834 Results Found

The suggested methods for solving fault diagnosis and estimation problems are based on the use of the Jordan canonical form. The diagnostic observer, virtual sensor, interval, and sliding mode observer design problems are considered. Algorithms have...

The Sturm–Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm–Liouville problem (SLP), this paper explores the intricacies of th...

This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order lin...

This paper aims to study a class of neutral differential equations of higher-order in canonical form. By using the comparison technique, we obtain sufficient conditions to ensure that the studied differential equations are oscillatory. The criteria t...

We address classification of permutation matrices, in terms of permutation similarity relations, which play an important role in investigating the reducible solutions of some symmetric matrix equations. We solve the three problems. First, what is the...

We study the semi-Riemannian geometry of the foliation $\mathcal{F}$ of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation $\omega =0$, provided that $\nabla \omega =0$ and $c=\parallel \omega \parallel \ne 0$ ($\omega$ is the Lee form of M). If M is conformally flat then every l...

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motion...

In this research work, we focus on the one-dimensional quaternion linear canonical transform (1-D QLCT). Under certain conditions, we first derive the symmetry property of the 1-D QLCT for real signals. The new form of the convolution theorem related...

Practical algorithms for computing canonical forms of multi-digraphs do not exist in the literature. This paper proposes two practical approaches for finding canonical forms, from the perspective of nD symbolic computation. Initially, the approaches...

In this paper, we consider various aspects of the Schur problem for a square complex matrix A, namely the similarity unitary transformation of A into upper triangular form containing the eigenvalues of A on its diagonal. Since the profound work of I....

This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermit...

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-ca...

In the paper, we transform the general Sturm–Liouville problem (SLP) into two canonical forms: one with the homogeneous Dirichlet boundary conditions and another with the homogeneous Neumann boundary conditions. A boundary shape function method...

The Weierstrass curve X is a smooth algebraic curve determined by the Weierstrass canonical form, $y^r+A_1\left(x\right)y^{r-1}+A_2\left(x\right)y^{r-2}+\cdots +A_{r-1}\left(x\right)y+A_r\left(x\right)=0$, where r is a positive integer, and each $A_j$ is a polynomial in x with a certain degree...

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal v...

The conversion between logic and algebraic expressions of Boolean control networks plays a worthy role in the analysis and design of digital circuits. In this paper, for a single Boolean function, a direct conversion between the minterm canonical for...

We develop and discuss a parameterization of vector autoregressive moving average processes with arbitrary unit roots and (co)integration orders. The detailed analysis of the topological properties of the parameterization—based on the state spa...

The integration of the HIV-1 genome into the host genome is an essential step in the life cycle of the virus and it plays a critical role in the expression, long-term persistence, and reactivation of HIV expression. To better understand the local gen...

G-quadruplexes (G4s) are unique non-canonical four-stranded nucleic acid secondary structures formed by guanine-rich DNA or RNA sequences. Sequences with the potential to form quadruplex motifs (pG4s) are prevalent throughout the genomes of all organ...

Nonlocal quantum theory of a one-component scalar field in D-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$ -matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling co...

The new adaptive fault estimation scheme is proposed for a class of hyperbolic partial differential equations in this paper. The multiplicative actuator and sensor faults are considered. There are two cases that require special consideration: (1). on...

In the era of big data and multimedia communication, securing color images against unauthorized access and attacks is a pressing challenge. While quaternion-based models provide a unified representation for color images, most existing encryption sche...

The transmission rate ($\beta \left(t\right)$) plays a crucial role in disease spread, making its measurement essential for effective control. However, existing techniques for its estimation are impractical as they rely on typically unavailable data. To address t...

This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canoni...

If $(A,B)$ is a reachable linear system over a commutative von Neumann regular ring R, a finite collection of idempotent elements is defined, constituting a complete set of invariants for the feedback equivalence. This collection allows us to construct...

We investigate a descriptor system of coupled generalized Sylvester matrix fractional differential equations in both non-homogeneous and homogeneous cases. All fractional derivatives considered here are taken in Caputo’s sense. We explain a 4-step pr...

Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the d dimensional Riemann space-time. Theory of canonical transformations, which relates equivalent Hamiltonian formulati...

For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can...

The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In this paper, we develop the method and...

In this paper, sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors for a list of complex numbers with nonnegative real part are obtained, and the corresponding nonnegative matrices are...

Examined in this paper is the Gray and Wyner source coding for a simple network of correlated multivariate Gaussian random variables, $Y_1:\Omega \to {\mathbb{R}}^{p_1}$ and $Y_2:\Omega \to {\mathbb{R}}^{p_2}$. The network consists of an encoder that produces two private rates $R_1$ a...

We present a graphical framework to represent entanglement in three-qubit states. The geometry associated with each entanglement class and type is analyzed, revealing distinct structural features. We explore the connection between this geometric pers...

This paper develops and analyzes new high-order iterative schemes for the effective evaluation of the matrix square root (MSR). By leveraging connections between the matrix sign function and the MSR, we design stable algorithms that exhibit fourth-or...

An algorithm for equivalence of linear codes over finite fields is presented. Its main advantage is that it can extract exactly one representative from each equivalence class among a large number of linear codes. It can also be used as a test for iso...

It is well known that in $\mathbb{C}\left[X\right]$, the product of two polynomials is equal to the product of their greatest common divisor and their least common multiple. In a recent paper, we proved a similar relation between the ranks of matrix polynomials. More prec...

In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model o...

In this paper, the global stabilization problem of control systems with input saturation and multiple input delays is studied, and a new method is proposed to design nonlinear stabilization control laws. First, based on Luenberger’s canonical d...

In this study, we aim to set new criteria regarding the asymptotic behavior of the neutral differential equation of the third order. These criteria are designed to ensure that this equation is oscillatory using comparisons with first-order differenti...

Presently, most of the common placement methods of actuators are based on the structural response and system energy to select the optimal locations. In these methods, the contribution of controllability and the energy of seismic excitations to each m...

This article provides a comprehensive examination of non-canonical DNA structures, particularly focusing on G-quadruplexes (G4s) and i-motifs. G-quadruplexes, four-stranded structures formed by guanine-rich sequences, are stabilized by Hoogsteen hydr...

This study is focused on the effects of the sulphur atom in position 2 of the cytosine molecule, 2-thiocytosine (2TC), on the molecular structural parameters in the isolated state, as well as in the hydration, solid state arrangement, Watson–Cr...

This study aims to establish novel iterative oscillation criteria for second-order half-linear advanced dynamic equations in non-canonical form. The results extend and enhance recently established criteria for this type of equation by various authors...

New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matric...

In the literature, Markowitz’s mean-variance model and its variants have been shown to yield portfolios that put excessive weights on only a few assets. Many diversity constraints were proposed and added to these models to avoid such overly concentra...

Nrf2 (nuclear factor erythroid 2 (NF-E2)-related factor 2) transcription factor is recognized for its pro-survival and cell protective role upon exposure to oxidative, chemical, or metabolic stresses. Nrf2 controls a number of cellular processes such...

In this study, the author attempts to analyze the canons of the Orthodox Church, which are still normative for all Orthodox Autocephalous Churches, in order to identify the image of Jews and the restrictions or prohibitions imposed by these canonical...

We show how a behavioral form of capital theory can be derived using canonical quantization. In particular, we introduce quantum cognition into capital theory by applying Dirac’s canonical quantization approach to Weitzman’s Hamiltonian f...

The quaternion linear canonical transform is an important tool in applied mathematics and it is closely related to the quaternion Fourier transform. In this work, using a symmetric form of the two-sided quaternion Fourier transform (QFT), we first de...

There have been misunderstandings regarding “narrative” in relation to games, in part due to the lack of a shared understanding of “narrative” and related terms. Instead, many contrasting perspectives exist, and this state of...

Many real-world problems have been modeled via delay differential equations. The pantograph delay differential equation $y^{\prime }\left(t\right)=ay\left(t\right)+by\left(ct\right)$ belongs to such a set of delay differential equations. To the authors’ knowledge, there are no standa...