Science.gov

Sample records for diagram algebras hecke

  1. Chain models on hecke algebra for corner type representations

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Ogievetsky, O. V.; Os'kin, A. F.

    2008-04-01

    We consider the integrable open chain models formulated in terms of generators of the Hecke algebra. The spectrum of Hamiltonians for the open Hecke chains of finite size with free boundary conditions is deduced for special (comer type) irreducible representations of the Hecke algebra.

  2. On Ternary Quotients of Cubic Hecke Algebras

    NASA Astrophysics Data System (ADS)

    Cabanes, Marc; Marin, Ivan

    2012-08-01

    We prove that the quotient of the group algebra of the braid group introduced by Funar (Commun Math Phys 173:513-558, 1995) collapses in characteristic distinct from 2. In characteristic 2 we define several quotients of it, which are connected to the classical Hecke and Birman-Wenzl-Murakami quotients, but which admit in addition a symmetry of order 3. We also establish conditions on the possible Markov traces factorizing through it.

  3. Baxter Operator and Archimedean Hecke Algebra

    NASA Astrophysics Data System (ADS)

    Gerasimov, A.; Lebedev, D.; Oblezin, S.

    2008-12-01

    In this paper we introduce Baxter integral {mathcal{Q}} -operators for finite-dimensional Lie algebras {mathfrak{gl}_{ell+1}} and {mathfrak{so}_{2ell+1}} . Whittaker functions corresponding to these algebras are eigenfunctions of the {mathcal{Q}}-operators with the eigenvalues expressed in terms of Gamma-functions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral representations of Whittaker functions, which are in a sense dual to each other. We define a dual Baxter operator and derive a family of mixed Mellin-Barnes-Givental integral representations. Givental and Mellin-Barnes integral representations are used to provide a short proof of the Friedberg-Bump and Bump conjectures for G = GL( ℓ + 1) proved earlier by Stade. We also identify eigenvalues of the Baxter {mathcal{Q}}-operator acting on Whittaker functions with local Archimedean L-factors. The Baxter {mathcal{Q}}-operator introduced in this paper is then described as a particular realization of the explicitly defined universal Baxter operator in the spherical Hecke algebra {mathcal {H}(G(mathbb{R}), K)} , K being a maximal compact subgroup of G. Finally we stress an analogy between {mathcal{Q}}-operators and certain elements of the non-Archimedean Hecke algebra {mathcal {H}(G(mathbb{Q}_p),G(mathbb{Z}_p))}.

  4. Eisenstein Hecke algebras and Iwasawa theory

    NASA Astrophysics Data System (ADS)

    Wake, Preston

    We show that if an Eisenstein component of the p-adic Hecke algebra associated to modular forms is Gorenstein, then it is necessary that the plus-part of a certain ideal class group is trivial. We also show that this condition is sufficient whenever a conjecture of Sharifi holds. We also formulate a weaker Gorenstein property, and show that this weak Gorenstein property holds if and only if a weak form of Sharifi's conjecture and a weak form of Greenberg's conjecture hold.

  5. Topological Strings, Double Affine Hecke Algebras, and Exceptional Knot Homology

    NASA Astrophysics Data System (ADS)

    Elliot, Ross F.

    In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory. In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems. In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

  6. Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation

    NASA Astrophysics Data System (ADS)

    Rim, Chaiho; Zhang, Hong

    2017-06-01

    AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.

  7. Spherical Hecke algebra in the Nekrasov-Shatashvili limit

    NASA Astrophysics Data System (ADS)

    Bourgine, Jean-Emile

    2015-01-01

    The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ɛ 2. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

  8. All exactly solvable U(1)-invariant quantum spin 1 chains from Hecke algebra

    SciTech Connect

    Alcarez, F.C. ); Koberle, R. ); Lima-Santos, A. )

    1992-12-10

    In this paper, the authors obtain all exactly integrable spin 1 quantum chains, which are U(1) invariant and satisfy the Hecke algebra. The authors present various generalizations for arbitrary spin S and discuss their solution via Bethe ansatz methods.

  9. A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank

    NASA Astrophysics Data System (ADS)

    Fu, Yuchen; Shelley-Abrahamson, Seth

    2016-06-01

    We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.

  10. On boundary fusion and functional relations in the Baxterized affine Hecke algebra

    SciTech Connect

    Babichenko, A.; Regelskis, V.

    2014-04-15

    We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

  11. On boundary fusion and functional relations in the Baxterized affine Hecke algebra

    NASA Astrophysics Data System (ADS)

    Babichenko, A.; Regelskis, V.

    2014-04-01

    We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

  12. On boundary fusion and functional relations in the Baxterized affine Hecke algebra

    SciTech Connect

    Babichenko, A.; Regelskis, V.

    2014-04-15

    We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

  13. Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations

    NASA Astrophysics Data System (ADS)

    Ito, Tatsuro; Terwilliger, Paul

    2010-08-01

    We consider the double affine Hecke algebra H=H(k0,k1,k0v,k1v;q) associated with the root system (C1v,C1). We display three elements x, y, z in H that satisfy essentially the Z3-symmetric Askey-Wilson relations. We obtain the relations as follows. We work with an algebra H^ that is more general than H, called the universal double affine Hecke algebra of type (C1v,C1). An advantage of H^ over H is that it is parameter free and has a larger automorphism group. We give a surjective algebra homomorphism H^ → H. We define some elements x, y, z in H^ that get mapped to their counterparts in H by this homomorphism. We give an action of Artin's braid group B3 on H^ that acts nicely on the elements x, y, z; one generator sends x → y → z → x and another generator interchanges x, y. Using the B3 action we show that the elements x, y, z in H^ satisfy three equations that resemble the Z3-symmetric Askey-Wilson relations. Applying the homomorphism H^ → H we find that the elements x, y, z in H satisfy similar relations.

  14. On certain Hecke rings

    PubMed Central

    Evens, Sam; Bressler, Paul

    1987-01-01

    We examine rings that embed into the smash product of the group algebra of the Weyl group with the field of meromorphic functions on the Cartan subalgebra and are generated by elements that satisfy braid relations. We prove that every such ring is isomorphic to either the Hecke algebra, the nil Hecke ring, or the group algebra of the Weyl group. PMID:16593804

  15. The Fermion Representation of Quantum Toroidal Algebra on 3D Young Diagrams

    NASA Astrophysics Data System (ADS)

    Cai, Li-Qiang; Wang, Li-Fang; Wu, Ke; Yang, Jie

    2014-07-01

    We develop an equivalence between the diagonal slices and the perpendicular slices of 3D Young diagrams via Maya diagrams. Furthermore, we construct the fermion representation of quantum toroidal algebra on the 3D Young diagrams perpendicularly sliced.

  16. Relation between large dimension operators and oscillator algebra of Young diagrams

    NASA Astrophysics Data System (ADS)

    Lin, Hai

    2015-02-01

    The operators with large scaling dimensions can be labeled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large N but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu-Wigner contraction of the u(2) algebra inside of the u(p) algebra of p giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large N limit.

  17. Twisted Trace Formula for Hecke Correspondences

    NASA Astrophysics Data System (ADS)

    Shokranian, Salahoddin

    2004-12-01

    By the twisted trace formula for the Hecke correspondences we understand the trace formulas for Hecke operators for a non-connected algebraic group acting on certain cohomology spaces. The traces of Hecke operators developed by Selberg in 1957 and the work of Arthur on the traces of Hecke operators of 1989 on L2 -cohomology are in some sense application of analysis and representation theory. On the other hand the work of Eichler in 1957 and of Goresky-MacPherson, Harder and Kottwitz from 1993 to present, reflects more geometric and topological applications. These may be seen as different solutions to the same problem, the calculation of the traces of Hecke operators. The present paper intends to be an introductory note about these operators and their applications.

  18. From Bar Diagrams to Letter-Symbolic Algebra: A Technology-Enabled Bridging

    ERIC Educational Resources Information Center

    Looi, C. -K.; Lim, K. -S.

    2009-01-01

    In the Singapore primary school Mathematics curriculum, students are taught the model method that uses bar diagrams to visualize the problem structure in a given word problem. When these students progress to secondary school, they learn the algebraic way of solving word problems. Studies (e.g. Ng et al.) have shown that poor bridging of students…

  19. From Bar Diagrams to Letter-Symbolic Algebra: A Technology-Enabled Bridging

    ERIC Educational Resources Information Center

    Looi, C. -K.; Lim, K. -S.

    2009-01-01

    In the Singapore primary school Mathematics curriculum, students are taught the model method that uses bar diagrams to visualize the problem structure in a given word problem. When these students progress to secondary school, they learn the algebraic way of solving word problems. Studies (e.g. Ng et al.) have shown that poor bridging of students…

  20. Phase diagrams of hard spheres with algebraic attractive interactions.

    PubMed

    Camp, Philip J

    2003-01-01

    The phase diagrams of systems made up of hard spheres interacting with attractive potentials of the form -1/r(3+sigma) are calculated using Monte Carlo simulations, second-order thermodynamic perturbation theory, and an augmented van der Waals theory. In simulations of the systems with sigma=0.1, 1, and 3, fluid-solid coexistence results are obtained using the Gibbs-Duhem integration technique; simulation data for the vapor-liquid coexistence envelopes and critical points are taken from previously published work [P. J. Camp and G. N. Patey, J. Chem. Phys. 114, 399 (2001)]. It is shown that the agreement between the theoretical and simulated phase diagrams improves as the range of the potential is increased, reflecting the decreasing role of short-range correlations in determining the bulk thermodynamics. In the extreme case of sigma=0.1 both theories are in excellent agreement with simulations. Phase diagrams for systems with sigma=4, 5, and 6 are computed using second-order thermodynamic perturbation theory. The results indicate that the vapor-liquid transition becomes metastable with respect to freezing when sigma > or approximately equal to 5, in broad agreement with results for the hard-sphere attractive Yukawa system which is commonly used to model colloidal particles, globular proteins, and nanoparticles.

  1. Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras

    SciTech Connect

    Konyaev, Andrei Yu

    2010-11-11

    A bifurcation diagram is a stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a bifurcation diagram {Sigma}-bar of the moment map defined by functions obtained by the method of argument shift with the closure of the discriminant D-bar{sub z} of a spectral curve is proved for the Lie algebras sl(n+1), sp(2n), so(2n+1), and g{sub 2}. Moreover, it is proved that these sets are distinct for the Lie algebra so(2n). Bibliography: 22 titles.

  2. One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms

    NASA Astrophysics Data System (ADS)

    Hirata, So; Doran, Alexander E.; Knowles, Peter J.; Ortiz, J. V.

    2017-07-01

    A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the Δ MPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except Δ MPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤n ≤3 but converges at the full-configuration-interaction (FCI) limit at n =∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or Δ MPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of Δ MPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤n ≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

  3. Visual Thinking, Algebraic Thinking, and a Full Unit-Circle Diagram.

    ERIC Educational Resources Information Center

    Shear, Jonathan

    1985-01-01

    The study of trigonometric functions in terms of the unit circle offer an example of how students can learn algebraic relations and operations while using visually oriented thinking. Illustrations are included. (MNS)

  4. Visual Thinking, Algebraic Thinking, and a Full Unit-Circle Diagram.

    ERIC Educational Resources Information Center

    Shear, Jonathan

    1985-01-01

    The study of trigonometric functions in terms of the unit circle offer an example of how students can learn algebraic relations and operations while using visually oriented thinking. Illustrations are included. (MNS)

  5. Solving Algebra Problems with Interactive Diagrams: Demonstration and Construction of Examples

    ERIC Educational Resources Information Center

    Naftaliev, Elena; Yerushalmy, Michal

    2011-01-01

    We investigated how students use the representation of data in a given example appearing in an interactive diagram (ID) and how they create additional examples with the ID. Students who worked with the ID that offered limited representations and tools ("illustrating ID") looked for ways to bypass the designed constraints: they changed the…

  6. Heck's disease: diagnosis and susceptibility.

    PubMed

    Bennett, Lindsey K; Hinshaw, Molly

    2009-01-01

    Focal epithelial hyperplasia, or Heck's disease, is an uncommon proliferation of oral mucosa that presents primarily in Native Central and South American populations. It presents as asymptomatic papules or nodules on the oral mucosa, gingiva, tongue, and lips. In the majority of cases, human papilloma virus 13 or 32 is detected. Factors that determine disease susceptibility are unclear, but genetics, and having the human lymphocytic antigen-DR4 (DRB1*0404) allele in particular, are thought to play a major role in disease vulnerability. We report another case of focal epithelial hyperplasia, hypothesize on disease susceptibility, and review the current understanding of this uncommon disorder.

  7. An algebraic/graphical tool to compare ecosystems with respect to their pollution V: cluster analysis and Hasse diagrams.

    PubMed

    Pudenz, S; Brüggemann, R; Luther, B; Kaune, A; Kreimes, K

    2000-06-01

    In case of large data matrices comparative evaluations of objects/regions with the technique of Hasse diagrams may be troublesome due to a messy system of lines in the graphical representation. Here fuzzy clustering leads to useful simplifications because regions with slightly different pollution pattern are grouped together. However, fuzzy clustering implies to introduce a threshold value for the membership of an object to a cluster and to select the best number of clusters. Therefore many arbitrarities evolve. Within the systematic study presented here we found that some objects are very stable against variations of the threshold value and the number of cluster whereas other objects behaves different. According to their behaviour we investigated a classification of the objects. Formal Concept Analysis shows that in some cases specific pollution pattern imply the membership to one of these classes. For example objects which are characterized by high Pb-, Zn-concentration and moderate S-concentration imply a high stability against variants of the clustering process. Further implications are described in the paper.

  8. Wilson Loop Diagrams and Positroids

    NASA Astrophysics Data System (ADS)

    Agarwala, Susama; Marin-Amat, Eloi

    2017-03-01

    In this paper, we study a new application of the positive Grassmannian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N= 4 Super Yang-Mill theory ( N = 4 SYM). There has been much interest in studying this theory via the positive Grassmannians using BCFW recursion. This is the first attempt to study MHV diagrams for planar Wilson loop calculations (or planar amplitudes) in terms of positive Grassmannians. We codify Wilson loop diagrams completely in terms of matroids. This allows us to apply the combinatorial tools in matroid theory used to identify positroids (non-negative Grassmannians) to Wilson loop diagrams. In doing so, we find that certain non-planar Wilson loop diagrams define positive Grassmannians. While non-planar diagrams do not have physical meaning, this finding suggests that they may have value as an algebraic tool, and deserve further investigation.

  9. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  10. Cremmer-Gervais r-Matrices and the Cherednik Algebras of Type GL 2

    NASA Astrophysics Data System (ADS)

    Johnson, Garrett

    2010-11-01

    We give an interpretation of the Cremmer-Gervais r-matrices for {mathfrak{sl}_n} in terms of actions of elements in the rational and trigonometric Cherednik algebras of type GL 2 on certain subspaces of their polynomial representations. This is used to compute the nilpotency index of the Jordanian r-matrices, thus answering a question of Gerstenhaber and Giaquinto. We also give an interpretation of the Cremmer-Gervais quantization in terms of the corresponding double affine Hecke algebra.

  11. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  12. W algebras are L∞ algebras

    NASA Astrophysics Data System (ADS)

    Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias

    2017-07-01

    It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W_3 algebra.

  13. Kinetic Study of the Heck Reaction: An Interdisciplinary Experiment

    ERIC Educational Resources Information Center

    Gozzi, Christel; Bouzidi, Naoual

    2008-01-01

    The aim of this experiment is to study and calculate the kinetic constant of a Heck reaction: the arylation of but-3-en-2-ol by iodobenzene catalyzed by palladium acetate in presence of triethylamine in DMF. The reaction leads to a mixture of two ketones. Students use GC analysis to quantify reagents and products of reaction. They control the…

  14. Kinetic Study of the Heck Reaction: An Interdisciplinary Experiment

    ERIC Educational Resources Information Center

    Gozzi, Christel; Bouzidi, Naoual

    2008-01-01

    The aim of this experiment is to study and calculate the kinetic constant of a Heck reaction: the arylation of but-3-en-2-ol by iodobenzene catalyzed by palladium acetate in presence of triethylamine in DMF. The reaction leads to a mixture of two ketones. Students use GC analysis to quantify reagents and products of reaction. They control the…

  15. [Focal epithelial hyperplasia (Heck's disease) in a Turkish family].

    PubMed

    Weidner, F

    1996-12-01

    A 31-year-old Turkish patient and some family members suffered from multiple hyperplastic oral mucosal papules. Intralesional papilloma virus was not found but the patient had elevated levels of CD8 lymphocytes in his peripheral blood. We diagnosed focal epithelial hyperplasia of Heck.

  16. Quark diagrams and the. cap omega. /sup -/ nonleptonic decays

    SciTech Connect

    Ponce, W.A.

    1980-09-01

    The quark-diagram model for nonleptonic two-body baryon decays is discussed and applied to the decay of the ..cap omega../sup -/ particle. Current algebra is not employed, but the relation between the quark diagrams and current algebra is explored.

  17. Hecke Groups, Dessins d'Enfants and the Archimedean Solids

    NASA Astrophysics Data System (ADS)

    He, Yang-Hui; Read, James

    2015-12-01

    Grothendieck's dessins d'enfants arise with ever-increasing frequency in many areas of 21st century mathematical physics. In this paper, we review the connections between dessins and the theory of Hecke groups. Focussing on the restricted class of highly symmetric dessins corresponding to the so-called Archimedean solids, we apply this theory in order to provide a means of computing representatives of the associated conjugacy classes of Hecke subgroups in each case. The aim of this paper is to demonstrate that dessins arising in mathematical physics can point to new and hitherto unexpected directions for further research. In addition, given the particular ubiquity of many of the dessins corresponding to the Archimedean solids, the hope is that the computational results of this paper will prove useful in the further study of these objects in mathematical physics contexts.

  18. Late-onset adenosine deaminase deficiency presenting with Heck's disease.

    PubMed

    Artac, Hasibe; Göktürk, Bahar; Bozdemir, Sefika Elmas; Toy, Hatice; van der Burg, Mirjam; Santisteban, Ines; Hershfield, Michael; Reisli, Ismail

    2010-08-01

    Focal epithelial hyperplasia, also known as Heck's disease, is a rare but distinctive entity of viral etiology with characteristic clinical and histopathological features. It is a benign, asymptomatic disease of the oral mucosa caused by human papilloma viruses (HPV). Previous studies postulated an association between these lesions and immunodeficiency. Genetic deficiency of adenosine deaminase (ADA) results in varying degrees of immunodeficiency, including neonatal onset severe combined immunodeficiency (ADA-SCID), and milder, later onset immunodeficiency. We report a 12-year-old girl with the late onset-ADA deficiency presenting with Heck's disease. Our case report should draw attention to the possibility of immunodeficiency in patients with HPV-induced focal epithelial hyperplasia.

  19. Non-Abelian Vortices, Hecke Modifications and Singular Monopoles

    NASA Astrophysics Data System (ADS)

    Baptista, J. M.

    2010-06-01

    In this note, we show that for the group G = U( N) the space of Hecke modifications of a rank N vector bundle over a Riemann surface C coincides with the moduli space of solutions of certain non-Abelian vortex equations over C. Through the recent work of Kapustin and Witten this then leads to an isomorphism between the moduli space of vortices and the moduli space of singular monopoles on the product of C with a closed interval I.

  20. Matrix Algebra.

    DTIC Science & Technology

    1998-06-01

    on courses being taught at NPS. LIST OF REFERENCES [1] Anton , Howard , Elementary Linear Algebra , John Wiley and Sons, New York, New York, 1994...and computational techniques for solving systems of linear equations. The goal is to enhance current matrix algebra textbooks and help the beginning... algebra is the study of algebraic operations on matrices and of their applications, primarily for solving systems of linear equations. Systems of

  1. Heck-type reactions of imine derivatives: a DFT study.

    PubMed

    Li, Zhe; Fu, Yao; Zhang, Song-Lin; Guo, Qing-Xiang; Liu, Lei

    2010-06-01

    The mechanism of a recently discovered intramolecular Heck-type coupling of oximes with aryl halides (Angew. Chem. Int. Ed. 2007, 46, 6325) was systematically studied by using density functional methods enhanced with a polarized continuum solvation model. The overall catalytic cycle of the reaction was found to consist of four steps: oxidative addition, migratory insertion, beta-H elimination, and catalyst regeneration, whereas an alternative base-promoted C-H activation pathway was determined to be less favorable. Migratory insertion was found to be the rate determining step in the catalytic cycle. The apparent activation barrier of migratory insertion of the (E)-oxime was +20.5 kcal mol(-1), whereas the barrier of (Z)-oxime was as high as +32.7 kcal mol(-1). However, (Z)-oxime could isomerize to form the more active (E)-oxime with the assistance of K(2)CO(3), so that both the (E)- and (Z)-oxime substrates could be transformed to the desired product. Our calculations also indicated that the Z product was predominant in the equilibrium of the isomerization of the imine double bond, which constituted the reason for the good Z-selectivity observed for the reaction. Furthermore, we examined the difference between the intermolecular Heck-type reactions of imines and of olefins. It was found that in the intermolecular Heck-type coupling of imines, the apparent activation barrier of migratory insertion was as high as +35 kcal mol(-1), which should be the main obstacle of the reaction. The analysis also revealed the main problem for the intermolecular Heck-type reactions of imines, which was that the breaking of a C=N pi bond was much more difficult than the breaking of a C=C pi bond. After systematic examination of a series of substituted imines, (Z)-N-amino imine and N-acetyl imine were found to have relatively low barriers of migratory insertion, so that they might be possible substrates for intermolecular Heck-type coupling.

  2. Synthesis of Phenylpropanoids via Matsuda-Heck Coupling of Arene Diazonium Salts.

    PubMed

    Schmidt, Bernd; Wolf, Felix

    2017-04-21

    The Pd-catalyzed Heck-type coupling (Matsuda-Heck reaction) of electron rich arene diazonium salts with electron deficient olefins has been exploited for the synthesis of phenylpropanoid natural products. Examples described herein are the naturally occurring benzofurans methyl wutaifuranate, wutaifuranol, wutaifuranal, their 7-methoxy derivatives, and the O-prenylated natural products boropinols A and C.

  3. Using geometric algebra to study optical aberrations

    SciTech Connect

    Hanlon, J.; Ziock, H.

    1997-05-01

    This paper uses Geometric Algebra (GA) to study vector aberrations in optical systems with square and round pupils. GA is a new way to produce the classical optical aberration spot diagrams on the Gaussian image plane and surfaces near the Gaussian image plane. Spot diagrams of the third, fifth and seventh order aberrations for square and round pupils are developed to illustrate the theory.

  4. On the Li Coefficients for the Hecke L-functions

    NASA Astrophysics Data System (ADS)

    Omar, Sami; Ouni, Raouf; Mazhouda, Kamel

    2014-06-01

    In this paper, we compute and verify the positivity of the Li coefficients for the Hecke L-functions using an arithmetic formula established in Omar and Mazhouda, J. Number Theory 125(1), 50-58 (2007) and J. Number Theory 130(4), 1098-1108 (2010) and the Serre trace formula. Additional results are presented, including new formulas for the Li coefficients and a formulation of a criterion for the partial Riemann hypothesis. Basing on the numerical computations made below, we conjecture that these coefficients are increasing in n.

  5. Thermodynamic Diagrams

    NASA Astrophysics Data System (ADS)

    Chaston, Scot

    1999-02-01

    Thermodynamic data such as equilibrium constants, standard cell potentials, molar enthalpies of formation, and standard entropies of substances can be a very useful basis for an organized presentation of knowledge in diverse areas of applied chemistry. Thermodynamic data can become particularly useful when incorporated into thermodynamic diagrams that are designed to be easy to recall, to serve as a basis for reconstructing previous knowledge, and to determine whether reactions can occur exergonically or only with the help of an external energy source. Few students in our chemistry-based courses would want to acquire the depth of knowledge or rigor of professional thermodynamicists. But they should nevertheless learn how to make good use of thermodynamic data in their professional occupations that span the chemical, biological, environmental, and medical laboratory fields. This article discusses examples of three thermodynamic diagrams that have been developed for this purpose. They are the thermodynamic energy account (TEA), the total entropy scale, and the thermodynamic scale diagrams. These diagrams help in the teaching and learning of thermodynamics by bringing the imagination into the process of developing a better understanding of abstract thermodynamic functions, and by allowing the reader to keep track of specialist thermodynamic discourses in the literature.

  6. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  7. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  8. Algebra Unplugged.

    ERIC Educational Resources Information Center

    Amdahl, Kenn; Loats, Jim

    This book discusses algebra in a non-threatening, fun way. It explains concepts, vocabulary, and strategies of algebra in understandable terms. Chapter titles include: "Numbers with Interesting Properties"; "Important Concepts"; "Fraction Refresher"; "Terms, Factors, and Polynomials"; "Rearranging Expressions"; "Handy Tricks and Magic Words";…

  9. Hubble Diagram

    NASA Astrophysics Data System (ADS)

    Djorgovski, S.; Murdin, P.

    2000-11-01

    Initially introduced as a way to demonstrate the expansion of the universe, and subsequently to determine the expansion rate (the HUBBLE CONSTANT H0), the Hubble diagram is one of the classical cosmological tests. It is a plot of apparent fluxes (usually expressed as magnitudes) of some types of objects at cosmological distances, against their REDSHIFTS. It is used as a tool to measure the glob...

  10. Magnetically Separable Fe3O4@DOPA-Pd: A Heterogeneous Catalyst for Aqueous Heck Reaction

    EPA Science Inventory

    Magnetically separable Fe3O4@DOPA-Pd catalyst has been synthesized via anchoring of palladium over dopamine-coated magnetite via non-covalent interaction and the catalyst is utilized for expeditious Heck coupling in aqueous media.

  11. Magnetically Separable Fe3O4@DOPA-Pd: A Heterogeneous Catalyst for Aqueous Heck Reaction

    EPA Science Inventory

    Magnetically separable Fe3O4@DOPA-Pd catalyst has been synthesized via anchoring of palladium over dopamine-coated magnetite via non-covalent interaction and the catalyst is utilized for expeditious Heck coupling in aqueous media.

  12. Ionic liquid effects on Mizoroki-Heck reactions: more than just carbene complex formation.

    PubMed

    Gyton, Matthew R; Cole, Marcus L; Harper, Jason B

    2011-08-28

    Reaction profiles for a Mizoroki-Heck reaction in either an ionic liquid or a molecular solvent with different palladium sources demonstrate that the rate enhancements observed in ionic liquids cannot be solely attributed to Pd-carbene complex formation.

  13. Heck coupling of haloaromatics with octavinylsilsesquioxane: solution processable nanocomposites for application in electroluminescent devices.

    PubMed

    Sellinger, Alan; Tamaki, Ryo; Laine, Richard M; Ueno, Kazunori; Tanabe, Hiroshi; Williams, Evan; Jabbour, Ghassan E

    2005-08-07

    A new solution processable nanocomposite material has been prepared via the Heck coupling of octavinylsilsesquioxane with a selected bromoaromatic hole transport compound. Resultant electroluminescent devices show an 18% improvement in external quantum efficiencies over their small molecule analogues.

  14. Weight diagram construction of Lax operators

    SciTech Connect

    Carbon, S.L.; Piard, E.J.

    1991-10-01

    We review and expand methods introduced in our previous paper. It is proved that cyclic weight diagrams corresponding to representations of affine Lie algebras allow one to construct the associated Lax operator. The resultant Lax operator is in the Miura-like form and generates the modified KdV equations. The algorithm is extended to the super-symmetric case.

  15. Constructing Causal Diagrams to Learn Deliberation

    ERIC Educational Resources Information Center

    Easterday, Matthew W.; Aleven, Vincent; Scheines, Richard; Carver, Sharon M.

    2009-01-01

    Policy problems like "What should we do about global warming?" are ill-defined in large part because we do not agree on a system to represent them the way we agree Algebra problems should be represented by equations. As a first step toward building a policy deliberation tutor, we investigated: (a) whether causal diagrams help students learn to…

  16. Phase Diagram

    NASA Astrophysics Data System (ADS)

    Walker, Matthew S.; Fruehan, Richard J.

    2014-08-01

    The thermodynamics of several aspects of the carbothermic reduction of alumina have been examined. In Part I, the results of measuring the evolved CO from the reaction between Al2O3 and C mixtures were used to determine the temperature and carbon contents for carbide formation at alumina saturation and at carbide saturation in the Al2O3-Al4C3 system. In this part of the paper, results are presented for a thermogravimetric study of the reactions of Al2O3 with carbon, as well as those for the determination of the Al2O3 liquidus line and the Al2O3-Al4O4C eutectic in the Al2O3-Al4C3 phase diagram. The critical temperature for Al2O3 and C to react, producing gas at 1 atm., was in agreement with that predicted from thermodynamics and measured in Part I of this paper. However, the Al2O3 liquidus appeared to be steeper and the eutectic temperature lower than the predicted phase diagram.

  17. Focal epithelial hyperplasia (Heck's disease) in two Chinese females.

    PubMed

    Liu, N; Li, Y; Zhou, Y; Zeng, X

    2012-08-01

    Focal epithelial hyperplasia, or Heck's disease, is a relatively rare virus-induced benign disease. To the best of the authors' knowledge it has not been reported in an ethnic Chinese population. The authors report two cases of focal epithelial hyperplasia (FEH) in Chinese patients, which were clinically and histologically in accord with FEH. In particular, the lesions in one case were located on the gingival mucosa, which is rarely affected by FEH. DNA extracted from paraffin-embedded specimens from the two patients was tested for the presence of human papilloma virus followed by specific polymerase chain reaction testing for 16, 18, 13, and 32 subtypes in order to confirm the clinical diagnosis.

  18. Direct carbocyclizations of benzoic acids: catalyst-controlled synthesis of cyclic ketones and the development of tandem aHH (acyl Heck-Heck) reactions.

    PubMed

    Miles, Kelsey C; Le, Chi Chip; Stambuli, James P

    2014-09-01

    The formation of exo-methylene indanones and indenones from simple ortho-allyl benzoic acid derivatives has been developed. Selective formation of the indanone or indenone products in these reactions is controlled by choice of ancillary ligand. This new process has a low environmental footprint as the products are formed in high yields using low catalyst loadings, while the only stoichiometric chemical waste generated from the reactants in the transformation is acetic acid. The conversion of the active cyclization catalyst into the Hermman-Beller palladacycle was exploited in a one-pot tandem acyl Heck-Heck (aHH) reaction, and utilized in the synthesis of donepezil.

  19. Color Algebras

    NASA Technical Reports Server (NTRS)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.

  20. Palladium-catalyzed oxidative Heck-type alkylation/aryl migration/desulfonylation between alkenes with α-carbonyl alkyl bromides.

    PubMed

    Fan, Jian-Hong; Yang, Ji; Song, Ren-Jie; Li, Jin-Heng

    2015-02-20

    A new Pd(II)-catalyzed alkene oxidative difunctionalization initiated by Heck insertion has been developed for the selective synthesis of acyclic and cyclic all-carbon quaternary stereocenters, which achieves an oxidative Heck-type alkylation, aryl migration, and desulfonylation sequence and represents a different input from those previously used Heck coupling in synthesis is reported.

  1. Steinberg conformal algebras

    NASA Astrophysics Data System (ADS)

    Mikhalev, A. V.; Pinchuk, I. A.

    2005-06-01

    The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.

  2. GENERAL: Mutual Information and Relative Entropy of Sequential Effect Algebras

    NASA Astrophysics Data System (ADS)

    Wang, Jia-Mei; Wu, Jun-De; Cho, Minhyung

    2010-08-01

    In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.

  3. Web Algebra.

    ERIC Educational Resources Information Center

    Capani, Antonio; De Dominicis, Gabriel

    This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…

  4. Phosphite-oxazole/imidazole ligands in asymmetric intermolecular Heck reaction.

    PubMed

    Mazuela, Javier; Tolstoy, Paivi; Pàmies, Oscar; Andersson, Pher G; Diéguez, Montserrat

    2011-02-07

    We describe the application of a new class of ligands--the phosphite-oxazole/imidazole (L1-L5a-g)--in asymmetric intermolecular Pd-catalyzed Heck reactions under thermal and microwave conditions. These ligands combine the advantages of the oxazole/imidazole moiety with those of the phosphite moiety: they are more stable than their oxazoline counterparts, less sensitive to air and other oxidizing agents than phosphines and phosphinites, and easy to synthesize from readily available alcohols. The results indicate that activities, regio- and enantioselectivities, are highly influenced by the type of nitrogen donor group (oxazole or imidazole), the oxazole and biaryl-phosphite substituents and the axial chirality of the biaryl moiety of the ligand. By carefully selecting the ligand components, we achieved high activities, regio- (up to 99%) and enantioselectivities (up to 99%) using several triflate sources. Under microwave-irradiation conditions, reaction times were considerably shorter (from 24 h to 30 min) and regio- and enantioselectivities were still excellent.

  5. Diastereoselective Intramolecular Heck Reaction Assisted by an Acetate Group: Synthesis of the Decahydrobenzofluorene Derivative Dasyscyphin E.

    PubMed

    Jiménez, Fermín; Fernández, Antonio; Boulifa, Ettahir; Mansour, Ahmed Ibn; Alvarez-Manzaneda, Ramón; Chahboun, Rachid; Alvarez-Manzaneda, Enrique

    2017-09-15

    The first synthesis of antifungal sesquiterpene quinol dasyscyphin E was achieved starting from trans-communic acid. The process described involves the first diastereoselective synthesis of this type of compound by cyclization of an aryl bicyclosesquiterpene. The acid was efficiently transformed into a sesquiterpene synthon, which was converted into the corresponding bromoaryl sesquiterpene. The key step of synthetic sequence was the cyclization of the latter under Heck reaction conditions, which yielded the tetracyclic skeleton of the target compound with complete diastereoselectivity. The participation of an acetate group is decisive, both for the course of the Heck reaction and for the stereoselectivity of the process.

  6. A rapid microwave protocol for Heck vinylation of aryl chlorides under air.

    PubMed

    Datta, Gopal K; Vallin, Karl S A; Larhed, Mats

    2003-01-01

    In modern high-throughput chemistry, the overall workflow is a crucial factor and much work is devoted to speeding up the process of chemistry development. Since automated microwave-based synthesizers are known to streamline the compound production and to accelerate slow organic transformations, this technology was implemented for Heck reactions with sluggish aryl chlorides. Furthermore, homogeneous palladium-catalyzed Heck vinylations of aryl chlorides can be performed under air under optimized conditions. Based on this finding, controlled microwave heating was utilized to accelerate model reactions down to 30 min employing a mixture of ionic liquid and 1,4-dioxane as solvent.

  7. Magnetically separable Fe3O4@DOPA??Pd: a heterogeneous catalyst for aqueous Heck reaction

    EPA Pesticide Factsheets

    Magnetically separable Fe3O4@DOPA??Pd catalyst has been synthesized via anchoring of palladium over dopamine-coated magnetite via co-ordinate interactionand the catalyst is utilized for expeditious Heck coupling in aqueous media.This dataset is associated with the following publication:Baig, N., J. Leazer , and R. Varma. Magnetically Separable Fe3O4@DOPA-Pd: A Heterogeneous Catalyst for Aqueous Heck Reaction. CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY. Springer-Verlag, New York, NY, USA, 17(7): 2073-2077, (2015).

  8. Γ-conformal algebras

    NASA Astrophysics Data System (ADS)

    Golenishcheva-Kutuzova, Maria I.; Kac, Victor G.

    1998-04-01

    Γ-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in terms of Lie algebras and their representations with an action of the group Γ. To every Γ-conformal algebra and a character of Γ we associate a Lie algebra generated by fields with the OPE with simple poles. Examples include twisted affine Kac-Moody algebras, the sin algebra (which is a "Γ-conformal" analogue of the general linear algebra) and its analogues, the algebra of pseudodifferential operators on the circle, etc.

  9. The local Hurwitz constant and Diophantine approximation on Hecke groups

    NASA Astrophysics Data System (ADS)

    Lehner, J.

    1990-10-01

    Define the Hecke group by {G_q} = < {( {begin{array}{*{20}{c}} 1 & {{⪉mb... ...{array}{*{20}{c}} 0 & { - 1} 1 & 0 } )} rangle , {λ _q} = 2cos π /q , q = 3,4, ldots . We call {G_q}(∞ ) the {G_q} -rationals, and R - {G_q}(∞ ) the {G_q} -irrationals. The problem we treat here is the approximation of {G_q} -irrationals by {G_q} -rationals. Let M(α ) be the upper bound of numbers c for which \\vertα - k/m\\vert < 1/c{m^2} for all {G_q} -irrationals and infinitely many k/m in {G_q}(∞ ) . Set h_q'= {inf _α }M(α ) . We call h_q' the Hurwitz constant for {G_q} . It is known that h_q'= 2 , q even; h_q'= 2{(1 + {(1 - {λ _q}/2)^2})^{1/2}} , q odd. In this paper we prove this result by using {λ _q} -continued fractions, as developed previously by D. Rosen. Write α - frac{{{P_{n - 1}}}}{{{Q_{n - 1}}}} = frac{{{{( - 1)}^{... ...}{\\varepsilon _2} \\cdots {\\varepsilon _n}}}{{{m_{n - 1}}(α )Q_{n - 1}^2}}, where {\\varepsilon _i} = ± 1 and {P_i}/{Q_i} are the convergents of the {λ _q} -continued fraction for α . Then M(α ) = {overline {lim } _n}{m_n}(α ) . We call {m_n}(α ) the local Hurwitz constant. In the final section we prove some results on the local Hurwitz constant. For example (Theorem 4), it is shown that if q is odd and {\\varepsilon _{n + 1}} = {\\varepsilon _{n + 2}} = + 1 , then {m_i} ≥ {(λ _q^2 + 4)^{1/2}} > h_q' for at least one of i = n - 1,n,n + 1 .

  10. Classification of Non-Affine Non-Hecke Dynamical R-Matrices

    NASA Astrophysics Data System (ADS)

    Avan, Jean; Billaud, Baptiste; Rollet, Geneviève

    2012-09-01

    A complete classification of non-affine dynamical quantum R-matrices obeying the Gl_n({C})-Gervais-Neveu-Felder equation is obtained without assuming either Hecke or weak Hecke conditions. More general dynamical dependences are observed. It is shown that any solution is built upon elementary blocks, which individually satisfy the weak Hecke condition. Each solution is in particular characterized by an arbitrary partition {{I}(i),; iin\\{1,dots,n}} of the set of indices {1,dots,n} into classes, {I}(i) being the class of the index i, and an arbitrary family of signs (ɛ_{I})_{{I}in{{I}(i), ; iin{1,dots,n}}} on this partition. The weak Hecke-type R-matrices exhibit the analytical behaviour R_{ij,ji}=f(ɛ_{{I}(i)}Λ_{{I}(i)}-ɛ_{{I}(j)}Λ_{{I}(j)}), where f is a particular trigonometric or rational function, Λ_{{I}(i)}=sumlimits_{jin{I}(i)}λ_j, and (λ_i)_{iin{1,dots,n}} denotes the family of dynamical coordinates.

  11. Intramolecular Imidoylative Heck Reaction: Synthesis of Cyclic Ketoimines from Functionalized Isocyanide.

    PubMed

    Wang, Jian; Tang, Shi; Zhu, Qiang

    2016-07-01

    Efficient access to five- to seven-membered cyclic ketoimines, through palladium-catalyzed intramolecular imidoylative Heck reaction of alkene-containing isocyanides, has been developed. Consecutive isocyanide and alkene insertion into aryl or alkyl Pd(II) intermediates takes place in this process. No byproduct derived from monoinsertion or reversed sequence is detected.

  12. Focal epithelial hyperplasia (Heck's disease) in three Kenyan girls: case reports.

    PubMed

    Chindia, M L; Awange, D O; Guthua, S W; Mwaniki, D L

    1993-09-01

    We report the first three patients diagnosed with focal epithelial hyperplasia (Heck's disease) in Kenya. Clinically they presented as focal or diffuse papillomatous lesions in the oral mucosa. Histopathological features rule out other similar lesions inter alia multiple fibro-epithelial and viral warts.

  13. Successful topical treatment of focal epithelial hyperplasia (Heck's disease) with interferon-beta.

    PubMed

    Steinhoff, M; Metze, D; Stockfleth, E; Luger, T A

    2001-05-01

    We report the successful topical treatment of focal epithelial hyperplasia (Heck's disease) with interferon-beta (Fiblaferon gel). Topical treatment with interferon-beta appears to be an effective, simple, non-invasive, cheap and low-risk alternative to other invasive or surgical therapeutic modalities.

  14. Ligand-free Heck reaction: Pd(OAc)2 as an active catalyst revisited.

    PubMed

    Yao, Qingwei; Kinney, Elizabeth P; Yang, Zhi

    2003-09-19

    Palladium acetate was shown to be an extremely active catalyst for the Heck reaction of aryl bromides. Both the base and the solvent were found to have a fundamental influence on the efficiency of the reaction, with K(3)PO(4) and N,N-dimethylacetamide being the optimal base and solvent, respectively.

  15. Preparation of Vinyl Silyl Ethers and Disiloxanes via the Silyl-Heck Reaction of Silyl Ditriflates

    PubMed Central

    Martin, Sara E. S.; Watson, Donald A.

    2013-01-01

    Vinyl silyl ethers and disiloxanes can now be prepared from aryl-substituted alkenes and related substrates using a silyl-Heck reaction. The reaction employs a commercially available catalyst system and mild conditions. This work represents a highly practical means of accessing diverse classes of vinyl silyl ether substrates in an efficient and direct manner with complete regio- and geometric selectivity. PMID:23984876

  16. Algebraic trigonometry

    NASA Astrophysics Data System (ADS)

    Vaninsky, Alexander

    2011-04-01

    This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.

  17. Global structure of curves from generalized unitarity cut of three-loop diagrams

    NASA Astrophysics Data System (ADS)

    Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang

    2015-02-01

    This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.

  18. Ternary algebraic approach to extended superconformal algebras

    NASA Astrophysics Data System (ADS)

    Günaydin, Murat; Hyun, Seungjoon

    1992-04-01

    The construction of extended ( N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4

  19. Derive Workshop Matrix Algebra and Linear Algebra.

    ERIC Educational Resources Information Center

    Townsley Kulich, Lisa; Victor, Barbara

    This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…

  20. Spinor representations of affine Lie algebras

    PubMed Central

    Frenkel, I. B.

    1980-01-01

    Let [unk] be an infinite-dimensional Kac-Moody Lie algebra of one of the types Dl+1(2), Bl(1), or Dl(1). These algebras are characterized by the property that an elimination of any endpoint of their Dynkin diagrams gives diagrams of types Bl or Dl of classical orthogonal Lie algebras. We construct two representations of a Lie algebra [unk], which we call spinor representations, following the analogy with the classical case. We obtain that every spinor representation is either irreducible or has two irreducible components. This provides us with an explicit construction of fundamental representations of [unk], two for the type Dl+1(2), three for Bl(1), and four for Dl(1). We note the profound connection of our construction with quantum field theory—in particular, with fermion fields. Comparing the character formulas of our representations with another construction of the fundamental representations of Kac-Moody Lie algebras of types Al(1), Dl(1), El(1), we obtain classical Jacobi identities and addition formulas for elliptic θ-functions. PMID:16592912

  1. A simple and facile Heck-type arylation of alkenes with diaryliodonium salts using magnetically recoverable Pd-catalyst

    EPA Science Inventory

    The Heck-type arylation of alkenes was achieved in aqueous polyethylene glycol using a magnetically recoverable heterogenized palladium catalyst employing diaryliodonium salts under ambient conditions. The benign reaction medium and the stability of the catalyst are the salient f...

  2. A simple and facile Heck-type arylation of alkenes with diaryliodonium salts using magnetically recoverable Pd-catalyst

    EPA Science Inventory

    The Heck-type arylation of alkenes was achieved in aqueous polyethylene glycol using a magnetically recoverable heterogenized palladium catalyst employing diaryliodonium salts under ambient conditions. The benign reaction medium and the stability of the catalyst are the salient f...

  3. Palladium-catalyzed heck coupling reaction of aryl bromides in aqueous media using tetrahydropyrimidinium salts as carbene ligands.

    PubMed

    Yaşar, Sedat; Ozcan, Emine Ozge; Gürbüz, Nevin; Cetinkaya, Bekir; Ozdemir, Ismail

    2010-01-28

    An efficient and stereoselective catalytic system for the Heck cross coupling reaction using novel 1,3-dialkyl-3,4,5,6-tetrahydropyrimidinium salts (1, LHX) and Pd(OAc)2 loading has been reported. The palladium complexes derived from the salts 1a-f prepared in situ exhibit good catalytic activity in the Heck coupling reaction of aryl bromides under mild conditions.

  4. Caution: Venn Diagrams Ahead!

    ERIC Educational Resources Information Center

    Kimmins, Dovie L.; Winters, J. Jeremy

    2015-01-01

    Two perspectives of the term "Venn diagram" reflect the typical differences in the uses of Venn diagrams in the subject areas of mathematics and language arts. These differences are subtle; nevertheless, they can potentially be confusing. In language arts, the circles in a Venn diagram typically represent things that can be compared and…

  5. Caution: Venn Diagrams Ahead!

    ERIC Educational Resources Information Center

    Kimmins, Dovie L.; Winters, J. Jeremy

    2015-01-01

    Two perspectives of the term "Venn diagram" reflect the typical differences in the uses of Venn diagrams in the subject areas of mathematics and language arts. These differences are subtle; nevertheless, they can potentially be confusing. In language arts, the circles in a Venn diagram typically represent things that can be compared and…

  6. Algebra for Everyone.

    ERIC Educational Resources Information Center

    Edwards, Edgar L., Jr., Ed.

    The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…

  7. On Exceptional Superconformal Algebras

    SciTech Connect

    Poletaeva, Elena

    2010-06-17

    We obtain realizations of superconformal algebras K(2), K'(4) and the exceptional N = 6 superconformal algebra in matrices over a Weyl algebra of size 2x2, 4x4 and 8x8, respectively. A general construction of these realizations is based on the spin representations of the orthogonal Lie algebras. We give explicit descriptions of these matrix realizations.

  8. Phase Equilibria Diagrams Database

    National Institute of Standards and Technology Data Gateway

    SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase)   The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.

  9. States and synaptic algebras

    NASA Astrophysics Data System (ADS)

    Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

    2017-02-01

    Different versions of the notion of a state have been formulated for various so-called quantum structures. In this paper, we investigate the interplay among states on synaptic algebras and on its sub-structures. A synaptic algebra is a generalization of the partially ordered Jordan algebra of all bounded self-adjoint operators on a Hilbert space. The paper culminates with a characterization of extremal states on a commutative generalized Hermitian algebra, a special kind of synaptic algebra.

  10. Using three-dimensional spacetime diagrams in special relativity

    NASA Astrophysics Data System (ADS)

    Dray, Tevian

    2013-08-01

    We provide three examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity. The examples are the "rising manhole" paradox, the "moving spotlight" problem, and Einstein's light-clock derivation of time dilation.

  11. Quantum cluster algebras and quantum nilpotent algebras.

    PubMed

    Goodearl, Kenneth R; Yakimov, Milen T

    2014-07-08

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.

  12. Quantum cluster algebras and quantum nilpotent algebras

    PubMed Central

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  13. Oxidative Heck vinylation for the synthesis of complex dienes and polyenes.

    PubMed

    Delcamp, Jared H; Gormisky, Paul E; White, M Christina

    2013-06-12

    We introduce an oxidative Heck reaction for selective complex diene and polyene formation. The reaction proceeds via oxidative Pd(II)/sulfoxide catalysis that retards palladium-hydride isomerizations which previously limited the Heck manifold's capacity for furnishing stereodefined conjugated dienes. Limiting quantities of nonactivated terminal olefins (1 equiv) and slight excesses of vinyl boronic esters (1.5 equiv) that feature diverse functionality can be used to furnish complex dienes and polyenes in good yields and excellent selectivities (generally E:Z = >20:1; internal:terminal = >20:1). Because this reaction only requires prior activation of a single vinylic carbon, improvements in efficiency are observed for synthetic sequences relative to ones featuring reactions that require activation of both coupling partners.

  14. Enantioselective Heck arylations of acyclic alkenyl alcohols using a redox-relay strategy.

    PubMed

    Werner, Erik W; Mei, Tian-Sheng; Burckle, Alexander J; Sigman, Matthew S

    2012-12-14

    Progress in the development of asymmetric Heck couplings of arenes and acyclic olefins has been limited by a tenuous understanding of the factors that dictate selectivity in migratory insertion and β-hydride elimination. On the basis of key mechanistic insight recently garnered in the exploration of selective Heck reactions, we report here an enantioselective variant that delivers β-, γ-, or δ-aryl carbonyl products from acyclic alkenol substrates. The catalyst system imparts notable regioselectivity during migratory insertion and promotes the migration of the alkene's unsaturation toward the alcohol to ultimately form the ketone product. The reaction uses aryldiazonium salts as the arene source, yields enantiomeric products from opposite starting alkene configurations, and uses a readily accessible ligand. The racemic nature of the alkenol substrate does not bias the enantioselection.

  15. A generalization of the Funk-Hecke theorem to the case of hyperbolic spaces

    NASA Astrophysics Data System (ADS)

    Shtepina, T. V.

    2004-10-01

    The well-known Funk-Hecke theorem states that for integral operators whose kernels depend only on the distance between points in spherical geometry and where the integral is taken over the surface of a hypersphere, every surface spherical harmonic is an eigenvector. In this paper we extend this theorem to the case of non-compact Lobachevsky spaces. We compute the corresponding eigenvalue in some physically important cases.

  16. Palladium-catalyzed Heck-type cross-couplings of unactivated alkyl iodides.

    PubMed

    McMahon, Caitlin M; Alexanian, Erik J

    2014-06-02

    A palladium-catalyzed, intermolecular Heck-type coupling of alkyl iodides and alkenes is described. This process is successful with a variety of primary and secondary unactivated alkyl iodides as reaction partners, including those with hydrogen atoms in the β position. The mild catalytic conditions enable intermolecular C-C bond formations with a diverse set of alkyl iodides and alkenes, including substrates containing base- or nucleophile-sensitive functionality.

  17. Focal epithelial hyperplasia (Heck's disease): report of two cases with PCR detection of human papillomavirus DNA.

    PubMed

    Jayasooriya, P R; Abeyratne, S; Ranasinghe, A W; Tilakaratne, W M

    2004-07-01

    Focal epithelial hyperplasia (FEH) (Heck's disease) is essentially a benign oral infection produced by the human papillomavirus (HPV). Although this condition is known to exist in numerous populations and ethnic groups, it is relatively rare in South-East Asia. The following report is based on two cases of adult FEH with histopathological features in favour of the disease. In addition, polymerase chain reaction was performed to detect the presence of HPV DNA in the lesions in order to confirm the histopathological diagnosis.

  18. Deformed Virasoro Algebras from Elliptic Quantum Algebras

    NASA Astrophysics Data System (ADS)

    Avan, J.; Frappat, L.; Ragoucy, E.

    2017-09-01

    We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.

  19. Palladium was supported on superparamagnetic nanoparticles: A magnetically recoverable catalyst for Heck reaction

    SciTech Connect

    Zhang, Fengwei; Niu, Jianrui; Wang, Haibo; Yang, Honglei; Jin, Jun; Liu, Na; Zhang, Yubin; Li, Rong; Ma, Jiantai

    2012-02-15

    Highlights: Black-Right-Pointing-Pointer Palladium-based heterogeneous catalyst was prepared facilely via the co-precipitation method. Black-Right-Pointing-Pointer The particles are nearly spherical in shape with an average size of 20 {+-} 1.0 nm. Black-Right-Pointing-Pointer The developed magnetic catalyst showed high activity for Heck reaction. Black-Right-Pointing-Pointer The catalyst was easily recovered from the reaction mixture with external magnetic field. Black-Right-Pointing-Pointer The catalytic efficiency for Heck reaction remains unaltered even after 6 repeated cycles. -- Abstract: A novel and high-performance palladium-based catalyst for Heck reaction was prepared easily by the co-precipitation method. The catalyst was characterized by transmission electron microscopy (TEM), X-ray powder diffraction (XRD), vibrating sample magnetometry (VSM), X-ray photoelectron spectroscopy (XPS) and atomic absorption spectrophotometry (AAS). The catalyst afforded a fast conversion of the 4-bromonitrobenzene to 4-nitrostilbene at a catalyst loading of 5 mol%, and the efficiency of the catalyst remains unaltered even after 6 repeated cycles. The excellent catalytic performance of the Pd/Fe{sub 3}O{sub 4} catalyst might be attributed to the enhanced synergistic effect between Pd nanoparticles and magnetite.

  20. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the…

  1. Hertzsprung-Russell Diagram

    NASA Astrophysics Data System (ADS)

    Chiosi, C.; Murdin, P.

    2000-11-01

    The Hertzsprung-Russell diagram (HR-diagram), pioneered independently by EJNAR HERTZSPRUNG and HENRY NORRIS RUSSELL, is a plot of the star luminosity versus the surface temperature. It stems from the basic relation for an object emitting thermal radiation as a black body: ...

  2. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  3. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  4. Writing to Learn Algebra.

    ERIC Educational Resources Information Center

    Miller, L. Diane; England, David A.

    1989-01-01

    Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)

  5. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  6. Arithmetic: Prerequisite to Algebra?

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…

  7. Year 7 Algebra

    ERIC Educational Resources Information Center

    Mitchell, Sarah

    2006-01-01

    Many students find the leap from arithmetic to algebra a difficult one to make, and current literature suggests that a number of the common misconceptions held by students arise as a result of the methods which teachers use to present algebra. The abstract nature of algebra makes it difficult for students to grasp; students also struggle with the…

  8. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  9. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  10. Ternary Virasoro - Witt algebra.

    SciTech Connect

    Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.

  11. Spin wave Feynman diagram vertex computation package

    NASA Astrophysics Data System (ADS)

    Price, Alexander; Javernick, Philip; Datta, Trinanjan

    Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.

  12. Permutation centralizer algebras and multimatrix invariants

    NASA Astrophysics Data System (ADS)

    Mattioli, Paolo; Ramgoolam, Sanjaye

    2016-03-01

    We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.

  13. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  14. Inductively generating Euler diagrams.

    PubMed

    Stapleton, Gem; Rodgers, Peter; Howse, John; Zhang, Leishi

    2011-01-01

    Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of well-formedness conditions; we present a series of results that identify properties of cycles that correspond to the well-formedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of well-formedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.

  15. Discrete Minimal Surface Algebras

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Hoppe, Jens

    2010-05-01

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  16. Longer Bars for Bigger Numbers? Children's Usage and Understanding of Graphical Representations of Algebraic Problems

    ERIC Educational Resources Information Center

    Lee, Kerry; Khng, Kiat Hui; Ng, Swee Fong; Ng Lan Kong, Jeremy

    2013-01-01

    In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems. However, little is known about students' understanding of these graphical representations. We investigated whether students use and think of the bar diagrams in a concrete or a more abstract fashion. We also…

  17. On Derivations Of Genetic Algebras

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh; Qaralleh, Izzat

    2014-11-01

    A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two.

  18. FormCalc 8: Better Algebra and Vectorization

    NASA Astrophysics Data System (ADS)

    Chokoufe Nejad, B.; Hahn, T.; Lang, J.-N.; Mirabella, E.

    2014-06-01

    We present Version 8 of the Feynman-diagram calculator FormCalc. New features include in particular significantly improved algebraic simplification as well as vectorization of the generated code. The Cuba Library, used in FormCalc, features checkpointing to disk for all integration algorithms.

  19. Synthesis of a Unique Isoindoline/Tetrahydroisoquinoline-based Tricyclic Sultam Library Utilizing a Heck-aza-Michael Strategy

    PubMed Central

    Zang, Qin; Javed, Salim; Porubsky, Patrick; Ullah, Farman; Neuenswander, Benjamin; Lushington, Gerald H.; Basha, Fatima Z.; Organ, Michael G.; Hanson, Paul R.

    2012-01-01

    The synthesis of a unique isoindoline- and tetrahydroisoquinoline (THIQ)-containing tricyclic sultam library, utilizing a Heck-aza-Michael (HaM) strategy is reported. Both isoindoline and THIQ rings are installed through a Heck reaction on a vinylsulfonamide, followed by one-pot deprotection and intramolecular aza-Michael reaction. Subsequent cyclization with either paraformaldehyde condensation or 1,1'-carbonyldiimidazole coupling generates a variety of tricyclic sultams. Overall, a 160-member library of these sultams, together with their isoindolines/THIQ and secondary sulfonamides precursors, were constructed using this strategy. PMID:22311745

  20. Synthesis of a unique isoindoline/tetrahydroisoquinoline-based tricyclic sultam library utilizing a Heck-aza-Michael strategy.

    PubMed

    Zang, Qin; Javed, Salim; Porubsky, Patrick; Ullah, Farman; Neuenswander, Benjamin; Lushington, Gerald H; Basha, Fatima Z; Organ, Michael G; Hanson, Paul R

    2012-03-12

    The synthesis of a unique isoindoline- and tetrahydroisoquinoline (THIQ)-containing tricyclic sultam library, utilizing a Heck-aza-Michael (HaM) strategy is reported. Both isoindoline and THIQ rings are installed through a Heck reaction on a vinylsulfonamide, followed by one-pot deprotection and intramolecular aza-Michael reaction. Subsequent cyclization with either paraformaldehyde condensation or 1,1'-carbonyldiimidazole coupling generates a variety of tricyclic sultams. Overall, a 160-member library of these sultams, together with their isoindolines/THIQ and secondary sulfonamides precursors, were constructed using this strategy.

  1. Palladium-catalyzed cyclization/Heck- and cyclization/conjugate-addition-type sequences in the preparation of polysubstituted furans.

    PubMed

    Aurrecoechea, José M; Durana, Aritz; Pérez, Elena

    2008-05-02

    Palladium-catalyzed heterocyclization-coupling sequences have been developed starting from buta-1,2,3-trienyl carbinols and electron-deficient alkenes. Polysubstituted furans are formed where the heterocyclic ring originates from the elements of the butatrienyl carbinol while the electron-deficient olefin is incorporated as a C-3 substituent. In most cases, the reaction proceeds via a Heck-type pathway leading to the efficient formation of 3-vinylfurans. However, couplings with methyl vinyl ketone display a divergent behavior to afford selectively either Heck- or hydroarylation-type products depending on reaction conditions.

  2. Square Source Type Diagram

    NASA Astrophysics Data System (ADS)

    Aso, N.; Ohta, K.; Ide, S.

    2014-12-01

    Deformation in a small volume of earth interior is expressed by a symmetric moment tensor located on a point source. The tensor contains information of characteristic directions, source amplitude, and source types such as isotropic, double-couple, or compensated-linear-vector-dipole (CLVD). Although we often assume a double couple as the source type of an earthquake, significant non-double-couple component including isotropic component is often reported for induced earthquakes and volcanic earthquakes. For discussions on source types including double-couple and non-double-couple components, it is helpful to display them using some visual diagrams. Since the information of source type has two degrees of freedom, it can be displayed onto a two-dimensional flat plane. Although the diagram developed by Hudson et al. [1989] is popular, the trace corresponding to the mechanism combined by two mechanisms is not always a smooth line. To overcome this problem, Chapman and Leaney [2012] developed a new diagram. This diagram has an advantage that a straight line passing through the center corresponds to the mechanism obtained by a combination of an arbitrary mechanism and a double-couple [Tape and Tape, 2012], but this diagram has some difficulties in use. First, it is slightly difficult to produce the diagram because of its curved shape. Second, it is also difficult to read out the ratios among isotropic, double-couple, and CLVD components, which we want to obtain from the estimated moment tensors, because they do not appear directly on the horizontal or vertical axes. In the present study, we developed another new square diagram that overcomes the difficulties of previous diagrams. This diagram is an orthogonal system of isotropic and deviatoric axes, so it is easy to get the ratios among isotropic, double-couple, and CLVD components. Our diagram has another advantage that the probability density is obtained simply from the area within the diagram if the probability density

  3. Noncovalent Substrate-Directed Enantioselective Heck Reactions: Synthesis of S- and P-Stereogenic Heterocycles.

    PubMed

    de Azambuja, Francisco; Carmona, Rafaela C; Chorro, Tomaz H D; Heerdt, Gabriel; Correia, Carlos Roque D

    2016-08-01

    S- and P-Stereogenic heterocycles were synthesized by a remarkably simple enantioselective Heck desymmetrization reaction based on the unprecedented noncovalent directing effect of S=O and P=O functionalities. Selected prochiral symmetric substrates were efficiently arylated using the recently disclosed chiral PyraBOx ligand under mild and open-flask reaction conditions. Several five-membered aryl- sulfones, sulfoxides, and phosphine oxides were synthesized in good to excellent yields, in good to high diastereoselectivity, and enantiomeric ratios up to 98:2. Theoretical calculations also support the noncovalent directing effect of the S=O and P=O functionalities during the arylation process.

  4. Metabolic alkene labeling and in vitro detection of histone acylation via the aqueous oxidative Heck reaction.

    PubMed

    Ourailidou, Maria E; Dockerty, Paul; Witte, Martin; Poelarends, Gerrit J; Dekker, Frank J

    2015-03-28

    The detection of protein lysine acylations remains a challenge due to lack of specific antibodies for acylations with various chain lengths. This problem can be addressed by metabolic labeling techniques using carboxylates with reactive functionalities. Subsequent chemoselective reactions with a complementary moiety connected to a detection tag enable the visualization and quantification of the protein lysine acylome. In this study, we present EDTA-Pd(II) as a novel catalyst for the oxidative Heck reaction on protein-bound alkenes, which allows employment of fully aqueous reaction conditions. We used this reaction to monitor histone lysine acylation in vitro after metabolic incorporation of olefinic carboxylates as chemical reporters.

  5. Linear polystyrene-stabilized PdO nanoparticle-catalyzed Mizoroki-Heck reactions in water.

    PubMed

    Ohtaka, Atsushi; Yamaguchi, Tomohiro; Teratani, Takuto; Shimomura, Osamu; Nomura, Ryôki

    2011-10-27

    Linear polystyrene-stabilized PdO nanoparticles (PS-PdONPs) were prepared by thermal decomposition of Pd(OAc)(2) in the presence of polystyrene. X-ray diffraction (XRD) and transmission electron microscopy (TEM) indicated the production of PdO nanoparticles. The loading of palladium was determined by inductively coupled plasma-atomic emission spectroscopy (ICP-AES). PS-PdONPs exhibited high catalytic activity for Mizoroki-Heck reactions under air in water and could be recycled without loss of activity.

  6. Catalyst-Controlled Regioselectivity in the Synthesis of Branched Conjugated Dienes via Aerobic Oxidative Heck Reactions

    PubMed Central

    Zheng, Changwu; Wang, Dian; Stahl, Shannon S.

    2012-01-01

    Pd-catalyzed aerobic oxidative coupling of vinylboronic acids and electronically unbiased alkyl olefins provides regioselective access to 1,3-disubstituted conjugated dienes. Catalyst-controlled regioselectivity is achieved by using 2,9-dimethylphenanthroline as a ligand. The observed regioselectivity is opposite to that observed from a traditional (non-oxidative) Heck reaction between a vinyl bromide and an alkene. DFT computational studies reveal that steric effects of the 2,9-dimethylphenanthroline ligand promote C–C bond-formation at the internal position of the alkene. PMID:22998540

  7. Classification of Normal Subgroups of Hecke Group H6 in Terms of Parabolic Class Number

    NASA Astrophysics Data System (ADS)

    Yurttas, Aysun; Demirci, Musa; Cangul, I. Naci

    2011-09-01

    In [3], Greenberg showed that n≤6t3 so that μ = nt≤6t4 for a normal subgroup N of level n and index μ having t parabolic classes in the modular group Γ. Accola, [1], improved these to n≤6t2 always and n≤t2 if Γ/N is not abelian. Newman, [5], obtained another generalisation of these results. Hecke groups are generalisations of the modular group. We particularly deal with one of the most important cases, q = 6.

  8. Rational design of cyclopropane-based chiral PHOX ligands for intermolecular asymmetric Heck reaction

    PubMed Central

    Rubina, Marina; Sherrill, William M; Barkov, Alexey Yu

    2014-01-01

    Summary A novel class of chiral phosphanyl-oxazoline (PHOX) ligands with a conformationally rigid cyclopropyl backbone was synthesized and tested in the intermolecular asymmetric Heck reaction. Mechanistic modelling and crystallographic studies were used to predict the optimal ligand structure and helped to design a very efficient and highly selective catalytic system. Employment of the optimized ligands in the asymmetric arylation of cyclic olefins allowed for achieving high enantioselectivities and significantly suppressing product isomerization. Factors affecting the selectivity and the rate of the isomerization were identified. It was shown that the nature of this isomerization is different from that demonstrated previously using chiral diphosphine ligands. PMID:25161709

  9. Asymptotic analysis of Bayesian generalization error with Newton diagram.

    PubMed

    Yamazaki, Keisuke; Aoyagi, Miki; Watanabe, Sumio

    2010-01-01

    Statistical learning machines that have singularities in the parameter space, such as hidden Markov models, Bayesian networks, and neural networks, are widely used in the field of information engineering. Singularities in the parameter space determine the accuracy of estimation in the Bayesian scenario. The Newton diagram in algebraic geometry is recognized as an effective method by which to investigate a singularity. The present paper proposes a new technique to plug the diagram in the Bayesian analysis. The proposed technique allows the generalization error to be clarified and provides a foundation for an efficient model selection. We apply the proposed technique to mixtures of binomial distributions.

  10. Prediction of Algebraic Instabilities

    NASA Astrophysics Data System (ADS)

    Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael

    2016-11-01

    A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.

  11. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  12. Infinite dimensional matrix algebras

    NASA Astrophysics Data System (ADS)

    Bordemann, M.; Hoppe, J.; Schaller, P.

    1989-11-01

    To each (finite dimensional) Lie algebra g we associate a class L λ(g) of infinite dimensional Lie algebras, induced by representations D λ(g). We show that in the case of sl(2, C) one obtains a series of pairwise non-isomorphic infinite dimensional Lie algebras depending continuously on a complex parameter λ. We connect this method with previous results on the relation between Diff AS 2 and su( N), and comment on a recent conjecture concerning higher spin algebras, and (2 + 1)-dimensional gravity.

  13. Weyl card diagrams

    SciTech Connect

    Jones, Gregory; Wang, John E.

    2005-06-15

    To capture important physical properties of a spacetime we construct a new diagram, the card diagram, which accurately draws generalized Weyl spacetimes in arbitrary dimensions by encoding their global spacetime structure, singularities, horizons, and some aspects of causal structure including null infinity. Card diagrams draw only nontrivial directions providing a clearer picture of the geometric features of spacetimes as compared to Penrose diagrams, and can change continuously as a function of the geometric parameters. One of our main results is to describe how Weyl rods are traversable horizons and the entirety of the spacetime can be mapped out. We review Weyl techniques and as examples we systematically discuss properties of a variety of solutions including Kerr-Newman black holes, black rings, expanding bubbles, and recent spacelike-brane solutions. Families of solutions will share qualitatively similar cards. In addition we show how card diagrams not only capture information about a geometry but also its analytic continuations by providing a geometric picture of analytic continuation. Weyl techniques are generalized to higher dimensional charged solutions and applied to generate perturbations of bubble and S-brane solutions by Israel-Khan rods.

  14. Reproducibility of maximum aerobic power (VO2max) among soccer players using a modified heck protocol.

    PubMed

    Santos-Silva, Paulo Roberto; Fonseca, Alfredo José; Castro, Anita Weigand de; Greve, Júlia Maria D'Andréa; Hernandez, Arnaldo José

    2007-08-01

    To determine the degree of reproducibility of maximum oxygen consumption (VO2max) among soccer players, using a modified Heck protocol. 2 evaluations with an interval of 15 days between them were performed on 11 male soccer players. All the players were at a high performance level; they were training for an average of 10 hours per week, totaling 5 times a week. When they were evaluated, they were in the middle of the competitive season, playing 1 match per week. The soccer players were evaluated on an ergometric treadmill with velocity increments of 1.2 km.h-1 every 2 minutes and a fixed inclination of 3% during the test. VO2max was measured directly using a breath-by-breath metabolic gas analyzer. The maximum running speed and VO2max attained in the 2 tests were, respectively: (15.6 +/- 1.1 vs. 15.7 +/- 1.2 km.h-1; [P = .78]) and (54.5 +/- 3.9 vs. 55.2 +/- 4.4 ml.kg-1.min-1; [P = .88]). There was high and significant correlation of VO2max between the 2 tests with a 15-day interval between them [r = 0.97; P < .001]. The modified Heck protocol was reproducible, and the 15-day interval between the ergospirometric testing was insufficient to significantly modify the soccer players' VO2max values.

  15. Mechanism, reactivity, and selectivity in palladium-catalyzed redox-relay Heck arylations of alkenyl alcohols.

    PubMed

    Xu, Liping; Hilton, Margaret J; Zhang, Xinhao; Norrby, Per-Ola; Wu, Yun-Dong; Sigman, Matthew S; Wiest, Olaf

    2014-02-05

    The enantioselective Pd-catalyzed redox-relay Heck arylation of acyclic alkenyl alcohols allows access to various useful chiral building blocks from simple olefinic substrates. Mechanistically, after the initial migratory insertion, a succession of β-hydride elimination and migratory insertion steps yields a saturated carbonyl product instead of the more general Heck product, an unsaturated alcohol. Here, we investigate the reaction mechanism, including the relay function, yielding the final carbonyl group transformation. M06 calculations predict a ΔΔG(‡) of 1 kcal/mol for the site selectivity and 2.5 kcal/mol for the enantioselectivity, in quantitative agreement with experimental results. The site selectivity is controlled by a remote electronic effect, where the developing polarization of the alkene in the migratory insertion transition state is stabilized by the C-O dipole of the alcohol moiety. The enantioselectivity is controlled by steric repulsion between the oxazoline substituent and the alcohol-bearing alkene substituent. The relay efficiency is due to an unusually smooth potential energy surface without high barriers, where the hydroxyalkyl-palladium species acts as a thermodynamic sink, driving the reaction toward the carbonyl product. Computational predictions of the relative reactivity and selectivity of the double bond isomers are validated experimentally.

  16. The Virasoro vertex algebra and factorization algebras on Riemann surfaces

    NASA Astrophysics Data System (ADS)

    Williams, Brian

    2017-08-01

    This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello-Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta-gamma system using the method of effective BV quantization.

  17. Efficient, regioselective palladium-catalyzed tandem Heck-isomerization reaction of aryl bromides and non-allylic benzyl alcohols.

    PubMed

    Crawley, Matthew L; Phipps, Kristin M; Goljer, Igor; Mehlmann, John F; Lundquist, Joseph T; Ullrich, John W; Yang, Cuijian; Mahaney, Paige E

    2009-03-05

    An efficient and mild method to couple aryl bromides and activated non-allylic alcohols in a Heck reaction with tandem isomerization to selectively afford high yields of 1,5-diarylalkan-1-ones has been developed. Mechanistic insight was gained through NMR studies of products derived from deuterium-labeled intermediates.

  18. Language Approaches to Beginning Algebra.

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    1990-01-01

    Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)

  19. To use or not to use diagrams: The effect of drawing a diagram in solving introductory physics problems

    NASA Astrophysics Data System (ADS)

    Maries, Alexandru; Singh, Chandralekha

    2013-01-01

    Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 111 students in an algebra-based introductory physics course were subjected to two different interventions during recitation quizzes throughout the semester. They were either (1) asked to solve problems in which the diagrams were drawn for them or (2) explicitly told to draw a diagram. A comparison group was not given any instruction regarding diagrams. We developed a rubric to score the problem-solving performance of students in different intervention groups. We investigated two problems involving electric field and electric force and found that students who draw expert-like diagrams are more successful problem solvers and that a higher level of detail in a student's diagram corresponds to a better score.

  20. Bicovariant quantum algebras and quantum Lie algebras

    NASA Astrophysics Data System (ADS)

    Schupp, Peter; Watts, Paul; Zumino, Bruno

    1993-10-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).

  1. Analytic real algebras.

    PubMed

    Seo, Young Joo; Kim, Young Hee

    2016-01-01

    In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d-algebra.

  2. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  3. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

  4. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  5. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  6. Learning Activity Package, Algebra.

    ERIC Educational Resources Information Center

    Evans, Diane

    A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

  7. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  8. Algebraic Reasoning through Patterns

    ERIC Educational Resources Information Center

    Rivera, F. D.; Becker, Joanne Rossi

    2009-01-01

    This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

  9. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

  10. Parastatistics Algebras and Combinatorics

    NASA Astrophysics Data System (ADS)

    Popov, T.

    2005-03-01

    We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.

  11. Catching Up on Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

  12. Remarks on Effect Algebras

    NASA Astrophysics Data System (ADS)

    Majewski, Władysław A.; Tylec, Tomasz I.

    2010-12-01

    Erik M. Alfsen and Frederic W. Shultz had recently developed the characterisation of state spaces of operator algebras. It established full equivalence (in the mathematical sense) between the Heisenberg and the Schrödinger picture, i.e. given a physical system we are able to construct its state space out of its observables as well as to construct algebra of observables from its state space. As an underlying mathematical structure they used the theory of duality of ordered linear spaces and obtained results are valid for various types of operator algebras (namely C *, von Neumann, JB and JBW algebras). Here, we show that the language they developed also admits a representation of an effect algebra.

  13. Impulse-Momentum Diagrams

    ERIC Educational Resources Information Center

    Rosengrant, David

    2011-01-01

    Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free-body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and…

  14. Understanding Network Diagrams.

    ERIC Educational Resources Information Center

    Waller, Robert

    A survey of a range of introductory university level textbooks in the social sciences found little use of network diagrams (NDs), i.e., graphic representations of processes, organizations, systems, and mechanisms. NDs can be viewed as a text/picture hybrid medium with titles and captions serving to qualify and identify the meaning and status of…

  15. Impulse-Momentum Diagrams

    ERIC Educational Resources Information Center

    Rosengrant, David

    2011-01-01

    Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free-body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and…

  16. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  17. Terminating Catalytic Asymmetric Heck Cyclizations by Stereoselective Intramolecular Capture of η3-Allylpalladium Intermediates: Total Synthesis of (−)-Spirotryprostatin B and Three Stereoisomers

    PubMed Central

    Overman, Larry E.; Rosen, Mark D.

    2010-01-01

    A catalytic intramolecular Heck reaction, followed by capture of the resulting η3-allylpalladium intermediate by a tethered diketopiperazine, is the central step in a concise synthetic route to (−)-spirotryprostatin B and three stereoisomers. This study demonstrates that an acyclic, chiral η3-allylpalladium fragment generated in a catalytic asymmetric Heck cyclization can be trapped by even a weakly nucleophilic diketopiperazine more rapidly than it undergoes diastereomeric equilibration. PMID:20725641

  18. Subsectors, Dynkin diagrams and new generalised geometries

    NASA Astrophysics Data System (ADS)

    Strickland-Constable, Charles

    2017-08-01

    We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin( d, d) × ℝ + for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case d = 8 provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider exam-ples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.

  19. Algebraic Nonlinear Collective Motion

    NASA Astrophysics Data System (ADS)

    Troupe, J.; Rosensteel, G.

    1998-11-01

    Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).

  20. Tectonic discrimination diagrams revisited

    NASA Astrophysics Data System (ADS)

    Vermeesch, Pieter

    2006-06-01

    The decision boundaries of most tectonic discrimination diagrams are drawn by eye. Discriminant analysis is a statistically more rigorous way to determine the tectonic affinity of oceanic basalts based on their bulk-rock chemistry. This method was applied to a database of 756 oceanic basalts of known tectonic affinity (ocean island, mid-ocean ridge, or island arc). For each of these training data, up to 45 major, minor, and trace elements were measured. Discriminant analysis assumes multivariate normality. If the same covariance structure is shared by all the classes (i.e., tectonic affinities), the decision boundaries are linear, hence the term linear discriminant analysis (LDA). In contrast with this, quadratic discriminant analysis (QDA) allows the classes to have different covariance structures. To solve the statistical problems associated with the constant-sum constraint of geochemical data, the training data must be transformed to log-ratio space before performing a discriminant analysis. The results can be mapped back to the compositional data space using the inverse log-ratio transformation. An exhaustive exploration of 14,190 possible ternary discrimination diagrams yields the Ti-Si-Sr system as the best linear discrimination diagram and the Na-Nb-Sr system as the best quadratic discrimination diagram. The best linear and quadratic discrimination diagrams using only immobile elements are Ti-V-Sc and Ti-V-Sm, respectively. As little as 5% of the training data are misclassified by these discrimination diagrams. Testing them on a second database of 182 samples that were not part of the training data yields a more reliable estimate of future performance. Although QDA misclassifies fewer training data than LDA, the opposite is generally true for the test data. Therefore LDA is a cruder but more robust classifier than QDA. Another advantage of LDA is that it provides a powerful way to reduce the dimensionality of the multivariate geochemical data in a similar

  1. Algebraic invariants for homotopy types

    NASA Astrophysics Data System (ADS)

    Blanc, David

    1999-11-01

    We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.

  2. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number,…

  3. Adaptive algebraic reconstruction technique

    SciTech Connect

    Lu Wenkai; Yin Fangfang

    2004-12-01

    Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency.

  4. Single-Site Palladium(II) Catalyst for Oxidative Heck Reaction: Catalytic Performance and Kinetic Investigations

    SciTech Connect

    Duan, Hui; Li, Mengyang; Zhang, Guanghui; Gallagher, James R.; Huang, Zhiliang; Sun, Yu; Luo, Zhong; Chen, Hongzhong; Miller, Jeffrey T.; Zou, Ruqiang; Lei, Aiwen; Zhao, Yanli

    2015-01-01

    ABSTRACT: The development of organometallic single-site catalysts (SSCs) has inspired the designs of new heterogeneous catalysts with high efficiency. Nevertheless, the application of SSCs in certain modern organic reactions, such as C-C bond formation reactions, has still been less investigated. In this study, a single-site Pd(II) catalyst was developed, where 2,2'-bipyridine-grafted periodic mesoporous organosilica (PMO) was employed as the support of a Pd(II) complex. The overall performance of the single-site Pd(II) catalyst in the oxidative Heck reaction was then investigated. The investigation results show that the catalyst displays over 99% selectivity for the product formation with high reaction yield. Kinetic profiles further confirm its high catalytic efficiency, showing that the rate constant is nearly 40 times higher than that for the free Pd(II) salt. X-ray absorption spectroscopy reveals that the catalyst has remarkable lifetime and recyclability.

  5. Enantioselective Heck-Matsuda Arylations through Chiral Anion Phase-Transfer of Aryl Diazonium Salts.

    PubMed

    Avila, Carolina M; Patel, Jigar S; Reddi, Yernaidu; Saito, Masato; Nelson, Hosea M; Shunatona, Hunter P; Sigman, Matthew S; Sunoj, Raghavan B; Toste, F Dean

    2017-05-15

    A mild, asymmetric Heck-Matsuda reaction of five-, six- and seven-membered ring alkenes and aryl diazonium salts is presented. High yields and enantioselectivities were achieved using Pd(0) and chiral anion co-catalysts, the latter functioning as a chiral anion phase-transfer (CAPT) reagent. For certain substrate classes, the chiral anion catalysts were modulated to minimize the formation of undesired by-products. More specifically, BINAM-derived phosphoric acid catalysts were shown to prevent alkene isomerization in cyclopentene and cycloheptene starting materials. DFT(B3LYP-D3) computations revealed that increased product selectivity resulted from a chiral anion dependent lowering of the activation barrier for the desired pathway. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  6. Arylboronic acids as versatile coupling partners in fast microwave promoted oxidative Heck chemistry.

    PubMed

    Andappan, Murugaiah M S; Nilsson, Peter; Larhed, Mats

    2003-01-01

    The useful and selective reactivity of arylboronic acids makes them favourite building blocks for many modern organic chemistry applications like the metal-mediated formation of C-C, C-O, C-N, and C-S bonds. This report describes oxidative Heck coupling reactions of arylboronic acids and olefins, which were conveniently and rapidly (5-30 min) carried out under air with temperature-controlled microwave heating. Different reaction conditions were investigated with regard to both microwave heating capability and chemical productivity. Copper(II) acetate was identified as a microwave compatible reoxidant of Pd(0). The scope and limitations of this high-speed chemistry protocol with diverse olefins and organoboronic acids are discussed.

  7. A Case Report of Focal Epithelial Hyperplasia (Heck's disease) with PCR Detection of Human Papillomavirus.

    PubMed

    Ozden, Bora; Gunduz, Kaan; Gunhan, Omer; Ozden, Feyza Otan

    2011-12-01

    Focal epithelial hyperplasia or Heck's disease, is a rare viral infection of the oral mucosa caused by human papillomavirus. The frequency of this disease varies widely from one geographic region to another. In Caucasians there have been only few cases reported. This paper reports a case of focal epithelial hyperplasia and demonstrates the association with HPV subtype 32 through polymerase chain reaction (PCR) and sequencing of PCR products. A 7-year-old Caucasian girl was admitted to our clinic for investigation of multiple oral mucosal lesions in the mouth. Lesion was excised under local anesthesia without any complication. The lesion was diagnosed as focal epithelial hyperplasia according to both clinical and histopathological features. Dental staff should be aware of these kind of lesions and histopathological examination together with a careful clinical observation should be carried out for a definitive diagnosis.

  8. Upper Bounds for the Level of Normal Subgroups of Hecke Groups

    NASA Astrophysics Data System (ADS)

    Demirci, Musa; Yurttas, Aysun; Cangul, I. Naci

    2011-09-01

    In [4], Greenberg showed that n≤6t3 so that μ = nt≤6t4 for a normal subgroup N of level n and index μ having t parabolic classes in the modular group Γ. Accola, [1], improved these to n≤6t2 always and n≤t2 if Γ/N is not abelian. In this work we generalise these results to Hecke groups. We get results between three parameters of a normal subgroup, i.e. the index μ, the level n and the parabolic class number t. We deal with the case q = 4, and then obtain the generalisation to other q. Two main problems here are the calculation of the number of normal subgroups and the determination of the bounds on the level n for a given t.

  9. Intramolecular Formal anti-Carbopalladation/Heck Reaction: Facile Domino Access to Carbo- and Heterooligocyclic Dienes.

    PubMed

    Pawliczek, Martin; Milde, Bastian; Jones, Peter G; Werz, Daniel B

    2015-08-24

    An intramolecular domino process consisting of a formal anti-carbopalladation followed by Heck reaction is realized. Complex oligo(hetero)cyclic scaffolds are efficiently obtained in one synthetic step from easily obtainable enyne precursors. In contrast to common syn-carbopalladation reactions of alkyne units, the carbopalladation employed here is designed to afford an anti-arrangement of the two new substituents across the emerging double bond. A prerequisite is that the residues next to the alkyne should lack any β-hydrogen atoms. The method paves the way to tri- and tetrasubstituted double-bond systems that have not been accessible by conventional Pd catalysis. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  10. Exploring a cascade Heck-Suzuki reaction based route to kinase inhibitors using design of experiments.

    PubMed

    Ekebergh, Andreas; Lingblom, Christine; Sandin, Peter; Wennerås, Christine; Mårtensson, Jerker

    2015-03-21

    Design of Experiments (DoE) has been used to optimize a diversity oriented palladium catalyzed cascade Heck-Suzuki reaction for the construction of 3-alkenyl substituted cyclopenta[b]indole compounds. The obtained DoE model revealed a reaction highly dependent on the ligand. Guided by the model, an optimal ligand was chosen that selectively delivered the desired products in high yields. The conditions were applicable with a variety of boronic acids and were used to synthesize a library of 3-alkenyl derivatized compounds. Focusing on inhibition of kinases relevant for combating melanoma, the library was used in an initial structure-activity survey. In line with the observed kinase inhibition, cellular studies revealed one of the more promising derivatives to inhibit cell proliferation via an apoptotic mechanism.

  11. TEP process flow diagram

    SciTech Connect

    Wilms, R Scott; Carlson, Bryan; Coons, James; Kubic, William

    2008-01-01

    This presentation describes the development of the proposed Process Flow Diagram (PFD) for the Tokamak Exhaust Processing System (TEP) of ITER. A brief review of design efforts leading up to the PFD is followed by a description of the hydrogen-like, air-like, and waterlike processes. Two new design values are described; the mostcommon and most-demanding design values. The proposed PFD is shown to meet specifications under the most-common and mostdemanding design values.

  12. Spinning Witten diagrams

    NASA Astrophysics Data System (ADS)

    Sleight, Charlotte; Taronna, Massimo

    2017-06-01

    We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS d+1. As an intermediate step, we identify convenient bases of three-point bulk and boundary structures to invert linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. Given a CFT d , this provides the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS d+1. Employing this framework, we determine the CPWE of a generic four-point exchange Witten diagram with spinning exchanged field. As a concrete application, we compute all four-point exchange Witten diagrams in the type A higher-spin gauge theory on AdS d+1, which is conjectured to be dual to the free scalar O ( N ) model.

  13. Pseudo-Riemannian Novikov algebras

    NASA Astrophysics Data System (ADS)

    Chen, Zhiqi; Zhu, Fuhai

    2008-08-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

  14. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems.

  15. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  16. Developing Algebraic Thinking.

    ERIC Educational Resources Information Center

    Alejandre, Suzanne

    2002-01-01

    Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)

  17. Jordan Algebraic Quantum Categories

    NASA Astrophysics Data System (ADS)

    Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander

    2015-03-01

    State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.

  18. An Abstract Algebra Story.

    ERIC Educational Resources Information Center

    Leron, Uri; Dubinsky, Ed

    1995-01-01

    Describes a constructivist, interactive approach for teaching undergraduate mathematics, abstract algebra in particular, using computer constructions programmed in ISETL to induce students' mental constructions and collaborative learning to help students reflect on these constructions. (18 references) (MKR)

  19. Accounting Equals Applied Algebra.

    ERIC Educational Resources Information Center

    Roberts, Sondra

    1997-01-01

    Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)

  20. Weyl n-Algebras

    NASA Astrophysics Data System (ADS)

    Markarian, Nikita

    2017-03-01

    We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.

  1. Aprepro - Algebraic Preprocessor

    SciTech Connect

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  2. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  3. Aprepro - Algebraic Preprocessor

    SciTech Connect

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  4. Global Geometric Deformations of the Virasoro Algebra, Current and Affine Algebras by Krichever Novikov Type Algebras

    NASA Astrophysics Data System (ADS)

    Fialowski, A.; Schlichenmaier, M.

    2007-11-01

    In two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever Novikov type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra, the Virasoro algebra, the classical current, and the affine Kac Moody Lie algebras respectively. The constructed families are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid. This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The algebras are of relevance in the global operator approach to the Wess Zumino Witten Novikov models appearing in the quantization of Conformal Field Theory.

  5. Crystalline hybrid solid materials of palladium and decamethylcucurbit[5]uril as recoverable precatalysts for Heck cross-coupling reactions.

    PubMed

    Li, Hongfang; Lü, Jian; Lin, Jingxiang; Huang, Yuanbiao; Cao, Minna; Cao, Rong

    2013-11-11

    A series of MPdMe10 CB[5] (M=Li, Na, K, Rb, and Cs; Me10 CB[5]=decamethylcucurbit[5]uril) hybrid solid materials have been successfully synthesized for the first time through a simple diffusion method. These as-prepared hybrid solids have been applied as phosphine-free precatalysts for Heck cross-coupling reactions with excellent catalytic performance and good recyclability. In the processes of the catalytic reactions, the activated Pd(II) species were released from the crystalline hybrid precatalysts and transformed into catalytically active Pd nanoparticles, which have been demonstrated as key to carry on the catalytic reactions for the recoverable precatalysts MPdMe10 CB[5] (M=K, Rb, and Cs). It has also been rationalized that the introduction of different alkali metals afforded crystalline hybrid precatalysts with different crystal structures, which are responsible for their diversified stability and reusability presented in Heck reactions.

  6. Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Chen, Baoyi; Chen, Gang; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan

    2017-02-01

    Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable.

  7. Using the Logarithmic Concentration Diagram, Log "C", to Teach Acid-Base Equilibrium

    ERIC Educational Resources Information Center

    Kovac, Jeffrey

    2012-01-01

    Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

  8. Using the Logarithmic Concentration Diagram, Log "C", to Teach Acid-Base Equilibrium

    ERIC Educational Resources Information Center

    Kovac, Jeffrey

    2012-01-01

    Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

  9. The topology of Liouville foliation for the Sokolov integrable case on the Lie algebra so(4)

    SciTech Connect

    Haghighatdoost, Gorbanali; Oshemkov, Andrey A

    2009-06-30

    Several new integrable cases for Euler's equations on some six-dimensional Lie algebras were found by Sokolov in 2004. In this paper we study topological properties of one of these integrable cases on the Lie algebra so(4). In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, the classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained. Bibliography: 9 titles.

  10. An in Situ Generated Palladium on Aluminum Oxide: Applications in Gram-Scale Matsuda-Heck Reactions.

    PubMed

    Pape, Simon; Daukšaitė, Lauryna; Lucks, Sandra; Gu, Xiaoting; Brunner, Heiko

    2016-12-16

    In situ generated palladium on aluminum oxide provides an active catalytic system for Matsuda-Heck reactions in gram-scale. The novel catalyst proceeded through a significantly higher catalytic activity compared to the classical Pd/C system. Based on the high catalytic activity the first α,β,β-triarylation of methyl acrylate in good yields could be provided in one-step.

  11. Reactions of nitroxides 15. Cinnamates bearing a nitroxyl moiety synthesized using a Mizoroki-Heck cross-coupling reaction.

    PubMed

    Zakrzewski, Jerzy; Huras, Bogumiła

    2015-01-01

    Cinnamic acid derivatives bearing a nitroxyl moiety (2,2,6,6-tetramethyl-1-oxyl-4-piperidyl 3-E-aryl acrylates) were synthesized in 30-100% yield using a Mizoroki-Heck cross-coupling reaction between 4-acryloyloxy-2,2,6,6-tetramethylpiperidine-1-oxyl and iodobenzene derivatives in the presence of palladium(II) acetate coordinated with a tri(o-tolyl)phosphine ligand immobilized in a polyurea matrix.

  12. Reactions of nitroxides 15. Cinnamates bearing a nitroxyl moiety synthesized using a Mizoroki–Heck cross-coupling reaction

    PubMed Central

    Huras, Bogumiła

    2015-01-01

    Summary Cinnamic acid derivatives bearing a nitroxyl moiety (2,2,6,6-tetramethyl-1-oxyl-4-piperidyl 3-E-aryl acrylates) were synthesized in 30–100% yield using a Mizoroki–Heck cross-coupling reaction between 4-acryloyloxy-2,2,6,6-tetramethylpiperidine-1-oxyl and iodobenzene derivatives in the presence of palladium(II) acetate coordinated with a tri(o-tolyl)phosphine ligand immobilized in a polyurea matrix. PMID:26199672

  13. A general synthesis of fluoroalkylated alkenes by palladium-catalyzed Heck-type reaction of fluoroalkyl bromides.

    PubMed

    Feng, Zhang; Min, Qiao-Qiao; Zhao, Hai-Yang; Gu, Ji-Wei; Zhang, Xingang

    2015-01-19

    An efficient palladium-catalyzed Heck-type reaction of fluoroalkyl halides, including perfluoroalkyl bromides, trifluoromethyl iodides, and difluoroalkyl bromides, has been developed. The reaction proceeds under mild reaction conditions with high efficiency and broad substrate scope, and provides a general and straightforward access to fluoroalkylated alkenes which are of interest in life and material sciences. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  14. The First Example of Nickel-Catalyzed Silyl-Heck Reactions: Direct Activation of Silyl Triflates Without Iodide Additives

    PubMed Central

    McAtee, Jesse R.; Martin, Sara E. S.; Cinderella, Andrew P.; Reid, William B.; Johnson, Keywan A.

    2014-01-01

    For the first time, nickel-catalyzed silyl-Heck reactions are reported. Using simple phosphine-supported nickel catalysts, direct activation of silyl triflates has been achieved. These results contrast earlier palladium-catalyzed systems, which require iodide additives to activate silyl-triflates. These nickel-based catalysts exhibit good functional group tolerance in the preparation of vinyl silanes, and unlike earlier systems, allows for the incorporation of trialkylsilanes larger than Me3Si. PMID:24914247

  15. Petersen diagram revolution

    NASA Astrophysics Data System (ADS)

    Smolec, Radoslaw; Dziembowski, Wojciech; Moskalik, Pawel; Netzel, Henryka; Prudil, Zdenek; Skarka, Marek; Soszynski, Igor

    2017-09-01

    Over the recent years, the Petersen diagram for classical pulsators, Cepheids and RR Lyr stars, populated with a few hundreds of new multiperiodic variables. We review our analyses of the OGLE data, which resulted in a significant extension of the known, and in the discovery of a few new and distinct forms of multiperiodic pulsation. The showcase includes not only radial mode pulsators, but also radial-non-radial pulsators and stars with significant modulation observed on top of the beat pulsation. First theoretical models explaining the new forms of stellar variability are briefly discussed.

  16. Nickel and cobalt-catalyzed coupling of alkyl halides with alkenes via heck reactions and radical conjugate addition.

    PubMed

    Qian, Qun; Zang, Zhenhua; Chen, Yang; Tong, Weiqi; Gong, Hegui

    2013-05-01

    Cross-coupling of alkyl halides with alkenes leading to Heck-type and addition products is summarized. The development of Heck reaction with aliphatic halides although has made significant progress in the past decade and particularly recently, it was much less explored in comparison with the aryl halides. The use of Ni- and Co-catalyzed protocols allowed efficient Heck coupling of activated and unactivated alkenes with 1°, 2° and 3° alkyl halides. In addition, radical conjugate addition to activated alkenes has become a well-established method that has led to efficient construction of many natural products. The utilization of Ni- and Co-catalyzed strategies would avoid toxic tin reagents, and therefore worth exploring. The recent development of Ni- and Co-catalyzed addition of alkyl halides to alkenes displays much improved reactivity and functional group tolerance. In this mini-review, we also attempt to overview the mechanisms that are proposed in the reactions, aiming at providing insight into the nickel and cobalt-catalyzed coupling of alkyl halides with alkenes.

  17. Bethe subalgebras in affine Birman-Murakami-Wenzl algebras and flat connections for q-KZ equations

    NASA Astrophysics Data System (ADS)

    Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O.

    2016-05-01

    Commutative sets of Jucys-Murphy elements for affine braid groups of {A}(1),{B}(1),{C}(1),{D}(1) types were defined. Construction of R-matrix representations of the affine braid group of type {C}(1) and its distinguished commutative subgroup generated by the {C}(1)-type Jucys-Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the {C}(1)-type Jucys-Murphy elements. We specify our general construction to the case of the Birman-Murakami-Wenzl algebras (BMW algebras for short). As an application we suggest a baxterization of the Dunkl-Cherednik elements {Y}\\prime {{s}} in the double affine Hecke algebra of type A. Dedicated to Professor Rodney Baxter on the occasion of his 75th Birthday.

  18. Warped penguin diagrams

    SciTech Connect

    Csaki, Csaba; Grossman, Yuval; Tanedo, Philip; Tsai, Yuhsin

    2011-04-01

    We present an analysis of the loop-induced magnetic dipole operator in the Randall-Sundrum model of a warped extra dimension with anarchic bulk fermions and an IR brane-localized Higgs. These operators are finite at one-loop order and we explicitly calculate the branching ratio for {mu}{yields}e{gamma} using the mixed position/momentum space formalism. The particular bound on the anarchic Yukawa and Kaluza-Klein (KK) scales can depend on the flavor structure of the anarchic matrices. It is possible for a generic model to either be ruled out or unaffected by these bounds without any fine-tuning. We quantify how these models realize this surprising behavior. We also review tree-level lepton flavor bounds in these models and show that these are on the verge of tension with the {mu}{yields}e{gamma} bounds from typical models with a 3 TeV Kaluza-Klein scale. Further, we illuminate the nature of the one-loop finiteness of these diagrams and show how to accurately determine the degree of divergence of a five-dimensional loop diagram using both the five-dimensional and KK formalism. This power counting can be obfuscated in the four-dimensional Kaluza-Klein formalism and we explicitly point out subtleties that ensure that the two formalisms agree. Finally, we remark on the existence of a perturbative regime in which these one-loop results give the dominant contribution.

  19. Markov Influence Diagrams.

    PubMed

    Díez, Francisco J; Yebra, Mar; Bermejo, Iñigo; Palacios-Alonso, Miguel A; Calleja, Manuel Arias; Luque, Manuel; Pérez-Martín, Jorge

    2017-02-01

    Markov influence diagrams (MIDs) are a new type of probabilistic graphical model that extends influence diagrams in the same way that Markov decision trees extend decision trees. They have been designed to build state-transition models, mainly in medicine, and perform cost-effectiveness analyses. Using a causal graph that may contain several variables per cycle, MIDs can model various patient characteristics without multiplying the number of states; in particular, they can represent the history of the patient without using tunnel states. OpenMarkov, an open-source tool, allows the decision analyst to build and evaluate MIDs-including cost-effectiveness analysis and several types of deterministic and probabilistic sensitivity analysis-with a graphical user interface, without writing any code. This way, MIDs can be used to easily build and evaluate complex models whose implementation as spreadsheets or decision trees would be cumbersome or unfeasible in practice. Furthermore, many problems that previously required discrete event simulation can be solved with MIDs; i.e., within the paradigm of state-transition models, in which many health economists feel more comfortable.

  20. Algebraic mesh quality metrics

    SciTech Connect

    KNUPP,PATRICK

    2000-04-24

    Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.

  1. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  2. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  3. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  4. Resonant algebras and gravity

    NASA Astrophysics Data System (ADS)

    Durka, R.

    2017-04-01

    The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.

  5. Quantum algebra of superspace

    SciTech Connect

    Hatcher, N.; Restuccia, A.; Stephany, J.

    2006-02-15

    We present the complete set of N=1, D=4 quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields. These solutions are expressed using the chiral, antichiral and tensorial projectors which define the three irreducible representations of the supersymmetry on the superfields. In each case the space-time variables are noncommuting and their commutators are proportional to the internal angular momentum of the representation. The quantum algebra associated to the chiral or the antichiral projector is the one obtained by the quantization of the Casalbuoni-Brink-Schwarz (superspin 0) massive superparticle. We present a new superparticle action for the (superspin 1/2) case and show that their wave functions are the ones associated to the irreducible tensor multiplet.

  6. Are diagrams always helpful tools? developmental and individual differences in the effect of presentation format on student problem solving.

    PubMed

    Booth, Julie L; Koedinger, Kenneth R

    2012-09-01

    High school and college students demonstrate a verbal, or textual, advantage whereby beginning algebra problems in story format are easier to solve than matched equations (Koedinger & Nathan, 2004). Adding diagrams to the stories may further facilitate solution (Hembree, 1992; Koedinger & Terao, 2002). However, diagrams may not be universally beneficial (Ainsworth, 2006; Larkin & Simon, 1987). To identify developmental and individual differences in the use of diagrams, story, and equation representations in problem solving. When do diagrams begin to aid problem-solving performance? Does the verbal advantage replicate for younger students? Three hundred and seventy-three students (121 sixth, 117 seventh, 135 eighth grade) from an ethnically diverse middle school in the American Midwest participated in Experiment 1. In Experiment 2, 84 sixth graders who had participated in Experiment 1 were followed up in seventh and eighth grades. In both experiments, students solved algebra problems in three matched presentation formats (equation, story, story + diagram). The textual advantage was replicated for all groups. While diagrams enhance performance of older and higher ability students, younger and lower-ability students do not benefit, and may even be hindered by a diagram's presence. The textual advantage is in place by sixth grade. Diagrams are not inherently helpful aids to student understanding and should be used cautiously in the middle school years, as students are developing competency for diagram comprehension during this time. ©2011 The British Psychological Society.

  7. On weak Lie 2-algebras

    NASA Astrophysics Data System (ADS)

    Roytenberg, Dmitry

    2007-11-01

    A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.

  8. A Holistic Approach to Algebra.

    ERIC Educational Resources Information Center

    Barbeau, Edward J.

    1991-01-01

    Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

  9. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  10. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  11. Algebra for Gifted Third Graders.

    ERIC Educational Resources Information Center

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  12. Selectivity control between Mizoroki-Heck and homo-coupling reactions for synthesising multinuclear metal complexes: unique addition effects of tertiary phosphines and O2.

    PubMed

    Yamazaki, Yasuomi; Ishitani, Osamu

    2017-04-05

    The addition of a tertiary phosphine and O2 to reaction solutions strongly affected the reactivity and selectivity of coupling reactions between transition metal complexes. The Mizoroki-Heck reaction between metal complexes with bromo and those with vinyl groups in the diimine ligand did not proceed using Pd(OAc)2 in the presence of 2-dicyclohexylphosphino-2',6'-dimethoxybiphenyl (Sphos) under Ar but proceeded selectively after injection of air into the reaction vessel. In the absence of the phosphine ligand, on the other hand, not only the Mizoroki-Heck reaction but also a homo-coupling reaction between the metal complexes with the bromo groups proceeded at the same time. Mechanistic investigation showed that nanoparticles of Pd species were produced in the absence of the phosphine ligand and worked as catalysts for both the Mizoroki-Heck and homo-coupling reactions. On the other hand, larger Pd particles, which were produced in the presence of Sphos but after addition of air for oxidising Sphos, selectively catalysed the Mizoroki-Heck reaction. 'Molecular' Pd species that were stabilised in the presence of non-oxidised Sphos could not catalyse both coupling reactions under the reaction conditions. Based on these results, reaction conditions were established for the selective progress of the Mizoroki-Heck and the homo-coupling reactions.

  13. Program Synthesizes UML Sequence Diagrams

    NASA Technical Reports Server (NTRS)

    Barry, Matthew R.; Osborne, Richard N.

    2006-01-01

    A computer program called "Rational Sequence" generates Universal Modeling Language (UML) sequence diagrams of a target Java program running on a Java virtual machine (JVM). Rational Sequence thereby performs a reverse engineering function that aids in the design documentation of the target Java program. Whereas previously, the construction of sequence diagrams was a tedious manual process, Rational Sequence generates UML sequence diagrams automatically from the running Java code.

  14. Algebra of Neuron Matrices,

    DTIC Science & Technology

    1985-03-13

    AD-Ri55 296 ALGEBRA OF NEURON MATRICES(U) FOREIGN TECHNOLOGY DIV i/i WRIGHT-PATTERSON RF8 ON K~ G RGRBRBYRN 13 MAR 85 FTD-ID(RS)T-8@4i-85...ANCLASSIFIED F/G6/6 NL I. 1j.2 U .611111 ’’ K1*10 Vl( PIH OPY Pl (iLUTION TL T CHART I-" FTD-ID(RS )T-0041-85 FOREIGN TECHNOLOGY DIVISION In ALGEBRA OF NEURON ... NEURON MATRICES DTIC TAB Unannounced Q By: K.G. Agababyan JustLficatlon English pages: 10 By Distribution/ Source: Doklady Akademii Nauk SSSR, Vol. 199

  15. An algebra of reversible computation.

    PubMed

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  16. On Weak-BCC-Algebras

    PubMed Central

    Thomys, Janus; Zhang, Xiaohong

    2013-01-01

    We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

  17. Visual Salience of Algebraic Transformations

    ERIC Educational Resources Information Center

    Kirshner, David; Awtry, Thomas

    2004-01-01

    Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

  18. Phenylenevinylene oligomers by Mizoroki-Heck cross coupling reaction. Structural and optoelectronic characterization

    NASA Astrophysics Data System (ADS)

    Estrada, Sandra E.; Ochoa-Puentes, Cristian; Sierra, Cesar A.

    2017-04-01

    In order to study the effect of the molecular structure on the optical properties of totally trans-trans phenylenevinylene oligomers (OPVs), sixteen 1,4-distyrylbenzene derivatives (1a-i and 2a-g) functionalized with different electron-donating (ED) and electron-withdrawing (EW) groups were synthesized by the Mizoroki-Heck cross coupling reaction in moderate to good yields (40-95%). The implemented methodology, with a small modification previously reported by our group, allows obtaining the desired vinyl configuration as well as one novel OPV compound (1h). After structural characterization by several techniques (e.g. FTIR, 1H, 13C and Solid-State NMR), particular emphasis was placed upon the investigation of their optical properties by UV-vis and fluorescence spectroscopies. The results showed that, with only one exception, the ED and EW groups at the ends of OPV systems lead to a bathochromic shift. This effect is intensified with the introduction of methoxy groups on the central ring. Consistent with these, the HOMO-LUMO gaps (ΔE) decreases as the strength of ED and EW substituents increases. The ED and EW substituents also lead to a decrease in the Φf values. This contribution in the area of organic electronics can be used as a reference to better select the most appropriate technological application for each OPV and this can be extrapolated to their respective structurally analogous segmented polymer.

  19. [Imiquimod for the topical treatment of focal epithelial hyperplasia (Heck disease) in a child].

    PubMed

    Maschke, Jan; Brauns, Tilmann C; Goos, Manfred

    2004-10-01

    Focal epithelial hyperplasia (FEH) or Heck disease is a rare skin disease caused by human papilloma viruses (HPV). The case of a 9-year old boy is presented to demonstrate the successful treatment of massive FEH with 5% imiquimod cream. Initially, the patient had noticed several separate papules, which spread and developed into multiple peri- and intraoral papillomatous nodules. The lesions were treated with carbon dioxide laser destruction. However, multiple, skin-coloured papillomatous nodules were found on the tongue, buccal mucosa and lips 1.5 years later. Treatment with imiquimod was initiated, because the patient suffered tremendously from the disease. 5% imiquimod cream was applied 3 times per week. Regression of lesions was obvious after 1 month of treatment. Complete clearance was achieved after 2 additional months of treatment and no recurrence was detected over a follow-up period of 5 months. Our case points out the clinical value of imiquimod for the non-traumatic and almost painless therapy of HPV-induced skin diseases in children.

  20. Relative reactivity of alkenyl alcohols in the palladium-catalyzed redox-relay Heck reaction.

    PubMed

    Hilton, Margaret J; Cheng, Bin; Buckley, Benjamin R; Xu, Liping; Wiest, Olaf; Sigman, Matthew S

    2015-09-16

    The relative rates of alkenyl alcohols in the Pd-catalyzed redox-relay Heck reaction were measured in order to examine the effect of their steric and electronic properties on the rate-determining step. Competition experiments between an allylic alkenyl alcohol and two substrates with differing chain lengths revealed that the allylic alcohol reacts 3-4 times faster in either case. Competition between di- and trisubstituted alkenyl alcohols provided an interesting scenario, in which the disubstituted alkene was consumed first followed by reaction of the trisubstituted alkene. Consistent with this observation, the transition structures for the migratory insertion of the aryl group into the di- and trisubstituted alkenes were calculated with a lower barrier for the former. An internal competition between a substrate containing two alcohols with differing chain lengths demonstrated the catalyst's preference for migrating towards the closest alcohol. Additionally, it was observed that increasing the electron density in the arene boronic acid promotes a faster reaction, which correlates with Hammett σp values to give a ρ of -0.87.

  1. Model Checking with Edge-Valued Decision Diagrams

    NASA Technical Reports Server (NTRS)

    Roux, Pierre; Siminiceanu, Radu I.

    2010-01-01

    We describe an algebra of Edge-Valued Decision Diagrams (EVMDDs) to encode arithmetic functions and its implementation in a model checking library. We provide efficient algorithms for manipulating EVMDDs and review the theoretical time complexity of these algorithms for all basic arithmetic and relational operators. We also demonstrate that the time complexity of the generic recursive algorithm for applying a binary operator on EVMDDs is no worse than that of Multi- Terminal Decision Diagrams. We have implemented a new symbolic model checker with the intention to represent in one formalism the best techniques available at the moment across a spectrum of existing tools. Compared to the CUDD package, our tool is several orders of magnitude faster

  2. Diagonal Slices of 3D Young Diagrams in the Approach of Maya Diagrams

    NASA Astrophysics Data System (ADS)

    Cai, Li-Qiang; Wang, Li-Fang; Wu, Ke; Yang, Jie

    2014-09-01

    According to the correspondence between 2D Young diagrams and Maya diagrams and the relation between 2D and 3D Young diagrams, we construct 3D Young diagrams in the approach of Maya diagrams. Moreover, we formulate the generating function of 3D Young diagrams, which is the MacMahon function in terms of Maya diagrams.

  3. From Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott

    2007-01-01

    Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

  4. Algebraic Thinking through Origami.

    ERIC Educational Resources Information Center

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  5. Pre-Algebra.

    ERIC Educational Resources Information Center

    Kennedy, John

    This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…

  6. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  7. Algebraic Thinking through Origami.

    ERIC Educational Resources Information Center

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  8. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  9. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  10. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  11. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  12. Nickel-Catalyzed Mizoroki–Heck Reaction of Aryl Sulfonates and Chlorides with Electronically Unbiased Terminal Olefins: High Selectivity for Branched Products**

    PubMed Central

    Tasker, Sarah Z.; Gutierrez, Alicia C.

    2014-01-01

    Achieving high selectivity in the Heck reaction of electronically unbiased alkenes has been a longstanding challenge. Using a nickel-catalyzed cationic Heck reaction, we were able to achieve excellent selectivity for branched products (≥19:1 in all cases) over a wide range of aryl electrophiles and aliphatic olefins. A bidentate ligand with a suitable bite angle and steric profile was key to obtaining high branched/linear selectivity, while the appropriate base suppressed alkene isomerization of the product. Though aryl triflates are traditionally used to access the cationic Heck pathway, we have shown that by using triethylsilyl trifluoromethanesulfonate (TESOTf), we can effect a counterion exchange of the catalytic nickel complex such that cheaper and more stable aryl chlorides, mesylates, tosylates, and sulfamates can be used to yield the same branched products with high selectivity. PMID:24402966

  13. Potential-pH Diagrams.

    ERIC Educational Resources Information Center

    Barnum, Dennis W.

    1982-01-01

    Potential-pH diagrams show the domains of redoxpotential and pH in which major species are most stable. Constructing such diagrams provides students with opportunities to decide what species must be considered, search literature for equilibrium constants and free energies of formation, and practice in using the Nernst equation. (Author/JN)

  14. Potential-pH Diagrams.

    ERIC Educational Resources Information Center

    Barnum, Dennis W.

    1982-01-01

    Potential-pH diagrams show the domains of redoxpotential and pH in which major species are most stable. Constructing such diagrams provides students with opportunities to decide what species must be considered, search literature for equilibrium constants and free energies of formation, and practice in using the Nernst equation. (Author/JN)

  15. Planar Para Algebras, Reflection Positivity

    NASA Astrophysics Data System (ADS)

    Jaffe, Arthur; Liu, Zhengwei

    2017-05-01

    We define a planar para algebra, which arises naturally from combining planar algebras with the idea of ZN para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects that are invariant under para isotopy. For each ZN, we construct a family of subfactor planar para algebras that play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras, which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), which we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity by relating the two reflections through the string Fourier transform.

  16. Genus Ranges of Chord Diagrams

    PubMed Central

    Burns, Jonathan; Jonoska, Nataša; Saito, Masahico

    2015-01-01

    A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges. PMID:26478650

  17. Genus Ranges of Chord Diagrams.

    PubMed

    Burns, Jonathan; Jonoska, Nataša; Saito, Masahico

    2015-04-01

    A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

  18. Algebraic connectivity and graph robustness.

    SciTech Connect

    Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.

    2009-07-01

    Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.

  19. On Dunkl angular momenta algebra

    NASA Astrophysics Data System (ADS)

    Feigin, Misha; Hakobyan, Tigran

    2015-11-01

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  20. On extensions of Leibniz algebras

    NASA Astrophysics Data System (ADS)

    Rakhimov, I. S.; Said Husain, Sh. K.; Mohammed, M. A.

    2017-09-01

    This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it to classify four-dimensional Leibniz algebras over a field K. We obtain complete classification of four-dimensional nilpotent Leibniz algebras. The main idea of the method is to transfer the “base change” action to an action of automorphism group of the algebras of smaller dimension on cocycles constructed by the annihilator extensions. The method can be used to classify low-dimensional Leibniz algebras over other finite fields as well.

  1. A general synthesis of alkenyl-substituted benzofurans, indoles, and isoquinolones by cascade palladium-catalyzed heterocyclization/oxidative Heck coupling.

    PubMed

    Alvarez, Rosana; Martínez, Claudio; Madich, Youssef; Denis, J Gabriel; Aurrecoechea, José M; de Lera, Angel R

    2010-11-08

    Structurally diverse C3-alkenylbenzofurans, C3-alkenylindoles, and C4-alkenylisoquinolones are efficiently prepared by using consecutive Sonogashira and cascade Pd-catalyzed heterocyclization/oxidative Heck couplings from readily available ortho-iodosubstituted phenol, aniline, and benzamide substrates, alkynes, and functionalized olefins. The cyclization of O- and N-heteronucleophiles follows regioselective 5-endo-dig- or 6-endo-dig-cyclization modes, whereas the subsequent Heck-type coupling with both mono- and disubstituted olefins takes place stereoselectively with exclusive formation of the E isomers in most cases.

  2. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  3. Algebraic Theories and (Infinity,1)-Categories

    NASA Astrophysics Data System (ADS)

    Cranch, James

    2010-11-01

    We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured objects from homotopy theory. A central example, treated at length, is the theory of E_infinity spaces: this has a tidy combinatorial description in terms of span diagrams of finite sets. We introduce a theory of distributive laws, allowing us to describe objects with two distributing E_infinity stuctures. From this we produce a theory of E_infinity ring spaces. We also study grouplike objects, and produce theories modelling infinite loop spaces (or connective spectra), and infinite loop spaces with coherent multiplicative structure (or connective ring spectra). We use this to construct the units of a grouplike E_infinity ring space in a natural manner. Lastly we provide a speculative pleasant description of the K-theory of monoidal quasicategories and quasicategories with ring-like structures.

  4. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    SciTech Connect

    Marquette, Ian

    2013-07-15

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.

  5. Brown Dwarf Microlensing Diagram

    NASA Image and Video Library

    2016-11-10

    For the first time, two space-based telescopes have teamed up with ground-based observatories to observe a microlensing event, a magnification of the light of a distant star due to the gravitational effects of an unseen object in the foreground. In this case, the cause of the microlensing event was a brown dwarf, dubbed OGLE-2015-BLG-1319, orbiting a star. In terms of mass, brown dwarfs fall somewhere between the size of the largest planets and the smallest stars. Curiously, scientists have found that, for stars roughly the mass of our sun, less than 1 percent have a brown dwarf orbiting within 3 AU (1 AU is the distance between Earth and the sun). This newly discovered brown dwarf may fall in that distance range. This microlensing event was observed by ground-based telescopes looking for these uncommon events, and subsequently seen by NASA's Spitzer and Swift space telescopes. As the diagram shows, Spitzer and Swift offer additional vantage points for viewing this chance alignment. While Swift orbits close to Earth, and saw (blue diamonds) essentially the same change in light that the ground-based telescopes measured (grey markers), Spitzer's location much farther away from Earth gave it a very different perspective on the event (red circles). In particular, Spitzer's vantage point resulted in a time lag in the microlensing event it observed, compared to what was seen by Swift and the ground-based telescope. This offset allowed astronomers to determine the distance to OGLE-2015-BLG-1319 as well as its mass: around 30-65 times that of Jupiter. http://photojournal.jpl.nasa.gov/catalog/PIA21077

  6. Aryl-phenyl scrambling in intermediate organopalladium complexes: a gas-phase study of the Mizoroki-Heck reaction.

    PubMed

    Fiebig, Lukas; Schlörer, Nils; Schmalz, Hans-Günther; Schäfer, Mathias

    2014-04-22

    The intramolecular aryl-phenyl scrambling reaction within palladium-DPPP-aryl complex (DPPP=1,3-bis(diphenylphosphino)propane) ions was analyzed by state-of-the-art tandem MS, including gas-phase ion/molecule reactions. The Mizoroki-Heck cross-coupling reaction was performed in the gas phase, and the intrinsic reactivity of important intermediates could be examined. Moreover, linear free-energy correlations were applied, and a mechanism for the scrambling reaction proceeding via phosphonium cations was assumed.

  7. Preparation of nonsymmetrically substituted stilbenes in a one-pot two-step heck strategy using ethene as a reagent.

    PubMed

    Kormos, Chad M; Leadbeater, Nicholas E

    2008-05-16

    We present here a strategy for the preparation of nonsymmetrically substituted stilbenes using a one-pot two-step double Heck strategy. First a protocol is developed for the selective preparation of a range of styrenes using ethene as the alkene coupling partner. Then conditions are found for the effective coupling of the styrenes with aryl halides using a 1:1 stoichiometric ratio of the two components. The use of the microwave apparatus to perform the reactions offers a convenient method for synthesis as well as for safely, easily, and accurately loading vessels with gaseous reagents.

  8. Selenium-ligated palladium(II) complexes as highly active catalysts for carbon-carbon coupling reactions: the Heck reaction.

    PubMed

    Yao, Qingwei; Kinney, Elizabeth P; Zheng, Chong

    2004-08-19

    Three selenium-ligated Pd(II) complexes were readily synthesized and shown to be extremely active catalysts for the Heck reaction of various aryl bromides, including deactivated and heterocyclic ones. The catalytic activity of the selenide-based Pd(II) complexes not only rivals but vastly outperforms that of the corresponding phosphorus and sulfur analogues. Practical advantages of the selenium-based catalysts include their straightforward synthesis and high activity in the absence of any additives as well as the enhanced stability of the selenide ligands toward air oxidation.

  9. Rectangular diagrams of surfaces: representability

    NASA Astrophysics Data System (ADS)

    Dynnikov, I. A.; Prasolov, M. V.

    2017-06-01

    Introduced here is a simple combinatorial way, which is called a rectangular diagram of a surface, to represent a surface in the three-sphere. It has a particularly nice relation to the standard contact structure on S^3 and to rectangular diagrams of links. By using rectangular diagrams of surfaces it is intended, in particular, to develop a method to distinguish Legendrian knots. This requires a lot of technical work of which the present paper addresses only the first basic question: which isotopy classes of surfaces can be represented by a rectangular diagram? Roughly speaking, the answer is this: there is no restriction on the isotopy class of the surface, but there is a restriction on the rectangular diagram of the boundary link arising from the presentation of the surface. The result extends to Giroux's convex surfaces for which this restriction on the boundary has a natural meaning. In a subsequent paper, transformations of rectangular diagrams of surfaces will be considered and their properties will be studied. By using the formalism of rectangular diagrams of surfaces an annulus in S^3 is produced here that is expected to be a counterexample to the following conjecture: if two Legendrian knots cobound an annulus and have zero Thurston-Bennequin numbers relative to this annulus, then they are Legendrian isotopic. Bibliography: 30 titles.

  10. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  11. The Algebra Artist

    ERIC Educational Resources Information Center

    Beigie, Darin

    2014-01-01

    Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

  12. Algebra of Majorana doubling.

    PubMed

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  13. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  14. The tensor hierarchy algebra

    SciTech Connect

    Palmkvist, Jakob

    2014-01-15

    We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.

  15. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  16. Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

    NASA Astrophysics Data System (ADS)

    Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.

    2016-10-01

    We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.

  17. Particles, Feynman Diagrams and All That

    ERIC Educational Resources Information Center

    Daniel, Michael

    2006-01-01

    Quantum fields are introduced in order to give students an accurate qualitative understanding of the origin of Feynman diagrams as representations of particle interactions. Elementary diagrams are combined to produce diagrams representing the main features of the Standard Model.

  18. Particles, Feynman Diagrams and All That

    ERIC Educational Resources Information Center

    Daniel, Michael

    2006-01-01

    Quantum fields are introduced in order to give students an accurate qualitative understanding of the origin of Feynman diagrams as representations of particle interactions. Elementary diagrams are combined to produce diagrams representing the main features of the Standard Model.

  19. Hierarchical structure of operations defined in nonextensive algebra

    NASA Astrophysics Data System (ADS)

    Nivanen, L.; Wang, Q. A.; Le Méhauté, A.; El Kaabouchi, A.; Basillais, P.; Donati, J. D.; Lacroix, A.; Paulet, J.; Perriau, S.; Sime Chuisse, S.; Simo Kamdem, E.; Théry, A.

    2009-04-01

    In the past few years, several generalized algebras were developed from physical background associated with the so-called nonextensive statistical mechanics. One of which, the q-generalized algebra, is a functional mimicking the morphisms between the standard algebraic operations through generalized exponential e ax = (1+ ax) 1/ a and logarithm ln(x)=x-1a. These functions and the resulting generalized operations possess very interesting mathematical properties and have been used in statistical physics for finite systems and nonextensive systems in general. We establish that the link between the two different operations can be either of functional or iterative nature. Both methods can be combined to introduce new nonextensive operations. The complete set of operations can be represented on a plane structured diagram. The generalized operations can be distributed into two classes, namely the "up" and "down" operations, depending on their localization in the diagram. The properties of generalized operations naturally arise from functional relations and equivalent properties of standard operations.

  20. Assessing Algebraic Solving Ability: A Theoretical Framework

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  1. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    PubMed

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  2. Quantum computation using geometric algebra

    NASA Astrophysics Data System (ADS)

    Matzke, Douglas James

    This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.

  3. The Hertzsprung-Russell Diagram.

    ERIC Educational Resources Information Center

    Woodrow, Janice

    1991-01-01

    Describes a classroom use of the Hertzsprung-Russell diagram to infer not only the properties of a star but also the star's probable stage in evolution, life span, and age of the cluster in which it is located. (ZWH)

  4. Atemporal diagrams for quantum circuits

    SciTech Connect

    Griffiths, Robert B.; Wu Shengjun; Yu Li; Cohen, Scott M.

    2006-05-15

    A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence 'atemporal'). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.

  5. The Hertzsprung-Russell Diagram.

    ERIC Educational Resources Information Center

    Woodrow, Janice

    1991-01-01

    Describes a classroom use of the Hertzsprung-Russell diagram to infer not only the properties of a star but also the star's probable stage in evolution, life span, and age of the cluster in which it is located. (ZWH)

  6. How Structure Sense for Algebraic Expressions or Equations Is Related to Structure Sense for Abstract Algebra

    ERIC Educational Resources Information Center

    Novotna, Jarmila; Hoch, Maureen

    2008-01-01

    Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…

  7. Applications of algebraic grid generation

    NASA Technical Reports Server (NTRS)

    Eiseman, Peter R.; Smith, Robert E.

    1990-01-01

    Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.

  8. Ion mixing and phase diagrams

    NASA Astrophysics Data System (ADS)

    Lau, S. S.; Liu, B. X.; Nicolet, M.-A.

    1983-05-01

    Interactions induced by ion irradiation are generally considered to be non-equilibrium processes, whereas phase diagrams are determined by phase equilibria. These two entities are seemingly unrelated. However, if one assumes that quasi-equilibrium conditions prevail after the prompt events, subsequent reactions are driven toward equilibrium by thermodynamical forces. Under this assumption, ion-induced reactions are related to equilibrium and therefore to phase diagrams. This relationship can be seen in the similarity that exists in thin films between reactions induced by ion irradiation and reactions induced by thermal annealing. In the latter case, phase diagrams have been used to predict the phase sequence of stable compound formation, notably so in cases of silicide formation. Ion-induced mixing not only can lead to stable compound formation, but also to metastable alloy formation. In some metal-metal systems, terminal solubilities can be greatly extended by ion mixing. In other cases, where the two constituents of the system have different crystal structures, extension of terminal solubility from both sides of the phase diagram eventually becomes structurally incompatible and a glassy (amorphous) mixture can form. The composition range where this bifurcation is likely to occur is in the two-phase regions of the phase diagram. These concepts are potentially useful guides in selecting metal pairs that from metallic glasses by ion mixing. In this report, phenomenological correlation between stable (and metastable) phase formation and phase diagram is discussed in terms of recent experimental data.

  9. Higher level twisted Zhu algebras

    NASA Astrophysics Data System (ADS)

    van Ekeren, Jethro

    2011-05-01

    The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by Γ /{Z} for some subgroup Γ of {R} containing {Z}, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras operatorname{Zhu}_{p, Γ }(V), and we prove the following theorems: For each p, there is a bijection between the irreducible operatorname{Zhu}_{p, Γ }(V)-modules and the irreducible Γ-twisted positive energy V-modules, and V is (Γ, H)-rational if and only if all its Zhu algebras operatorname{Zhu}_{p, Γ }(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra operatorname{Vir}^c and the universal affine Kac-Moody vertex algebra V^k({g}) at non-critical level. We also compute the inverse limits of these directed systems of algebras.

  10. Epetra Linear Algebra Services Package

    SciTech Connect

    2011-09-09

    Epetra provides the fundamental construction routines and service functions that are required for serial and paraliellinear algebra libraries using double precision scalar values and int ordinal values.

  11. Continuous-flow Heck synthesis of 4-methoxybiphenyl and methyl 4-methoxycinnamate in supercritical carbon dioxide expanded solvent solutions

    PubMed Central

    Lau, Phei Li; Allen, Ray W K

    2013-01-01

    Summary The palladium metal catalysed Heck reaction of 4-iodoanisole with styrene or methyl acrylate has been studied in a continuous plug flow reactor (PFR) using supercritical carbon dioxide (scCO2) as the solvent, with THF and methanol as modifiers. The catalyst was 2% palladium on silica and the base was diisopropylethylamine due to its solubility in the reaction solvent. No phosphine co-catalysts were used so the work-up procedure was simplified and the green credentials of the reaction were enhanced. The reactions were studied as a function of temperature, pressure and flow rate and in the case of the reaction with styrene compared against a standard, stirred autoclave reaction. Conversion was determined and, in the case of the reaction with styrene, the isomeric product distribution was monitored by GC. In the case of the reaction with methyl acrylate the reactor was scaled from a 1.0 mm to 3.9 mm internal diameter and the conversion and turnover frequency determined. The results show that the Heck reaction can be effectively performed in scCO2 under continuous flow conditions with a palladium metal, phosphine-free catalyst, but care must be taken when selecting the reaction temperature in order to ensure the appropriate isomer distribution is achieved. Higher reaction temperatures were found to enhance formation of the branched terminal alkene isomer as opposed to the linear trans-isomer. PMID:24367454

  12. Pd loaded amphiphilic COF as catalyst for multi-fold Heck reactions, C-C couplings and CO oxidation

    PubMed Central

    Mullangi, Dinesh; Nandi, Shyamapada; Shalini, Sorout; Sreedhala, Sheshadri; Vinod, Chathakudath P.; Vaidhyanathan, Ramanathan

    2015-01-01

    COFs represent a class of polymers with designable crystalline structures capable of interacting with active metal nanoparticles to form excellent heterogeneous catalysts. Many valuable ligands/monomers employed in making coordination/organic polymers are prepared via Heck and C-C couplings. Here, we report an amphiphilic triazine COF and the facile single-step loading of Pd0 nanoparticles into it. An 18–20% nano-Pd loading gives highly active composite working in open air at low concentrations (Conc. Pd(0) <0.05 mol%, average TON 1500) catalyzing simultaneous multiple site Heck couplings and C-C couplings using ‘non-boronic acid’ substrates, and exhibits good recyclability with no sign of catalyst leaching. As an oxidation catalyst, it shows 100% conversion of CO to CO2 at 150 °C with no loss of activity with time and between cycles. Both vapor sorptions and contact angle measurements confirm the amphiphilic character of the COF. DFT-TB studies showed the presence of Pd-triazine and Pd-Schiff bond interactions as being favorable. PMID:26057044

  13. Pd loaded amphiphilic COF as catalyst for multi-fold Heck reactions, C-C couplings and CO oxidation.

    PubMed

    Mullangi, Dinesh; Nandi, Shyamapada; Shalini, Sorout; Sreedhala, Sheshadri; Vinod, Chathakudath P; Vaidhyanathan, Ramanathan

    2015-06-09

    COFs represent a class of polymers with designable crystalline structures capable of interacting with active metal nanoparticles to form excellent heterogeneous catalysts. Many valuable ligands/monomers employed in making coordination/organic polymers are prepared via Heck and C-C couplings. Here, we report an amphiphilic triazine COF and the facile single-step loading of Pd(0) nanoparticles into it. An 18-20% nano-Pd loading gives highly active composite working in open air at low concentrations (Conc. Pd(0) <0.05 mol%, average TON 1500) catalyzing simultaneous multiple site Heck couplings and C-C couplings using 'non-boronic acid' substrates, and exhibits good recyclability with no sign of catalyst leaching. As an oxidation catalyst, it shows 100% conversion of CO to CO2 at 150 °C with no loss of activity with time and between cycles. Both vapor sorptions and contact angle measurements confirm the amphiphilic character of the COF. DFT-TB studies showed the presence of Pd-triazine and Pd-Schiff bond interactions as being favorable.

  14. Synthesis of epoxybenzo[d]isothiazole 1,1-dioxides via a reductive-Heck, metathesis-sequestration protocol†‡

    PubMed Central

    Asad, Naeem; Hanson, Paul R.; Long, Toby R.; Rayabarapu, Dinesh K.; Rolfe, Alan

    2011-01-01

    An atom-economical purification protocol, using solution phase processing via ring-opening metathesis polymerization (ROMP) has been developed for the synthesis of tricyclic sultams. This chromatography-free method allows for convenient isolation of reductive-Heck products and reclamation of excess starting material via sequestration involving metathesis catalysts and a catalyst-armed Si-surface. PMID:21727956

  15. Synthesis of Pd-N-heterocyclic carbene Pd-catalyst and its application in MW-assisted Heck and Suzuki reaction

    EPA Science Inventory

    The first Pd-N-heterocyclic carbene (NHC) complex in the form of organic silica is prepared using sol-gel method and its application in Heck and Suzuki reactions are demonstrated. These C-C coupling reactions proceeded efficiently under the influence of microwave irradiation, wit...

  16. Synthesis of Pd-N-heterocyclic carbene Pd-catalyst and its application in MW-assisted Heck and Suzuki reaction

    EPA Science Inventory

    The first Pd-N-heterocyclic carbene (NHC) complex in the form of organic silica is prepared using sol-gel method and its application in Heck and Suzuki reactions are demonstrated. These C-C coupling reactions proceeded efficiently under the influence of microwave irradiation, wit...

  17. Scope and limitations of the Heck-Matsuda-coupling of phenol diazonium salts and styrenes: a protecting-group economic synthesis of phenolic stilbenes.

    PubMed

    Schmidt, Bernd; Elizarov, Nelli; Berger, René; Hölter, Frank

    2013-06-14

    4-Phenol diazonium salts undergo Pd-catalyzed Heck reactions with various styrenes to 4'-hydroxy stilbenes. In almost all cases higher yields and fewer side products were observed, compared to the analogous 4-methoxy benzene diazonium salts. In contrast, the reaction fails completely with 2- and 3-phenol diazonium salts. For these substitution patterns the methoxy-substituted derivatives are superior.

  18. A versatile approach to flavones via a one-pot Pd(II)-catalyzed dehydrogenation/oxidative boron-Heck coupling sequence of chromanones.

    PubMed

    Lee, Jun; Yu, Jihyun; Son, Seung Hwan; Heo, Jinyuk; Kim, Taelim; An, Ji-Young; Inn, Kyung-Soo; Kim, Nam-Jung

    2016-01-14

    A variety of flavones were expediently synthesized from readily accessible chromanones via a one-pot sequence involving Pd(II)-catalyzed dehydrogenation and oxidative boron-Heck coupling with arylboronic acid pinacol esters. In particular, the use of arylboronic acid pinacol esters was found to significantly improve the yield of the reaction.

  19. From α-arylation of olefins to acylation with aldehydes: a journey in regiocontrol of the Heck reaction.

    PubMed

    Ruan, Jiwu; Xiao, Jianliang

    2011-08-16

    The Pd-catalyzed Mizoroki-Heck reaction of olefins with aryl halides, more often simply called the Heck reaction, was recently recognized with the 2010 Nobel Prize in chemistry. Although highly selective with electron-deficient olefins, which generally yield the linear β-arylated product exclusively, the Heck reaction is less satisfactory with electron-rich olefins. This substrate typically generates a mixture of both α- and β-arylated regioisomeric products, hampering wider application of the reaction in chemical synthesis. Pioneering studies by a number of researchers revealed that high α-regioselectivity could be obtained under Pd-diphosphine catalysis either through (i) the substitution of aryl triflates for halides or (ii) the addition of stoichiometric silver or thallium salts when aryl halides are used. Under these conditions, the arylation is believed to proceed via an ionic pathway. However, silver introduces added cost, thallium salts are toxic, and triflates are generally commercially unavailable, base sensitive, and thermally labile. Believing that the ionic pathway would be promoted in an ionic medium, in the early 2000s, we attempted the Pd-catalyzed arylation of the benchmark electron-rich olefin butyl vinyl ether with aryl bromides in an imidazolium ionic liquid. We were delighted to observe that highly regioselective α-arylation could readily be accomplished, with no need for silver additives, thallium additives, or aryl triflates. A range of other electron-rich olefins has since been shown to be viable as well. The high α-selectivity probably results from the high ionic strength of the medium, which facilitates the dissociation of halide anions from the [L(2)Pd(Ar)X] intermediate, channeling the arylation into the ionic pathway. Hydrogen bonding interactions may also play a role, however. We subsequently discovered that the α-arylation can indeed be significantly accelerated by a hydrogen bond donor salt, in both ionic liquids and common

  20. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  1. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  2. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  3. Algebra and Algebraic Thinking in School Math: 70th YB

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2008

    2008-01-01

    Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

  4. Adaptive Algebraic Smoothers

    SciTech Connect

    Philip, Bobby; Chartier, Dr Timothy

    2012-01-01

    methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.

  5. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  6. Patterns to Develop Algebraic Reasoning

    ERIC Educational Resources Information Center

    Stump, Sheryl L.

    2011-01-01

    What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

  7. Viterbi/algebraic hybrid decoder

    NASA Technical Reports Server (NTRS)

    Boyd, R. W.; Ingels, F. M.; Mo, C.

    1980-01-01

    Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.

  8. Teaching Algebra Conceptually: Student Achievement

    ERIC Educational Resources Information Center

    Linsell, Chris; Tozer, Lynn; Anakin, Megan; Cox, Anna; Jones, Rachel; McAuslan, Eric; Smith, Donna; Turner, Garry

    2012-01-01

    This paper reports findings from the second year of a two-year study designed to develop approaches to teaching algebra in years 9 and 10. The aim of the research was to explore and develop teaching approaches to assist students to acquire a conceptual understanding of algebra, and to document the impact of these approaches on student outcomes.…

  9. SICs and Algebraic Number Theory

    NASA Astrophysics Data System (ADS)

    Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon

    2017-08-01

    We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.

  10. Patterns to Develop Algebraic Reasoning

    ERIC Educational Resources Information Center

    Stump, Sheryl L.

    2011-01-01

    What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

  11. Learning Algebra from Worked Examples

    ERIC Educational Resources Information Center

    Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

    2014-01-01

    For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

  12. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  13. Linear algebra and image processing

    NASA Astrophysics Data System (ADS)

    Allali, Mohamed

    2010-09-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty.

  14. Multiplier operator algebras and applications.

    PubMed

    Blecher, David P; Zarikian, Vrej

    2004-01-20

    The one-sided multipliers of an operator space X are a key to "latent operator algebraic structure" in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals.

  15. Astro Algebra [CD-ROM].

    ERIC Educational Resources Information Center

    1997

    Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

  16. Elementary maps on nest algebras

    NASA Astrophysics Data System (ADS)

    Li, Pengtong

    2006-08-01

    Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.

  17. The Algebra of the Arches

    ERIC Educational Resources Information Center

    Buerman, Margaret

    2007-01-01

    Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

  18. Linear Algebra and Image Processing

    ERIC Educational Resources Information Center

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  19. Online Algebraic Tools for Teaching

    ERIC Educational Resources Information Center

    Kurz, Terri L.

    2011-01-01

    Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)

  20. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  1. Automatically Assessing Graph-Based Diagrams

    ERIC Educational Resources Information Center

    Thomas, Pete; Smith, Neil; Waugh, Kevin

    2008-01-01

    To date there has been very little work on the machine understanding of imprecise diagrams, such as diagrams drawn by students in response to assessment questions. Imprecise diagrams exhibit faults such as missing, extraneous and incorrectly formed elements. The semantics of imprecise diagrams are difficult to determine. While there have been…

  2. Automatically Assessing Graph-Based Diagrams

    ERIC Educational Resources Information Center

    Thomas, Pete; Smith, Neil; Waugh, Kevin

    2008-01-01

    To date there has been very little work on the machine understanding of imprecise diagrams, such as diagrams drawn by students in response to assessment questions. Imprecise diagrams exhibit faults such as missing, extraneous and incorrectly formed elements. The semantics of imprecise diagrams are difficult to determine. While there have been…

  3. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  4. Matched designs and causal diagrams

    PubMed Central

    Mansournia, Mohammad A; Hernán, Miguel A; Greenland, Sander

    2013-01-01

    We use causal diagrams to illustrate the consequences of matching and the appropriate handling of matched variables in cohort and case-control studies. The matching process generally forces certain variables to be independent despite their being connected in the causal diagram, a phenomenon known as unfaithfulness. We show how causal diagrams can be used to visualize many previous results about matched studies. Cohort matching can prevent confounding by the matched variables, but censoring or other missing data and further adjustment may necessitate control of matching variables. Case-control matching generally does not prevent confounding by the matched variables, and control of matching variables may be necessary even if those were not confounders initially. Matching on variables that are affected by the exposure and the outcome, or intermediates between the exposure and the outcome, will ordinarily produce irremediable bias. PMID:23918854

  5. Symplectic Clifford Algebraic Field Theory.

    NASA Astrophysics Data System (ADS)

    Dixon, Geoffrey Moore

    We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.

  6. Electrochemical Phase Diagrams for Aqueous Redox Systems

    DTIC Science & Technology

    1989-12-22

    theoretical analysis permits a classification of potential-pH diagrams into two basic types: 1) Pourbaix diagrams , in which 1 the stability field of solid...property" diagrams will contain conventional Pourbaix and Ellingham diagrams as subsets. 3. Improve the data-base supporting the computations by...research grant DAAL03-86-K-0062 and the preceding grant DAAG29-84-K-0074. 1. John C. Angus and Charles T. Angus, "Computation of Pourbaix Diagrams Using

  7. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  8. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  9. Macdonald index and chiral algebra

    NASA Astrophysics Data System (ADS)

    Song, Jaewon

    2017-08-01

    For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

  10. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  11. Constraint algebra in bigravity

    SciTech Connect

    Soloviev, V. O.

    2015-07-15

    The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.

  12. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  13. The algebraic method

    NASA Astrophysics Data System (ADS)

    Grassi, P. A.; Hurth, T.; Steinhauser, M.

    2001-09-01

    Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process b→ sγ.

  14. Voronoi Diagrams and Spring Rain

    ERIC Educational Resources Information Center

    Perham, Arnold E.; Perham, Faustine L.

    2011-01-01

    The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…

  15. Voronoi Diagrams and Spring Rain

    ERIC Educational Resources Information Center

    Perham, Arnold E.; Perham, Faustine L.

    2011-01-01

    The goal of this geometry project is to use Voronoi diagrams, a powerful modeling tool across disciplines, and the integration of technology to analyze spring rainfall from rain gauge data over a region. In their investigation, students use familiar equipment from their mathematical toolbox: triangles and other polygons, circumcenters and…

  16. A unique Pd-catalysed Heck arylation as a remote trigger for cyclopropane selective ring-opening.

    PubMed

    Singh, Sukhdev; Bruffaerts, Jeffrey; Vasseur, Alexandre; Marek, Ilan

    2017-02-07

    Combining functionalization at a distant position from a reactive site with the creation of several consecutive stereogenic centres, including the formation of a quaternary carbon stereocentre, in acyclic system represents a pinnacle in organic synthesis. Here we report the regioselective Heck arylation of terminal olefins as a distant trigger for the ring-opening of cyclopropanes. This Pd-catalysed unfolding of the strained cycle, driving force of the chain-walking process, remarkably proved its efficiency and versatility, as the reaction proceeded regardless of the molecular distance between the initiation (double bond) and termination (alcohol) sites. Moreover, employing stereodefined polysubstituted cyclopropane vaults allowed to access sophisticated stereoenriched acyclic scaffolds in good yields. Conceptually, we demonstrated that merging catalytically a chain walking process with a selective C-C bond cleavage represents a powerful approach to construct linear skeleton possessing two stereogenic centres.

  17. A unique Pd-catalysed Heck arylation as a remote trigger for cyclopropane selective ring-opening

    NASA Astrophysics Data System (ADS)

    Singh, Sukhdev; Bruffaerts, Jeffrey; Vasseur, Alexandre; Marek, Ilan

    2017-02-01

    Combining functionalization at a distant position from a reactive site with the creation of several consecutive stereogenic centres, including the formation of a quaternary carbon stereocentre, in acyclic system represents a pinnacle in organic synthesis. Here we report the regioselective Heck arylation of terminal olefins as a distant trigger for the ring-opening of cyclopropanes. This Pd-catalysed unfolding of the strained cycle, driving force of the chain-walking process, remarkably proved its efficiency and versatility, as the reaction proceeded regardless of the molecular distance between the initiation (double bond) and termination (alcohol) sites. Moreover, employing stereodefined polysubstituted cyclopropane vaults allowed to access sophisticated stereoenriched acyclic scaffolds in good yields. Conceptually, we demonstrated that merging catalytically a chain walking process with a selective C-C bond cleavage represents a powerful approach to construct linear skeleton possessing two stereogenic centres.

  18. Palladium-meta-terarylphosphine catalyst for the Mizoroki-Heck reaction of (hetero)aryl bromides and functional olefins.

    PubMed

    Tay, Daniel Weiliang; Jong, Howard; Lim, Yee Hwee; Wu, Wenqin; Chew, Xinying; Robins, Edward G; Johannes, Charles W

    2015-04-17

    The evolutionary meta-terarylphosphine ligand architecture of Cy*Phine was recently shown to be a key feature that imposed outstanding performance in palladium-catalyzed copper-free Sonogashira applications. Herein, the Pd-Cy*Phine combination has similarly proven to be a powerful catalyst system for the Mizoroki-Heck reaction. Using high-throughput screening (HTS) methodology, DMF and NaHCO3 were rapidly identified as the most effective solvent and base pair for the cross-coupling catalysis of challenging and industrially valuable substrates including highly electron-rich heteroaryl bromides and unactivated olefins. Unprotected functional groups were well tolerated using low catalyst loadings, and the simple protocol produced excellent yields (up to 99%) with unprecedented substrate diversity. The Pd-Cy*Phine system broadly outperformed many state-of-the-art commercial alternatives, which demonstrated its potential as a next-generation cross-coupling catalyst.

  19. A unique Pd-catalysed Heck arylation as a remote trigger for cyclopropane selective ring-opening

    PubMed Central

    Singh, Sukhdev; Bruffaerts, Jeffrey; Vasseur, Alexandre; Marek, Ilan

    2017-01-01

    Combining functionalization at a distant position from a reactive site with the creation of several consecutive stereogenic centres, including the formation of a quaternary carbon stereocentre, in acyclic system represents a pinnacle in organic synthesis. Here we report the regioselective Heck arylation of terminal olefins as a distant trigger for the ring-opening of cyclopropanes. This Pd-catalysed unfolding of the strained cycle, driving force of the chain-walking process, remarkably proved its efficiency and versatility, as the reaction proceeded regardless of the molecular distance between the initiation (double bond) and termination (alcohol) sites. Moreover, employing stereodefined polysubstituted cyclopropane vaults allowed to access sophisticated stereoenriched acyclic scaffolds in good yields. Conceptually, we demonstrated that merging catalytically a chain walking process with a selective C–C bond cleavage represents a powerful approach to construct linear skeleton possessing two stereogenic centres. PMID:28169276

  20. Investigating the nature of palladium chain-walking in the enantioselective redox-relay Heck reaction of alkenyl alcohols.

    PubMed

    Hilton, Margaret J; Xu, Li-Ping; Norrby, Per-Ola; Wu, Yun-Dong; Wiest, Olaf; Sigman, Matthew S

    2014-12-19

    The mechanism of the redox-relay Heck reaction was investigated using deuterium-labeled substrates. Results support a pathway through a low energy palladium-alkyl intermediate that immediately precedes product formation, ruling out a tautomerization mechanism. DFT calculations of the relevant transition structures at the M06/LAN2DZ+f/6-31+G* level of theory show that the former pathway is favored by 5.8 kcal/mol. Palladium chain-walking toward the alcohol, following successive β-hydride eliminations and migratory insertions, is also supported in this study. The stereochemistry of deuterium labels is determined, lending support that the catalyst remains bound to the substrate during the relay process and that both cis- and trans-alkenes form from β-hydride elimination.

  1. Case Report of Focal Epithelial Hyperplasia (Heck's Disease) with Polymerase Chain Reaction Detection of Human Papillomavirus 13.

    PubMed

    Brehm, Mary A; Gordon, Katie; Firan, Miahil; Rady, Peter; Agim, Nnenna

    2016-05-01

    Focal epithelial hyperplasia (FEH), or Heck's disease, is an uncommon benign proliferation of oral mucosa caused by the human papillomavirus (HPV), particularly subtypes 13 and 32. The disease typically presents in young Native American patients and is characterized by multiple asymptomatic papules and nodules on the oral mucosa, lips, tongue, and gingiva. The factors that determine susceptibility to FEH are unknown, but the ethnic and geographic distribution of FEH suggests that genetic predisposition, particularly having the human lymphocytic antigen DR4 type, may be involved in pathogenesis. We report a case of FEH with polymerase chain reaction detection of HPV13 in a healthy 11-year-old Hispanic girl and discuss the current understanding of disease pathogenesis, susceptibility, and treatment.

  2. Particle-like structure of Lie algebras

    NASA Astrophysics Data System (ADS)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  3. Investigating Teacher Noticing of Student Algebraic Thinking

    ERIC Educational Resources Information Center

    Walkoe, Janet Dawn Kim

    2013-01-01

    Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…

  4. Investigating Teacher Noticing of Student Algebraic Thinking

    ERIC Educational Resources Information Center

    Walkoe, Janet Dawn Kim

    2013-01-01

    Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…

  5. Generalized Lie algebras of type An

    NASA Astrophysics Data System (ADS)

    Lyubashenko, Volodymyr; Sudbery, Anthony

    1998-06-01

    It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz's. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré-Birkhoff-Witt basis.

  6. Readiness and Preparation for Beginning Algebra.

    ERIC Educational Resources Information Center

    Rotman, Jack W.

    Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…

  7. Loop Virasoro Lie conformal algebra

    SciTech Connect

    Wu, Henan Chen, Qiufan; Yue, Xiaoqing

    2014-01-15

    The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

  8. Central extensions of Lax operator algebras

    NASA Astrophysics Data System (ADS)

    Schlichenmaier, M.; Sheinman, O. K.

    2008-08-01

    Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.

  9. Asymptotic aspect of derivations in Banach algebras.

    PubMed

    Roh, Jaiok; Chang, Ick-Soon

    2017-01-01

    We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  10. Computing Matrix Representations of Filiform Lie Algebras

    NASA Astrophysics Data System (ADS)

    Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.

    In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.

  11. Ada Linear-Algebra Program

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  12. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  13. Cartooning in Algebra and Calculus

    ERIC Educational Resources Information Center

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  14. Semiclassical states on Lie algebras

    SciTech Connect

    Tsobanjan, Artur

    2015-03-15

    The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.

  15. An "Arithmetic" Thinker Tackles Algebra

    ERIC Educational Resources Information Center

    Armstrong, Alayne C.

    2006-01-01

    Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.

  16. Graphical tensor product reduction scheme for the Lie algebras so(5) = sp(2) , su(3) , and g(2)

    NASA Astrophysics Data System (ADS)

    Vlasii, N. D.; von Rütte, F.; Wiese, U.-J.

    2016-08-01

    We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2) , su(3) , and g(2) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a "landscape" of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic "girdle" method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

  17. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  18. Quantum Process Algebra with Priorities

    NASA Astrophysics Data System (ADS)

    Ren, Xingtian; Wang, Yong; Dai, Guiping

    2017-08-01

    One of the most fascinating characteristics is the modularity of ACP (Algebra of Communicating Processes), that is, ACP can be extended easily. qACP also inherents the modularity characteristics of ACP. By introducing new operators or new constants, qACP can have more properties. In this paper, we extend the quantum process algebra qACP with priorities support in an elegant way. And we obtain the soundness and completeness of the extension.

  19. Coherent States for Hopf Algebras

    NASA Astrophysics Data System (ADS)

    Škoda, Zoran

    2007-07-01

    Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.

  20. Multiplier operator algebras and applications

    PubMed Central

    Blecher, David P.; Zarikian, Vrej

    2004-01-01

    The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990

  1. Algebraic Systems and Pushdown Automata

    NASA Astrophysics Data System (ADS)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  2. Efficient synthesis of PtPd/Fe3O4 nanoparticles and its magnetic recoverability and stable recyclability for the Heck and Suzuki reactions

    NASA Astrophysics Data System (ADS)

    Sun, Yuanxu; Zhu, Xiaoqing; Guo, Dandan; Chen, Xiao; Dai, Jingtao

    2017-07-01

    Platinum and palladium bimetal nanoparticles on ferroferric oxide (PtPd/Fe3O4 NPs) nanocomposite catalysts were successfully synthesized with polyvinyl pyrrolidone as a stabilizing agent. The resultant samples were characterized by x-ray diffraction, x-ray photoelectron spectroscopy, transmission electron microscopy, high-resolution transmission electron microscopy, inductively coupled plasma, and magnetic studies. The catalytic performance of the PtPd/Fe3O4 NPs in the Heck and Suzuki coupling reactions was evaluated. Results showed that the cubic phase of Pt and Pd bimetal nanoparticles coexists with that of Fe3O4. The PtPd/Fe3O4 NP catalysts, which were approximately 22 nm in size, showed excellent catalytic activity in the Heck and Suzuki reactions. Moreover, the catalyst can be recovered with a magnet and reused several times without the significant loss of catalytic activity.

  3. Development of Stereocontrolled Palladium(II)-Catalyzed Domino Heck/Suzuki β,α-Diarylation Reactions with Chelating Vinyl Ethers and Arylboronic Acids.

    PubMed

    Trejos, Alejandro; Odell, Luke R; Larhed, Mats

    2012-02-01

    A stereoselective and 1,4-benzoquinone-mediated palladium(II)-catalyzed Heck/Suzuki domino reaction involving metal coordinating cyclic methylamino vinyl ethers and a number of electronically diverse arylboronic acids has been developed and studied. Diastereomeric ratios up to 39:1 and 78 % isolated yields were obtained. The stereoselectivity of the reaction was found to be highly dependent on the nature of the arylboronic acid and the amount of water present in the reaction mixture. Thus, a domino β,α-diarylation-reduction of chelating vinyl ethers can now be accomplished and stereochemically controlled, given that optimized conditions and an appropriate chiral auxiliary are used. To the best of our knowledge, this represents the first example of a stereoselective, oxidative Heck/Suzuki domino reaction in the literature.

  4. Orbifold singularities, Lie algebras of the third kind (LATKes), and pure Yang-Mills with matter

    SciTech Connect

    Friedmann, Tamar

    2011-02-15

    We discover the unique, simple Lie algebra of the third kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a new kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is one-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism. The World in a Point?; Blow-up ofC{sup 3}/Z{sub 3}| Dynkin diagram of the LATKe; {center_dot}; Pure Yang-Mills with matter

  5. Spectral Determinants on Mandelstam Diagrams

    NASA Astrophysics Data System (ADS)

    Hillairet, Luc; Kalvin, Victor; Kokotov, Alexey

    2016-04-01

    We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact Riemann surface equipped with a conformal flat singular metric {|ω|^2}, where {ω} is a meromorphic one-form with simple poles such that all its periods are pure imaginary and all its residues are real. The main result is an explicit formula for the determinant of the Laplacian in terms of the basic objects on the underlying Riemann surface (the prime form, theta-functions, the canonical meromorphic bidifferential) and the divisor of the meromorphic form {ω}. As an important intermediate result we prove a decomposition formula of the type of Burghelea-Friedlander-Kappeler for the determinant of the Laplacian for flat surfaces with cylindrical ends and conical singularities.

  6. Hero's journey in bifurcation diagram

    NASA Astrophysics Data System (ADS)

    Monteiro, L. H. A.; Mustaro, P. N.

    2012-06-01

    The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.

  7. Anatomy of geodesic Witten diagrams

    NASA Astrophysics Data System (ADS)

    Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki

    2017-05-01

    We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

  8. Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.

    ERIC Educational Resources Information Center

    Stoutemyer, David R.

    1983-01-01

    Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)

  9. Quantum Dimer Model: Phase Diagrams

    NASA Astrophysics Data System (ADS)

    Goldstein, Garry; Chamon, Claudio; Castelnovo, Claudio

    We present new theoretical analysis of the Quantum Dimer Model. We study dimer models on square, cubic and triangular lattices and we reproduce their phase diagrams (which were previously known only numerically). We show that there are several types of dimer liquids and solids. We present preliminary analysis of several other models including doped dimers and planar spin ice, and some results on the Kagome and hexagonal lattices.

  10. Reliability computation from reliability block diagrams

    NASA Technical Reports Server (NTRS)

    Chelson, P. O.; Eckstein, E. Y.

    1975-01-01

    Computer program computes system reliability for very general class of reliability block diagrams. Four factors are considered in calculating probability of system success: active block redundancy, standby block redundancy, partial redundancy, and presence of equivalent blocks in the diagram.

  11. Mizoroki-Heck Cross-coupling Reactions Catalyzed by Dichloro{bis[1,1',1''-(phosphinetriyl)tripiperidine]}palladium Under Mild Reaction Conditions

    PubMed Central

    Oberholzer, Miriam; Frech, Christian M.

    2014-01-01

    Dichloro-bis(aminophosphine) complexes of palladium with the general formula of [(P{(NC5H10)3-n(C6H11)n})2Pd(Cl)2] (where n = 0-2), belong to a new family of easy accessible, very cheap, and air stable, but highly active and universally applicable C-C cross-coupling catalysts with an excellent functional group tolerance. Dichloro{bis[1,1',1''-(phosphinetriyl)tripiperidine]}palladium [(P(NC5H10)3)2Pd(Cl)2] (1), the least stable complex within this series towards protons; e.g. in the form of water, allows an eased nanoparticle formation and hence, proved to be the most active Heck catalyst within this series at 100 °C and is a very rare example of an effective and versatile catalyst system that efficiently operates under mild reaction conditions. Rapid and complete catalyst degradation under work-up conditions into phosphonates, piperidinium salts and other, palladium-containing decomposition products assure an easy separation of the coupling products from catalyst and ligands. The facile, cheap, and rapid synthesis of 1,1',1"-(phosphinetriyl)tripiperidine and 1 respectively, the simple and convenient use as well as its excellent catalytic performance in the Heck reaction at 100 °C make 1 to one of the most attractive and greenest Heck catalysts available. We provide here the visualized protocols for the ligand and catalyst syntheses as well as the reaction protocol for Heck reactions performed at 10 mmol scale at 100 °C and show that this catalyst is suitable for its use in organic syntheses. PMID:24686532

  12. Palladium(II)-catalyzed coupling reactions with a chelating vinyl ether and arylboronic acids: a new Heck/Suzuki domino diarylation reaction.

    PubMed

    Trejos, Alejandro; Fardost, Ashkan; Yahiaoui, Samir; Larhed, Mats

    2009-12-28

    A mild and novel palladium(II)-catalyzed domino Heck/Suzuki alpha,beta-diarylation-reduction of a dimethylaminoethyl substituted chelating vinyl ether was developed by using electron-rich arylboronic acids in combination with p-benzoquinone. Based on the preparative results, a catalytic cycle is proposed. Further, highly regioselective palladium(II)-catalyzed alpha- or beta-monoarylation of the chelating vinyl ether was achieved using either a bidentate ligand or by employing ligand-less conditions.

  13. Domino Heck-Aza-Michael Reactions: A One-Pot, Sequential Three-Component Approach to 1,1-Dioxido-1,2-benzisothiazoline-3-acetic Acid.

    PubMed

    Rolfe, Alan; Young, Kyle; Hanson, Paul R

    2008-01-01

    The development of a new method for the synthesis of 1,1-dioxido-1,2-benzisothiazoline-3-acetic acid by a domino process is reported whereby a classical Heck reaction is coupled to an intramolecular aza-Michael reaction. Ultimately, this method has been expanded to a one-pot, sequential three-component protocol to generate diverse benzofused γ-sultams from a range of commercially available α-bromobenzenesulfonyl chlorides, amines and Michael acceptors.

  14. Scheil-Gulliver Constituent Diagrams

    NASA Astrophysics Data System (ADS)

    Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.

    2017-06-01

    During solidification of alloys, conditions often approach those of Scheil-Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil-Gulliver constituent diagrams which play the same role as that in the case of Scheil-Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.

  15. Scheil-Gulliver Constituent Diagrams

    NASA Astrophysics Data System (ADS)

    Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.

    2017-03-01

    During solidification of alloys, conditions often approach those of Scheil-Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil-Gulliver constituent diagrams which play the same role as that in the case of Scheil-Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.

  16. Phase diagram of crushed powders

    NASA Astrophysics Data System (ADS)

    Bodard, Sébastien; Jalbaud, Olivier; Saurel, Richard; Burtschell, Yves; Lapebie, Emmanuel

    2016-12-01

    Compression of monodisperse powder samples in quasistatic conditions is addressed in a pressure range such that particles fragmentation occurs while the solid remains incompressible (typical pressure range of 1-300 MPa for glass powders). For a granular bed made of particles of given size, the existence of three stages is observed during compression and crush up. First, classical compression occurs and the pressure of the granular bed increases along a characteristic curve as the volume decreases. Then, a critical pressure is reached for which fragmentation begins. During the fragmentation process, the granular pressure stays constant in a given volume range. At the end of this second stage, 20%-50% of initial grains are reduced to finer particles, depending on the initial size. Then the compression undergoes the third stage and the pressure increases along another characteristic curve, in the absence of extra fragmentation. The present paper analyses the analogies between the phase transition in liquid-vapour systems and powder compression with crush-up. Fragmentation diagram for a soda lime glass is determined by experimental means. The analogues of the saturation pressure and latent heat of phase change are determined. Two thermodynamic models are then examined to represent the crush-up diagram. The first one uses piecewise functions while the second one is of van der Waals type. Both equations of state relate granular pressure, solid volume fraction, and initial particle diameter. The piecewise functions approach provides reasonable representations of the phase diagram while the van der Waals one fails.

  17. Causal diagrams in systems epidemiology

    PubMed Central

    2012-01-01

    Methods of diagrammatic modelling have been greatly developed in the past two decades. Outside the context of infectious diseases, systematic use of diagrams in epidemiology has been mainly confined to the analysis of a single link: that between a disease outcome and its proximal determinant(s). Transmitted causes ("causes of causes") tend not to be systematically analysed. The infectious disease epidemiology modelling tradition models the human population in its environment, typically with the exposure-health relationship and the determinants of exposure being considered at individual and group/ecological levels, respectively. Some properties of the resulting systems are quite general, and are seen in unrelated contexts such as biochemical pathways. Confining analysis to a single link misses the opportunity to discover such properties. The structure of a causal diagram is derived from knowledge about how the world works, as well as from statistical evidence. A single diagram can be used to characterise a whole research area, not just a single analysis - although this depends on the degree of consistency of the causal relationships between different populations - and can therefore be used to integrate multiple datasets. Additional advantages of system-wide models include: the use of instrumental variables - now emerging as an important technique in epidemiology in the context of mendelian randomisation, but under-used in the exploitation of "natural experiments"; the explicit use of change models, which have advantages with respect to inferring causation; and in the detection and elucidation of feedback. PMID:22429606

  18. Palladium catalysts supported on mesoporous molecular sieves bearing nitrogen donor groups: preparation and use in Heck and Suzuki C-C bond-forming reactions.

    PubMed

    Demel, Jan; Lamac, Martin; Cejka, Jirí; Stepnicka, Petr

    2009-01-01

    A series of supported catalysts is prepared by treatment of SBA-15-type mesoporous molecular sieve bearing [triple chemical bond]SiCH(2)CH(2)CH(2)NHCH(2)CH(2)NEt(2) groups with palladium(II) acetate. These catalysts are studied in Suzuki biaryl couplings and in Heck reactions to establish the influence of metal loading and innocent surface modifications (trimethylsilylation). The Suzuki reaction proceeded efficiently with model and practically relevant substrates; the catalyst performance increasing with an increasing degree of metalation (decreasing N/Pd ratio). Catalyst poisoning tests revealed that the reaction takes place in the liquid phase with the catalyst serving as a reservoir of active metal species and also as a stabilizing support once the reaction is performed. In the Heck reactions, on the other hand, the catalyst performance strongly changed with the reaction temperature and with the N/Pd ratio. The material with the lowest metal loading (0.01 mmol palladium per gram of material, N/Pd ratio ca. 100:1) proved particularly attractive in the Heck coupling, being highly active at elevated temperatures, recyclable, and capable of acting as a bifunctional catalyst (i.e., functioning without any external base.

  19. Heck-type coupling vs. conjugate addition in phosphine-rhodium catalyzed reactions of aryl boronic acids with alpha,beta-unsaturated carbonyl compounds: a systematic investigation.

    PubMed

    Zou, Gang; Guo, Jianping; Wang, Zhiyong; Huang, Wen; Tang, Jie

    2007-07-28

    The competition between Heck-type coupling and conjugate addition in phosphine-rhodium catalyzed reactions of aryl boronic acids with alpha,beta-unsaturated carbonyls has been systematically investigated in a toluene-H(2)O biphasic system. Aside from the intrinsic nature of rhodium and the enolization of carbonyls, the phosphine supporting ligand on rhodium, the ratio of aryl boronic acid to alpha,beta-unsaturated carbonyl and the pH value of the aqueous phase were found to affect the competition significantly. Highly selective rhodium-based catalyst systems have therefore been developed for both Heck-type coupling and conjugate addition by synergistically tuning the supporting ligand, the boronic acid to olefin ratio and other reaction conditions. Conjugate addition with selectivity >99% and Heck-type coupling with selectivity of up to 100%, 98% and 84% for acrylates, acrylamides and methyl vinyl ketone, respectively, could be achieved in the rhodium-catalyzed reactions of aryl boronic acids with alpha,beta-unsaturated carbonyls using the corresponding optimized rhodium-based catalyst systems.

  20. Recursive graphical construction of feynman diagrams and their multiplicities in straight phi(4) and straight phi2A theory

    PubMed

    Kleinert; Pelster; Kastening; Bachmann

    2000-08-01

    The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation that can be turned into a recursion relation. This is solved order by order in the coupling constant to find all connected vacuum diagrams with their proper multiplicities. The procedure is applied to a multicomponent scalar field theory with a straight phi(4) self-interaction and then to a theory of two scalar fields straight phi and A with an interaction straight phi2A. All Feynman diagrams with external lines are obtained from functional derivatives of the connected vacuum diagrams with respect to the free correlation function. Finally, the recursive graphical construction is automatized by computer algebra with the help of a unique matrix notation for the Feynman diagrams.

  1. Novikov algebras with associative bilinear forms

    NASA Astrophysics Data System (ADS)

    Zhu, Fuhai; Chen, Zhiqi

    2007-11-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  2. Arrows in Comprehending and Producing Mechanical Diagrams

    ERIC Educational Resources Information Center

    Heiser, Julie; Tversky, Barbara

    2006-01-01

    Mechanical systems have structural organizations--parts, and their relations--and functional organizations--temporal, dynamic, and causal processes--which can be explained using text or diagrams. Two experiments illustrate the role of arrows in diagrams of mechanical systems. In Experiment 1, people described diagrams with or without arrows,…

  3. Differential Effectiveness of Two Science Diagram Types.

    ERIC Educational Resources Information Center

    Holliday, William G.

    Reported is an Aptitude Treatment Instruction (ATI) Study designed to evaluate the aptitude of verbal comprehension in terms of two unitary complex science diagram types: a single complex block word diagram and a single complex picture word diagram.. ATI theory and research indicate that different effective instructional treatments tend to help…

  4. Quantum Q systems: from cluster algebras to quantum current algebras

    NASA Astrophysics Data System (ADS)

    Di Francesco, Philippe; Kedem, Rinat

    2017-02-01

    This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.

  5. Model-Checking with Edge-Valued Decision Diagrams

    NASA Technical Reports Server (NTRS)

    Roux, Pierre; Siminiceanu, Radu I.

    2010-01-01

    We describe an algebra of Edge-Valued Decision Diagrams (EVMDDs) to encode arithmetic functions and its implementation in a model checking library along with state-of-the-art algorithms for building the transition relation and the state space of discrete state systems. We provide efficient algorithms for manipulating EVMDDs and give upper bounds of the theoretical time complexity of these algorithms for all basic arithmetic and relational operators. We also demonstrate that the time complexity of the generic recursive algorithm for applying a binary operator on EVMDDs is no worse than that of Multi-Terminal Decision Diagrams. We have implemented a new symbolic model checker with the intention to represent in one formalism the best techniques available at the moment across a spectrum of existing tools: EVMDDs for encoding arithmetic expressions, identity-reduced MDDs for representing the transition relation, and the saturation algorithm for reachability analysis. We compare our new symbolic model checking EVMDD library with the widely used CUDD package and show that, in many cases, our tool is several orders of magnitude faster than CUDD.

  6. Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams

    ERIC Educational Resources Information Center

    Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde

    2013-01-01

    This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…

  7. Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams

    ERIC Educational Resources Information Center

    Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde

    2013-01-01

    This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…

  8. (Fuzzy) Ideals of BN-Algebras.

    PubMed

    Dymek, Grzegorz; Walendziak, Andrzej

    2015-01-01

    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.

  9. Phase diagrams of polyelectrolyte solutions

    NASA Astrophysics Data System (ADS)

    Mahdi, Khaled A.

    We study the phase diagram of polyelectrolyte solutions in salt and salt-free environments. We examine the phase behavior of polyelectrolyte solutions, in the semidilute regime, using different physical models, namely the Random Phase Approximation (RPA) and the cross-linked model. In the RPA, we calculate the electrostatic free energy by summing all the fluctuations of the chains and all present ionic species. Within this approximation, the phase diagrams of salt-free polyelectrolyte solutions show phase separation even without including short-range attractions or ion condensation. We find that the phase behavior of large chains resembles the phase diagram of polymer network solutions. That is, the equilibrium is established between a network phase and a chain-free phase. Upon the addition of salt, the dissociated ions increase the entropy of the system and overcome the energy from the electrostatic fluctuations. When the short-range attraction between monomers is included in the model, the free energy predicts phase segregation for all salt valences at high salt concentrations (1 mol/l and higher). The phenomenon is called salting-out and occurs simply because the addition of salt reduces the quality of the solvent and induces precipitation. However, phase segregation in the presence of multivalent ions in polyelectrolyte solutions occurs at low salt concentrations (less than 1 mol/l). We propose that this phase separation is due to polyions cross-linked by multivalent ions. We constructed a phenomenological two-state model to examine this phenomenon. The two phases coexisting in the solution are a network-like phase and a polymer-free phase. The polymer-free phase is modeled using Debye-Huckel theory. In the cross-linked phase, each condensed multivalent ion attracts an equal number of monomers creating a neutral cluster. The energy of the cluster is evaluated by a simple Coulombic energy. The bare monomer charges between the linkages are treated as line of

  10. Voronoi Diagrams Without Bounding Boxes

    NASA Astrophysics Data System (ADS)

    Sang, E. T. K.

    2015-10-01

    We present a technique for presenting geographic data in Voronoi diagrams without having to specify a bounding box. The method restricts Voronoi cells to points within a user-defined distance of the data points. The mathematical foundation of the approach is presented as well. The cell clipping method is particularly useful for presenting geographic data that is spread in an irregular way over a map, as for example the Dutch dialect data displayed in Figure 2. The automatic generation of reasonable cell boundaries also makes redundant a frequently used solution to this problem that requires data owners to specify region boundaries, as in Goebl (2010) and Nerbonne et al (2011).

  11. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  12. A Metric Conceptual Space Algebra

    NASA Astrophysics Data System (ADS)

    Adams, Benjamin; Raubal, Martin

    The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.

  13. Using Number Theory to Reinforce Elementary Algebra.

    ERIC Educational Resources Information Center

    Covillion, Jane D.

    1995-01-01

    Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)

  14. Colored Quantum Algebra and Its Bethe State

    NASA Astrophysics Data System (ADS)

    Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun

    2014-12-01

    We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.

  15. Comments on /N=4 superconformal algebras

    NASA Astrophysics Data System (ADS)

    Rasmussen, Jørgen

    2001-01-01

    We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)⊗U(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2|2) current superalgebra. Replacing SL(2|2) with the coset SL(2|2)/U(1), results directly in the small N=4 superconformal algebra.

  16. Tensor models and 3-ary algebras

    NASA Astrophysics Data System (ADS)

    Sasakura, Naoki

    2011-10-01

    Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.

  17. Phase diagrams for sonoluminescing bubbles

    NASA Astrophysics Data System (ADS)

    Hilgenfeldt, Sascha; Lohse, Detlef; Brenner, Michael P.

    1996-11-01

    Sound driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL have been proposed: diffusively stable and diffusively unstable SL. We present phase diagrams in the gas concentration versus forcing pressure state space and also in the ambient radius versus gas concentration and versus forcing pressure state spaces. These phase diagrams are based on the thresholds for energy focusing in the bubble and two kinds of instabilities, namely (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of large forcing pressure amplitude Pa˜1.2-1.5 atm and low gas concentration of less than 0.4% of the saturation. The upper concentration threshold becomes smaller with increased forcing. Our results quantitatively agree with experimental results of Putterman's UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if in addition (iii) chemical instabilities are considered. All statements are based on the Rayleigh-Plesset ODE approximation of the bubble dynamics, extended in an adiabatic approximation to include mass diffusion effects. This approximation is the only way to explore considerable portions of parameter space, as solving the full PDEs is numerically too expensive. Therefore, we checked the adiabatic approximation by comparison with the full numerical solution of the advection diffusion PDE and find good agreement.

  18. Asteroseismology Across the HR Diagram

    NASA Astrophysics Data System (ADS)

    Thompson, M. J.; Cunha, M. S.; Monteiro, M. J. P. F. G.

    2003-05-01

    Ground-based observations have detected solar-like oscillations on Sun-like stars, and diagnostics similar to those used in helioseismology are now being used to test and constrain the physics and evolutionary state of these stars. Multi-mode oscillations are being observed in an abundance of other stars, including slowly pulsating B stars (SPB stars), delta-Scuti stars, Ap stars and the pulsating white dwarfs. New classes of pulsators continue to be discovered across the Herzsprung-Russell diagram. Yet the chances still to be faced to make asteroseismology across the HR diagram a reality are formidable. Observation, data analysis and theory all pose hard problems to be overcome. This book, reflecting the goal of the meeting, aims to facilitate a cross-fertilisation of ideas and approaches between fields covering different pulsators and with different areas of expertise. The book successfully covers most known types of pulsators, reflecting a highly productive and far reaching interchange of ideas which we believe is conveyed by the papers and posters published, making it a reference for researchers and postgraduate students working on stellar structure and evolution. Link: http://www.wkap.nl/prod/b/1-4020-1173-3

  19. Phase Diagrams of Nuclear Pasta

    NASA Astrophysics Data System (ADS)

    Caplan, Matthew; Horowitz, Chuck; Berry, Don; da Silva Schneider, Andre

    2016-03-01

    In the inner crust of neutrons stars, where matter is near the saturation density, protons and neutrons arrange themselves into complex structures called nuclear pasta. Early theoretical work predicted a simple graduated hierarchy of pasta phases, consisting of spheres, cylinders, slabs, and uniform matter with voids. Previous work has simulated these phases with a simple classical model and has shown that the formation of these structures is dependent on the temperature, density, and proton fraction. However, previous work only studied a limited range of these parameters due to computational limitations. Thanks to recent advances in computing it is now possible to survey the structure of nuclear pasta for a larger range of parameters. By simulating nuclear pasta with constant temperature and proton fraction in an expanding simulation volume we are able to study the phase transitions in nuclear pasta, and thus produce a set of phase diagrams. We report on these phase diagrams as well as newly identified phases of nuclear pasta and discuss their implications for neutron star observables.

  20. Scalable Parallel Algebraic Multigrid Solvers

    SciTech Connect

    Bank, R; Lu, S; Tong, C; Vassilevski, P

    2005-03-23

    The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

  1. Algebraic orbifold conformal field theories

    PubMed Central

    Xu, Feng

    2000-01-01

    The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383

  2. Entropic Forms and Related Algebras

    NASA Astrophysics Data System (ADS)

    Scarfone, Antonio

    2013-02-01

    Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.

  3. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  4. Symmetry algebras of linear differential equations

    NASA Astrophysics Data System (ADS)

    Shapovalov, A. V.; Shirokov, I. V.

    1992-07-01

    The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.

  5. Discrimination in a General Algebraic Setting

    PubMed Central

    Fine, Benjamin; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421

  6. Post-Lie algebras and factorization theorems

    NASA Astrophysics Data System (ADS)

    Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

    2017-09-01

    In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

  7. Twining characters and orbit Lie algebras

    SciTech Connect

    Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph

    1996-12-05

    We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.

  8. Discrimination in a General Algebraic Setting.

    PubMed

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.

  9. Applications of Algebraic Logic and Universal Algebra to Computer Science

    DTIC Science & Technology

    1989-06-21

    conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords

  10. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  11. Difficulties in Initial Algebra Learning in Indonesia

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-01-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

  12. Teaching Strategies to Improve Algebra Learning

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  13. Build an Early Foundation for Algebra Success

    ERIC Educational Resources Information Center

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  14. Teacher Actions to Facilitate Early Algebraic Reasoning

    ERIC Educational Resources Information Center

    Hunter, Jodie

    2015-01-01

    In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

  15. Unifying the Algebra for All Movement

    ERIC Educational Resources Information Center

    Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

    2015-01-01

    There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

  16. Unifying the Algebra for All Movement

    ERIC Educational Resources Information Center

    Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

    2015-01-01

    There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

  17. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  18. Cyclic homology for Hom-associative algebras

    NASA Astrophysics Data System (ADS)

    Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan

    2015-12-01

    In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.

  19. Algebra? A Gate! A Barrier! A Mystery!

    ERIC Educational Resources Information Center

    Mathematics Educatio Dialogues, 2000

    2000-01-01

    This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

  20. Embedding Algebraic Thinking throughout the Mathematics Curriculum

    ERIC Educational Resources Information Center

    Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph

    2005-01-01

    This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…

  1. Constraint-Referenced Analytics of Algebra Learning

    ERIC Educational Resources Information Center

    Sutherland, Scot M.; White, Tobin F.

    2016-01-01

    The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

  2. Difficulties in Initial Algebra Learning in Indonesia

    ERIC Educational Resources Information Center

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-01-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

  3. Teaching Strategies to Improve Algebra Learning

    ERIC Educational Resources Information Center

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  4. Build an Early Foundation for Algebra Success

    ERIC Educational Resources Information Center

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  5. A Balancing Act: Making Sense of Algebra

    ERIC Educational Resources Information Center

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  6. Algebra? A Gate! A Barrier! A Mystery!

    ERIC Educational Resources Information Center

    Mathematics Educatio Dialogues, 2000

    2000-01-01

    This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

  7. Quadratic Dynamical Systems and Algebras

    NASA Astrophysics Data System (ADS)

    Kinyon, M. K.; Sagle, A. A.

    1995-03-01

    Quadratic dynamical systems come from differential or discrete systems of the form Ẋ = Q(X) or X(k+1)=Q(X(k)), where Q:Rn→Rn is homogeneous of degree 2; i.e., Q(αX) = α2Q(X) for all α∈R, X∈Rn. Defining a bilinear mapping β:Rn × Rn→Rn by β(X, Y) ≔ {1}/{2}[Q(X+Y)-Q(X)-Q(Y)], we view XY≡β(X, Y) as a multiplication, and thus consider A=(Rn, β) to be a commutative, nonassociative algebra. The quadratic systems are then studied with the general theme that the structure of the algebras helps determine the behavior of the solutions. For example, semisimple algebras give a decoupling of the original system into systems occurring in simple algebras, and solvable algebras give solutions to differential systems via linear differential equations; the general three-dimensional example of the latter phenomenon is described. There are many classical examples and the scope of quadratic systems is large; every polynomial system can be embedded into a higher dimensional quadratic system such that solutions of the original system are obtained from the quadratic system. For differential systems, nilpotents of index 2 (N2=0) are equilibria and idempotents (E2=E) give ray solutions. The origin is never asymptotically stable, and the existence of nonzero idempotents implies that the origin is actually unstable. Nonzero equilibria are not hyperbolic, but can be studied by standard algebra techniques using nondegenerate bilinear forms as Lyapunov functions. Periodic orbits lie on "cones." They cannot occur in dimension 2 or in power-associative algebras. No periodic orbit can be an attractor but "limit cycles" (invariant cones) can exist. Automorphisms of the algebra A leave equilibria, periodic orbits, and domains of attraction invariant. Also, explicit solutions can be given by the action of automorphisms on an initial point; the general three-dimensional example of this is described. Thus if there are sufficient automorphisms, Hilbert‧s sixteenth problem in R3 has

  8. Focal Epithelial Hyperplasia (Heck's Disease) in a 57-Year-Old Brazilian Patient: A Case Report and Literature Review.

    PubMed

    de Castro, Luciano Alberto; de Castro, Joao Gabriel Leite; da Cruz, Alexandre Duarte Lopes; Barbosa, Bruno Henrique de Sousa; de Spindula-Filho, Jose Vieira; Costa, Mauricio Barcelos

    2016-04-01

    Focal epithelial hyperplasia (FEH), or Heck's disease, is a rare disease of the oral mucosa associated with infection by some subtypes of human papilloma virus, especially subtypes 13 or 32. The disease is predominantly found in children and adolescents with indigenous heritage, but other ethnic groups can be affected worldwide. To the best of the authors' knowledge, it has not been reported in Brazil's elderly population. This article describes a case of FEH in a 57-year-old Brazilian patient presenting since childhood, with multiple lesions in the lips, buccal mucosa and tongue. The solitary tongue lesion underwent excisional biopsy and the histopathological analysis showed parakeratosis, acanthosis, rete pegs with a club-shaped appearance, koilocytosis and the presence of mitosoid cells. These microscopic findings in conjunction with clinical presentation were sufficient to establish the accurate diagnosis of FEH. Polymerase chain reaction (PCR) was performed, but no one human papillomavirus (HPV) subtype could be identified. Clinicians must be aware of this rare oral disease, which can even affect elderly patients, as we described here. Treatment may be indicated in selected cases due to esthetic and/or functional problems.

  9. Phase diagrams for high Tc superconductors

    SciTech Connect

    Whitler, J.D.; Roth, R.S. NIST, Gaithersburg, MD )

    1991-01-01

    The phase diagrams of ternary and quaternary systems containing superconducting phases are presented, as are the phase diagrams of the associated binary systems. The diagrams are divided into two large groups: (1) alkaline earth-rare earth-copper-oxygen diagrams, and (2) alkaline earth-bismuth/lead-copper-oxygen diagrams. The first group includes BaO-REO-CuO systems followed by SrO-REO-CuO or Nd2O3-CeO-CuO systems. The second group includes systems related to the AE-Bi2O3-CuO and AE-PbO-CuO systems. The phase diagrams are accompanied by notes relating procedures used in the studies, results obtained, and comparisons with the results in the literature for the same system.

  10. Continuation of point clouds via persistence diagrams

    NASA Astrophysics Data System (ADS)

    Gameiro, Marcio; Hiraoka, Yasuaki; Obayashi, Ippei

    2016-11-01

    In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D‧, we gradually move from D to D‧, by successively computing intermediate point clouds until we finally find a point cloud P‧ having D‧ as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.

  11. Mechanistic studies on the Heck-Mizoroki cross-coupling reaction of a hindered vinylboronate ester as a key approach to developing a highly stereoselective synthesis of a C1-C7 Z,Z,E-triene synthon for viridenomycin.

    PubMed

    Batsanov, Andrei S; Knowles, Jonathan P; Whiting, Andrew

    2007-03-30

    Mechanistic studies of the Heck-Mizoroki reaction of a vinylboronate ester with electronically different (four-substituted) aryl iodides shows that electron donors accelerate the cross-coupling, demonstrating that the oxidative addition step is not rate determining and that there is development of some degree of positive charge in the rate determining step. These results were used as a basis to allow the development of reaction conditions for the Heck-Mizoroki coupling of a hindered vinylboronate ester with electron deficient methyl cis-2-iodoacrylate. The resulting dienylboronate ester was converted through a series of highly stereoselective iodo-deboronations and Heck-Mizoroki reactions into a trienyl iodide precursor for further application in the total synthesis of viridenomycin.

  12. Adventures in Flipping College Algebra

    ERIC Educational Resources Information Center

    Van Sickle, Jenna

    2015-01-01

    This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

  13. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  14. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  15. Dimension independence in exterior algebra.

    PubMed

    Hawrylycz, M

    1995-03-14

    The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity.

  16. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

  17. Experts Question California's Algebra Edict

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2008-01-01

    Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…

  18. Celestial mechanics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

  19. Weaving Geometry and Algebra Together

    ERIC Educational Resources Information Center

    Cetner, Michelle

    2015-01-01

    When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

  20. Algebraic Activities Aid Discovery Lessons

    ERIC Educational Resources Information Center

    Wallace-Gomez, Patricia

    2013-01-01

    After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

  1. Kleene Algebra and Bytecode Verification

    DTIC Science & Technology

    2016-04-27

    Languages, ACM SIGPLAN/SIGACT, 1998, pp. 149–160. [2] Coglio, A., Simple verification technique for complex Java bytecode subroutines, Concurrency and...of Programming Languages (POPL’73), ACM , 1973, pp. 194–206. [6] Kot, L. and D. Kozen, Second-order abstract interpretation via Kleene algebra

  2. Algebra for All. Research Brief

    ERIC Educational Resources Information Center

    Bleyaert, Barbara

    2009-01-01

    The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless…

  3. Algebra from Chips and Chopsticks

    ERIC Educational Resources Information Center

    Yun, Jeong Oak; Flores, Alfinio

    2012-01-01

    Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

  4. Implementing Change in College Algebra

    ERIC Educational Resources Information Center

    Haver, William E.

    2007-01-01

    In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…

  5. Algebraic methods in system theory

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Willems, J. C.; Willsky, A. S.

    1975-01-01

    Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

  6. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

  7. Celestial mechanics with geometric algebra

    NASA Technical Reports Server (NTRS)

    Hestenes, D.

    1983-01-01

    Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

  8. Algebra, Home Mortgages, and Recessions

    ERIC Educational Resources Information Center

    Mariner, Jean A. Miller; Miller, Richard A.

    2009-01-01

    The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

  9. Easing Students' Transition to Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2006-01-01

    Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

  10. Algebra, Home Mortgages, and Recessions

    ERIC Educational Resources Information Center

    Mariner, Jean A. Miller; Miller, Richard A.

    2009-01-01

    The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

  11. Generalized electromagnetism and Dirac algebra

    SciTech Connect

    Fryberger, D.

    1989-02-01

    Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the variation of the action associated with the cross terms of the interaction Lagrangian in terms of a surface integral. The surface integral has an equivalent path-integral form, showing that the contribution of the cross terms is local in nature. The form of these cross terms derives in a natural way from a Dirac algebraic formulation, and, in fact, the use of the geometric product of Dirac algebra is an essential aspect of this derivation. No kinematic restrictions are associated with the derivation, and no relationship between magnetic and electric charge evolves from the (classical) formulations. However, it is indicated that in bound states quantum mechanical considerations will lead to a version of Dirac's quantization condition. A discussion of parity violation of the generalized electromagnetic theory is given, and a new approach to the incorporation of this violation into the formalism is suggested. Possibilities for extensions are mentioned.

  12. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  13. Carry Groups: Abstract Algebra Projects

    ERIC Educational Resources Information Center

    Miller, Cheryl Chute; Madore, Blair F.

    2004-01-01

    Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

  14. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  15. Adventures in Flipping College Algebra

    ERIC Educational Resources Information Center

    Van Sickle, Jenna

    2015-01-01

    This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

  16. Dimension independence in exterior algebra.

    PubMed Central

    Hawrylycz, M

    1995-01-01

    The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520

  17. Carry Groups: Abstract Algebra Projects

    ERIC Educational Resources Information Center

    Miller, Cheryl Chute; Madore, Blair F.

    2004-01-01

    Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.

  18. Monitoring Student Learning in Algebra

    ERIC Educational Resources Information Center

    Accardo, Amy L.; Kuder, S. Jay

    2017-01-01

    Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…

  19. Algebraic Activities Aid Discovery Lessons

    ERIC Educational Resources Information Center

    Wallace-Gomez, Patricia

    2013-01-01

    After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…

  20. Weaving Geometry and Algebra Together

    ERIC Educational Resources Information Center

    Cetner, Michelle

    2015-01-01

    When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

  1. Math Sense: Algebra and Geometry.

    ERIC Educational Resources Information Center

    Howett, Jerry

    This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

  2. Hubble's diagram and cosmic expansion.

    PubMed

    Kirshner, Robert P

    2004-01-06

    Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168-173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velocities come chiefly from Vesto Melvin Slipher, and the interpretation in terms of the de Sitter effect is out of the mainstream of modern cosmology, this article opened the way to investigation of the expanding, evolving, and accelerating universe that engages today's burgeoning field of cosmology.

  3. Gravity on-shell diagrams

    DOE PAGES

    Herrmann, Enrico; Trnka, Jaroslav

    2016-11-22

    Here, we study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N = 8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinitymore » are present, in complete agreement with the conjecture presented in.« less

  4. Gravity on-shell diagrams

    SciTech Connect

    Herrmann, Enrico; Trnka, Jaroslav

    2016-11-22

    Here, we study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N = 8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in.

  5. Hubble's diagram and cosmic expansion

    PubMed Central

    Kirshner, Robert P.

    2004-01-01

    Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168–173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velocities come chiefly from Vesto Melvin Slipher, and the interpretation in terms of the de Sitter effect is out of the mainstream of modern cosmology, this article opened the way to investigation of the expanding, evolving, and accelerating universe that engages today's burgeoning field of cosmology. PMID:14695886

  6. A Regime Diagram for Subduction

    NASA Astrophysics Data System (ADS)

    Stegman, D. R.; Farrington, R.; Capitanio, F. A.; Schellart, W. P.

    2009-12-01

    Regime diagrams and associated scaling relations have profoundly influenced our understanding of planetary dynamics. Previous regime diagrams characterized the regimes of stagnant-lid, small viscosity contrast, transitional, and no-convection for temperature-dependent (Moresi and Solomatov, 1995), and non-linear power law rheologies (Solomatov and Moresi, 1997) as well as stagnant-lid, sluggish-lid, and mobile-lid regimes once the finite strength of rock was considered (Moresi and Solomatov, 1998). Scalings derived from such models have been the cornerstone for parameterized models of thermal evolution of rocky planets and icy moons for the past decade. While such a theory can predict the tectonic state of a planetary body, it is still rather incomplete in regards to predicting tectonics. For example, the mobile-lid regime is unspecific as to how continuous lithospheric recycling should occur on a terrestrial planet. Towards this goal, Gerya et al., (2008) advanced a new regime diagram aiming to characterize when subduction would manifest itself as a one-sided or two-sided downwelling and either symmetric or asymmetric. Here, we present a regime diagram for the case of a single-sided, asymmetric type of subduction (most Earth-like type). Using a 3-D numerical model of a free subduction, we describe a total of 5 different styles of subduction that can possibly occur. Each style is distinguished by its upper mantle slab morphology resulting from the sinking kinematics. We provide movies to illustrate the different styles and their progressive time-evolution. In each regime, subduction is accommodated by a combination of plate advance and slab rollback, with associated motions of forward plate velocity and trench retreat, respectively. We demonstrate that the preferred subduction mode depends upon two essential controlling factors: 1) buoyancy of the downgoing plate and 2) strength of plate in resisting bending at the hinge. We propose that a variety of subduction

  7. Gravity on-shell diagrams

    NASA Astrophysics Data System (ADS)

    Herrmann, Enrico; Trnka, Jaroslav

    2016-11-01

    We study on-shell diagrams for gravity theories with any number of super-symmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only d log-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for {N}=8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in [1].

  8. Phase diagram of Hertzian spheres

    NASA Astrophysics Data System (ADS)

    Pàmies, Josep C.; Cacciuto, Angelo; Frenkel, Daan

    2009-07-01

    We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structures. For this, we defined a general primitive unit cell that allows for the simulation of any lattice. We found multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal, and hexagonal symmetries.

  9. Phase diagram of ammonium nitrate

    NASA Astrophysics Data System (ADS)

    Dunuwille, M.; Yoo, C. S.

    2014-05-01

    Ammonium Nitrate (AN) has often subjected to uses in improvised explosive devices, due to its wide availability as a fertilizer and its capability of becoming explosive with slight additions of organic and inorganic compounds. Yet, the origin of enhanced energetic properties of impure AN (or AN mixtures) is neither chemically unique nor well understood -resulting in rather catastrophic disasters in the past1 and thereby a significant burden on safety in using ammonium nitrates even today. To remedy this situation, we have carried out an extensive study to investigate the phase stability of AN at high pressure and temperature, using diamond anvil cells and micro-Raman spectroscopy. The present results confirm the recently proposed phase IV-to-IV' transition above 17 GPa2 and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400 °C.

  10. Phase diagram of ammonium nitrate

    NASA Astrophysics Data System (ADS)

    Dunuwille, Mihindra; Yoo, Choong-Shik

    2013-12-01

    Ammonium Nitrate (AN) is a fertilizer, yet becomes an explosive upon a small addition of chemical impurities. The origin of enhanced chemical sensitivity in impure AN (or AN mixtures) is not well understood, posing significant safety issues in using AN even today. To remedy the situation, we have carried out an extensive study to investigate the phase stability of AN and its mixtures with hexane (ANFO-AN mixed with fuel oil) and Aluminum (Ammonal) at high pressures and temperatures, using diamond anvil cells (DAC) and micro-Raman spectroscopy. The results indicate that pure AN decomposes to N2, N2O, and H2O at the onset of the melt, whereas the mixtures, ANFO and Ammonal, decompose at substantially lower temperatures. The present results also confirm the recently proposed phase IV-IV' transition above 17 GPa and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400°C.

  11. Influence Diagrams: Automated Analysis with Dynamic Programming

    DTIC Science & Technology

    1988-12-01

    demonstrating both the efficiency of the dynamic programming features and the limitations of influence diagrams in modeling problems with significant...Introduction 1.1 General Background Influence diagrams are a -eccntly developed graphical modeling tool for repre- senting both the conceptual elements and the...the model [9:10]. The types of node included in basic influence diagrams are (see Figure 1): Chance Node The chance node represents a random variable

  12. Process Flow Diagrams for Training and Operations

    NASA Astrophysics Data System (ADS)

    Venter, Jacobus

    This paper focuses on the use of process flow diagrams for training first responders who execute search and seizure warrants at electronic crime scenes. A generic process flow framework is presented, and the design goals and layout characteristics of process flow diagrams are discussed. An evaluation of the process flow diagrams used in training courses indicates that they are beneficial to first responders performing searches and seizures, and they speed up investigations, including those conducted by experienced personnel.

  13. Teachers' Understanding of Algebraic Generalization

    NASA Astrophysics Data System (ADS)

    Hawthorne, Casey Wayne

    Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive

  14. Explicit field realizations of W algebras

    NASA Astrophysics Data System (ADS)

    Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong

    2009-06-01

    The fact that certain nonlinear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W2,s algebras are presented. The results show that all these realizations are Romans-type realizations.

  15. Roughness in lattice ordered effect algebras.

    PubMed

    Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi

    2014-01-01

    Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras.

  16. Roughness in Lattice Ordered Effect Algebras

    PubMed Central

    Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi

    2014-01-01

    Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras. PMID:25170523

  17. Array algebra estimation in signal processing

    NASA Astrophysics Data System (ADS)

    Rauhala, U. A.

    A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.

  18. On special classes of n-algebras

    NASA Astrophysics Data System (ADS)

    Vainerman, L.; Kerner, R.

    1996-05-01

    We define n-algebras as linear spaces on which the internal composition law involves n elements: m:V⊗n■V. It is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics. Using the notion of a commutant of two subalgebras of an n-algebra, we distinguish certain classes of n-algebras with reasonable properties: semisimple, Abelian, nilpotent, solvable. We also consider a few examples of n-algebras of different types, and show their properties.

  19. Origin and use of crystallization phase diagrams

    PubMed Central

    Rupp, Bernhard

    2015-01-01

    Crystallization phase diagrams are frequently used to conceptualize the phase relations and also the processes taking place during the crystallization of macromolecules. While a great deal of freedom is given in crystallization phase diagrams owing to a lack of specific knowledge about the actual phase boundaries and phase equilibria, crucial fundamental features of phase diagrams can be derived from thermodynamic first principles. Consequently, there are limits to what can be reasonably displayed in a phase diagram, and imagination may start to conflict with thermodynamic realities. Here, the commonly used ‘crystallization phase diagrams’ are derived from thermodynamic excess properties and their limitations and appropriate use is discussed. PMID:25760697

  20. Infinite order decompositions of C*-algebras.

    PubMed

    Nematjonovich, Arzikulov Farhodjon

    2016-01-01

    The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-algebra if and only if this C*-algebra is a von Neumann algebra. As a summary we obtain that the norm of an infinite dimensional matrix is equal to the supremum of norms of all finite dimensional main diagonal submatrices of this matrix and an infinite dimensional matrix is positive if and only if all finite dimensional main diagonal submatrices of this matrix are positive.

  1. Deformed Kac Moody and Virasoro algebras

    NASA Astrophysics Data System (ADS)

    Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.

    2007-07-01

    Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.

  2. Filiform Lie algebras of order 3

    SciTech Connect

    Navarro, R. M.

    2014-04-15

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

  3. Recursion and feedback in image algebra

    NASA Astrophysics Data System (ADS)

    Ritter, Gerhard X.; Davidson, Jennifer L.

    1991-04-01

    Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.

  4. REDUCE 2: A computer program for the symbolic reduction of large block diagrams

    NASA Technical Reports Server (NTRS)

    Lorenzo, C. F.; Riehl, J. P.

    1974-01-01

    REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.

  5. Algebraic complexities and algebraic curves over finite fields

    PubMed Central

    Chudnovsky, D. V.; Chudnovsky, G. V.

    1987-01-01

    We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816

  6. Stereoselective Synthesis of Spiro Bis-C,C-α-arylglycosides by Tandem Heck Type C-Glycosylation and Friedel-Crafts Cyclization.

    PubMed

    Chen, Yen-Bo; Liu, Shi-Hao; Hsieh, Min-Tsang; Chang, Chih-Shiang; Lin, Chun-Hung; Chen, Chen-Yin; Chen, Po-Yen; Lin, Hui-Chang

    2016-04-01

    Spiro bis-C,C-α-arylglycosides were synthesized in three steps in 78-85% overall yields starting from exo-glycals. The initial Heck type C-aryl addition of exo-glycals with arylboronic acids afforded α-aryl-β-substituted C-glycosides with exclusive α-stereoselectivity. Among the products, β-ethanal α-aryl C-glycosides further reacted with alkylthiol in the presence of InCl3, followed by in situ Friedel-Crafts cyclization to yield the desirable final products. We proposed a mechanism to explain how the α-aryl group serves as a main determinant of the cyclization.

  7. Palladium-catalyzed direct heck arylation of dual pi-deficient/pi-excessive heteroaromatics. Synthesis of C-5 arylated imidazo[1,5-a]pyrazines.

    PubMed

    Wang, Jian-Xin; McCubbin, J Adam; Jin, Meizhong; Laufer, Radoslaw S; Mao, Yunyu; Crew, Andrew P; Mulvihill, Mark J; Snieckus, Victor

    2008-07-17

    A general and efficient synthesis of 5-aryl imidazo[1,5- a]pyrazines by palladium-catalyzed coupling of the corresponding 8-substituted derivatives with aryl halides is described. The scope of this new reaction for the imidazo[1,5- a]pyrazine ring system was explored using three readily available 8-substituted precursors, X = NH2, NMe2, and OMe, as well as 8-aryl derivatives, X = Ar'. On the basis of these results as well as studies using a deuterated derivative, a Heck-like mechanism is proposed for this transformation.

  8. Quaternary Stereogenic Centers through Enantioselective Heck Arylation of Acyclic Olefins with Aryldiazonium Salts: Application in a Concise Synthesis of (R)-Verapamil.

    PubMed

    Oliveira, Caio C; Pfaltz, Andreas; Correia, Carlos Roque Duarte

    2015-11-16

    We describe herein a highly regio- and enantioselective Pd-catalyzed Heck arylation of unactivated trisubstituted acyclic olefins to provide all-carbon quaternary stereogenic centers. Chiral N,N ligands of the pyrimidine- and pyrazino-oxazoline class were developed for that purpose, providing the desired products in good to high yields with enantiomeric ratios up to >99:1. Both linear and branched substituents on the olefins were well-tolerated. The potential of this new method is demonstrated by the straightforward synthesis of several O-methyl lactols and lactones containing quaternary stereocenters, together with a concise enantioselective total synthesis of the calcium channel blocker verapamil.

  9. Diagrams Benefit Symbolic Problem-Solving

    ERIC Educational Resources Information Center

    Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R.

    2017-01-01

    Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…

  10. Pressure-temperature phase diagrams of biomolecules.

    PubMed

    Smeller, László

    2002-03-25

    The pressure-temperature phase diagram of various biomolecules is reviewed. Special attention is focused on the elliptic phase diagram of proteins. The phenomenological thermodynamic theory describing this diagram explains the heat, cold and pressure denaturations in a unified picture. The limitations and possible developments of this theory are discussed as well. It is pointed out that a more complex diagram can be obtained when the intermolecular interactions are also taken into account. In this case metastable states appear on the pressure-temperature (p-T) diagram due to intermolecular interactions. Pressure-temperature phase diagrams of other biopolymers are also discussed. While the p-T diagrams of helix-coil transition of nucleic acids and of gel-liquid crystal transition of lipid bilayers are non-elliptical, those of gelatinization of starch and of phase separation of some synthetic polymers show an elliptic profile, similar to that of proteins. Finally, the p-T diagram of bacterial inactivation is shown to be elliptic. From the point of view of basic science, this fact shows that the key factor of inactivation should be the protein type, and from the viewpoint of practical applications, it serves as the theoretical basis of pressure treatment of biosystems.

  11. Vesicle deformation by microtubules: A phase diagram

    NASA Astrophysics Data System (ADS)

    Emsellem, Virginie; Cardoso, Olivier; Tabeling, Patrick

    1998-10-01

    The experimental investigation of vesicles deformed by the growth of encapsulated microtubules shows that the axisymmetric morphologies can be classified into ovals, lemons, φ, cherries, dumbbells, and pearls. A geometrical phase diagram is established. Numerical minimization of the elastic energy of the membrane reproduces satisfactorily well the observed morphologies and the corresponding phase diagram.

  12. The morphological diagram of spinels

    SciTech Connect

    Ziolkowski, J.

    1996-02-01

    Catalytic anisotropy in mild oxidation reactions results from the varying activity of different crystal faces. Here, spinels exposing (100), (110), and (111) faces have been considered and their Curie-Wulff plots have been drawn, admitting that the relative G(hkl) surface free energies may change in a wide range as a function of composition, inversion, and segregation degree. The normalized free surface energies are defined as A = G(100)/G(111), B = G(110)/G(111), and C = G(111)/G(111) = 1 = const. This made it possible to construct bidimensional morphological diagrams (morphology = f(A,B) at C = const) in the exposed-face-type, solid-type, and exposure-percentage versions. Eleven morphological habits of grains have been identified, including (100)-cube, (110)-dodecahedron, (111)-hexagons, 18-hedron, 20-hedron, and up to 26-hedra bordered with (i) 6 (100)-octagons, 12 (110)-rectangles, and 8 (111)-hexagons, (ii) 6 (100)-squares, 12 (110)-rectangles, and 8 (111)-triangles, or (iii) 6 (100)-squares, 12 (110)-octagons, and 8 (100)-triangles. The analysis is valid for all compounds crystallizing in the cubic system and preferentially exposing the three enumerated faces.

  13. Phase diagram of ammonium nitrate

    SciTech Connect

    Dunuwille, Mihindra; Yoo, Choong-Shik

    2013-12-07

    Ammonium Nitrate (AN) is a fertilizer, yet becomes an explosive upon a small addition of chemical impurities. The origin of enhanced chemical sensitivity in impure AN (or AN mixtures) is not well understood, posing significant safety issues in using AN even today. To remedy the situation, we have carried out an extensive study to investigate the phase stability of AN and its mixtures with hexane (ANFO–AN mixed with fuel oil) and Aluminum (Ammonal) at high pressures and temperatures, using diamond anvil cells (DAC) and micro-Raman spectroscopy. The results indicate that pure AN decomposes to N{sub 2}, N{sub 2}O, and H{sub 2}O at the onset of the melt, whereas the mixtures, ANFO and Ammonal, decompose at substantially lower temperatures. The present results also confirm the recently proposed phase IV-IV{sup ′} transition above 17 GPa and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400°C.

  14. Phase Diagram of Ammonium Nitrate

    NASA Astrophysics Data System (ADS)

    Dunuwille, Mihindra; Yoo, Choong-Shik

    2013-06-01

    Ammonium Nitrate (AN) has often been subjected to uses in improvised explosive devices, due to its wide availability as a fertilizer and its capability of becoming explosive with slight additions of organic and inorganic compounds. Yet, the origin of enhanced energetic properties of impure AN (or AN mixtures) is neither chemically unique nor well understood - resulting in rather catastrophic disasters in the past1 and thereby a significant burden on safety, in using ammonium nitrates even today. To remedy this situation, we have carried out an extensive study to investigate the phase stability of AN, in different chemical environments, at high pressure and temperature, using diamond anvil cells and micro-Raman spectroscopy. The present results confirm the recently proposed phase IV-to-IV' transition above 15 GPa2 and provide new constraints for the melting and phase diagram of AN to 40 GPa and 673 K. The present study has been supported by the U.S. DHS under Award Number 2008-ST-061-ED0001.

  15. Phase diagram of elastic spheres.

    PubMed

    Athanasopoulou, L; Ziherl, P

    2017-02-15

    Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant-Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.

  16. Alternative algebraic approaches in quantum chemistry

    SciTech Connect

    Mezey, Paul G.

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  17. Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams

    SciTech Connect

    Willow, Soohaeng Yoo; Hirata, So

    2014-01-14

    A new, alternative set of interpretation rules of Feynman–Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE{sub h} after 10{sup 6} Monte Carlo steps.

  18. Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams

    NASA Astrophysics Data System (ADS)

    Willow, Soohaeng Yoo; Hirata, So

    2014-01-01

    A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 106 Monte Carlo steps.

  19. Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.

    PubMed

    Willow, Soohaeng Yoo; Hirata, So

    2014-01-14

    A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 10(6) Monte Carlo steps.

  20. Surface defects and chiral algebras

    DOE PAGES

    Córdova, Clay; Gaiotto, Davide; Shao, Shu-Heng

    2017-05-26

    Here, we investigate superconformal surface defects in four-dimensional N = 2 superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfield-Sokolov reduction and spectral flow can be interpreted as constructions involving four-dimensional surface defects. We compute the index of these defects in the free hypermultiplet theory and Argyres-Douglas theories, using both infrared techniques involving BPS states, as well as renormalization group flows onto Higgs branches. We find perfect agreement with the predicted characters, in eachmore » case.« less

  1. Synthesis of Pd(0) nanocatalyst using lignin in water for the Mizoroki-Heck reaction under solvent-free conditions.

    PubMed

    Marulasiddeshwara, M B; Kumar, P Raghavendra

    2016-02-01

    Palladium(0) nanospheres with an average size of 1-5 nm were synthesized and stabilized by lignin in water without any reducing agent. The lignin supported palladium(0) nanoparticles (lignin@Pd-NPs) were characterized by UV-vis., FT-IR, SEM, TEM, HRICP-AES, EDX and PXRD. Absence of the peak at 430 nm in UV-vis., spectrum confirmed the reduction of Pd(II) to Pd(0). The five characteristic peaks at (111), (200), (220), (311) and (222) corresponding to the 2θ values 40°, 46.7°, 67.9°, 81.9° and 86.9°, respectively, appeared in PXRD spectrum indicated the crystallographic planes of Pd(0) with fcc structure. The Pd(0) loaded on lignin was 0.0467 mmol/g determined by HRICP-AES and 0.89% (w/w) by EDX. The performance of lignin@Pd-NPs catalyst have been investigated for the Mizoroki-Heck CC bond formation reactions between n-butyl propene-2-enoate and halobenzenes and substituted halobenzenes in polar to highly polar solvents as well as under solvent-free conditions in the presence of organic or inorganic bases. The lignin@Pd-NPs was found to be a highly efficient catalyst to yield the desired products of up to 94% under solvent-free conditions in short reaction times. The catalyst was heterogeneous and hence recovered by filtration and reused several times in the subsequent batches of the same reaction.

  2. Bagger-Lambert theory for general Lie algebras

    NASA Astrophysics Data System (ADS)

    Gomis, Jaume; Milanesi, Giuseppe; Russo, Jorge G.

    2008-06-01

    We construct the totally antisymmetric structure constants fABCD of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants fABCD can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the ``center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large gYM.

  3. Algebraic Methods to Design Signals

    DTIC Science & Technology

    2015-08-27

    whose out-of-phase autocorrelation values are very small. We call the constructed sequences perfect sequences and they serve as perfect algebraic...matrices DISTRIBUTION A: Distribution approved for public release. 2. Gauss sum factorizations yield perfect sequences, (with John Dillon and...the p- ary case, the prefix " perfect " for the underlying sequence (i.e. 1-dimensional array) refers to the case when all the out-of-phase

  4. Algebraic learning for language acquisition

    NASA Astrophysics Data System (ADS)

    Farrell, Kevin R.; Mammone, Richard J.; Gorin, Allen

    1994-02-01

    This paper explores the application of new algorithms to the adaptive language acquisition model formulated by Gorin. The new methods consists of incremental approaches for the algebraic learning of statistical associations proposed by Tishby. The incremental methods are evaluated on a text-based natural language experiment, namely the inward call manager task. Performance is evaluated with respect to the alternative methods, namely the smooth mutual information method and the pseudo-inverse solution.

  5. Introduction to Image Algebra Ada

    NASA Astrophysics Data System (ADS)

    Wilson, Joseph N.

    1991-07-01

    Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.

  6. BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1994-01-01

    The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

  7. BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1994-01-01

    The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.

  8. Computer algebra and transport theory.

    SciTech Connect

    Warsa, J. S.

    2004-01-01

    Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.

  9. Algebra: A Challenge at the Crossroads of Policy and Practice

    ERIC Educational Resources Information Center

    Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

    2011-01-01

    The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

  10. Algebra: A Challenge at the Crossroads of Policy and Practice

    ERIC Educational Resources Information Center

    Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

    2011-01-01

    The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

  11. The topology of the Liouville foliation for the Kovalevskaya integrable case on the Lie algebra so(4)

    SciTech Connect

    Kozlov, I K

    2014-04-30

    In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra so(4), which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the momentum mapping are constructed, the types of critical points of rank 0 are determined, the bifurcations of Liouville tori are described, and the loop molecules are computed for all singular points of the bifurcation diagrams. It follows from the obtained results that some topological properties of the classical Kovalevskaya case can be obtained from the corresponding properties of the considered integrable case on the Lie algebra so(4) by taking a natural limit. Bibliography: 21 titles.

  12. (Fuzzy) Ideals of BN-Algebras

    PubMed Central

    Walendziak, Andrzej

    2015-01-01

    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

  13. Bilinear forms on fermionic Novikov algebras

    NASA Astrophysics Data System (ADS)

    Chen, Zhiqi; Zhu, Fuhai

    2007-05-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.

  14. Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Tianjie; Gao, Xing; Guo, Li

    2016-10-01

    The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

  15. Lie algebras of classical and stochastic electrodynamics

    NASA Astrophysics Data System (ADS)

    Neto, J. J. Soares; Vianna, J. D. M.

    1994-03-01

    The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.

  16. On classification of m-dimensional algebras

    NASA Astrophysics Data System (ADS)

    Bekbaev, U.

    2017-03-01

    A constructive approach to the classification and invariance problems, with respect to basis changes, of the finite dimensional algebras is offered. A construction of an invariant open, dense (in the Zariski topology) subset of the space of structure constants of algebras is given. A classification of all algebras with structure constants from this dense set is given by providing canonical representatives of their orbits. A finite system of generators for the corresponding field of invariant rational functions of structure constants is shown.

  17. Symbolic Lie algebras manipulations using COMMON LISP

    NASA Astrophysics Data System (ADS)

    Cecchini, R.; Tarlini, M.

    1989-01-01

    We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LISP knowledge is unnecessary.

  18. Numerical linear algebra algorithms and software

    NASA Astrophysics Data System (ADS)

    Dongarra, Jack J.; Eijkhout, Victor

    2000-11-01

    The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.

  19. Algebraic logic of concepts and its machine implementation in the algebras of deontic and axiological notions

    NASA Astrophysics Data System (ADS)

    Manerowska, Anna; Nieznański, Edward; Mulawka, Jan

    2013-10-01

    Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.

  20. Direct olefination of benzaldehydes into hydroxy functionalized oligo (p-phenylenevinylene)s via Pd-catalyzed heterodomino Knoevenagel-decarboxylation-Heck sequence and its application for fluoride sensing pi-conjugated units.

    PubMed

    Sharma, Abhishek; Sharma, Naina; Kumar, Rakesh; Shard, Amit; Sinha, Arun K

    2010-05-21

    A new approach for one step olefination of benzaldehydes into hydroxy functionalized OPVs is achieved through the first domino Knoevenagel-decarboxylation-Heck sequence using a single catalyst system. The methodology also led to new oxygen based OPV scaffolds capable of selective and visible fluoride recognition in organic or aqueous medium.