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The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the…

Nuclear Theory · Physics 2009-11-10 Cuneyt Berkdemir , Ayse Berkdemir , Ramazan Sever

We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…

Numerical Analysis · Mathematics 2018-06-20 Martin Neuenhofen

The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…

Computational Complexity · Computer Science 2018-11-20 Antonios Syreloglou

A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…

Numerical Analysis · Mathematics 2020-08-18 Desheng Li , Ruijing Wang

In this article we present a unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces). The lower bounds we derive via the linear programming (LP) techniques of…

Metric Geometry · Mathematics 2018-04-23 Peter Boyvalenkov , Peter Dragnev , Douglas Hardin , Edward Saff , Maya Stoyanova

Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…

Artificial Intelligence · Computer Science 2017-01-19 Manuele Leonelli , Eva Riccomagno , Jim Q. Smith

We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x:…

Quantum Physics · Physics 2025-11-19 Daniel Stilck França , Ngoc Hoang Anh Mai

We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…

Soft Condensed Matter · Physics 2025-12-16 Paolo Amore , Victor Figueroa , Raymundo Ramos

The polynomial solution of the N-dimensional space Schrodinger equation for a special case of Mie potential is obtained for any arbitrary $% l-state. The exact bound-state energy eigenvalues and the corresponding eigenfunctions are…

Quantum Physics · Physics 2008-07-15 Sameer M. Ikhdair , Ramazan Sever

The purpose of this paper is to determine the asymptotic of the average energy of a configuration of N zeros of system of random polynomials of degree N as N tends to infinity and more generally the zeros of random holomorphic sections of a…

Complex Variables · Mathematics 2007-05-23 Qi Zhong

The one-dimensional Schroedinger's equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential's parameters, we show that the decatic polynomial potential…

Mathematical Physics · Physics 2015-06-15 David Brandon , Nasser Saad

The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…

Numerical Analysis · Mathematics 2015-03-10 Peter Benner , Steffen Börm , Thomas Mach , Knut Reimer

The authors present a unified method for calculating the zeros of the classical orthogonal polynomials based upon the electrostatic interpretation and its connection to the energy minimization problem. Examples are given with error…

Classical Analysis and ODEs · Mathematics 2021-09-21 Ridha Moussa , James Tipton

We introduce a numerical method for generating the approximating polynomials used in fermionic calculations with smeared link actions. We investigate the stability of the algorithm and determine the optimal weight function and the optimal…

High Energy Physics - Lattice · Physics 2009-11-10 S. D. Katz , B. C. Toth

Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…

Quantum Physics · Physics 2021-01-26 Theerapat Tansuwannont , Surachate Limkumnerd , Sujin Suwanna , Pruet Kalasuwan

Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem,…

Computational Complexity · Computer Science 2024-10-15 Ferucio Laurenţiu Ţiplea , Simona-Maria Lăzărescu

We present the results of systematic numerical computations relating to the extreme value statistics of the characteristic polynomials of random unitary matrices drawn from the Circular Unitary Ensemble (CUE) of Random Matrix Theory. In…

Statistical Mechanics · Physics 2018-10-24 Yan V. Fyodorov , Sven Gnutzmann , Jonathan P. Keating

Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…

Mathematical Physics · Physics 2020-11-11 Gernot Akemann , Eugene Strahov , Tim R. Würfel

While previous work on energy-efficient algorithms focused on assumption that tasks can be assigned to any processor, we initially study the problem of task scheduling on restricted parallel processors. The objective is to minimize the…

Data Structures and Algorithms · Computer Science 2013-09-17 Xibo Jin , Fa Zhang , Ying Song , Liya Fan , Zhiyong Liu

We search for first- and second-order corrections to the energy levels of the Pauli-Dirac equation within the Rayleigh-Schr\"odinger theory. We use some identities satisfied by the associated Laguerre polynomials to reach this aim. We give…

Quantum Physics · Physics 2021-09-17 Altug Arda