The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realizati...
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The fuzzy optimization problem is one of the prominent topics in the broad area of artificial intelligence. It is applicable in the field of non-linear fuzzy programming. Its application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem was solved by hybrid optimization techniques like Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). An industrial production planning problem with a cubic objective function, eight decision variables and 29 constraints was solved successfully using the LS-SA-PS hybrid optimization techniques. The computational results for the objective function with respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem. (C) 2011 Elsevier Ltd. All rights reserved.
Group fairness requires that different protected groups, characterized by a given sensitive attribute, receive equal outcomes overall. Typically, the level of group fairness is measured by the statistical gap between ...
We show that in the ground states of the infinite-volume limits of both the spin-1/2 anisotropic antiferromagnetic Heisenberg model (in dimensions d greater-than-or-equal-to 2), and the ferromagnetic Ising model in a ...
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We show that in the ground states of the infinite-volume limits of both the spin-1/2 anisotropic antiferromagnetic Heisenberg model (in dimensions d greater-than-or-equal-to 2), and the ferromagnetic Ising model in a strong transverse field (in dimensions d greater-than-or-equal-to 1) there is an interval in the spectrum above the mass gap which contains a continuous band of energy levels. We use the methods of Bricmont and Frohlich to develop our expansions, as well as a method of Kennedy and Tasaki to do the expansions in the quantum mechanical limit. Where the expansions converge, they are then shown to have spectral measures which have absolutely continuous parts on intervals above the mass gaps.
Although normal ordering (NO) is often used as a quantization procedure for classical problems that are based on complex mode amplitudes, an alternate choice, called ''symmetric ordering'' (SO), is cha...
Although normal ordering (NO) is often used as a quantization procedure for classical problems that are based on complex mode amplitudes, an alternate choice, called ''symmetric ordering'' (SO), is championed here. In normal form the SO operator is simply related to zero order Laguerre polynomials that are implied by Weyl's quantization rule. Thus SO is as convenient as NO, and it is more accurate when the rotating wave approximation is used for a mass-spring oscillator with a slightly nonlinear spring. The two quantization methods are compared for a Hartree analysis of the discrete self-trapping equation with an arbitrary power of the nonlinearity.
This paper addresses the possible connections between chaos, the unpredictable behavior of solutions of finite dimensional systems of ordinary differential and difference equations and turbulence, the unpredictable be...
This paper addresses the possible connections between chaos, the unpredictable behavior of solutions of finite dimensional systems of ordinary differential and difference equations and turbulence, the unpredictable behavior of solutions of partial differential equations. It is dedicated to Martin Kruskal on the occasion of his 60th birthday.
For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is prim...
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For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is primarily of interest to show two things: First, it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool for computing the measure of the accessible set. We use this to compute the measure of the bounded orbits for the Henon quadratic map. (C) 1997 American Institute of Physics.
For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the di...
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For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the diameter of the d-dimensional lattice is given by L, the absolute value of the difference of the ground-state energy per site and its limit is asymptotically exp(-xiL) L(-d/2) for some positive constant xi. We also show that the correlation function has the same behavior. Our results are derived by cluster expansions, using a method of Bricmont and Frohlich which we extend to the quantum mechanical case.
In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-fr...
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Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt found...
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The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use...
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. ''Counting lemmas'' for the non-selfadjoint operator L, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite disc D in the complex eigenvalue plane. The radius of the disc D is controlled by the H-1 norm of the potential q. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds - ''whiskered tori'' for the NLS pde. The Floquet discriminant DELTA(lambda;q) used to introduce a natural sequence of NLS constants of motion, [F(j)(q) = DELTA(lambda = lambda(j)c(q);q), where lambda(j)c denotes the j(th) critical point of the Floquet discriminant DELTA(lambda)]. A Taylor series expansion of the constants F(j)(q), with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of F(j)(q), which themselves are expressed in terms of quadratic products of eigenfunctions of L. The second variation permits identification, within the disc D, of important bifurcations m the spectral configurations of the operator L. The constant F(j)(q), as the height of the Floquet discriminant over the critical point lambda(j)c, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, {F(j)(q)}\j\>N, which is associated with critical points outside the disc D. Within this disc, the interpretation is only valid locally, with the s
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