Related papers: Cycle products and efficient vectors in reciprocal…
Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of…
The concept of a fully interlacing matrix of formal power series with real coefficients is introduced. This concept extends and strengthens that of an interlacing sequence of real-rooted polynomials with nonnegative coefficients, in the…
We prove that the space $l^2$ contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.
We introduce an alternative route for obtaining reliable cyclic engines, based on interacting Brownian particles under time-periodic drivings. General expressions for the thermodynamic fluxes, such as power and heat, are obtained using the…
The randomised Horn problem, in both its additive and multiplicative version, has recently drawn increasing interest. Especially, closed analytical results have been found for the rank-1 perturbation of sums of Hermitian matrices and…
Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
In this paper, we first introduce the new class of vertically-recurrent matrices, using a generalization of "the Hockey stick and Puck theorem" in Pascal's triangle. Then, we give an interesting formula for the lower triangular…
Let $S_1, \cdots, S_N$ simple finite-dimensional modules of a quantum affine algebra. We prove that if $S_i\otimes S_j$ is cyclic for any $i < j$ (i.e. generated by the tensor product of the highest weight vectors), then $S_1\otimes \cdots…
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles…
Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $\sigma$ and that of its symmetric tensor power $\sigma ^{\odot k}$. In this paper, we investigate this question and give formulas…
In this paper, the determinants of $n\times n$ matrices over commutative finite chain rings and over commutative finite principal ideal rings are studied. The number of $n\times n$ matrices over a commutative finite chain ring ${R}$ of a…
In this note, we discuss the shift retrieval problems, both classical and compressed, and provide connections between them using circulant matrices. We review the properties of circulant matrices necessary for our calculations and then show…
We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions we obtain…
We obtain the closed form expressions for the densities of the product, quotient, power and scalar multiple of independent stable subordinators. Similar results for the independent inverse stable subordinators are discussed. This is…
Consider the set of scalars $\alpha$ for which the $\alpha$th Hadamard power of any $n\times n$ positive semi-definite (p.s.d.) matrix with non-negative entries is p.s.d. It is known that this set is of the form $\{0, 1, \dots, n-3\}\cup…
The loss of particles due to highly inelastic reactions has previously been taken into account in effective field theories for low-energy particles by adding local anti-Hermitian terms to the effective Hamiltonian. An additional…
A conjecture by Higman asserts that the number of conjugacy classes in the unipotent group of upper triangular matrices over a finite field depends polynomially on the number of elements of the field. We will study several alternative…