arXiv preprints from January 1, 2026 through September 22, 2026 — 02:16:28 EST
Purpose: The model allocates the system components orders to the suppliers to minimize the parts price and the system construction delay penalties and maximize the system availability during its use. It considers the quantity-based discount and variation of delivery lead time by ordering similar components. The model also reflects the...
We study null controllability for linear heat-type systems in finite dimensions that incorporate both memory and time-delay effects. A strengthened notion of controllability, referred to as delay and memory-type null controllability, is introduced, which requires the state, the memory functional, and the delayed history to vanish at...
We consider parabolic variational inequalities in a Hilbert space $V$, which have a non-monotone nonlinearity of Navier--Stokes type represented by a bilinear operator $B: V \times V \to V'$ and a monotone type nonlinearity described by a convex, proper, and lower-semicontinuous functional $\varphi : V \to (-\infty, +\infty]$....
The three dimensional primitive equations with full viscosity are considered in a horizontally periodic box $Ω$, which are subject to either the homogeneous Neumann or Dirichlet conditions on the upper and bottom parts of the boundary. For a strong solution $v$ with initial data $a$, we establish \emph{a priori} bounds in $L^\infty(0,...
The aim of this paper is to improve the compactness of the multilinear commutators in Morrey spaces generated by VMO functions and fractional integral operators. In this paper, we will use the decomposition of the tilde closed subspaces of Morrey spaces. This gives us more understanding about commutators.
A line multigraph is obtained from a hypergraph as follows: the vertices of the multigraph correspond to the hyperedges of the hypergraph, and the number of edges between two vertices is given by the number of vertices shared by the corresponding hyperedges. In this paper, we establish several structural and spectral properties of...
A Roman dominating function of a graph $G=(V,E)$ is a labeling $f: V \rightarrow{} \{0 ,1, 2\}$ such that for each vertex $u \in V$ with $f(u) = 0$, there exists a vertex $v \in N(u)$ with $f(v) =2$. A Roman dominating function $f$ is a global Roman dominating function if it is a Roman dominating function for both $G$ and its...
For a tuple $A=(A_0,A_1,\cdots,A_n)$ of elements in a Banach algebra $\mathfrak{B}$, its projective (joint) spectrum $p(A)$ is the collection of $z\in \mathbb{P}^n$ such that $A(z)=z_0A_0+z_1A_1+\cdots+z_nA_n$ is not invertible. If $\mathfrak{B}$ is the group $C^*$-algebra for a discrete group $G$ generated by $A_0, A_1,\dots, A_n$...
In this paper, we present and prove that the coefficients $u_n$ and $v_n$ in the series expansions $F^2(a,b;c;z) = \sum_{n=0}^\infty u_n z^n$ and $F^3(a,b;c;z) = \sum_{n=0}^\infty v_n z^n$ ($a,b,c,z \in \mathbb{C}$ and $-c \notin \mathbb{N} \cup \{0\}$) satisfy second- and third-order linear recurrence relations, respectively, where...
The Emergent Order Spectrum $Ω(x,y)$ is a topological invariant of dynamical systems providing order-types induced by the limit order of order-compatible nested $\varepsilon_n$-chains (with $\varepsilon_n\to 0$) from $x$ to $y$. In this paper, we investigate how rich these spectra can be under natural dynamical hypotheses. For a...
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically suited to continuous stochastic volatility models. Our approach accommodates both small...
In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance, in the case of a bone tumor in a femur) initial colony. In particular we derive and study a new weakly nonlinear asymptotic model of multilayer tumor...
We study the tail behavior of Markov-modulated generalized Ornstein-Uhlenbeck processes -- that is, solutions to Langevin-type stochastic differential equations driven by a background continuous-time Markov chain. To this end, we consider a sequence of Markov modulated random affine functions $ Ψ_{n} : \mathbb{R} \to \mathbb{R} $, $ n...
We study a class of mean-field control problems under partial observation. The controlled dynamics are of McKean-Vlasov type and are subject to regime switching driven by a hidden Markov chain. The observation process depends on the control and on the joint distribution of the state and control, which prevents the direct application...
We show that a certain triangulation of CAT(0) triangle-pentagon complexes is $7$-located and locally $5$-large. Hereby we give examples of $7$-located, locally $5$-large groups.
In this paper, we introduce a new infinite-dimensional Lie superalgebra $\mathcal{S}$ called the super extended Ovsienko--Roger algebra. This algebra is obtained by determining the annihilation superalgebra of the Lie conformal superalgebra $S=S_{\bar0}\oplus S_{\bar{1}}$ with...
In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating $ζ(s)-ψ(1-s)$ as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary...
In this note, we characterize affine and non-affine Coxeter systems among all Coxeter systems in terms of the structure of their reflection orders. For an infinite irreducible system $(W,S)$, we show that affineness can be characterized in three equivalent ways: by the scatteredness of all reflection orders, by the existence of a...
We construct explicit examples of really perverse central configurations in the spatial Newtonian $N$-body problem. A central configuration is called really perverse if it satisfies the central configuration equations for two distinct mass distributions having the same total mass. While such configurations were previously known only...
This article develops a self-contained affine $Γ$-scheme theory for a class of commutative ternary $Γ$-semirings. By establishing all geometric and spectral results internally, the work provides a unified framework for triadic symmetry and spectral analysis. The central thesis is that a triadic $Γ$-algebra canonically induces two...
Given a graph $F$, the $r$-expansion $F^r$ of $F$ is the $r$-uniform hypergraph obtained from $F$ by inserting $r-2$ new distinct vertices in each edge of $F$. Given $r$-uniform hypergraphs $\mathcal{H}$ and $\mathcal{F}$, the generalized Turán number, denoted by $\textrm{ex}_r(n,\mathcal{H},\mathcal{F})$, is the maximum number of...
In recent years, several efforts have focused on identifying new families of scattered polynomials. Currently, only three families in $\mathbb{F}_{q^n}[X]$ are known to exist for infinitely many values of $n$ and $q$: (i) pseudoregulus-type monomials, (ii) Lunardon-Polverino-type binomials, and (iii) a family of quadrinomials studied...
We show that a bilinear radial Fourier multiplier operator with symbol $σ$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $σ$ satisfies the smoothness condition $σ(2^j\cdot)Φ\in L^2_{1/2 +ε}(\mathbb R^{2n})$ for some $ε>0$ and every $j\in \mathbb Z,$ where $Φ$ is a smooth cutoff function...
The shape of a number field $K$ of degree $n$ is defined as the equivalence class of the lattice of integers with respect to linear operations that are composites of rotations, reflections, and positive scalar dilations. The shape is a point in the space of shapes $\mathscr{S}_{n-1}$, which is the double quotient...
Let $[\, x\,]$ denote the integer part of a real number $x$. Assume that $λ_1,λ_2,λ_3$ are nonzero real numbers, not all of the same sign, that $λ_1/λ_2$ is irrational, and that $η$ is real. Let $\frac{219}{220}<γ<1$ and $θ>0$. We establish that, there exist infinitely many triples of primes $p_1,\, p_2,\, p_3$ satisfying the...