111 Results Found

In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Lagu...

This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. Th...

Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is...

Time evolution of open quantum systems is governed by the master equation. The master equation, which is a matrix formalism, is the time derivative of the density matrix, which contains the complete information on the state of a quantum system. Inste...

In this paper, we employ a generalization of the Boas–Bellman inequality for inner products, as developed by Mitrinović–Pečarić–Fink, to derive several upper bounds for the $2p$-th power with $p\ge 1$ of the numerical rad...

The incorporation of ductile reinforcements into ceramics helps restrain crack deflection, which can enhance ceramics’ toughness and overcome the matrix’s brittleness. In this paper, we produced a ceramic composite reinforced by carbon fi...

This paper explores the application of Random Matrix Theory (RMT) as a methodological enhancement for portfolio selection within financial markets. Traditional approaches to portfolio optimization often rely on historical estimates of correlation mat...

This work presents the first systematic development of the inverse scattering transform for matrix nonlinear Schrödinger equations in the case where the discrete spectrum has triple poles, under nonzero boundary conditions at infinity. These sys...

In this study, we obtain the ${\ell }_p$-norms of six classes of operators that commute with the infinite Hilbert operators.

The quantum evolution of wave functions controlled by the spectrum of Lévy random matrices is considered. An analytical treatment of quantum recurrences and revivals in the Hilbert space is performed in the framework of a theory of almost periodic fu...

For $G\in {\mathbb{R}}^{m\times n}$ and $g\in {\mathbb{R}}^m$, the minimization ${min\parallel G\psi -g\parallel }_2$, with $\psi \in {\mathbb{R}}^n$, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is $min\parallel T\left(h\right)\&m$...

In this short paper, we describe natural logit population games dynamics that explain equilibrium models of origin-destination matrix estimation and (stochastic) traffic assignment models (Beckmann, Nesterov–de Palma). Composition of the propos...

The identification and classification of acoustic emission (AE) based failure modes are complex due to the fact that AE waves are generally released simultaneously from all AE-emitting damage sources. To fully understand the occurrence of damage and...

We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geomet...

This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties. We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergences...

We establish multiple novel upper estimates for the numerical radius associated with off-diagonal operator matrices defined on a complex Hilbert space $\mathfrak{H}$. The operators considered have a specific structure, with zero diagonal entries and anti-diagonal...

Quantum-inspired language models have been introduced to Information Retrieval due to their transparency and interpretability. While exciting progresses have been made, current studies mainly investigate the relationship between density matrices of d...

The final goal of this paper is to organize the tools needed to study digital Quantum Communications, where classical information is entrusted to quantum states represented by density operators. A density operator is usually defined starting from a s...

This survey provides a review of the theoretical research on the classic system of matrix equations $AX=C$ and $XB=D$, which has wide-ranging applications across fields such as control theory, optimization, image processing, and robotics. The paper discu...

The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as m...

A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being...

In this paper, a kind of nonlinear Schrödinger (NLS) equation, called an NLS-like equation, is Riemann–Hilbert investigated. We construct a $2\times 2$ Lax pair associated with the NLS equation and combine the spectral analysis to...

This paper explores the reverse space-time mKdV equation through the application of the Riemann–Hilbert problem. Under the zero boundary condition, we derive the Jost solutions, examine their the analytic and symmetry properties alongside those...

Let \(S=\{1,2,..., n\}\) be a set of positive integers. The \(n\times n\) matrix \([S]=(i,j)\), where \(s_{ij}=(x_{i},x_{j})\) the greatest common divisor of \(x_{i}\) and \(x_{j}\), is called the greatest common divisor GCD matrix on \(S\). In this...

When rolling bearing failure occurs, vibration signals generally contain different signal components, such as impulsive fault feature signals, background noise and harmonic interference signals. One of the most challenging aspects of rolling bearing...

In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann–Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equati...

The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms...

The energy-momentum relocalization in classical and quantum theory is addressed with specific impact on non-perturbative QCD and hadronic structure. The relocalization is manifested in the existence of canonical and symmetric (Belinfante and Hilbert)...

An improved variational inequality strategy for dealing with variational inequality in a Hilbert space is proposed in this article as an alternative; if Hilbert space is used as the domain of interest, the original extra-gradient method is proposed f...

We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a $4\times 4$ matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based...

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative obl...

In this paper, we investigate the long-term asymptotic behavior of solutions to the Cauchy problem for the n-component coupled higher-order nonlinear Schrödinger (nC-HNLS) equation on a line with decaying initial data. Through the application of...

We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is pi...

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying pa...

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality p...

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered proble...

We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce add...

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^2\left(\mu \right)$ , with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix wi...

This paper presents a unified framework for controllability and minimum-energy control of linear fractional differential systems with Caputo derivative order $\gamma \in (0,1)$ and fully time-varying state and control delays. An explicit mild solutio...

As an effective method for image security protection, image encryption is widely used in data hiding and content protection. This paper proposes an image encryption algorithm based on an improved Hilbert curve with DNA coding. Firstly, the discrete w...

The problem of diffraction of a TE-polarized electromagnetic wave by a circular slotted cylinder is investigated. The boundary value problem in question for the Helmholtz equation is reduced to an infinite system of linear algebraic equations of the...

In order to increase the security and robustness of quantum images, this study combined the quantum DNA codec with quantum Hilbert scrambling to offer an enhanced quantum image encryption technique. Initially, to accomplish pixel-level diffusion and...

In this paper, using the technique of operator matrix, we consider the positive solution of the system of operator equations $AX=B,XC=D$ in the framework of the Hilbert space; here, the ranges $R\left(A\right)$ of A and $R\left(C\right)$ of C are not necessarily closed. Firstly...

We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensiona...

The assessment of dermal alterations is necessary to monitor skin aging, cancer, and other skin diseases and alterations. The gold standard of morphologic diagnostics is still histopathology. Here, we proposed parameters to distinguish morphologicall...

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in...

We consider a Markov chain that can be termed a discrete version of Blackwell’s example from 1958. It is constructed with the aid of a sequence of independent Markov chains with two states. It turns out its stationary distribution $\pi$ and tran...

In this article, a system of two coupled matrix Riccati differential equations (CMRDEs) arising in connection with mean-field linear quadratic (LQ) control problems is considered. Our aim is to provide conditions that guarantee the existence and uniq...

We develop a semi-inner product framework for $2\times 2$ block operator matrices acting on the direct sum $\mathcal{K}=\mathcal{H}\oplus \mathcal{H}$ of a complex Hilbert space $\mathcal{H}$, generated by the diagonal operator matrix $\mathbb{A}=\mathrm{diag}(\mathrm{A},\mathrm{B})$, where $\mathrm{A}$ and $\mathrm{B}$ are distinct positive operators ac...

Let $\epsilon >0$ and $\mathcal{TB}(\mathcal{X}\times \mathcal{X})$ be the Banach algebra of all $2\times 2$ bounded upper triangular operator matrices on a separable Hilbert space $\mathcal{X}\times \mathcal{X}$. In this paper, we first establish the spectrum equalities for special cases of upper triang...