Related papers: Harmonic Representation of Combinations and Partit…
A combined method for analyzing quantum dynamical equations which uses the Bohmian mechanics and the quantum phase space representation is proposed. It is based on a presentation of the wave function in phase space in a polar form. The…
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…
This paper presents a novel application of compositional data analysis methods in the context of color image processing. A vector decomposition method is proposed to reveal compositional components of any vector with positive components…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
We use the symmetric product to describe the resultant scheme and discriminant scheme of polynomials two variables.
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
We construct generalized regular representations of the wreath product of a compact group with the infinite symmetric group. The characters of these representations are determined by probability measures on families of partitions called the…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…