Related papers: Blends in Maple
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstrate that Hermite splines are maximally localized in the sense…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…
In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of…
A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not…
Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the…
Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation we derive some new identities about operator Hermite polynomials in both single- and two-variable, we…
We give two widest Mehler's formulas for the univariate complex Hermite polynomials $H_{m,n}^\nu$, by performing double summations involving the products $u^m H_{m,n}^\nu (z,\overline{z}) \overline{H_{m,n}^\nu (w,\overline{w})}$ and $u^m…