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# Matrix - Science topic

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This study proposes a new assembly method to address the problems of using the conventional direct assembly method for assembling elemental damping matrices for a global damping matrix. These problems include the challenges in calibrating an elemental damping ratio for a desired global damping ratio, significantly low and high global damping ratios...

To broaden the family of available matrices for auxetic composites, an auxetic TPU frame with cubic matrix cases is proposed, tested, and optimized. Quasi-static compression was applied to the new structure to investigate its mechanical performance. Verified finite element models were established for demonstrating the programmable strength and stif...

With the deterioration growth of water pipes, the frequency of identifying segments and unintended isolation in water distribution networks is expected to increase, because it can help identify the number of nodes that cannot be supplied and their locations when a failure occurs. Therefore, a methodology for identifying segments and unintended isol...

In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are independent. The dependency is modeled through correlations between the Brownian motions driving the diffusion processe...

The internal oxide precipitates were supposed to be spherical in Wagner’s original theory, while the following research demonstrated that this assumption is an exception rather than the truth, which caused deviations in the application of this theory. In this study, the internal oxide precipitates have a needle-like and a near-spherical morphology...

In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the “state transition matrix method” is introduced and some necessary and sufficie...

In this study, a new two-parameter biased estimator for estimating the parameter of a multicollinearity linear regression model is developed. We compared the performance of the proposed estimator with some existing estimators in terms of the mean squared error matrix. The theoretical comparisons and simulation results revealed that the proposed two...

The effect of C content on the formation of V carbide layer on carbon steels by a powder packed method was investigated. The continuous duplex carbide layer consisting of an outer V2C and inner V6C5 and V8C7 layers was formed on Fe-0.7C and Fe-0.3C (in wt.%), but it was discontinuous on Fe-0.1C. Internal carbide precipitates were observed within th...

Increasing demand for individualised products has led to the concept of mass customisation, combining high product variety with production efficiency coming along with mass production. Companies are moving to matrix production systems with complex product flows for mass customisation. One challenge in such systems is the determination of optimal sy...

The academic article presents a Directional states based averaging approach to describe the array structure of strictly rectangular complex matrices. Using this approach, an approximation to a non zero strictly rectangular complex matrix is formulated and the proximity of this matrix approximation to the input matrix is appropriately quantified.

The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of ordinary derivatives in the first and second order that, are unstable before feedback gain. More precisely, we inv...

Let \(\{G_n\}_1^{\infty }\) be a sequence of non-trivial finite groups. In this paper, we study the properties of a random walk on the complete monomial group \(G_n\wr S_n\) generated by the elements of the form \(({{\,\textrm{e}\,}},\dots ,{{\,\textrm{e}\,}},g;{{\,\textrm{id}\,}})\) and \(({{\,\textrm{e}\,}},\dots ,{{\,\textrm{e}\,}},g^{-1},{{\,\t...

Various parameters of a melt blending processing including the extruders’ type, processing conditions (barrel temperature, screw speed and screw configuration), shear rate, residence time and distribution in relation to the mechanical properties of polymer nanocomposites were qualitatively reviewed. The tensile, flexural and impact strengths and th...

At present, there is a problem that the growth quality is reduced due to damage to the plug seedling pot during the transplanting process. In this study, the pressure distribution measurement system was used to measure the contact area of plug seedlings when they collided with the ground. The effects of seedling age and forward speed on the charact...

The increased volume of rumors and attention on related topics during the COVID-19 pandemic have had a significant negative social impact. To combat rumors, it is crucial to study the actors involved in their spread. In this study, we first introduce prospect theory and construct an evolutionary game model between network operators and government r...

The concept of sustainable development, in recent years if not decades, has been introduced into all individual forms of development regardless of sector or economy. It has been realized internationally that when development does not become sustainable it will soon cease to exist. In previous years, there have been attempts to measure development a...

Motivated by the recent experimental realization of minimal Kitaev chains using quantum dots, we investigate the Majorana zero modes (MZM) in Y-shape Kitaev wires. We solve the associated Kitaev models analytically at the sweet spot (th = Δ) and derive the exact form of MZM wave-functions in this geometry. We observed exotic multi-site MZMs located...

We investigate the gravitational form factors of a strongly coupled scalar theory that mimic the interaction between the nucleon and the pion. The nonperturbative calculation is based on the light-front Hamiltonian formalism. We renormalize the energy-momentum tensor with a Fock sector dependent scheme. We also systematically analyze the Lorentz st...

This paper focuses on the Hyers-Ulam stability to linear nonhomogeneous quaternion-valued matrix difference equations via complex representation. Then one can transfer the second-order and higher-order linear nonhomogeneous quaternion-valued difference equations into the first-order linear nonhomogeneous quaternion-valued matrix difference equation...

We extend the framework of analyzing the 2HDM in its orbit space to study the one-loop effective potential before and after electroweak symmetry breaking. In this framework, we present a comprehensive analysis of global symmetries of the one-loop thermal effective potential in the Higgs family space, demonstrating when the global symmetries in the...

In this paper, the Ulam’s type stability of delayed discrete systems with a second-order difference is investigated. Firstly, we introduce the Hyers–Ulam stability and Hyers–Ulam–Rassias stability concepts for delayed discrete systems with a second-order difference. Secondly, the uniqueness and existence of the solution of delayed nonlinear discret...

Let f:(0,∞)→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f: (0,\infty )\rightarrow {\mathbb {R}}$$\end{document} be an operator monotone function and A∈Mn\documentc...

The article focuses on creating matrix models for machining error in multi-tool multi-carriage adjustments (setups) where tools are spatially arranged. These models take into account the elastic deformations of the technological system in all coordinate directions, along with the simultaneous impact of cutting forces from all adjustment tools. Thes...

SO(3). Проведены модельные расчеты главных компонент тензора эффективной теплопроводности образца композита с эпоксидной системой типа ЭД-20 в качестве матрицы и графеновыми включениями в за-висимости от объемной доли включений. Расчеты производятся при различных аспектных отношениях включений и при различных разбросах в ориентациях осей включений,...

The fact that the adjacency matrix of every finite graph is diagonalizable plays a fundamental role in spectral graph theory. Since this fact does not hold in general for digraphs, it is natural to ask whether it holds for digraphs with certain level of symmetry. Interest in this question dates back to the early 1980 s, when P. J. Cameron asked for...

The stakeholder commitments of higher education institutions (HEIs) continuously strengthen sustainable practices and ethical governance. In addition, stakeholders' internal decision-making activities must seek operational excellence at all workplaces. Participants in the HEI should promote scientific development and improve the results of students...

The location identification of dynamic load is an important part of load-identification technology. Traditional methods are mostly aimed at the identification of dynamic load’s amplitude and phase. A new method for dynamic load location identification is proposed in this paper. An amplitude ratio or a phase difference between structural dynamic res...

The status of a power network, as well as the techniques for estimating it, are important in assessing the power network’s operation and control, as well as determining its future expansion. Power flow analysis, which estimates the magnitudes of the bus voltages as well as the power flowing through the system’s lines, may be utilized to identify th...

For a marked surface \(\Sigma \) and a semisimple algebraic group G of adjoint type, we study the Wilson line morphism \(g_{[c]}:{\mathcal {P} }_{G,\Sigma } \rightarrow G\) associated with the homotopy class of an arc c connecting boundary intervals of \(\Sigma \), which is the comparison element of pinnings via parallel-transport. The matrix coeff...

We develop a game-theoretical model of a classroom scenario, where n students collaborate on a common task. We assume that there exists an objective truth known to the students but not to the course instructor. Each of the students estimates the contributions of all team members and reports her estimates to the instructor. Thus, a matrix A of peer...

In this paper, we obtain tight lower bounds for the trace norm || ||_1 of some matrices with diagonal zero, in terms of the entry-wise l1-norm (denoted by || ||_(1)). It is shown that on the space of nonzero real symmetric matrices A of order n with diagonal zero, the miniumum value of the quantity ||A||_1 / ||A||_(1) is equal to 2/n. The answer fo...

Multi-task learning (MTL) improves generalization by sharing information among related tasks. Structured sparsity-inducing regularization has been widely used in MTL to learn interpretable and compact models, especially in high-dimensional settings. These methods have achieved much success in practice, however, there are still some key limitations,...

We present three reduced integrable hierarchies of nonlocal integrable nonlinear Schrödinger-type equations, starting from a given vector integrable hierarchy generated from a matrix Lie algebra of B type. The basic tool is the zero curvature formulation. Three similarity transformations are taken to keep the invariance of the involved zero curvatu...

We employ implicit regularization (IReg) in quark-antiquark decays of the Z, or of a scalar (CP-even or odd) boson at NLO, and compare with dimensional schemes to reveal subtleties involving infrared divergence cancellation and $$\gamma _5$$ γ 5 -matrix issues. Besides the absence of evanescent fields in IReg, such as $$\epsilon $$ ϵ -scalars requi...

We propose a variational quantum algorithm for estimating microcanonical expectation values in models obeying the eigenstate thermalization hypothesis. Using a relaxed criterion for convergence of the variational optimization loop, the algorithm generates weakly entangled superpositions of eigenstates at a given target energy density. An ensemble o...

This paper deals with a high-resolution algorithm that engages fuzzy transform to solve three-dimensional nonlinear elliptic partial differential equations. The scheme approximates the fuzzy components, which estimate fourth-order accurate solutions at the interior mesh points of the solution domain. The fuzzy components and triangular base functio...

The stability and dynamic performance of the system are impacted by the uncertainties present in the converter model and controller parameters. This paper introduces a robust non-fragile control approach that addresses the influence of these uncertainties. The approach involves developing a control law that achieves quadratic stabilization of the c...

Unlike histogram-based reversible data hiding (RDH), the general distortion-based framework considers pixel-by-pixel distortions, which is a new research direction in RDH. The advantage of the general distortion-based RDH method is that it can enhance the visual quality of the marked image by embedding data into visually insensitive regions (e.g.,...

Recent researches have shown that the success of Transformers comes from their macro-level framework and advanced components, not just their self-attention (SA) mechanism. Comparable results can be obtained by replacing SA with spatial pooling, shifting, MLP, fourier transform and constant matrix, all of which have spatial information encoding capa...

Purpose
While intolerance of uncertainty (IU) is widely recognized as a transdiagnostic risk factor for psychopathology, there is limited research on its internal structure and core features. This study aimed to employ network analysis to examine IU as a system of interconnected beliefs among a large sample of Chinese adolescents.
Methods
A total...

The main intent of this manuscript is to formulate the Controllability conditions for the impulsive fractional order differential systems with proportional delay. The solution representation is derived by employing Laplace transformation and Mittag–Leffler matrix function. Also, theoretical study for controllability is described by appropriate Gram...

Addressing the complex issue of multi-attribute decision-making within a probabilistic dual hesitant fuzzy context, where attribute weights are unknown, a novel decision-making method based on cumulative prospect theory is proposed, named the probabilistic dual hesitant fuzzy multi-attribute decision-making method based on cumulative prospect theor...

In the context of the debate between the perspective of structural racism (Almeida, 2019) and the fascism of color (Sodré, 2023)), we develop, in this article, several inferences about fascism from the perspective of mediatization. At first, we compare the two contributions, in an approach that accentuates the contradictions, without necessarily an...

We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix A, defined as tr(f(A))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}...

A procedure to obtain relativistic expressions for photoionisation angular distribution parameters using the helicity formulation is discussed for open-shell atoms. Electric dipole and quadrupole transition matrix elements were considered in the present work, to study the photoionisation dynamics of the 3s electron of the sodium atom in the vicinit...

Existing deep subspace clustering algorithms are difficult to scale to large-scale data. There are two reasons: Firstly, the existing subspace clustering algorithms almost all need to find the self-expressive coefficient matrix whose size is proportional to the square of the data set size at once. Secondly, spectral clustering needs to solve the ei...

Interference with a nonlinear cavity mode undergoing a self-sustained limit cycle can lead to superradiant amplification of incident waves. This effect, which results from nonlinear wave-mode coupling, is theoretically predicted and experimentally confirmed in this work. On the theoretical side, we present a nonlinear coupled-mode framework to deri...

In this paper, we consider a linear constraint system with a set constraint. We investigate the Lipschitz-like property of such systems with an explicit set constraint under full perturbations (including the matrix perturbation) and derive some sufficient and necessary conditions for this property. We also make use of some other approaches like out...

In this paper, a new efficient weighted correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking and impact events for the first time. It is well known that the original kernel gradient correction (KGC) encounters numerical i...

An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results...

Among the list of one-dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen–Morse II potential. The first objective is to analyse the scattering matrix corresponding to this potential. We show that it includes a series of poles corresponding to the types of redundant poles or anti-bound poles. In some cases, there are even bound...

A Flocking obstacle avoidance algorithm based on the extensive game with perfect information is proposed for the blockage problem of UAV swarm in front of multi‐narrow type obstacles. The two UAVs closest to the target are selected as participants of the game, and the game tree is defined to determine the combination of the motion strategies of the...

In the present paper, for the first time, we consider the problem of non-fragile finite-time guaranteed cost control for a class of fractional-order singular systems with norm-bounded uncertainties. Firstly, we establish a linear quadratic cost function based on the integral of integer order, which serves practical purposes and acts as a performanc...

Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams with arbitrarily axially varying cross-sections, materials, foundations, loads, and general bou...

Risk analysis of investment decision-making behavior is to improve the ability to prevent investment risks in order to guarantee the success rate of investment decisions. In this paper, the risk evaluation level is determined by calculating the correlation degree of risk indicators through the establishment of the material topology matrix, and the...

We show that Majorana neutrino flavor mixing can be driven by transition dipole moments in the presence of external electromagnetic fields. We demonstrate the sensitivity of the rotation mixing matrix to strong fields obtaining dynamical mass eigenstates in the two-flavor model. The three-flavor case and extensions to the quark sector are introduce...

This article presents two new algebraic algorithms to perform fast matrix-vector product for $N$-body problems in $d$ dimensions, namely \emph{nHODLR$d$D} (nested algorithm) and \emph{s-nHODLR$d$D} (semi-nested or partially nested algorithm). The \emph{nHODLR$d$D} and \emph{s-nHODLR$d$D} algorithms are the nested and semi-nested version of our prev...

The primary mechanism in cancer metastasis, collective invasion is becoming more widely recognized. Leader cells are specially trained cancer cells that invading the tumors. They are crucial in establishing invasion pathways, organizing follower cells, and facilitating the survival of cancer cells throughout the metastatic cascade. To aid group inv...

A bstract
The possibility to reanalyse data taken by the HERA experiments offers the chance to study modern QCD jet and event-shape observables in deep-inelastic scattering. To address this, we compute resummed and matched predictions for the 1-jettiness distribution in neutral current DIS with and without grooming the hadronic final state using th...

A 3 × 3 Mueller matrix polarimeter, as one of the primary polarization measurement tools, has attracted intensive interest in various fields of polarization optics. In this paper, from a novel viewpoint with more mathematical analysis of the basic configuration and the working performance of a 3 × 3 Mueller matrix polarimeter, we systematically stu...

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using t...

Matrix mechanics is very convenient to express all the operations in quantum mechanics that are vague to use probabilities. However, we are not always aware of disadvantages of matrix mechanics. Matrices have generally properties of asymmetric, and the symmetric are very limited as in the case of the diagonal ones of matrices. So far, most experime...

Facing the increasing annual cybersecurity costs, threat modelling (TM) is a method to consider security as early as possible in the software development life cycle (SDLC). Thereby, TM helps to identify and address security-related design flaws in information systems. As the original TM approach is based on sequential development, it is not aligned...

The known constructive tests for the shapes of the numerical ranges in the 3-by-3 case are further specified when the matrices in question are row stochastic. Auxiliary results on the unitary (ir)reducibility of such matrices are also obtained.

In this work, we consider the inverse spectral problem for the impulsive Dirac systems on (0,π) with the jump condition at the point π2. We conclude that the matrix potential Q(x) on the whole interval can be uniquely determined by a set of eigenvalues for two cases: (i) the matrix potential Q(x) is given on 0,(1+α)π4; (ii) the matrix potential Q(x...

We consider the classical field integrable system whose evolution equation is the nonlinear Schrödinger equation with defocusing non-linearities, which is the classical limit of the quantum Lieb-Liniger model. We propose a simple derivation of the relation between two sets of conserved quantities: on the one hand the trace of the monodromy matrix,...

Exact cancellation of quantum amplitudes in multiphoton interferences with Fock states at the input, the so-called suppression or zero transmission laws generalizing the Hong-Ou-Mandel dip, are useful tools in quantum information and computation. It was recently suggested that all bosonic suppression laws follow from a common permutation symmetry i...

The Payoff Matrix.
The Hurwiz Rule.
The Minimax Rule.
The Laplace Rule.
The Maximin Rule.

On configurations with 2+1-flavor dynamical domain-wall fermions, we calculate the RI/(S)MOM renormalization constants (RC) of overlap quark bilinears. Hypercubic (HYP) smearing is used to construct the overlap Dirac operator. We investigate the possible effects of the smearing on discretization errors in the RCs by varying the level of smearing fr...

environmental concerns are pushing industries for the use of renewable and bio-based materials. Considerable interest has been devoted to poly(lactic acid) (PLA) since this polymer has shown promising and excellent results in mechanical and environmental properties. Poly(lactic acid) properties can be improved by incorporation of nanoplatelets , na...

LT-базисе Bartini. Инвариант определяется по передаточной матрице пропорциональности между входной и выходной матрицами эффекта. Эффекты с одинаковым инвариантом образуют тренды развития пространственных, временных и вещественно-полевых ресурсов. Одним из примеров является известный тренд «точка-линия-поверхность-объем». По закону свертывания-разве...

D. A. Hejhal showed the positive definiteness of the matrix H=(hjk)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=(h_{jk})$$\end{document} appearing in Schiffer’s id...

In this paper, we optimize the secrecy capacity of the legitimate user under resource allocation and security constraints for a multi-antenna environment for the simultaneous transmission of wireless information and power in a dynamic downlink scenario. We study the relationship between secrecy capacity and harvested energy in a power-splitting con...

Elektrische Transitionsvehikel, mit der Fähigkeit senkrecht zu starten und zu landen (eVTOLs), werden häufig mithilfe von nichtlinearen Regelungsstrategien betrieben. Ein Beispiel stellt das in diesem Paper betrachtete Starrflügler-eVTOL-Konzept dar, welches mithilfe von zwei Impellern und Schubvektorsteuerungen angetrieben wird und die Regelungsst...

It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearr...

The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT hardware implementation efficiency. Until now, most hardware implementations used Digital Signal Proc...