Achievements and Problems in Diophantine Approximation Theory
NASA Astrophysics Data System (ADS)
Sprindzhuk, V. G.
1980-08-01
ContentsIntroduction I. Metrical theory of approximation on manifolds § 1. The basic problem § 2. Brief survey of results § 3. The principal conjecture II. Metrical theory of transcendental numbers § 1. Mahler's classification of numbers § 2. Metrical characterization of numbers with a given type of approximation § 3. Further problems III. Approximation of algebraic numbers by rationals § 1. Simultaneous approximations § 2. The inclusion of p-adic metrics § 3. Effective improvements of Liouville's inequality IV. Estimates of linear forms in logarithms of algebraic numbers § 1. The basic method § 2. Survey of results § 3. Estimates in the p-adic metric V. Diophantine equations § 1. Ternary exponential equations § 2. The Thue and Thue-Mahler equations § 3. Equations of hyperelliptic type § 4. Algebraic-exponential equations VI. The arithmetic structure of polynomials and the class number § 1. The greatest prime divisor of a polynomial in one variable § 2. The greatest prime divisor of a polynomial in two variables § 3. Square-free divisors of polynomials and the class number § 4. The general problem of the size of the class number Conclusion References
The diophantine equation hard problem (DEHP) as an asymmetric primitive - Is it possible?
NASA Astrophysics Data System (ADS)
Kamel Ariffin, Muhammad Rezal
2013-09-01
We put forward a probable hard problem based on a Diophantine equation that has characteristics to become an asymmetric primitive. Motivated by rearranging the equation representing the RSA modulus, N together with its Euler-phi function, φ(N) we define the Diophantine Equation Hard Problem (DEHP) on a definitive setting. Relation between the RSA factorization problem, RSA's e-th root problem and the DEHP is also discussed. A proposed asymmetric cryptosystem that manipulates DEHP together with the difficulty of factoring a product of strong primes is presented.
ERIC Educational Resources Information Center
Gauthier, N.
2008-01-01
A general method is presented for evaluating the sums of "m"th powers of the integers that can, and that cannot, be represented in the two-element Frobenius problem. Generating functions are introduced and used for that purpose. Explicit formulas for the desired sums are obtained and specific examples are discussed.
NASA Astrophysics Data System (ADS)
Rouan, D.
2016-09-01
What I call Diophantine optics is the exploitation in optics of some remarkable algebraic relations between powers of integers. The name comes from Diophantus of Alexandria, a greek mathematician, known as the father of algebra. He studied polynomial equations with integer coefficients and integer solutions, called diophantine equations. Since constructive or destructive interferences are playing with optical path differences which are multiple integer (odd or even) of λ/2 and that the complex amplitude is a highly non-linear function of the optical path difference (or equivalently of the phase), one can understand that any Taylor development of this amplitude implies powers of integers. This is the link with Diophantine equations. We show how, especially in the field of interferometry, remarkable relations between powers of integers can help to solve several problems, such as achromatization of a phase shifter or deep nulling efficiency. It appears that all the research that was conducted in this frame of thinking, relates to the field of detection of exoplanets, a very active domain of astrophysics today.
NASA Astrophysics Data System (ADS)
Bedogne', C.; Masucci, A. P.; Rodgers, G. J.
2008-03-01
We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques between M vertices every time that M distinct integers satisfy the equation. We analyse the network generated by the Pythagorean equation x2 +y2 =z2 showing that its degree distribution is well approximated by a power law with exponential cut-off. We also show that the properties of this network differ considerably from the features of scale-free networks generated through preferential attachment. Remarkably we also recover a power law for the clustering coefficient. We then study the network associated with the equation x2 +y2 = z showing that the degree distribution is consistent with a power law for several decades of values of k and that, after having reached a minimum, the distribution begins rising again. The power-law exponent, in this case, is given by γ ∼ 4.5 We then analyse clustering and ageing and compare our results to the ones obtained in the Pythagorean case.
Recent Progress on Certain Quartic Diophantine Equations
NASA Astrophysics Data System (ADS)
Walsh, P. G.
2008-01-01
Wilhelm Ljunggren proved many results on quartic Diophantine equations of the form aX4-bY2 = c, with c∈{±1,-2,±4}. Noticeably absent from this set of values of c is c = 2. We describe some recent progress on this problem, and discuss some open problems which require further study.
Diophantine Equations and Computation
NASA Astrophysics Data System (ADS)
Davis, Martin
Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{
NASA Astrophysics Data System (ADS)
Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.
2013-04-01
This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.
Diophantine frequency synthesis.
Sotiriadis, Paul Peter
2006-11-01
A methodology for fine-step, fast-hopping, low-spurs phase-locked loop based frequency synthesis is presented. It uses mathematical properties of integer numbers and linear Diophantine equations to overcome the constraining relation between frequency step and phase-comparator frequency that is inherent in conventional phase-locked loop based frequency synthesis. The methodology leads to fine-step, fast-hopping, modular-structured frequency synthesizers with potentially very low spurs, especially in the vicinity of the carrier. The paper focuses on the mathematical principles of the new methodology and the related number theoretic algorithms. PMID:17091835
Un scindage du morphisme de Frobenius quantique
NASA Astrophysics Data System (ADS)
Gros, Michel; Kaneda, Masaharu
2015-10-01
We show that the quantum Frobenius morphism constructed by Lusztig in the setting of the quantum enveloping algebra specialized at a root of unity admits a (nonunital) multiplicative splitting. We construct the splitting using a basis of the toral part of the small quantum algebra consisting of pairwise orthogonal idempotents summing up to 1, and likewise in the modular case of the algebra of distributions for a semisimple algebraic group.
New Hardness Results for Diophantine Approximation
NASA Astrophysics Data System (ADS)
Eisenbrand, Friedrich; Rothvoß, Thomas
We revisit simultaneous Diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input to the decision version of this problem consists of a rational vector α ∈ ℚ n , an error bound ɛ and a denominator bound N ∈ ℕ + . One has to decide whether there exists an integer, called the denominator Q with 1 ≤ Q ≤ N such that the distance of each number Q ·α i to its nearest integer is bounded by ɛ. Lagarias has shown that this problem is NP-complete and optimization versions have been shown to be hard to approximate within a factor n c/ loglogn for some constant c > 0. We strengthen the existing hardness results and show that the optimization problem of finding the smallest denominator Q ∈ ℕ + such that the distances of Q·α i to the nearest integer are bounded by ɛ is hard to approximate within a factor 2 n unless {textrm{P}} = NP.
Symmetry and Lie-Frobenius reduction of differential equations
NASA Astrophysics Data System (ADS)
Gaeta, G.
2015-01-01
Twisted symmetries, widely studied in the last decade, have proved to be as effective as standard ones in the analysis and reduction of nonlinear equations. We explain this effectiveness in terms of a Lie-Frobenius reduction; this requires focus not just on the prolonged (symmetry) vector fields, but on the distributions spanned by these and on systems of vector fields in involution in the Frobenius sense, not necessarily spanning a Lie algebra. Research partially supported by MIUR-PRIN program under project 2010-JJ4KPA.
On some applications of diophantine approximations
Chudnovsky, G. V.
1984-01-01
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to “almost all” numbers. In particular, any such number has the “2 + ε” exponent of irrationality: ǀΘ - p/qǀ > ǀqǀ-2-ε for relatively prime rational integers p,q, with q ≥ q0 (Θ, ε). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162]. PMID:16593441
On some applications of diophantine approximations.
Chudnovsky, G V
1984-03-01
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions at rational points have measures of diophantine approximations typical to "almost all" numbers. In particular, any such number has the "2 + epsilon" exponent of irrationality: Theta - p/q > q(-2-epsilon) for relatively prime rational integers p,q, with q >/= q(0) (Theta, epsilon). These results answer some problems posed by Lang. The methods used here are based on the introduction of graded Padé approximations to systems of functions satisfying linear differential equations with rational function coefficients. The constructions and proofs of this paper were used in the functional (nonarithmetic case) in a previous paper [Chudnovsky, D. V. & Chudnovsky, G. V. (1983) Proc. Natl. Acad. Sci. USA 80, 5158-5162]. PMID:16593441
Average Frobenius distribution for the degree two primes of a number field
NASA Astrophysics Data System (ADS)
James, Kevin; Smith, Ethan
2013-05-01
Let $K$ be a number field and $r$ an integer. Given an elliptic curve $E$, defined over $K$, we consider the problem of counting the number of degree two prime ideals of $K$ with trace of Frobenius equal to $r$. Under certain restrictions on $K$, we show that "on average" the number of such prime ideals with norm less than or equal to $x$ satisfies an asymptotic identity that is in accordance with standard heuristics. This work is related to the classical Lang-Trotter conjecture and extends the work of several authors.
Evolution equations: Frobenius integrability, conservation laws and travelling waves
NASA Astrophysics Data System (ADS)
Prince, Geoff; Tehseen, Naghmana
2015-10-01
We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these equations. We also discuss ‘local’ conservations laws for evolution equations in general and demonstrate all the results for the Korteweg-de Vries equation.
NASA Astrophysics Data System (ADS)
Calogero, Francesco; Yi, Ge
2013-06-01
By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi polynomial {pN (0, 1; γ; x )} and by the Jacobi polynomial {PN^{(-N-1,-N-1 )} (x )} (or, equivalently, by the Gegenbauer polynomial {CN^{-N-1/2}( x ) }) are identified, as well as Diophantine properties of the zeros and coefficients of these polynomials.
ON FROBENIUS PAIRS OF THE FORM (F\\leftthreetimes V,\\, V)
NASA Astrophysics Data System (ADS)
Shunkov, V. P.
1991-02-01
A nonsimplicity test for groups is obtained which is connected with certain Frobenius pairs. In the case of finite groups it is a natural complement to Glauberman's familiar Z^*-theorem.Bibliography: 10 titles.
On a conjecture on exponential Diophantine equations
NASA Astrophysics Data System (ADS)
Cipu, Mihai; Mignotte, Maurice
We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\\equiv 2 \\pmod 4$, $b\\equiv 3 \\pmod 4$ and $\\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We also prove the uniqueness of such a solution if any of $a$, $b$, $c$ is a prime power. In a different vein, we obtain various inequalities that must be satisfied by the components of a putative second solution.
Integer Solutions of a Special Diophantine Equation
NASA Astrophysics Data System (ADS)
Özkoç, Arzu; Tekcan, Ahmet
2011-09-01
Let t≠1 be an integer. In this work, we determine the integer solutions of Diophantine equation D:x2+(2-t2)y2+(-2t2-2t+2)x+(2t5-6t3+4t)y-t8+4t6-4t4+2t3+t2-2t = 0 over Z and also over finite fields Fp for primes p≥2. Also we derive some recurrence relations on the integer solutions (xn,yn) of D and formulate the the n—th solution (xn,yn) by using the simple continued fraction expansion of xn/yn.
Frobenius-norm-based measures of quantum coherence and asymmetry.
Yao, Yao; Dong, G H; Xiao, Xing; Sun, C P
2016-01-01
We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physical meanings, we observe that these quantities are intimately related to the purity (or linear entropy) of the corresponding quantum states. Remarkably, we demonstrate that the proposed coherence quantifier is not only a measure of mixedness, but also an intrinsic (basis-independent) quantification of quantum coherence contained in quantum states, which can also be viewed as a normalized version of Brukner-Zeilinger invariant information. In our context, the asymmetry of N-qubit quantum systems is considered under local independent and collective transformations. In- triguingly, it is illustrated that the collective effect has a significant impact on the asymmetry measure, and quantum correlation between subsystems plays a non-negligible role in this circumstance. PMID:27558009
Frobenius-norm-based measures of quantum coherence and asymmetry
Yao, Yao; Dong, G. H.; Xiao, Xing; Sun, C. P.
2016-01-01
We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physical meanings, we observe that these quantities are intimately related to the purity (or linear entropy) of the corresponding quantum states. Remarkably, we demonstrate that the proposed coherence quantifier is not only a measure of mixedness, but also an intrinsic (basis-independent) quantification of quantum coherence contained in quantum states, which can also be viewed as a normalized version of Brukner-Zeilinger invariant information. In our context, the asymmetry of N-qubit quantum systems is considered under local independent and collective transformations. In- triguingly, it is illustrated that the collective effect has a significant impact on the asymmetry measure, and quantum correlation between subsystems plays a non-negligible role in this circumstance. PMID:27558009
Diophantine exponents for mildly restricted approximation
NASA Astrophysics Data System (ADS)
Bugeaud, Yann; Kristensen, Simon
2009-10-01
We are studying the Diophantine exponent μ n, l defined for integers 1≤ l< n and a vector α∈ℝ n by letting μ_{n,l}=sup\\{μ≥0: 0 < Vertx\\cdotαVert
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
ERIC Educational Resources Information Center
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Superconformal block quivers, duality trees and Diophantine equations
NASA Astrophysics Data System (ADS)
Hanany, Amihay; He, Yang-Hui; Sun, Chuang; Sypsas, Spyros
2013-11-01
We generalize previous results on = 1, (3 + 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice.
The Diophantine equation 8(x) + p(y) = z(2).
Qi, Lan; Li, Xiaoxue
2015-01-01
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ± 3(mod 8), then the equation 8 (x) + p (y) = z (2) has no positive integer solutions (x, y, z); (ii) if p ≡ 7(mod 8), then the equation has only the solutions (p, x, y, z) = (2 (q) - 1, (1/3)(q + 2), 2, 2 (q) + 1), where q is an odd prime with q ≡ 1(mod 3); (iii) if p ≡ 1(mod 8) and p ≠ 17, then the equation has at most two positive integer solutions (x, y, z). PMID:25654128
The Diophantine Equation 8x + py = z2
Qi, Lan; Li, Xiaoxue
2015-01-01
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ±3(mod 8), then the equation 8x + py = z2 has no positive integer solutions (x, y, z); (ii) if p ≡ 7(mod 8), then the equation has only the solutions (p, x, y, z) = (2q − 1, (1/3)(q + 2), 2, 2q + 1), where q is an odd prime with q ≡ 1(mod 3); (iii) if p ≡ 1(mod 8) and p ≠ 17, then the equation has at most two positive integer solutions (x, y, z). PMID:25654128
NASA Astrophysics Data System (ADS)
Kimura, Yusuke
2015-07-01
It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.
Bounds for departure from normality and the Frobenius norm of matrix eigenvalues
Lee, S.L.
1994-12-01
New lower and upper bounds for the departure from normality and the Frobenius norm of the eigenvalues of a matrix axe given. The significant properties of these bounds axe also described. For example, the upper bound for matrix eigenvalues improves upon the one derived by Kress, de Vries and Wegmann in [Lin. Alg. Appl., 8 (1974), pp. 109-120]. The upper bound for departure from normality is sharp for any matrix whose eigenvalues are collinear in the complex plane. Moreover, the latter formula is a practical estimate that costs (at most) 2m multiplications, where m is the number of nonzeros in the matrix. In terms of applications, the results can be used to bound from above the sensitivity of eigenvalues to matrix perturbations or bound from below the condition number of the eigenbasis of a matrix.
Lepton mixing, residual symmetries, and trigonometric Diophantine equations
NASA Astrophysics Data System (ADS)
Hu, Bo
2014-10-01
In this paper, we study residual symmetries in the lepton sector. Our first concern is the symmetry of the charged lepton mass matrix in the basis where the Majorana neutrino mass matrix is diagonal, which is strongly constrained by the requirement that the symmetry group generated by residual symmetries is finite. In a recent work, R. M. Fonseca and W. Grimus found that there exists a set of constraint equations that can be completely solved, which is essential in their approach to the classification of lepton mixing matrices that are fully determined by residual symmetries. In this paper, a method to handle trigonometric Diophantine equations is introduced. We will show that the constraint equations found by Fonseca and Grimus can also be solved by this method. Detailed derivation and discussion will be presented in a self-contained way. In addition, we will also show that, in the case where residual symmetries satisfy a reality condition, this method can be used to solve the equation constraining parameters in the symmetry assignment that controls the group structure generated by residual symmetries and is directly related to mixing matrix elements.
Spectrum and eigenfunctions of the Frobenius-Perron operator of the tent map
NASA Astrophysics Data System (ADS)
Dörfle, M.
1985-07-01
The spectrum and eigenfunctions of the Frobenius-Perron operator induced by the tent map are discussed in detail. Special attention is paid to the case where the critical point of the map lies on an aperiodic trajectory and the differences from maps with a periodic critical trajectory are stressed. It is shown that the relevant eigenvalues of the spectrum are not sensitive to the aperiodicity of the critical trajectory. All other parts of the spectrum and all eigenfunctions in particular are changed drastically if the critical trajectory becomes aperiodic. The intimate connection between the point spectrum and the kneading invariant is established and the critical slowing down as well as the band splitting are a consequence of its properties. The structure of the infinite sequence of null spaces and its implications on the spectrum of the operator are discussed. It is shown that any initial distribution P(0, x) of bounded variation can be projected uniquely onto the eigenfunctions of the relevant eigenvalues and that the time dependence of P(n, x) is determined by this expansion up to an error O(η n). From this the stationary and the asymptotic behavior of the correlation function < x(n) x> can be derived exactly.
A study of the ambiguity in the solutions to the Diophantine equation for Chern numbers
NASA Astrophysics Data System (ADS)
Avron, J. E.; Kenneth, O.; Yehoshua, G.
2014-05-01
The Chern numbers for Hofstadter models with rational flux 2πp/q are partially determined by a Diophantine equation. A mod q ambiguity remains. The resolution of this ambiguity is only known for the rectangular lattice with nearest neighbors hopping where it has the form of a ‘window condition’. We study a Hofstadter butterfly on the triangular lattice for which the resolution of ambiguity is open. In the model many pairs (p, q) satisfy a window condition which is shifted relative to the window of the square model. However, we also find pairs (p, q) where the Chern numbers do not belong to any contiguous window. This shows that the rectangular model and the one we study on the triangular lattice are not adiabatically connected: many gaps must close. Our results suggest the conjecture that the mod q ambiguity in the Diophantine equation generically reduces to a sign ambiguity.
On the Diophantine equation x^2+q^2m=2y^p
NASA Astrophysics Data System (ADS)
Tengely, Sz
In this paper we consider the Diophantine equation $x^2+q^{2m}=2y^p$ where $m,p,q,x,y$ are integer unknowns with $m>0,$ $p$ and $q$ are odd primes and $\\gcd(x,y)=1.$ We prove that there are only finitely many solutions $(m,p,q,x,y)$ for which $y$ is not a sum of two consecutive squares. We also study the above equation with fixed $y$ and with fixed $q.$
On the System of Diophantine Equations x2 − 6y2 = −5 and x = az2 − b
Zhang, Silan; Chen, Jianhua; Hu, Hao
2014-01-01
Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x2 − 6y2 = −5 and x = 2z2 − 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x2 − 6y2 = −5 and x = az2 − b for each pair of integral parameters a, b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals. PMID:25045739
On the system of Diophantine equations x2 - 6y2 = -5 and x = az2 - b.
Zhang, Silan; Chen, Jianhua; Hu, Hao
2014-01-01
Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) - 6y (2) = -5 and x = 2z (2) - 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x (2) - 6y (2) = -5 and x = az (2) - b for each pair of integral parameters a, b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals. PMID:25045739
NASA Astrophysics Data System (ADS)
Fortunati, Alessandro; Wiggins, Stephen
2014-09-01
The aim of this paper is to prove a Kolmogorov type result for a nearly integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists in the possibility to choose an arbitrarily small decaying coefficient consistently with the perturbation size. The proof, based on the Lie series formalism, is a generalization of a work by A. Giorgilli.
NASA Astrophysics Data System (ADS)
Trell, Erik
2012-09-01
Emulating Nature by observation and ground-up application of its patterns, structures and processes is a classical scientific practice which under the designation of Biomimetics has now been brought to the Nanotechnology scale where even highly complex systems can be replicated by continuous or cyclically reiterated assembly of the respective self-similar real-world eigen-elements, modules and algorithms right from their infinitesimal origin. This is actually quite akin to the genuine mathematical art and can find valuable renewed use as here exemplified by an onedimensional prime-number line and a three-dimensional Diophantine Equation Universe embodiment.
Linear forms in p-adic logarithms and the Diophantine equation formula here
NASA Astrophysics Data System (ADS)
Bugeaud, Yann
1999-11-01
A longstanding conjecture claims that the Diophantine equationformula herehas finitely many solutions and, maybe, only those given byformula hereAmong the known results, let us mention that Ljunggren [9] solved (1) completely when q = 2 and that very recently Bugeaud et al. [3] showed that (1) has no solution when x is a square. For more information and in particular for finiteness type results under some extra hypotheses, we refer the reader to Nagell [11], Shorey & Tijdeman [16, 17] and to the recent survey of Shorey [15]. One of the main tools used in most of the proofs is Baker's theory of linear form in archimedean logarithms of algebraic numbers and especially a dramatic sharpening obtained when the algebraic numbers involved are closed to 1. This was first noticed by Shorey [14], and has been applied in numerous works relating to (1) or to the Diophantine equationformula heresee for instance [1, 5, 10]. The purpose of the present work is to prove a similar sharpening for linear forms in p-adic logarithms and to show how it can be applied in the context of (1). Further, following previous investigations by Sander [12] and Saradha & Shorey [13], we derive from our results an irrationality statement for Mahler's numbers.
Modelling Problem-Solving Situations into Number Theory Tasks: The Route towards Generalisation
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…
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 .
Ergodic theory and Diophantine approximation for translation surfaces and linear forms
NASA Astrophysics Data System (ADS)
Athreya, Jayadev; Parrish, Andrew; Tseng, Jimmy
2016-08-01
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli space of translation surfaces. Our techniques, together with an approximation argument, also give an alternative proof of a weak version of a classical theorem in multi-dimensional Diophantine approximation due to Schmidt (1960 Can. J. Math. 12 619–31, 1964 Trans. Am. Math. Soc. 110 493–518). The approximation argument allows us to deduce the Birkhoff genericity of almost all lattices in a certain submanifold of the space of unimodular lattices from the Birkhoff genericity of almost all lattices in the whole space and similarly for the space of affine unimodular lattices.
NASA Astrophysics Data System (ADS)
Sato, Masatoshi; Tobe, Daijiro; Kohmoto, Mahito
2008-12-01
We consider a tight-binding model with the nearest-neighbor hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote by ta , can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong ta regions, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak ta region shows the unconventional quantization of the Hall conductance, σxy=-(e2/h)(2n+1) (n=0,±1,±2,…) , near the half filling, while the strong ta region shows only the conventional one, σxy=-(e2/h)n (n=0,±1,±2,…) . From the topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate ta region is concluded. We also study numerically the quantum phase structure in detail and find that even when ta=1 , namely, in graphene case, the system is in the weak ta phase except when the Fermi energy is located near the Van Hove singularity or the lower and upper edges of the spectrum.
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.; Droghei, R.
2009-12-01
The isochronous variant is exhibited of the dynamical system corresponding to the Mth ordinary differential equation of the stationary Korteweg-de Vries (KdV) hierarchy. New Diophantine relations are thereby obtained, in the guise of matrices of arbitrary order having integer eigenvalues or equivalently of polynomials of arbitrary degree having integer zeros. Generalizations of these formulas to relations among rational functions are also obtained. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings.
On solving the Diophantine equation x^3+y^3+z^3=k on a vector computer
NASA Astrophysics Data System (ADS)
Heath-Brown, D. R.; Lioen, W. M.; Riele, H. J. J. Te
1993-07-01
Recently, the first author has proposed a new algorithm for solving the Diophantine equation {x^3} + {y^3} + {z^3} = k , where k is a given nonzero integer. In this paper we present the detailed versions of this algorithm for some values of k given below, and we describe how we have optimized and run the algorithm on a Cyber 205 vector computer. A vectorized version of the Euclidean algorithm was written, which is capable of solving the equations {w_i}{x_i} ≡ 1 bmod {n_i},i = 1,2, ldots , at vector speed. Moreover, the basic double-precision arithmetic operations ( + , - , × ,/) were vectorized. The following cases were implemented and run: k = 3,30,2,20,39 , and 42. For k = 3 a range was searched which includes the cube \\vert x\\vert,\\vert y\\vert,\\vert z\\vert ≤ {10^8} ; this considerably extends an earlier search in the cube \\vert x\\vert,\\vert y\\vert,\\vert z\\vert ≤ {2^{16}} . No solutions were found apart from the known ones (1, 1, 1) and (4,4, - 5) . For k = 30 , which probably is, with k = 3 , the case which has attracted most attention in the literature, no solution was found. It is the smallest case for which no solution is known and for which one has not been able to find a proof that no solution exists. For k = 2 a parametric form solution is known, but we also found one which does not belong to this parametric form, viz., (1214928,3480205, - 3528875) . For k = 20 , several new large solutions were found in addition to several known ones; this case served as a (partial) check of the correctness of our program. Finally, for k = 39 we found the first solution: (134476,117367, - 159380) . Hence, this case can be dropped from the list of values of k (k = 30,33,39,42, ldots ) for which no solution is known (yet).
Goldfishing: A new solvable many-body problem
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-10-01
A recent technique allows one to identify and investigate solvable dynamical systems naturally interpretable as classical many-body problems, being characterized by equations of motion of Newtonian type (generally in two-dimensional space). In this paper we tersely review results previously obtained in this manner and present novel findings of this kind: mainly solvable variants of the goldfish many-body model, including models that feature isochronous classes of completely periodic solutions. Different formulations of these models are presented. The behavior of one of these isochronous dynamical systems in the neighborhood of its equilibrium configuration is investigated, and in this manner some remarkable Diophantine findings are obtained.
Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem
NASA Astrophysics Data System (ADS)
Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang
2008-08-01
The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert’s tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.
Public channel cryptography: chaos synchronization and Hilbert's tenth problem.
Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang
2008-08-22
The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols. PMID:18764616
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2013-01-01
Some properties of a solvable N-body problem featuring several free parameters ("coupling constants") are investigated. Restrictions on its parameters are reported which guarantee that all its solutions are completely periodic with a fixed period independent of the initial data (isochrony). The restrictions on its parameters which guarantee the existence of equilibria are also identified. In this connection a remarkable second-order ODE—generally not of hypergeometric type, hence not reducible to those characterizing the classical polynomials—is studied: if its parameters satisfy a Diophantine condition, its general solution is a polynomial of degree N, the N zeros of which identify the equilibria of the N-body system.
Baroclinic Instability in the Solar Tachocline. II. The Eady Problem
NASA Astrophysics Data System (ADS)
Gilman, Peter A.
2016-02-01
We solve the nongeostrophic baroclinic instability problem for the tachocline for a continuous model with a constant vertical rotation gradient (the Eady problem), using power series generated by the Frobenius method. The results confirm and greatly extend those from a previous two-layer model. For effective gravity G independent of height, growth rates and ranges of unstable longitudinal wavenumbers m and latitudes increase with decreasing G. As with the two-layer model, the overshoot tachocline is much more unstable than the radiative tachocline. The e-folding growth times range from as short as 10 days to as long as several years, depending on latitude, G, and wavenumber. For a more realistic effective gravity that decreases linearly from the radiative interior to near zero at the top of the tachocline, we find that only m = 1, 2 modes are unstable, with growth rates somewhat larger than for constant G, with the same value as at the bottom of the tachocline. All results are the same whether we assume that the vertical velocity or the perturbation pressure is zero at the top of the layer; this is a direct consquence of not employing the geostrophic assumption for perturbations. We explain most of the properties of the instability in terms of the Rossby deformation radius. We discuss further improvements in the realism of the model, particularly adding toroidal fields that vary in height, and including latitudinal gradients of both rotation and toroidal fields.
Diophantine equations in the primes
NASA Astrophysics Data System (ADS)
Cook, Brian; Magyar, Ákos
2014-12-01
Let $\\mathfrak{p}=(\\mathfrak{p}_1,...,\\mathfrak{p}_r)$ be a system of $r$ polynomials with integer coefficients of degree $d$ in $n$ variables $\\mathbf{x}=(x_1,...,x_n)$. For a given $r$-tuple of integers, say $\\mathbf{s}$, a general local to global type statement is shown via classical Hardy-Littlewood type methods which provides sufficient conditions for the solubility of $\\mathfrak{p}(\\mathbf{x})=\\mathbf{s}$ under the condition that each of the $x_i$'s is prime.
On applications of diophantine approximations
Chudnovsky, G. V.
1984-01-01
This paper is devoted to the study of the arithmetic properties of values of G-functions introduced by Siegel [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1]. One of the main results is a theorem on the linear independence of values of G-functions at rational points close to the origin. In this theorem, no conditions are imposed on the p-adic convergence of a G-function at a generic point. The theorem finally realizes Siegel's program on G-function values outlined in his paper. PMID:16593530
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-12-01
We take advantage of the simple approach, recently discussed, which associates to (solvable) matrix equations (solvable) dynamical systems interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. Starting from a solvable matrix evolution equation, we obtain the corresponding many-body model and note that in one case the auxiliary variables can be altogether eliminated, obtaining thereby an (also Hamiltonian) extension of the "goldfish" model. The solvability of this novel model, and of its isochronous variant, is exhibited. A related, as well solvable, model, is also introduced, as well as its isochronous variant. Finally, the small oscillations of the isochronous models around their equilibrium configurations are investigated, and from their isochronicity certain diophantine relations are evinced.
... gov/ Home Body Getting your period Problem periods Problem periods It’s common to have cramps or feel ... doctor Some common period problems Signs of period problems top One way to know if you may ...
... it could be a sign of a balance problem. Balance problems can make you feel unsteady or as if ... related injuries, such as hip fracture. Some balance problems are due to problems in the inner ear. ...
... often, it could be a sign of a balance problem. Balance problems can make you feel unsteady or as ... fall-related injuries, such as hip fracture. Some balance problems are due to problems in the inner ...
... labor starts before 37 completed weeks of pregnancy Problems with the umbilical cord Problems with the position of the baby, such as ... feet first Birth injuries For some of these problems, the baby may need to be delivered surgically ...
... version of this page please turn Javascript on. Balance Problems About Balance Problems Have you ever felt dizzy, lightheaded, or ... dizziness problem during the past year. Why Good Balance is Important Having good balance means being able ...
... daily activities, get around, and exercise. Having a problem with walking can make daily life more difficult. ... walk is called your gait. A variety of problems can cause an abnormal gait and lead to ...
... re not getting enough air. Sometimes mild breathing problems are from a stuffy nose or hard exercise. ... emphysema or pneumonia cause breathing difficulties. So can problems with your trachea or bronchi, which are part ...
... cord injury In some cases, your emotions or relationship problems can lead to ED, such as: Poor ... you stressed, depressed, or anxious? Are you having relationship problems? You may have a number of different ...
... ankles and toes. Other types of arthritis include gout or pseudogout. Sometimes, there is a mechanical problem ... for more information on osteoarthritis, rheumatoid arthritis and gout. How Common are Joint Problems? Osteoarthritis, which affects ...
ERIC Educational Resources Information Center
Foster, Colin
2012-01-01
This is the story of a real problem, not a problem that is contrived, or invented for the convenience of the appropriate planning tool. This activity by a group of students, defined simply as "8FN", might be likened to an "end of term concert". If you just happened to be a delegate at the ATM Conference 2003 you might remember the analogy. Social…
... our e-newsletter! Aging & Health A to Z Balance Problems Basic Facts & Information What are Balance Problems? Having good balance means being able to ... Only then can you “keep your balance.” Why Balance is Important Your feelings of dizziness may last ...
... treated differently. Common thyroid disorders and problems include: Hypothyroidism Hypothyroidism is a disorder in which your thyroid doesn’ ... normal after you get better. If you have hypothyroidism, however, the levels of T4 in your blood ...
... back or groin? Yes You may have a KIDNEY STONE or another serious problem. EMERGENCY See your doctor ... the bladder, called INTERSTITIAL CYSTITIS, or from a KIDNEY STONE stuck in the bladder, or a chemical in ...
... our e-newsletter! Aging & Health A to Z Kidney Problems Basic Facts & Information The kidneys are two ... the production of red blood cells. What are Kidney Diseases? For about one-third of older people, ...
... This flow chart will help direct you if hearing loss is a problem for you or a family ... may damage the inner ear. This kind of hearing loss is called OCCUPATIONAL. Prevent occupational hearing loss by ...
... For Consumers Consumer Information by Audience For Women Sleep Problems Share Tweet Linkedin Pin it More sharing ... PDF 474KB) En Español Medicines to Help You Sleep Tips for Better Sleep Basic Facts about Sleep ...
... a person's ability to speak clearly. Some Common Speech Disorders Stuttering is a problem that interferes with fluent ... is a language disorder, while stuttering is a speech disorder. A person who stutters has trouble getting out ...
... the home Dry mouth during cancer treatment Enteral nutrition - child - managing problems Gastrostomy feeding tube - bolus Jejunostomy feeding tube Mouth and neck radiation - discharge Multiple sclerosis - discharge Stroke - discharge Update Date 5/15/2014 ...
... Inverted nipple; Nipple problems Images Female breast Intraductal papilloma Mammary gland Abnormal discharge from the nipple Normal ... 8. Read More Breast cancer Endocrine glands Intraductal papilloma Update Date 11/16/2014 Updated by: Cynthia ...
... which nothing can be seen) Vision loss and blindness are the most severe vision problems. Causes Vision ... that look faded. The most common cause of blindness in people over age 60. Eye infection, inflammation, ...
Hopf and Frobenius algebras in conformal field theory
NASA Astrophysics Data System (ADS)
Singh, Sukreet
With the current rapid depletion of non-renewable resources to generate power, energy conservation and on site generation have become the most critical aspects of the equation. Buildings should be so designed or retrofitted in order to generate its own electricity and cater to its own demand. This thesis looks as the ways in which we can do a post occupancy analysis of an existing institutional building of about 95,000 square feet that was built in 1960's in order to reduce usage and approach a Zero Net Energy goal. This case study building is Von Kleinsmid Centre (VKC) which is located at the heart of USC (University of Southern California). It is challenging to retrofit an existing institutional building because of its complexity and make it achieve a 'Zero Net Energy' goal. All the roadblocks, real life delays, software limitations that had to be overcome to achieve this result are explained in this thesis. The Zero Net Energy goal was achieved by calibrating energy model to the utility data of the building, providing various energy efficiency measures and generating on-site electricity.
ERIC Educational Resources Information Center
Murphy, Pat, Ed.
1993-01-01
"Exploring" is a magazine of science, art, and human perception, produced by Exploratorium in collaboration with other participating museums. This issue focuses on puzzles and problem solving. Brain teasers, puzzles, and the strategies for solving them are included. Features include: (1) "Homework Assignment #3" (Paul Doherty); (2) "The Case of…
ERIC Educational Resources Information Center
Connors, G. Patrick
Heat problems and heat cramps related to jogging can be caused by fluid imbalances, medications, dietary insufficiency, vomiting or diarrhea, among other factors. If the condition keeps reoccurring, the advice of a physician should be sought. Some preventive measures that can be taken include: (1) running during the cooler hours of the day; (2)…
Padé approximations and diophantine geometry
Chudnovsky, D. V.; Chudnovsky, G. V.
1985-01-01
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves. PMID:16593552
LETTER TO THE EDITOR: Diophantine integrability
NASA Astrophysics Data System (ADS)
Halburd, R. G.
2005-04-01
The heights of iterates of the discrete Painlevé equations over number fields appear to grow no faster than polynomials while the heights of generic solutions of non-integrable discrete equations grow exponentially. This gives rise to a simple and effective numerical test for the integrability of discrete equations. Numerical evidence and theoretical results are presented. Connections with other tests for integrability and Vojta's dictionary are discussed.
Centaurs: Here, There, Everywhere!
ERIC Educational Resources Information Center
Dzlabenko, Dimitri; Ivril, Oleg
2008-01-01
Motivated by centaurs jumping around a circular stadium, we derive Kronecker's Approximation Theorem, which in turn provides elementary solutions to difficult problems in the theory of Diophantine approximations.
Waring's problem with the Ramanujan \\tau-function
NASA Astrophysics Data System (ADS)
Garaev, M. Z.; Garcia, V. C.; Konyagin, S. V.
2008-02-01
We prove that for every integer N the Diophantine equation \\sum_{i=1}^{74000}\\tau(n_i)=N, where \\tau(n) is the Ramanujan \\tau-function, has a solution in positive integers n_1, n_2,\\dots, n_{74000} satisfying the condition \\max_{1\\le i\\le 74000}n_i\\,{\\ll}\\vert N\\vert^{2/11}+1. We also consider similar questions in residue fields modulo a large prime p.
Problems with "n"th-Term Problems
ERIC Educational Resources Information Center
Matteson, Shirley M.
2010-01-01
An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…
Class and Home Problems: Optimization Problems
ERIC Educational Resources Information Center
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
ERIC Educational Resources Information Center
Reeves, Charles A.
2000-01-01
Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)
f AQ FREQUENTLY ASKED QUESTIONS FAQ178 GYNECOLOGIC PROBLEMS Mammography and Other Screening Tests for Breast Problems • What ... used to screen for breast problems? • What is mammography? • Why is mammography done? • When should I start ...
... problems may also be factors. Occasional problems with sexual function are common. If problems last more than a few months or cause distress for you or your partner, you should see your health care provider.
... this page please turn Javascript on. Problems with Smell About Problems with Smell Our sense of smell helps us enjoy life. ... sec Click to watch this video Aging and Smell Loss Problems with smell increase as people get ...
... correct pelvic support problems? • Glossary What are pelvic support problems? The pelvic organs include the vagina , cervix , uterus , bladder , urethra , small intestines, and rectum . The pelvic ...
Problem? "No Problem!" Solving Technical Contradictions
ERIC Educational Resources Information Center
Kutz, K. Scott; Stefan, Victor
2007-01-01
TRIZ (pronounced TREES), the Russian acronym for the theory of inventive problem solving, enables a person to focus his attention on finding genuine, potential solutions in contrast to searching for ideas that "may" work through a happenstance way. It is a patent database-backed methodology that helps to reduce time spent on the problem,…
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
The Algorithm Selection Problem
NASA Technical Reports Server (NTRS)
Minton, Steve; Allen, John; Deiss, Ron (Technical Monitor)
1994-01-01
Work on NP-hard problems has shown that many instances of these theoretically computationally difficult problems are quite easy. The field has also shown that choosing the right algorithm for the problem can have a profound effect on the time needed to find a solution. However, to date there has been little work showing how to select the right algorithm for solving any particular problem. The paper refers to this as the algorithm selection problem. It describes some of the aspects that make this problem difficult, as well as proposes a technique for addressing it.
Pérez, Diana I
2005-01-01
In this paper I present, in the first place, two of the main problems in the philosophy of mind: 1) the problem of the criteria of the mental, and 2) the problem of the relationship between the mental and the physical. In the last part, I mention two problems highly discussed nowadays which, in my view, will produce the most important advance in the knowledge of our minds in the next decades: the problem of consciousness and its neural basis, and the problem of the origin and development of a theory of mind. PMID:16220149
Locating Problems with Quality Circles.
ERIC Educational Resources Information Center
White, Donald D.; Bednar, David A.
1985-01-01
Five categories of common quality circles problems are identified to help firms anticipate difficulties and avert circle failures. These categories include encountered internal problems, encountered external problems, created internal problems, created external problems, and interface problems. Solutions are suggested. (CT)
IT Problem Management â process responsible for managing Lifecycle of all IT problems. The primary objective is to prevent incidents from occurring and to minimize impact of incidents that cannot...
ERIC Educational Resources Information Center
Choate, Joyce S.
1990-01-01
The initial step of a strategic process for solving mathematical problems, "studying the question," is discussed. A lesson plan for teaching students to identify and revise arithmetic problems is presented, involving directed instruction and supervised practice. (JDD)
Traveling with breathing problems
If you have breathing problems and you: Are short of breath most of the time Get short of breath when you walk 150 ... or less Have been in the hospital for breathing problems recently Use oxygen at home, even if ...
Problem: Heart Valve Regurgitation
... Pressure High Blood Pressure Tools & Resources Stroke More Problem: Heart Valve Regurgitation Updated:May 26,2016 What ... content was last reviewed May 2016. Heart Valve Problems and Disease • Home • About Heart Valves • Heart Valve ...
... Pressure High Blood Pressure Tools & Resources Stroke More Problem: Heart Valve Stenosis Updated:Aug 10,2016 About ... content was last reviewed May 2016. Heart Valve Problems and Disease • Home • About Heart Valves • Heart Valve ...
... gov/ency/patientinstructions/000663.htm Women and sexual problems To use the sharing features on this page, ... feel better about your sex life. Common Sexual Problems You may have sexual dysfunction if you are ...
... review our exit disclaimer . Subscribe Increases in Problem Drinking Alcohol use disorder is becoming more common, a ... the need to better educate people about problem drinking and its treatment. Alcohol use disorder, or AUD, ...
There are many problems that can keep a woman from enjoying sex. They include Lack of sexual desire Inability to become aroused Lack of orgasm, or sexual climax Painful intercourse These problems may have physical or psychological causes. Physical causes ...
... this can damage your eyes. The most common problem is diabetic retinopathy. It is a leading cause ... surgery, with follow-up care. Two other eye problems can happen to people with diabetes. A cataract ...
ERIC Educational Resources Information Center
Karrison, Joan; Carroll, Margaret Kelly
1991-01-01
Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)
ERIC Educational Resources Information Center
Eperson, D. B.
1991-01-01
This section includes eight problems to which the journal invites readers to respond. Problem topics include angles in alternate segments, pentominoes, a new triangle of numbers, cricket scores, symmetrical pentagons, inequalities, a pythagorean dissection, and magic squares. (MDH)
... Disease, and Other Dental Problems Diabetic Eye Disease Diabetes and Foot Problems How can diabetes affect my feet? Too much glucose, also called ... you have any of these signs. How can diabetes change the shape of my feet? Nerve damage ...
The molecular matching problem
NASA Technical Reports Server (NTRS)
Kincaid, Rex K.
1993-01-01
Molecular chemistry contains many difficult optimization problems that have begun to attract the attention of optimizers in the Operations Research community. Problems including protein folding, molecular conformation, molecular similarity, and molecular matching have been addressed. Minimum energy conformations for simple molecular structures such as water clusters, Lennard-Jones microclusters, and short polypeptides have dominated the literature to date. However, a variety of interesting problems exist and we focus here on a molecular structure matching (MSM) problem.
Exploratory Problems in Mathematics.
ERIC Educational Resources Information Center
Stevenson, Frederick W.
This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…
NASA Astrophysics Data System (ADS)
Marx, G.
Drake's formula for the possible number of independent civilizations in the Galaxy is discussed in the light of several new hypotheses (e.g., Lovelock's Gaia hypothesis). Emphasis is placed on ways to overcome the time problem, i.e., the problem of how to communicate with civilizations that may arise in the future. Electronic, nucleonic, and bionic approaches to this problem are discussed.
ERIC Educational Resources Information Center
DEVANE, J.R.; RIMOLDI, H.J.A.
CHANGES WERE STUDIED IN THE PROBLEM-SOLVING BEHAVIOR OF HIGH SCHOOL STUDENTS AS A FUNCTION OF A CAREFULLY DESIGNED TRAINING PROGRAM. TRAINING WAS DEFINED AS THE DEVELOPMENT OF STUDENT AWARENESS OF PROBLEM-SOLVING STRATEGIES USED. INSTRUMENTS WERE DEVELOPED AND REFINED TO MEASURE PROBLEM-SOLVING BEHAVIOR. SPECIFICALLY TESTED WAS THE FOLLOWING…
Mathematics as Problem Solving.
ERIC Educational Resources Information Center
Soifer, Alexander
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
ERIC Educational Resources Information Center
Green, Gary J.
This paper presents two actual problems involving grievance procedures. Both problems involve pending litigation and one of them involves pending arbitration. The first problem occurred in a wealthy Minnesota school district and involved a seniority list. Because of changes in the financial basis for supporting public schools, it became necessary…
ERIC Educational Resources Information Center
Capobianco, Brenda M.; Tyrie, Nancy
2009-01-01
In a unique school-university partnership, methods students collaborated with fifth graders to use the engineering design process to build their problem-solving skills. By placing the problem in the context of a client having particular needs, the problem took on a real-world appeal that students found intriguing and inviting. In this article, the…
Techniques of Problem Solving.
ERIC Educational Resources Information Center
Krantz, Steven G.
The purpose of this book is to teach the basic principles of problem solving in both mathematical and non-mathematical problems. The major components of the book consist of learning to translate verbal discussion into analytical data, learning problem solving methods for attacking collections of analytical questions or data, and building a…
Florkowski, Antoni; Gruszczyński, Wojciech; Gałecki, Piotr; Szubert, Sławomir; Klus, Marek; Zboralski, Krzysztof
2008-01-01
An overusing and an addiction to alcoholic drinks are important problems in a medical society. The studies made in the United States had documented that about 8-12% doctors were addicted to alcohol. In many cases the doctors are able to keep their problem as a secret and their activity is satisfied up to the moment when a decrease is noticed. Some factors--such as a high level of stress--predispose doctors to alcoholic problems especially surgeons. Alcohol problems should be identified as early as possible, and therapy ought to be given as well. There is no reason to hide the problem. PMID:19025048
Pan, Feng; Kasiviswanathan, Shiva
2010-01-01
In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove k columns such that the sum over all rows of the maximum entry in each row is minimized. This combinatorial problem is closely related to bipartite network interdiction problem which can be applied to prioritize the border checkpoints in order to minimize the probability that an adversary can successfully cross the border. After introducing the matrix interdiction problem, we will prove the problem is NP-hard, and even NP-hard to approximate with an additive n{gamma} factor for a fixed constant {gamma}. We also present an algorithm for this problem that achieves a factor of (n-k) mUltiplicative approximation ratio.
ROV overcomes deepwater problems
Frisbie, F.R.; Hughes, E.W.
1984-09-01
The use of remotely operated vehicles (ROVs) in supportive drill ships operating in more than 200 meters of water poses severe technical and operational problems. Defining these problems beforehand and addressing them during design, manufacture, testing and installation ensures a functional and effective support capability. Such problems as the availability of desk space, and the subsequent installation, maintenance, and the launch/recovery of the system are described.
Specific Pronunciation Problems.
ERIC Educational Resources Information Center
Avery, Peter; And Others
1987-01-01
Reviews common pronunciation problems experienced by learners of English as a second language who are native speakers of Vietnamese, Cantonese, Spanish, Portuguese, Italian, Polish, Greek, and Punjabi. (CB)
Egorov, Yurii V
2013-04-30
We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.
Known TCP Implementation Problems
NASA Technical Reports Server (NTRS)
Paxson, Vern (Editor); Allman, Mark; Dawson, Scott; Fenner, William; Griner, Jim; Heavens, Ian; Lahey, K.; Semke, J.; Volz, B.
1999-01-01
This memo catalogs a number of known TCP implementation problems. The goal in doing so is to improve conditions in the existing Internet by enhancing the quality of current TCP/IP implementations. It is hoped that both performance and correctness issues can be resolved by making implementors aware of the problems and their solutions. In the long term, it is hoped that this will provide a reduction in unnecessary traffic on the network, the rate of connection failures due to protocol errors, and load on network servers due to time spent processing both unsuccessful connections and retransmitted data. This will help to ensure the stability of the global Internet. Each problem is defined as follows: Name of Problem The name associated with the problem. In this memo, the name is given as a subsection heading. Classification one or more problem categories for which the problem is classified: "congestion control", "performance", "reliability", "resource management". Description A definition of the problem, succinct but including necessary background material. Significance A brief summary of the sorts of environments for which the problem is significant.
Tactical missile turbulence problems
NASA Technical Reports Server (NTRS)
Dickson, Richard E.
1987-01-01
Of particular interest is atmospheric turbulence in the atmospheric boundary layer, since this affects both the launch and terminal phase of flight, and the total flight for direct fire systems. Brief discussions are presented on rocket artillery boost wind problems, mean wind correction, turbulent boost wind correction, the Dynamically Aimed Free Flight Rocket (DAFFR) wind filter, the DAFFR test, and rocket wake turbulence problems. It is concluded that many of the turbulence problems of rockets and missiles are common to those of aircraft, such as structural loading and control system design. However, these problems have not been solved at this time.
Finsterle, S.
1997-11-01
This report contains a collection of ITOUGH2 sample problems. It complements the ITOUGH2 User`s Guide [Finsterle, 1997a], and the ITOUGH2 Command Reference [Finsterle, 1997b]. ITOUGH2 is a program for parameter estimation, sensitivity analysis, and uncertainty propagation analysis. It is based on the TOUGH2 simulator for non-isothermal multiphase flow in fractured and porous media [Preuss, 1987, 1991a]. The report ITOUGH2 User`s Guide [Finsterle, 1997a] describes the inverse modeling framework and provides the theoretical background. The report ITOUGH2 Command Reference [Finsterle, 1997b] contains the syntax of all ITOUGH2 commands. This report describes a variety of sample problems solved by ITOUGH2. Table 1.1 contains a short description of the seven sample problems discussed in this report. The TOUGH2 equation-of-state (EOS) module that needs to be linked to ITOUGH2 is also indicated. Each sample problem focuses on a few selected issues shown in Table 1.2. ITOUGH2 input features and the usage of program options are described. Furthermore, interpretations of selected inverse modeling results are given. Problem 1 is a multipart tutorial, describing basic ITOUGH2 input files for the main ITOUGH2 application modes; no interpretation of results is given. Problem 2 focuses on non-uniqueness, residual analysis, and correlation structure. Problem 3 illustrates a variety of parameter and observation types, and describes parameter selection strategies. Problem 4 compares the performance of minimization algorithms and discusses model identification. Problem 5 explains how to set up a combined inversion of steady-state and transient data. Problem 6 provides a detailed residual and error analysis. Finally, Problem 7 illustrates how the estimation of model-related parameters may help compensate for errors in that model.
A Stochastic Employment Problem
ERIC Educational Resources Information Center
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Problem Solving Techniques Seminar.
ERIC Educational Resources Information Center
Massachusetts Career Development Inst., Springfield.
This booklet is one of six texts from a workplace literacy curriculum designed to assist learners in facing the increased demands of the workplace. Six problem-solving techniques are developed in the booklet to assist individuals and groups in making better decisions: problem identification, data gathering, data analysis, solution analysis,…
Medical problems affecting musicians.
Potter, P. J.; Jones, I. C.
1995-01-01
The physical demands of performing on musical instruments can cause pain, sensory loss, and lack of coordination. Five cases illustrate common problems. Knowledge of the interaction between the technique of playing the instrument and the particular musician can help physicians diagnose and resolve problems. Images Figure 1 PMID:8680295
ERIC Educational Resources Information Center
Cassidy, Jack
1991-01-01
Presents suggestions for teaching math word problems to elementary students. The strategies take into consideration differences between reading in math and reading in other areas. A problem-prediction game and four self-checking activities are included along with a magic password challenge. (SM)
NASA Astrophysics Data System (ADS)
Harper, Kathleen A.; Etkina, Eugenia
2002-10-01
As part of weekly reports,1 structured journals in which students answer three standard questions each week, they respond to the prompt, If I were the instructor, what questions would I ask or problems assign to determine if my students understood the material? An initial analysis of the results shows that some student-generated problems indicate fundamental misunderstandings of basic physical concepts. A further investigation explores the relevance of the problems to the week's material, whether the problems are solvable, and the type of problems (conceptual or calculation-based) written. Also, possible links between various characteristics of the problems and conceptual achievement are being explored. The results of this study spark many more questions for further work. A summary of current findings will be presented, along with its relationship to previous work concerning problem posing.2 1Etkina, E. Weekly Reports;A Two-Way Feedback Tool, Science Education, 84, 594-605 (2000). 2Mestre, J.P., Probing Adults Conceptual Understanding and Transfer of Learning Via Problem Posing, Journal of Applied Developmental Psychology, 23, 9-50 (2002).
Current Social Problem Novels.
ERIC Educational Resources Information Center
Kenney, Donald J.
This review of social problem novels for young adults opens with a brief background of the genre, then lists the dominant themes of social problem fiction and nonfiction novels that have been published in the last two years, such as alcoholism, alienation, death, growing up and self-awarness, drugs, and divorce. Other themes mentioned are…
Problems in baryon spectroscopy
Capstick, S.
1994-04-01
Current issues and problems in the physics of ground- and excited-state baryons are considered, and are classified into those which should be resolved by CEBAF in its present form, and those which may require CEBAF to undergo an energy upgrade to 8 GeV or more. Recent theoretical developments designed to address these problems are outlined.
ERIC Educational Resources Information Center
Wilmington Public Schools, DE.
The general purpose of the twelfth grade course is to help the student assume his role as a decision-maker in a democratic society. The nature and complexity of contemporary problems are examined using this guide to enable the student: 1) to analyze alternative solutions to these problems; 2) to develop attitudes and values appropriate to a…
ERIC Educational Resources Information Center
Mann, Philip H.; Suiter, Patricia A.
This teacher training module classifies visual channel problems into the following four main areas: visual perception, revisualization (memory), visual-motor (eye-hand coordination), and ocular-motor tasks. Specific deficits are listed under these main headings, behaviors are given to help identify the problem, and ways to improve the condition…
ERIC Educational Resources Information Center
Martinez, Michael E.
1998-01-01
Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…
Teaching through Problem Solving
ERIC Educational Resources Information Center
Fi, Cos D.; Degner, Katherine M.
2012-01-01
Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…
ERIC Educational Resources Information Center
Thorson, Annette, Ed.
1999-01-01
This issue of ENC Focus focuses on the topic of inquiry and problem solving. Featured articles include: (1) "Inquiry in the Everyday World of Schools" (Ronald D. Anderson); (2) "In the Cascade Reservoir Restoration Project Students Tackle Real-World Problems" (Clint Kennedy with Advanced Biology Students from Cascade High School); (3) "Project…
Problems Facing Rural Schools.
ERIC Educational Resources Information Center
Stewart, C. E.; And Others
Problems facing rural Scottish schools range from short term consideration of daily operation to long term consideration of organizational alternatives. Addressed specifically, such problems include consideration of: (1) liaison between a secondary school and its feeder primary schools; (2) preservice teacher training for work in small, isolated…
NASA Astrophysics Data System (ADS)
1981-01-01
The problems related to aircraft noise were studied. Physical origin (sound), human reaction (noise), quantization of noise and sound sources of aircraft noise are discussed. Noise abatement at the source, technical, fleet-political and air traffic measures are explained. The measurements and future developments are also discussed. The position of Lufthansa as regards aircraft noise problems is depicted.
ERIC Educational Resources Information Center
MARTONFFY, ANDREA PONTECORVO; AND OTHERS
A CURRICULUM GUIDE IS PRESENTED FOR A 10-WEEK STUDY OF ANCIENT GREEK CIVILIZATION AT THE 10TH-GRADE LEVEL. TEACHING MATERIALS FOR THE UNIT INCLUDE (1) PRIMARY AND SECONDARY SOURCES DEALING WITH THE PERIOD FROM THE BRONZE AGE THROUGH THE HELLENISTIC PERIOD, (2) GEOGRAPHY PROBLEMS, AND (3) CULTURAL MODEL PROBLEM EXERCISES. THOSE CONCEPTS WITH WHICH…
NASA Technical Reports Server (NTRS)
Lippisch, Espenlaub
1922-01-01
Any one endeavoring to solve the problem of soaring flight is confronted not only by structural difficulties, but also by the often far more difficult aerodynamic problem of flight properties and efficiency, which can only be determined by experimenting with the finished glider.
Stabilization of Kepler's problem
NASA Technical Reports Server (NTRS)
Stokes, A.
1977-01-01
A regularization of Kepler's problem due to Moser (1970) is used to stabilize the equations of motion. In other words, a particular solution of Kepler's problem is imbedded in a Liapunov stable system. Perturbations can be introduced into the stabilized equations.
... problems that can lead to dislocation of the hip bones. This is also called dysplasia (say: "diss-play-see-uh"). This means that ... problems later in life? Source Screening for Developmental Dysplasia of the Hip by LM French, M.D., and FR Dietz, ...
ERIC Educational Resources Information Center
Ross, Robert
This paper focusses on problems involved in adopting the newer modes of social science and professionalism. The complexities which precede these problems are recognized. It is mentioned that many recent entrants to these fields have made value commitments in their professionalism without very long detention at the portals of objectivity or…
ERIC Educational Resources Information Center
Allen, Deborah E.; Donham, Richard S.; Bernhardt, Stephen A.
2011-01-01
In problem-based learning (PBL), students working in collaborative groups learn by resolving complex, realistic problems under the guidance of faculty. There is some evidence of PBL effectiveness in medical school settings where it began, and there are numerous accounts of PBL implementation in various undergraduate contexts, replete with…
Problem Solving and Intelligence.
ERIC Educational Resources Information Center
Resnick, Lauren B.; Glaser, Robert
This paper argues that a major aspect of intelligence is the ability to solve problems and that careful analysis of problem-solving behavior is a means of specifying many of the psychological processes that make up intelligence. The focus is on the mechanisms involved when, in the absence of complete instruction, a person must "invent" a new…
ERIC Educational Resources Information Center
Karns, Phyllis Spear
The relationship of educational preparation to the problem- solving performance of 55 hospital employed baccalaureate and associate degree nurses working in Wyoming hospitals was studied. Participant data were collected that might correlate with problem-solving ability: age, years of experience in nursing, years of work experience in a…
ERIC Educational Resources Information Center
Mann, Philip H.; Suiter, Patricia A.
This teacher's guide contains a list of general auditory problem areas where students have the following problems: (a) inability to find or identify source of sound; (b) difficulty in discriminating sounds of words and letters; (c) difficulty with reproducing pitch, rhythm, and melody; (d) difficulty in selecting important from unimportant sounds;…
Problem Solving in Electricity.
ERIC Educational Resources Information Center
Caillot, Michel; Chalouhi, Elias
Two studies were conducted to describe how students perform direct current (D-C) circuit problems. It was hypothesized that problem solving in the electricity domain depends largely on good visual processing of the circuit diagram and that this processing depends on the ability to recognize when two or more electrical components are in series or…
ERIC Educational Resources Information Center
Cannon, Lawrence O.; Elich, Joe
In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…
ERIC Educational Resources Information Center
Wheatley, Judy; Sudman, Rita Schmidt, Ed.
This packet of instructional materials is designed to give social science students in grades 6-9 a first-hand experience in working out solutions to real-life problems involving the management of California's water. Students work in groups on one of three problems presented in the packet: (1) the management of the Sacramento-San Joaquin Delta that…
The Guderley problem revisited
Ramsey, Scott D; Kamm, James R; Bolstad, John H
2009-01-01
The self-similar converging-diverging shock wave problem introduced by Guderley in 1942 has been the source of numerous investigations since its publication. In this paper, we review the simplifications and group invariance properties that lead to a self-similar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the self-similar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the so-called similarity exponent for the converging flow, and that of the second is a trajectory multiplier for the diverging regime. We provide a clear exposition concerning the reflected shock configuration. Additionally, we introduce a new approximation for the similarity exponent, which we compare with other estimates and numerically computed values. Lastly, we use the Guderley problem as the basis of a quantitative verification analysis of a cell-centered, finite volume, Eulerian compressible flow algorithm.
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations. PMID:12005916
NASA Technical Reports Server (NTRS)
1992-01-01
CBR Express software solves problems by adapting sorted solutions to new problems specified by a user. It is applicable to a wide range of situations. The technology was originally developed by Inference Corporation for Johnson Space Center's Advanced Software Development Workstation. The project focused on the reuse of software designs, and Inference used CBR as part of the ACCESS prototype software. The commercial CBR Express is used as a "help desk" for customer support, enabling reuse of existing information when necessary. It has been adopted by several companies, among them American Airlines, which uses it to solve reservation system software problems.
NASA Technical Reports Server (NTRS)
Lesso, W. G.; Kenyon, E.
1972-01-01
Consideration of the problems involved in choosing appropriate menus for astronauts carrying out SKYLAB missions lasting up to eight weeks. The problem of planning balanced menus on the basis of prepackaged food items within limitations on the intake of calories, protein, and certain elements is noted, as well as a number of other restrictions of both physical and arbitrary nature. The tailoring of a set of menus for each astronaut on the basis of subjective rankings of each food by the astronaut in terms of a 'measure of pleasure' is described, and a computer solution to this problem by means of a mixed integer programming code is presented.
... orientation. This information is for people who have mouth (oral) problems related to HIV infection. It explains ... look like. It also describes where in the mouth they occur and how they are treated. They ...
ERIC Educational Resources Information Center
Pool, Ithiel de Sola
1979-01-01
Presents several anticipated problems to be handled at the 1979 World Administrative Conference including an orbital allocation plan, political and ideological issues concerning sovereignty and prior consent, spectrum assignments, and sharing of TV frequencies with land mobile radio. (JMF)
ERIC Educational Resources Information Center
Cunningham, Luvern L.
1969-01-01
Evaluation of school administrators to determine whether they are truly performing their functions adequately has presented a problem of long standing since most administrators find excuses to avoid appraisal of their performance. (CK)
... problems may include: Getting older: a woman's sex drive often decreases with age. This is normal. It ... pressure, depression, and chemotherapy can decrease your sex drive or make it hard to have an orgasm. ...
ERIC Educational Resources Information Center
Bosch, Van Den Robert
1979-01-01
Contains a discussion of insects' ability to survive, of the development of pesticides and the introduction of DDT, of the problems of pesticide use and resistance to insecticides, and of the advantages of integrated pest control. (BB)
Overcoming breastfeeding problems
Plugged milk ducts; Nipple soreness when breastfeeding; Breastfeeding - overcoming problems; Let-down reflex ... Breastfeeding (nursing) your baby can be a good experience for both the mother and the baby. It ...
... life expectancy. Do children with Down syndrome have eye problems? Individuals with Down syndrome are at increased ... When should children with Down syndrome receive an eye exam? The American Academy of Pediatrics recommends that ...
... days, such as in painting and carpentry Poor posture over many years Aging Rotator cuff tears TEARS ... also help prevent rotator cuff problems. Practice good posture to keep your rotator cuff tendons and muscles ...
ERIC Educational Resources Information Center
Wilson, James Q.; And Others
1972-01-01
Argues that most of the underlying assumptions of presently recommended solutions to the problem of heroin addiction are unreasonable, unwarranted, or at least open to more than one interpretation. (DM)
... too high. Over time, this can damage your eyes. The most common problem is diabetic retinopathy. It ... light-sensitive tissue at the back of your eye. You need a healthy retina to see clearly. ...
... the biggest health problem for people with diabetes. LDL cholesterol. LDL cholesterol is known as the bad cholesterol because it ... you often eat foods that are high in LDL cholesterol high cholesterol runs in your family HDL cholesterol. ...
ERIC Educational Resources Information Center
Carpenter, Thomas P.; And Others
1980-01-01
Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).
Scheper, W A; Lobbezoo, F; Eijkman, M A J
2005-05-01
Divers can have several oral problems. Firstly, problems caused by pressure changes. These are barodontalgia and odontocrexis. Barodontalgia is toothache by barotrauma. Odontocrexis is restorations coming lose or breaking or tooth fractures by expansion of air beneath restorations. Other problems can occur by cements used to fix casted restorations, by inflammations in the orofacial region, and by not yet fully healed oral wounds. Secondly, there are problems related to the diver's mouthpiece. To keep the mouthpiece in place, the mandible has to be forced in a forward position. Holding this position often and for long periods of time, may develop or aggravate temporomandibular dysfunction. Insufficient fit of the mouthpiece may induce oral mucosal lesions. Therefore, it is recommended to produce individual diver mouthpieces. It is also recommended to produce individual diver mouthpieces for complete dentures wearing divers and for divers with fixed orthodontic appliances. PMID:15932043
ERIC Educational Resources Information Center
McDonald, James E.
1978-01-01
Several theories and treatments of enuresis are described. The authors conclude that enuresis is a social problem (perhaps due to maturational lag, developmental delay or faulty learning) which requires teacher and parental tolerance and understanding. (SE)
Solving Tommy's Writing Problems.
ERIC Educational Resources Information Center
Burdman, Debra
1986-01-01
The article describes an approach by which word processing helps to solve some of the writing problems of learning disabled students. Aspects considered include prewriting, drafting, revising, and completing the story. (CL)
... words, whereas motor clumsiness or defective visual-spatial perception affects only handwriting, not spelling. Dyscalculia Dyscalculia is ... related to memory, problem solving skills, logical thought, perception and attention span. Like parents of other adolescents ...
Nicholson, Keith; Martelli, Michael F
2004-01-01
Pain problems, especially posttraumatic headache, are very common following head trauma. Pain may be the most significant problem, more disabling than any brain or other injuries, and interfering with aspects of cognition or other function. However, posttraumatic headache and most other chronic posttraumatic pain problems remain poorly understood. This article reviews fundamental issues that should be considered in understanding the nature of chronic pain including the distinction between acute and chronic pain; neurobiological distinctions between the lateral and medial pain system; nociceptive versus neuropathic or other central pain; sensitization effects; the widely accepted view of chronic pain as a multidimensional subjective experience involving sensory, motivational-affective and cognitive-behavioral components; the problem of mind-body dualism; the role of psychosocial factors in the onset, maintenance, exacerbation or severity of pain; plus issues of response bias and malingering. PMID:14732827
... less frequently than problems with smell. How Our Sense of Taste Works Our sense of taste, along ... may start to lose taste buds. Five Taste Sensations We can experience five basic taste sensations: sweet, ...
... or legs? Yes Your symptoms may be from FIBROIDS, noncancerous tumors of the uterus. See your doctor. ... premature MENOPAUSE. Irregular periods may be due to FIBROIDS, HORMONE PROBLEMS, or other medical conditions. See your ...
ERIC Educational Resources Information Center
Eperson, D. B.
1985-01-01
Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr.; Rankin, Charles C.
2006-01-01
This document summarizes the STructural Analysis of General Shells (STAGS) development effort, STAGS performance for selected demonstration problems, and STAGS application problems illustrating selected advanced features available in the STAGS Version 5.0. Each problem is discussed including selected background information and reference solutions when available. The modeling and solution approach for each problem is described and illustrated. Numerical results are presented and compared with reference solutions, test data, and/or results obtained from mesh refinement studies. These solutions provide an indication of the overall capabilities of the STAGS nonlinear finite element analysis tool and provide users with representative cases, including input files, to explore these capabilities that may then be tailored to other applications.
The cosmological constant problem
Dolgov, A.D.
1989-05-01
A review of the cosmological term problem is presented. Baby universe model and the compensating field model are discussed. The importance of more accurate data on the Hubble constant and the Universe age is stressed. 18 refs.
Overcoming breastfeeding problems
... position Reducing distractions during nursing, performing a gentle massage, and applying heat to the breast Nursing often ( ... JL, et al, eds. Obstetrics: Normal and Problem Pregnancies . 6th ed. Philadelphia, PA: Elsevier Saunders; 2012:chap ...
NASA Technical Reports Server (NTRS)
Gejji, Raghvendra, R.
1992-01-01
Network transmission errors such as collisions, CRC errors, misalignment, etc. are statistical in nature. Although errors can vary randomly, a high level of errors does indicate specific network problems, e.g. equipment failure. In this project, we have studied the random nature of collisions theoretically as well as by gathering statistics, and established a numerical threshold above which a network problem is indicated with high probability.
NASA Astrophysics Data System (ADS)
Schröer, H.
In basketball there is the problem of hitting a basket at a determined distance and a determined height. The quantities that can be changed during the inclined throw are the initial velocity and the angle of throw. At first we neglect the air resistance. Then we treat the same problem in a medium (liquid, gas) with constant density. We obtain two differential equations. Then we view special cases of the retarding force. There is an english and a german edition.
Sinn, H
1988-01-01
Problems concerning the provision of development aid to the Sahel region of Africa are discussed. The author argues that the population already exceeds the area's carrying capacity, and that the provision of direct aid to the region will only encourage further in-migration and exacerbate the problem. He argues that aid should be provided to neighboring areas with the capacity to support larger populations, which will eventually improve the standard of living of the whole region. PMID:12315680
Smoothers for Optimization Problems
NASA Technical Reports Server (NTRS)
Arian, Eyal; Ta'asan, Shlomo
1996-01-01
We present a multigrid one-shot algorithm, and a smoothing analysis, for the numerical solution of optimal control problems which are governed by an elliptic PDE. The analysis provides a simple tool to determine a smoothing minimization process which is essential for multigrid application. Numerical results include optimal control of boundary data using different discretization schemes and an optimal shape design problem in 2D with Dirichlet boundary conditions.
Living with Bowel Control Problems
... Home Living with Bowel Control Problems Resources Bowel Control Awareness Campaign Home Resources for Health Care Providers ... Living with Bowel Control Problems Living with Bowel Control Problems Living with a bowel control problem can ...
Dzamonja, Mirna
2006-12-15
This is a paper in mathematics, specifically in set theory. On the example of the measure recognition problem (MRP), the paper highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular, the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra, B, and a property, Phi, of measures, one can recognize by purely combinatorial means if B supports a strictly positive measure with property Phi. The most famous instance of this problem is MRP (countable additivity), and in the first part of the paper, we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP (non-atomic) and MRP (separable). Then, we show how our recent work gives an easy solution to the former of these problems and some partial information about the latter. The long-term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem, which gives such a structure theorem for measure algebras. PMID:17090453
Exceptional cases of Terai's conjecture on Diophantine equations
NASA Astrophysics Data System (ADS)
Miyazaki, Takafumi
2011-09-01
Let p,q,r be positive integers with p,q,r≥2, and let a,b,c be relatively prime positive integers with ap+bq = cr. Terai conjectured that (apart from a handful of known exceptions) the only solution of the equation ax+by = cz in positive integers x,y,z is (x,y,z) = (p,q,r). In this article, we consider the case q = r = 2 and give some results related to exceptional cases.
The Exponential Diophantine Equation 2x + by = cz
Yu, Yahui; Li, Xiaoxue
2014-01-01
Let b and c be fixed coprime odd positive integers with min{b, c} > 1. In this paper, a classification of all positive integer solutions (x, y, z) of the equation 2x + by = cz is given. Further, by an elementary approach, we prove that if c = b + 2, then the equation has only the positive integer solution (x, y, z) = (1,1, 1), except for (b, x, y, z) = (89,13,1, 2) and (2r − 1, r + 2,2, 2), where r is a positive integer with r ≥ 2. PMID:24959613
Bicriteria network design problems
Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III
1997-11-20
The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, they develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same they present a black box parametric search technique. This black box takes in as input an (approximation) algorithm for the criterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs they use a cluster based approach to devise approximation algorithms. The solutions violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, they provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. The authors show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
The Guderley problem revisited
NASA Astrophysics Data System (ADS)
Ramsey, Scott D.; Kamm, James R.; Bolstad, John H.
2012-02-01
The self-similar converging-diverging shock wave problem introduced by Guderley in 1942 has been the source of considerable mathematical and physical interest. We investigate a novel application of the Guderley solution as a unique and challenging code verification test problem for compressible flow algorithms; this effort requires a unified understanding of the problem's mathematical and computational subtleties. Hence, we review the simplifications and group invariance properties that reduce the compressible flow equations for a polytropic gas to two coupled nonlinear eigenvalue problems: the first for the similarity exponent in the converging regime, and the second for a trajectory multiplier in the diverging regime. The information we provide, together with previously published material, gives a complete description of the computational steps required to construct a semi-analytic Guderley solution. We employ the problem in a quantitative code verification analysis of a cell-centred, finite volume, Eulerian compressible flow algorithm. Lastly, in appended material, we introduce a new approximation for the similarity exponent, which may prove useful in the future construction of certain semi-analytic Guderley solutions.
Colored Traveling Salesman Problem.
Li, Jun; Zhou, MengChu; Sun, Qirui; Dai, Xianzhong; Yu, Xiaolong
2015-11-01
The multiple traveling salesman problem (MTSP) is an important combinatorial optimization problem. It has been widely and successfully applied to the practical cases in which multiple traveling individuals (salesmen) share the common workspace (city set). However, it cannot represent some application problems where multiple traveling individuals not only have their own exclusive tasks but also share a group of tasks with each other. This work proposes a new MTSP called colored traveling salesman problem (CTSP) for handling such cases. Two types of city groups are defined, i.e., each group of exclusive cities of a single color for a salesman to visit and a group of shared cities of multiple colors allowing all salesmen to visit. Evidences show that CTSP is NP-hard and a multidepot MTSP and multiple single traveling salesman problems are its special cases. We present a genetic algorithm (GA) with dual-chromosome coding for CTSP and analyze the corresponding solution space. Then, GA is improved by incorporating greedy, hill-climbing (HC), and simulated annealing (SA) operations to achieve better performance. By experiments, the limitation of the exact solution method is revealed and the performance of the presented GAs is compared. The results suggest that SAGA can achieve the best quality of solutions and HCGA should be the choice making good tradeoff between the solution quality and computing time. PMID:25494521
Preventing remediation problems
Fleming, W.H.
1994-12-31
Remediation, the design and construction of a remedy, typically represents the most significant portion of the cleanup process. The cost may be 5 to 10 times the cost of earlier investigation and feasibility efforts. Furthermore, the risks associated with remediation activities and their ability to meet ultimate cleanup goals and objectives are far greater than those associated with earlier efforts. Often times there are unrealistic expectations interjected throughout the design and construction process in the remediation field. The simple fact that most problems are buried, and one cannot see all that is below the ground surface provides sufficient uncertainty to result in problems. There are three key points during the remediation process which provide opportunities to prevent and avoid problems. These are: (1) during design; (2) during procurement and contracting; and (3) during construction. This paper examines actions which the author has found or believes will assist in providing a formula for success.
NASA Astrophysics Data System (ADS)
Izzo, Dario
2015-01-01
The orbital boundary value problem, also known as Lambert problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revolution case, in only two iterations. The resulting algorithm is compared, for single and multiple revolutions, to Gooding's procedure revealing to be numerically as accurate, while having a significantly smaller computational complexity.
NASA Technical Reports Server (NTRS)
Harriss, R. C.
1980-01-01
Application of remote sensing techniques to the solution of geochemical problems is considered with emphasis on the 'carbon-cycle'. The problem of carbon dioxide sinks and the areal extent of coral reefs are treated. In order to assess the problems cited it is suggested that remote sensing techniques be utilized to: (1)monitor globally the carbonate and bicarbonate concentrations in surface waters of the world ocean; (2)monitor the freshwater and oceanic biomass and associated dissolved organic carbon; (3) inventory the coral reef areas and types and the associated oceanographic climatic conditions; and (4)measure the heavy metal fluxes from forested and vegetated areas, from volcanos, from different types of crustal rocks, from soils, and from sea surfaces.
Moran, B
2007-08-08
We present analytic solutions to two test problems that can be used to check the hydrodynamic implementation in computer codes designed to calculate the propagation of shocks in spherically convergent geometry. Our analysis is restricted to fluid materials with constant bulk modulus. In the first problem we present the exact initial acceleration and pressure gradient at the outer surface of a sphere subjected to an exponentially decaying pressure of the form P(t) = P{sub 0}e{sup -at}. We show that finely-zoned hydro-code simulations are in good agreement with our analytic solution. In the second problem we discuss the implosions of incompressible spherical fluid shells and we present the radial pressure profile across the shell thickness. We also discuss a semi-analytic solution to the time-evolution of a nearly spherical shell with arbitrary but small initial 3-dimensional (3-D) perturbations on its inner and outer surfaces.
NASA Astrophysics Data System (ADS)
Kranakis, Evangelos; Krizanc, Danny
A man walks into a men's room and observes n empty urinals. Which urinal should he pick so as to maximize his chances of maintaining privacy, i.e., minimize the chance that someone will occupy a urinal beside him? In this paper, we attempt to answer this question under a variety of models for standard men's room behavior. Our results suggest that for the most part one should probably choose the urinal furthest from the door (with some interesting exceptions). We also suggest a number of variations on the problem that lead to many open problems.
Fung, Jimmy; Masser, Thomas; Morgan, Nathaniel R.
2012-06-25
The Sedov test is classically defined as a point blast problem. The Sedov problem has led us to advances in algorithms and in their understanding. Vorticity generation can be physical or numerical. Both play a role in Sedov calculations. The RAGE code (Eulerian) resolves the shock well, but produces vorticity. The source definition matters. For the FLAG code (Lagrange), CCH is superior to SGH by avoiding spurious vorticity generation. FLAG SGH currently has a number of options that improve results over traditional settings. Vorticity production, not shock capture, has driven the Sedov work. We are pursuing treatments with respect to the hydro discretization as well as to artificial viscosity.
NASA Astrophysics Data System (ADS)
Voitkevich, Georgii V.
The main problems of space chemistry are examined, including the origin and abundance of chemical elements, their migration to different regions of the universe, the formation of the chemical composition of cosmic bodies, and the chemical evolution of the solar system and the origin of life. Based on current astrophysical and space-chemical data, the main stages of the evolution of matter from the beginning of universe expansion to the formation of the solar system are described. The problem of the origin of life is examined in the light of space-chemical data on the formation of high-molecular compounds before the formation of the planets.
Assessing the Quality of Problems in Problem-Based Learning
ERIC Educational Resources Information Center
Sockalingam, Nachamma; Rotgans, Jerome; Schmidt, Henk
2012-01-01
This study evaluated the construct validity and reliability of a newly devised 32-item problem quality rating scale intended to measure the quality of problems in problem-based learning. The rating scale measured the following five characteristics of problems: the extent to which the problem (1) leads to learning objectives, (2) is familiar, (3)…
Every pregnancy has some risk of problems. The causes can be conditions you already have or conditions you develop. They also include being pregnant with ... health care provider about how to minimize your risk before you get pregnant. Once you are pregnant, ...
LEXICOGRAPHICAL PROBLEMS IN PASHTO.
ERIC Educational Resources Information Center
CHAVARRIS-AGUILAR, O.L.; PENZL, HERBERT
PROBLEMS IN DEVELOPING SUITABLE DICTIONARIES OF PASHTO WERE REPORTED. PASHTO WAS DESCRIBED AS A MEMBER OF THE IRANIAN BRANCH OF THE INDO-EUROPEAN LANGUAGES SPOKEN IN EASTERN AND SOUTHERN AFGHANISTAN AND IN NORTHEASTERN PAKISTAN. FIVE TOPICS DEALING WITH THE PASHTO LANGUAGE WERE DISCUSSED--(1) STATISTICS, (2) WRITTEN CORPUS AND LEXICAL STUDIES, (3)…
Circumference and Problem Solving.
ERIC Educational Resources Information Center
Blackburn, Katie; White, David
The concept of pi is one of great importance to all developed civilization and one that can be explored and mastered by elementary students through an inductive and problem-solving approach. Such an approach is outlined and discussed. The approach involves the following biblical quotation: "And he made a moltin sea ten cubits from one brim to the…
... age 6 months. That's because children start learning speech and language long before they talk. Hearing problems can be temporary or permanent. Sometimes, ear infections, injuries or diseases affect hearing. If your child does not hear well, get help. NIH: National ...
ERIC Educational Resources Information Center
Cook, Martin
1995-01-01
Students studying water as a class project were concerned by levels of pollution at a nearby river and the local beach. They identified three environmental problems for research including sewage discharge, beach litter, and quality of swimming water. Research consisted of field trips which allowed for opportunities to improve skills in collecting…
Universal Design Problem Solving
ERIC Educational Resources Information Center
Sterling, Mary C.
2004-01-01
Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…
Correct Problems, Desperate Solutions.
ERIC Educational Resources Information Center
Donohue, William A.
1996-01-01
Argues that the social problems confronting America have been bombarded with ill-conceived and unsuccessful social policy largely driven by fear. Explains that parental licensing is a draconian and unworkable solution. Vouchers for indigent youth to attend Catholic schools, developing after-school and summer programs, and reforming welfare are…
Problems in Graduate Education...
ERIC Educational Resources Information Center
Whaley, W. Gordon
The Commission on Graduate Education of the National Association of State Universities and Land Grant Colleges has assembled in this booklet the nature of the fundamental problems of graduate education accompanied by recommendations for action. Nine areas of concern include redesigning graduate education for the twentieth century, distinguishing…
Dermatologic problems of musicians.
Rimmer, S; Spielvogel, R L
1990-04-01
The unique occupational dermatologic disorders of musicians are reviewed and compiled to provide the clinician with a reference list. Our results were obtained by a survey of 24 members of a professional symphony orchestra. The results of the survey revealed a significant incidence of occupationally related skin problems in musicians. PMID:2138638
NASA Technical Reports Server (NTRS)
Douglas, G.
1972-01-01
The problems of excess capacity in the airline industry are discussed with focus on the following topics: load factors; fair rate of return on investment; service-quality rivalry among airlines; pricing (fare) policies; aircraft production; and the impacts of excess capacity on operating costs. Also included is a discussion of the interrelationships among these topics.
"Righting" the Writing Problem.
ERIC Educational Resources Information Center
Shaughnessy, Michael F.; Eastham, Nicholas
The problem of college students' writing skills or lack thereof is generally agreed upon in academia. One cause is the inordinate amount of multiple choice/true false/fill in the blank type of tests that students take in high school and college. Not only is there is a dearth of actual classes in writing available, few students recognize the need…
Transformation Problem Solving Abilities.
ERIC Educational Resources Information Center
Harmel, Sarah Jane
The relationship between transformation problem performance and Guilford Structure of Intellect (SI) abilities is explored. During two group sessions 42 females and 35 males, age 18-39, were administered 12 Guilford SI tests exemplifying all five symbolic content (numeric) operations, and three contents in the divergent production area. Logical…
and Internalizing Behavior Problems
ERIC Educational Resources Information Center
Hofer, Claire; Eisenberg, Nancy; Spinrad, Tracy L.; Morris, Amanda S.; Gershoff, Elizabeth; Valiente, Carlos; Kupfer, Anne; Eggum, Natalie D.
2013-01-01
Stability and change in mother-adolescent conflict reactions (CRs) and the prediction of CRs from adolescents' earlier behavior problems (and vice versa) were examined with 131 mothers and their adolescents (63 boys). Dyads engaged in a 6-min conflict discussion twice, 2 years apart ["M" age was 13 at Time 1 (T1)]. Non-verbal expressive and verbal…
ERIC Educational Resources Information Center
Hoyer, William J.; And Others
1975-01-01
Many of the clinically disabling behaviors of elderly persons may be viewed as operants. Research bearing on the efficacy of operant techniques for programming individualized, group based, and ward-wide therapeutic intervention is reviewed. Suggests the operant view is useful for conceptualizing and treating many problem behaviors of elderly…
ERIC Educational Resources Information Center
Olson, Alton T.
1993-01-01
Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)
ERIC Educational Resources Information Center
Wisconsin Univ. - Stout, Menomonie. Center for Vocational, Technical and Adult Education.
The teacher directed problem solving activities package contains 17 units: Future Community Design, Let's Build an Elevator, Let's Construct a Catapult, Let's Design a Recreational Game, Let's Make a Hand Fishing Reel, Let's Make a Wall Hanging, Let's Make a Yo-Yo, Marooned in the Past, Metrication, Mousetrap Vehicles, The Multi System…
Bicriteria network design problems
Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III
1995-05-01
We study several bicriteria network design problems phrased as follows: given an indirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. First, we develop a formalism for bicriteria problems and their approximations. Secondly, we use a simple parametric search technique to provide bicriteria approximation algorithms for problems with two similar criteria, where both criteria are the same measure (such as the diameter or the total cost of a tree) but differ only in the cost function under which the measure is computed. Thirdly, we present an (O(log n), O(log n))-approximation algorithm for finding a diameter-constrained minimum cost spanning tree of an undirected graph on n nodes. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. These pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
ERIC Educational Resources Information Center
Currier, Sarah Cox
2015-01-01
In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…
ERIC Educational Resources Information Center
Aznar, Mercedes Martinez; Orcajo, Teresa Ibanez
2005-01-01
A teaching unit on genetics and human inheritance using problem-solving methodology was undertaken with fourth-level Spanish Secondary Education students (15 year olds). The goal was to study certain aspects of the students' learning process (concepts, procedures and attitude) when using this methodology in the school environment. The change…
Chemical Reaction Problem Solving.
ERIC Educational Resources Information Center
Veal, William
1999-01-01
Discusses the role of chemical-equation problem solving in helping students predict reaction products. Methods for helping students learn this process must be taught to students and future teachers by using pedagogical skills within the content of chemistry. Emphasizes that solving chemical reactions should involve creative cognition where…
Problem Solving Using Calculators.
ERIC Educational Resources Information Center
Billings, Karen; Moursund, David
1978-01-01
The first part in the serialized version of a book on the use of calculators for problem solving is presented. It contains prefaces for teachers and students and a chapter on getting started which includes topics such as symmetries, operations, powers, and chaining. (MP)
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Learning through Problem Solving.
ERIC Educational Resources Information Center
Murray, Hanlie; Olivier, Alwyn; Human, Piet
After conducting several studies on young students' understanding of particular concepts before, during, and after instruction, this paper focuses on the two small scale and several informal teaching experiments based on the idea that the teacher should pose problems to students for which they do not yet have a routine solution method available,…
ERIC Educational Resources Information Center
Emmel, Thomas C.; Sligh, Michael M.
1970-01-01
Asserts that overpopulation is the most pressing world problem. Topics discussed include population control in primitive societies, population growth and control in modern societies, methods of motivational population control, consequences of no population control, and mass famines during the 1970's in underdeveloped countries. Cities 33…
ERIC Educational Resources Information Center
Vagianos, Louis
1972-01-01
The library problem consists of equal parts of external and internal noise. The external noise consists of the volume of publication. The internal noise can be characterized by the present and continuing brouhaha concerning reform of library education. Scientists frankly regard librarians as impediments to information. (Author/NH)
Environmental Health Problems.
ERIC Educational Resources Information Center
Environmental Health Service (DHEW/PHS), Rockville, MD.
Aimed at a society which is forced to make decisions relative to their total environment, this pamphlet discusses a few of the problems associated with restoring and maintaining an environmental relationship conducive to the health and well-being of man. The topics covered include: air pollution, noise, solid waste, the urban environment, drinking…
Emery, V.J.; Kivelson, S.A.
1993-12-31
In the past few years there has been a resurgence of interest in dynamical impurity problems, as a result of developments in the theory of correlated electron systems. The general dynamical impurity problem is a set of conduction electrons interacting with an impurity which has internal degrees of freedom. The simplest and earliest example, the Kondo problem, has attracted interest since the mid-sixties not only because of its physical importance but also as an example of a model displaying logarithmic divergences order by order in perturbation theory. It provided one of the earliest applications of the renormalization group method, which is designed to deal with just such a situation. As we shall see, the antiferromagnetic Kondo model is controlled by a strong-coupling fixed point, and the essence of the renormalization group solution is to carry out the global renormalization numerically starting from the original (weak-coupling) Hamiltonian. In these lectures, we shall describe an alternative route in which we identify an exactly solvable model which renormalizes to the same fixed point as the original dynamical impurity problem. This approach is akin to determining the critical behavior at a second order phase transition point by solving any model in a given universality class.
ERIC Educational Resources Information Center
Moore, Jerilou; Sumrall, William J.
2008-01-01
Exploring our patent system is a great way to engage students in creative problem solving. As a result, the authors designed a teaching unit that uses the study of patents to explore one avenue in which scientists and engineers do science. Specifically, through the development of an idea, students learn how science and technology are connected.…
ERIC Educational Resources Information Center
Onions, Chris
1991-01-01
Presented are the solutions generated by a fifth grade class to the problem of finding the sum of the number of blocks in a pyramid with a bottom layer containing seven blocks. Three methods were recorded: a levels method, a columns method, and a vertical slice method. (MDH)
Solving Problems through Circles
ERIC Educational Resources Information Center
Grahamslaw, Laura; Henson, Lisa H.
2015-01-01
Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…
Symmetries of Spectral Problems
NASA Astrophysics Data System (ADS)
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
ERIC Educational Resources Information Center
Hanson, Deroy L.
Designed to motivate eighth-grade civics students in the study of the United States Constitution, this game is intended to simulate the basic problems faced by the delegates to the Philadelphia Convention of 1787. The four parts of the game introduce the governmental concepts of the bicameral legislature, the executive branch, the judicial branch,…
ERIC Educational Resources Information Center
De Bono, Edward
A group of children were presented with several tasks, including the invention of a sleep machine and a machine to weigh elephants. The tasks were chosen to involve the children in coping with problems of a distinct character. A study of the children's drawings and interpretations shows that children's thinking ability is not very different from…
ERIC Educational Resources Information Center
Nelson, Norman N.; Fisch, Forest N.
1973-01-01
Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)
ERIC Educational Resources Information Center
Crick, Francis; Koch, Christof
1992-01-01
Discusses approaches to the problem presented in understanding consciousness as a yet undiscovered process of interacting neuron activity. Presents the historical context of research in the area of human awareness and identifies research necessary to scientifically explain how the brain relates to the mind. (MCO)
Thermodynamics with Design Problems.
ERIC Educational Resources Information Center
Cilento, E. V.; Sears, J. T.
1983-01-01
Discusses how basic thermodynamics concepts are integrated with design problems. Includes course goals, instructional strategies, and major advantages/disadvantages of the integrated design approach. Advantages include making subject more concrete, emphasizing interrelation of variables, and reinforcing concepts by use in design analysis; whereas…
A Multifaceted Minimization Problem.
ERIC Educational Resources Information Center
Pomeranz, Janet Bellcourt
1983-01-01
The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)
Cognitive Problems (Disorientation, Perception, Attention, Learning and Problem-Solving)
... SOMEONE WITH EMOTIONAL & BEHAVIORAL NEEDS Cognitive Problems (Disorientation, Perception, Attention, Learning & Problem-Solving) Cognition is the process ... What Are Some Other Cognitive Problems? What Is Perception? Remember What Is Attention or Concentration? More Resources ...
Bicriteria network design problems
Marathe, M.V.; Ravi, R.; Sundaram, R.; Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III
1994-12-31
We study several bicriteria network design problems phrased as follows: given an undirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. Define an ({alpha}, {beta})-approximation algorithm as a polynomial-time algorithm that produces a solution in which the first objective value is at most {alpha} times the budget, and the second objective value is at most {alpha} times the minimum cost of a network obeying the budget oil the first objective. We, present the first approximation algorithms for bicriteria problems obtained by combining classical minimization objectives such as the total edge cost of the network, the diameter of the network and a weighted generalization of the maximum degree of any node in the network. We first develop some formalism related to bicriteria problems that leads to a clean way to state bicriteria approximation results. Secondly, when the two objectives are similar but only differ based on the cost function under which they are computed we present a general parametric search technique that yields approximation algorithms by reducing the problem to one of minimizing a single objective of the same type. Thirdly, we present an O(log n, log n)-approximation algorithm for finding a diameter-constrained minimum cost spanning tree of an undirected graph on n nodes generalizing the notion of shallow, light trees and light approximate shortest-path trees that have been studied before. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. These pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
Physics Problem Workbook, Student Manual.
ERIC Educational Resources Information Center
Jones, John L.
This workbook contains 50 undergraduate physics problems designed for use in conjunction with a computer in a time-sharing mode. Each of the problems includes a statement of the problem topic, a background description of the problem, problem objectives, suggested readings, and a related graph or figure. Various topics in general physics are…
Gravitational Many-Body Problem
Makino, J.
2008-04-29
In this paper, we briefly review some aspects of the gravitational many-body problem, which is one of the oldest problems in the modern mathematical science. Then we review our GRAPE project to design computers specialized to this problem.
Buffon's Coin Problem and beyond
ERIC Educational Resources Information Center
Schneiter, Kady
2011-01-01
This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.
The inhibiting bisection problem.
Pinar, Ali
2010-11-01
Given a graph where each vertex is assigned a generation or consumption volume, we try to bisect the graph so that each part has a significant generation/consumption mismatch, and the cutsize of the bisection is small. Our motivation comes from the vulnerability analysis of distribution systems such as the electric power system. We show that the constrained version of the problem, where we place either the cutsize or the mismatch significance as a constraint and optimize the other, is NP-complete, and provide an integer programming formulation. We also propose an alternative relaxed formulation, which can trade-off between the two objectives and show that the alternative formulation of the problem can be solved in polynomial time by a maximum flow solver. Our experiments with benchmark electric power systems validate the effectiveness of our methods.
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Elor, Gilly; Hall, Lawrence J.
2012-01-01
We revisit the cosmology of the supersymmetric QCD axion, highlighting the existence of a serious cosmological axino problem that is fully analogous to the gravitino problem of overclosure via thermal production. A general analysis implies that the QCD axino has a mass greater than or equal to that of the gravitino in the absence of unnatural fine-tuning or sequestering. As a consequence, bounds from thermal gravitino and QCD axino production are complementary in parameter space, and together provide a quite stringent limit on the reheating temperature after inflation given by TR<103-106GeV for an axion decay constant of fa=109-1012GeV. Motivated by this result, we explore the cosmology of gravitino lightest supersymmetric particle and axino next to lightest supersymmetric particle at low TR and present three realistic scenarios for dark matter.
FBST for Cointegration Problems
NASA Astrophysics Data System (ADS)
Diniz, M.; Pereira, C. A. B.; Stern, J. M.
2008-11-01
In order to estimate causal relations, the time series econometrics has to be aware of spurious correlation, a problem first mentioned by Yule [21]. To solve the problem, one can work with differenced series or use multivariate models like VAR or VEC models. In this case, the analysed series are going to present a long run relation i.e. a cointegration relation. Even though the Bayesian literature about inference on VAR/VEC models is quite advanced, Bauwens et al. [2] highlight that "the topic of selecting the cointegrating rank has not yet given very useful and convincing results." This paper presents the Full Bayesian Significance Test applied to cointegration rank selection tests in multivariate (VAR/VEC) time series models and shows how to implement it using available in the literature and simulated data sets. A standard non-informative prior is assumed.
Modern problems of thermodynamics
NASA Astrophysics Data System (ADS)
Novikov, I. I.
2012-12-01
The role of energy and methods of its saving for the development of human society and life are analyzed. The importance of future use of space energy flows and energy of water and air oceans is emphasized. The authors consider the idea of the unit for production of electric energy and pure substances using sodium chloride which reserves are limitless on the planet. Looking retrospectively at the development of power engineering from the elementary fire to modern electric power station, we see that the used method of heat production, namely by direct interaction of fuel and oxidizer, is the simplest. However, it may be possible to combust coal, i.e., carbon in salt melt, for instance, sodium chloride that would be more rational and efficient. If the stated problems are solved positively, we would master all energy properties of the substance; and this is the main problem of thermodynamics being one of the sciences on energy.
Hematological Problems of Pregnancy
Ballem, P.J.
1988-01-01
Hematologic complications are relatively common in pregnancy. Furthermore, many chronic hematologic disorders require special surveillance and intervention in pregnancy. In this brief review, the author discusses common nutritional anemias in pregnancy. She reviews the disorders of hemoglobin synthesis and the need for early genetic counselling and prenatal diagnosis, as well as the special requirements and problems affected patients encounter in pregnancy. An overview of the frequent causes of thrombocytopenia in pregnancy is given and an approach suggested to the management of both the mother and the fetus. An approach is also presented to the management of women at risk for thrombosis in pregnancy, a particularly vexing and controversial problem. The risks of the various forms of anticoagulation are reviewed. Finally, a brief review of obstetrical hemorrhage is presented along with some guidelines useful in its management. PMID:21253125
MCNP: Photon benchmark problems
Whalen, D.J.; Hollowell, D.E.; Hendricks, J.S.
1991-09-01
The recent widespread, markedly increased use of radiation transport codes has produced greater user and institutional demand for assurance that such codes give correct results. Responding to these pressing requirements for code validation, the general purpose Monte Carlo transport code MCNP has been tested on six different photon problem families. MCNP was used to simulate these six sets numerically. Results for each were compared to the set's analytical or experimental data. MCNP successfully predicted the analytical or experimental results of all six families within the statistical uncertainty inherent in the Monte Carlo method. From this we conclude that MCNP can accurately model a broad spectrum of photon transport problems. 8 refs., 30 figs., 5 tabs.
Solving bearing overheating problems
Jendzurski, T.
1995-05-08
Overheating is a major indicator, along with vibration and noise, of an underlying problem affecting a bearing or related components. Because normal operating temperatures vary widely from one application to another, no single temperature is a reliable sign of overheating in every situation. By observing an application when it is running smoothly, a technician can establish a benchmark temperature for a particular bearing arrangement. Wide deviations from this accepted norm generally indicate troublesome overheating. The list of possible causes of over-heating ranges from out-of-round housings and oversize shaft diameters to excessive lubrication and bearing preloading. These causes fall into two major categories: improper or faulty lubrication and mechanical problems, such as incorrect fits and tolerances. These are discussed along with solutions.
Momotani, Hiroko; Yamamoto, Haruyoshi
2014-02-01
This paper describes current issues in occupational mental health, occupational mental health activities currently underway, and priorities to improve the situation in Japan. A new tool to support these activities is then discussed. The incidence of employee mental health problems is rising, despite efforts to promote occupational mental health activities. The adoption of such activities is lagging behind in medium and small-sized enterprises. Priorities to improve occupational mental health include motivating business operators to address mental health issues, focusing more on prevention, and promoting mental health initiatives in medium and small-sized enterprises. Mental-Rosai, a web-based mental health check system, is a useful tool for the prevention of mental health problems and can provide support for medium and small-sized enterprises. PMID:24605529
The Boolean Isomorphism problem
Agrawal, M.; Thierauf, T.
1996-12-31
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be {sigma}{sup p}{sub 2} complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And- and Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.
A Perron-Frobenius theory for block matrices associated to a multiplex network
NASA Astrophysics Data System (ADS)
Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino
2015-03-01
The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.
Working on interesting problems
NASA Astrophysics Data System (ADS)
Smith, Arfon M.
2015-01-01
BSc Chemistry, The University of Sheffield 2001... PhD Astrochemistry, The University of Nottingham 2006... Scientist at GitHub Inc. 2013.From the outside, the path an individual has taken from academia to industry is not an obvious one. In this session I'll (try and) explain how an interest in software, engineering and chasing interesting problems makes internet startup in San Francisco a great home.
NASA Technical Reports Server (NTRS)
Bourke, Roger D.
1982-01-01
Energy management in its most comprehensive sense encompasses economic, technical, environmental, and political problems. The present evaluation of prospects notes that opportunities for energy conservation are widespread, in such fields as building air conditioning, transportation, electrical appliances, and industrial processes. Further conservation is expected to be achieved through a combination of technology development and economics; the latter factor must not be unduly influenced by political measures that shield consumers from the true cost of energy.
Novak, L L
1996-01-01
Educating parents about normal, age-appropriate behavior in their children, teaching them basic behavioral techniques (such as the time-out and positive-reward systems) and giving them specific suggestions for intervention can increase parental confidence and decrease anxiety. Anticipating problems before they develop can help parents prevent inappropriate behavior patterns from developing in their children and may decrease abusive behavior. PMID:8546052
NASA Astrophysics Data System (ADS)
Santos, Emilio
1992-10-01
The problem of hidden variables in quantum mechanics is formalized as follows. A general or contextual (noncontextual) hidden-variables theory is defined as a mapping f: Q×M → C (f: Q→C) where Q is the set of projection operators in the appropriate (quantum) Hilbert space, M is the set of maximal Boolean subalgebras of Q and C is a (classical) Boolean algebra. It is shown that contextual (noncontextual) hidden-variables always exist (do not exist).
Wang, Mao-Che; Liu, Chia-Yu; Shiao, An-Suey; Wang, Tyrone
2005-08-01
Acute diffuse otitis externa (swimmer's ear), otomycosis, exostoses, traumatic eardrum perforation, middle ear infection, and barotraumas of the inner ear are common problems in swimmers and people engaged in aqua activities. The most common ear problem in swimmers is acute diffuse otitis externa, with Pseudomonas aeruginosa being the most common pathogen. The symptoms are itching, otalgia, otorrhea, and conductive hearing loss. The treatment includes frequent cleansing of the ear canal, pain control, oral or topical medications, acidification of the ear canal, and control of predisposing factors. Swimming in polluted waters and ear-canal cleaning with cotton-tip applicators should be avoided. Exostoses are usually seen in people who swim in cold water and present with symptoms of accumulated debris, otorrhea and conductive hearing loss. The treatment for exostoses is transmeatal surgical removal of the tumors. Traumatic eardrum perforations may occur during water skiing or scuba diving and present with symptoms of hearing loss, otalgia, otorrhea, tinnitus and vertigo. Tympanoplasty might be needed if the perforations do not heal spontaneously. Patients with chronic otitis media with active drainage should avoid swimming, while patients who have undergone mastoidectomy and who have no cavity problems may swim. For children with ventilation tubes, surface swimming is safe in a clean, chlorinated swimming pool. Sudden sensorineural hearing loss and some degree of vertigo may occur after diving because of rupture of the round or oval window membrane. PMID:16138712
NASA Astrophysics Data System (ADS)
Ruskey, Frank; Williams, Aaron
In the classic Josephus problem, elements 1, 2,...,n are placed in order around a circle and a skip value k is chosen. The problem proceeds in n rounds, where each round consists of traveling around the circle from the current position, and selecting the kth remaining element to be eliminated from the circle. After n rounds, every element is eliminated. Special attention is given to the last surviving element, denote it by j. We generalize this popular problem by introducing a uniform number of lives ℓ, so that elements are not eliminated until they have been selected for the ℓth time. We prove two main results: 1) When n and k are fixed, then j is constant for all values of ℓ larger than the nth Fibonacci number. In other words, the last surviving element stabilizes with respect to increasing the number of lives. 2) When n and j are fixed, then there exists a value of k that allows j to be the last survivor simultaneously for all values of ℓ. In other words, certain skip values ensure that a given position is the last survivor, regardless of the number of lives. For the first result we give an algorithm for determining j (and the entire sequence of selections) that uses O(n 2) arithmetic operations.
Medical problems of musicians.
Lockwood, A H
1989-01-26
Surveys of performing musicians indicate that almost half of them experience playing-related medical problems, some of which threaten or end their careers. Overuse injuries involving the muscle--tendon unit are the most common problem, with symptoms ranging from mild pain while the musician is playing to pain severe enough to preclude any use of the affected hand. String players are the most commonly affected, and percussionists the least. The most important predisposing characteristic is the use of repetitive movements during long hours of practice, but awkward body positions mandated by the shape and weight of the instrument, the technical difficulty of the repertoire, and unfamiliar instruments may also play a part. Women are more commonly affected than men. Rest is the cornerstone of therapy. Neural impingement syndromes affecting the median or ulnar nerves or the thoracic outlet affect many musicians. Focal dystonias may involve part or all of a hand or the muscles forming the embouchure (the position of the lips in wind players). These are very resistant to therapy and may terminate or drastically alter a career. Stress, especially performance anxiety, may impede performance. Beta-adrenergic blocking agents prevent the symptoms of performance anxiety and are frequently used by musicians without medical supervision. A recognition of the unique problems of musician-patients has led to the formation of successful specialty clinics in a number of cities. PMID:2643048