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This paper asks which parts of the standard Zadeh truth-value algebra can be represented by normalized positive physical contents from Newtonian mechanics, Schrödinger quantum mechanics, perturbative string theory, selected M2/M5-brane sectors o...

Learning-based distribution system state estimation (DSSE) predictors trained with the squared loss estimate the conditional mean of the state given the measurements. Under contaminated measurements, the conditional mean shifts, and the unbounded inf...

Physics-informed neural networks (PINNs) provide a framework for approximating solutions of partial differential equations (PDEs), but their accuracy depends on the input representation and optimization procedure. We investigated a Legendre-expanded...

We study non-negative solutions to the reciprocal cost law on positive rationals and determine which of them admit regular extensions to positive reals. Using the substitution $H=1+F$, we reduce the reciprocal composition law to d’Alembert’...

For a graph G, let $V\left(G\right)$ and $E\left(G\right)$ denote its vertex and edge sets, and put $n=\left|V\right(G\left)\right|$ and $m=\left|E\right(G\left)\right|$. For a supereulerian graph G, let $\ell \left(G\right)$ be the maximum number of edges in a spanning Eulerian subgraph of G. Haghparast and Kiani proved that each si...

This paper investigates null-framed curves in Minkowski 3-space with particular emphasis on curves admitting singular points. The null-framed structure is defined by choosing u and $\psi$ as null vector fields and v as a spacelike vector field. An add...

Quasilinear hyperbolic conservation law equations are of great significance in mathematical physics. Characterizing their meromorphic solutions provides valuable insight into the qualitative behaviors of these equations. In this paper, we investigate...

Cozero-divisor graphs ${\Gamma }^{\prime }\left({\mathbb{Z}}_n\right)$ have been studied from structural, combinatorial and spectral points of view. The edge ideals they define appear to have received much less attention, and the purpose of this paper is to begin their homologica...

Motivated by call center systems, we investigate the optimal admission control problem for a retrial queueing system with multiple customer classes. Arrivals follow independent Poisson processes, service times are exponentially distributed, and the d...

We develop two-sided, order-free bounds for the Sylvester matrix differential equation $\dot{X}\left(t\right)=AX\left(t\right)+X\left(t\right)B+C,X\left(t_0\right)=X_0,$ allowing rectangular and nonsymmetric solutions. We derive upper and lower bounds for each singular value of $X\left(t\right)$. A Dini-deriva...

This paper develops a class of anisotropic spaces of eight-dimensional numbers with real components. Starting from a general bilinear multiplication law, we impose commutativity and associativity and derive the resulting relations among the structure...

We investigate the finite ultrametric spaces $(X,d)$ that have a given cardinality of the center of distances and a minimal cardinality of the set X. It is shown that such spaces are isometric if and only if their centers of distances are the same. The...

This paper investigates refined Hardy-type inequalities on time scales associated with nonnegative kernels and superquadratic functions. Starting from a generalized Hardy operator, we derive an inequality involving explicit remainder terms through a...

We investigate gradient $\rho$-Einstein solitons and quasi-Yamabe solitons on $\eta$-Einstein para-Kenmotsu manifolds, with particular emphasis on the Zamkovoy and Schouten–van Kampen connections. For gradient $\rho$-Einstein solitons, we derive a...

Scalar centrality measures assign one score to each sector of a production network and cannot compare its exposure to two shock sources. We develop a matrix-algebraic framework for this comparison. The Asymmetry Multiplier ${\gamma }_j(\alpha ,\beta )=L_j^{}$...

This study extends our previous investigations of $(\overline{m},m)$-conformal mappings. While the earlier studies were primarily theoretical and included only limited applications, the present study focuses on the applicability of these mappings to problem...

The generalized-$c\mu$ (G$c\mu$) rule is asymptotically optimal for a single multiclass queue with convex delay costs, no setups and traffic intensity near one. We ask what it is worth when used only at the bottleneck of a job shop with sequence-depend...

The Yang–Baxter equation is one of the most celebrated equations in science. There exist some correspondences between Yang–Baxter operators and Hopf algebras. For example, the quasitriangular Hopf algebras are used to define ribbon Hopf a...

Motivated by sparse principal component analysis (PCA), this paper proposes ATE-ManPG, a safeguarded transport-extrapolated proximal gradient method for minimizing the sum of a smooth function and a convex, possibly nonsmooth function over the Stiefe...

This work addresses the issue of robust iterative learning tracking for heterogeneous multi-agent systems in the presence of random impulsive disturbances. Unlike existing literature focusing solely on bounded deterministic impulsive perturbations, t...

In this paper, we introduce a generalized $(\epsilon$-$\delta )$-type contractive condition and develop a unified framework that extends a wide spectrum of classical fixed-point results for self-mappings in complete metric spaces, with or without contin...

We formulate an Information-Geometric Grammar Principle (IGGP) for adaptive systems in which grammatical admissibility, probabilistic realization, and statistical geometry are treated as distinct but connected levels of description. A grammar is repr...

Let $\mathsf{Q}$ be an integral, commutative quantale with a completely distributive underlying lattice. It is known that there is a one-to-one correspondence between the category of quantale-valued tolerance spaces and tolerance-preserving mappings, denoted by...

For a connected graph, the Fermat difference of three vertices is defined as the minimum sum of their distances to a common vertex minus half the sum of their pairwise distances. In this paper, we investigate the average Fermat difference of unicycli...

We study a parameterized SOR-like (PSOR-like) representation of the parameterized inexact Uzawa (PIU) iteration for generalized saddle point systems. An explicit parameter change establishes equivalence to PIU with an exact first-block solve, and to...

The present article is mainly concerned with radius problems for a newly defined subclass of meromorphic starlike functions having the punctured open unit disk as its domain. This subclass is introduced by using differential subordination with the ge...

The article examines alpha-rhythm spindles. The importance of studying alpha rhythm spindles for improving the reliability of nervous system diagnostics is substantiated. The analysis employs a mathematical framework based on the Hilbert transform as...

$\mu$–$\tau$ flavor reflection symmetry (RS) of the PMNS mixing matrix implies $|U_{\mu i}| = |U_{\tau i}|$, leading to the atmospheric mixing angle ${\theta }_{23}={45}^{°}$ and maximal Dirac CP violation phase, ${\delta }_{\mathrm{CP}}=\pm {90}^{°}$. Here, we est...

A dense $G_{\delta }$ subset of a Polish group is large in the sense of Baire category. We study a configuration consequence of this largeness. If G is a Polish abelian group, $R\subseteq G$ is dense $G_{\delta }$, and $A\subseteq G$ is countable, then the set of translat...

We establish several upper bounds for the Berezin number and Berezin norms of products of three bounded operators. Let $({\mathcal{H}}_{\mathrm{\Gamma }},⟨·,·⟩)$ be a reproducing kernel Hilbert space (RKHS) on a set $\mathrm{\Gamma }$ with inner product $f$...

We study bias-corrected empirical-likelihood inference for single-index expectile regression when responses are missing at random. Local-linear expectile estimation is combined with conditional centering to construct three procedures based on complet...

Gamma models are natural for positive, right-skewed quality characteristics and grouped time-between-event observations. Fixed Gamma cumulative sum (CUSUM) charts can detect persistent scale changes, but their deployed performance depends on the in-c...

We further develop Kernel Quantum State Estimation (KQSE), a fully data-driven nonparametric method for continuous variable quantum state reconstruction and characterization, introduced in our recent work and rooted in nonparametric kernel density es...

In this paper, a second-order implicit difference scheme for the time-fractional subdiffusion equation is constructed using a corrected L1 approximation of the fractional derivative. Estimates for the generating functions and resolvent coefficients a...

Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney sum, it is...

In this research paper, we develop a relation-theoretic $\Phi$-contraction framework in multiplicative metric spaces. We introduce the concept of a relation-theoretic $\Phi$-contraction, in which the contractive condition is imposed only on pairs satis...

Secondary infections and reactivation of latent pathogens pose prominent public-health challenges in the post-pandemic era. To account for spatiotemporal heterogeneity, host relapse transitions, and the coupling of multi-stage infection processes, th...

We compute the generalized noncommutative Castelnuovo-Mumford regularity of irreducible highest-weight modules over the Virasoro algebra Vir. Working over the graded negative universal enveloping algebra $A=U\left({\mathfrak{n}}_{-}\right)\subset U(Vir)$ equipped with the lev...

This paper develops a unified framework for continuous distributional characterizations based on conditional expectations of functions of a random variable. The proposed framework expresses several characterization identities through a single differe...

The averaged Gauss–Radau quadrature rule assigns equal weights to the left and right Gauss–Radau formulas regardless of the behavior of the integrand. This choice is generally not optimal for integrands possessing algebraic endpoint singu...

This paper investigates a mixed Volterra–Fredholm integral equation of the first kind involving a hypergeometric spatial kernel and a continuous Volterra kernel in time. The analysis is formulated in an admissible even spatial space: the unweig...

This paper investigates optimal resource allocation in multi-agent networks subject to simultaneous measurement and communication delays. We propose a distributed stochastic extremum seeking (SES) algorithm for connected undirected graphs with hetero...

The present work is concerned with a class of biharmonic elliptic equations involving critical and singular nonlinearities. Under the assumption that $p\left(x\right)$ attains its global maximum at some point, we derive that the problem admits a mountain pass typ...

Clausen’s series ₃F₂$(a,b,c;d,e;1)$, a generalized hypergeometric series with three numerator and two denominator parameters taken at unit argument, has classical closed forms when its denominator parameters exceed two of its numerator parameters by in...

The Shortest Vector Problem (SVP) is the computational foundation of lattice-based cryptography, and its hardness on structured lattices directly impacts the security of NIST-standardized schemes such as Kyber and Dilithium. This paper investigates t...

In this paper, we investigate robust model averaging for high-dimensional data with outlier contamination. Most existing model averaging methods rely on ordinary least squares (OLS) estimation and are therefore highly sensitive to outliers. Moreover,...

In this paper, we develop an operator-based framework for laser–plasma interactions, providing a compact and systematic description of the coupled dynamics of laser fields and plasma response, with particular relevance to laser wakefield accele...

This paper investigates the oscillatory behavior of second-order noncanonical neutral differential equations involving a neutral term with continuous delay and distributed deviating arguments. The main contribution is the establishment of a new and s...

We study estimation of the integrated squared latent density from two measurements per subject with independent, unknown measurement errors. The error distributions may differ and need not be symmetric or centered, but their characteristic functions...

In this paper, we generalize the notions of pure derived and pure singularity categories by introducing $\mathcal{X}$-pure derived and $\mathcal{X}$-pure singularity categories for a module class $\mathcal{X}$ satisfying suitable conditions. We prove that the main classical results for...