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The purpose of the present paper is to investigate on a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding…
In geometry of nonlinear partial differential equations, recursion operators that act on symmetries of an equation $\mathcal{E}$ are understood as B\"{a}cklund auto-transformations of the equation $\mathcal{TE}$ tangent to $\mathcal{E}$. We…
In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…
Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…
Rational Lax hierarchies introduced by Krichever are generalized. A systematic construction of infinite multi-Hamiltonian hierarchies and related conserved quantities is presented. The method is based on the classical R-matrix approach…
In this paper we introduce and study an alternative definition of tense operators on residuated lattices. We give a categorical equivalence for the class of tense residuated lattices, which is motivated by an old construction due to J.…
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised. The relationship with the Lie-algebraic integrability…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states.…
Special matrix functions have recently been investigated for regions of convergence, integral representations and the systems of matrix differential equation that these functions satisfy. In this paper, we find the recursion formulas for…
Modern machine learning systems represent their computations as dataflow graphs. The increasingly complex neural network architectures crave for more powerful yet efficient programming abstractions. In this paper we propose an efficient…
The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the…
In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyavlensky equation and has the Kaup-Kupershmidt equation in its…
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic…
Various formulas for reciprocals of densely defined weighted composition operators in $L^2$-spaces as well as for their adjoints are provided. The relation between the reciprocal of a weighted composition operator and the product of the…
This article presents a formula for some dispersionless equations and a brief review of the operators which have been used for the dispersionless KP hierarchy.
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
A recursive calculational scheme is developed for matrix elements in the generalized seniority scheme for the nuclear shell model. Recurrence relations are derived which permit straightforward and efficient computation of matrix elements of…
The rationality of the parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra and any nonnegative integer is established and the irreducible modules are determined.
Several definitions of differential operators on modules over noncommutative rings are discussed.