相关论文: Partition function for general multi-level systems
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
A model of a geometric algorithm is introduced and methodology of its operation is presented for the dynamic partitioning of data spaces.
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out.…
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…
The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…