arXiv preprints from January 1, 2026 through July 20, 2026 — 23:07:06 EST
This paper aims to investigate a Harnack inequality for non-negative solutions of the normalized infinity Laplacian with nonlinear absorption and gradient terms. More specifically, we establish a Harnack inequality for non-negative viscosity solutions of the PDE $Δ_\infty^Nu=f(u)+g(u)|Du|^q$, where $0\le q\le 1$, and for a large class...
Chemical reaction networks are a widely accepted modeling framework for diverse science phenomena stemming from all disciplines of science, such as biochemistry, ecology, epidemiology, social and political science. In this paper we prove that every first order endotactic stochastic mass-action reaction system (SMART) is essential...
We define a grid graph $G$ as a Cartesian product of path-graphs $P_n$ or cycle-graphs $C_n$ as shown in Figure 1, and we ask, when can the edge set of a complete graph be expressed as a disjoint union of graphs isomorphic to $G$? That is, we are asking for which grid graphs a $G$-design exists, where a $G$-design is defined as a...
We present an NPT extension of Ewald summation with prolates (ESP), a spectrally accurate and scalable particle-mesh method for molecular dynamics simulations of periodic, charged systems. Building on the recently introduced ESP framework, this work focuses on rigorous and thermodynamically consistent pressure/stress evaluation in the...
Using Watt's mean value theorem and a delicate sieve decomposition, the author shows that the interval $[x, x+x^{\frac{1}{2}+\varepsilon}]$ contains an integer with a prime factor larger than $x^{\frac{35}{36}-\varepsilon}$ for sufficiently large $x$. This gives a solution with $γ= \frac{1}{36}$ to the Exercise 5.1 in Harman's...
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schrödinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle and a finite number $N$ of infinite half--lines attached to a common vertex. The model is endowed...
We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth projective surface. Having fixed the Chern character of E, the resulting moduli space is isomorphic to some subscheme of the Quot-scheme parametrising...
We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and Marchand for the dissipative SQG equation are not necessarily unique. Second, this establishes...
Pisier's celebrated counterexample to Halmos's similarity-to-contractions problem was based on $2 \times 2$ upper triangular block operator matrices involving three classical operators: forward and backward shifts on the diagonal and Hankel operators in the off-diagonal entry. Together with another classical object, namely Toeplitz...
In this article, we study the fixed-point subgroups of the solvable Baumslag-Solitar groups $\BS(1,n)= \langle a, t \mid t a t^{-1} = a^{n} \rangle$, $n>1$ of automorphisms and endomorphisms. We also investigate the stabilizers of subgroups of $\BS(1,n)$, considered as subgroups of the group of automorphisms and submonoids of the...
In this paper we study parameter-dependent structured moment matrices with a canonical block form arising from weighted quadratic histopolation on simplicial meshes. For a strictly positive density on a simplex, we construct compatible face densities and an orthogonal decomposition of the quadratic polynomial space into face and...
In this paper, we introduce multiple zeta dagger values and special values of Carlitz multiple dagger polylogarithms, and study their properties. In particular, using these values, we construct a non-trivial involution on a certain quotient space of multiple zeta values in positive characteristic.
We establish improved bounds for bilinear forms with Kloosterman fractions of the form ${\sum\sum}_{m,n} α_m β_n e(a\overline{m}/(bn))$ with $M<m\le 2M$, $N < n \le 2N$ and $(m,n)=1$. Our approach works directly with arbitrary coefficient sequences $(α_m), (β_n) \in \mathbb{C}$, avoiding the temporary restriction to squarefree support...
A popular question in Bernoulli percolation models is if the probability of connection between two vertices in a transitive graph decays monotonically with the distance between these two vertices. For example, on the square lattice is an open question to prove that the probability of the origin being connected to the vertex $(0,n)$ is...
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic continuity of operators from ordered Frechet spaces to topological vector spaces are included. Levi and Lebesgue operators especially are investigated.
This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information...
In our earlier work, we studied the link surgery modules of two component L-space links. Therein, we computed two of the four idempotents of such modules. In this article, we use Koszul duality to give an alternate account of this proof, and also to extend it to compute the entire link surgery modules of such links, modulo a technical...
This text contains some notes on the Griesmer bound. In particular, we give a geometric proof of the Griesmer bound for the generalized weights and show that a Solomon--Stiffler type construction attains it if the minimum distance is sufficiently large. We also determine the parameters of optimal binary codes for dimensions at most...
We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of the resulting module decomposition, we establish a general result on fusion rules for commutant...
A series of vertex operator algebras are constructed by GKO-construction, which is a generalization of 3A-algebra and 6A-algebra. It is proved their vertex operator algebra structures are unique under nonzero assumptions on some elements of braiding matrices. Furthermore, we show each of them is generated by weight two subspace,...
We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.
The convexity number of a set $X \subset \mathbb{R}^2$ is the minimum number of convex subsets required to cover it. We study the following question: what is the largest possible convexity number $f(n)$ of $\mathbb{R}^2 \setminus S$, where $S$ is a set of $n$ points in general position in the plane? We prove that for all $n \geq 4$,...
We consider general bilinear products defined by positive semidefinite matrices. Typically non-commutative, non-associative, and non-unital, these products preserve positivity and include the classical Hadamard, Kronecker, and convolutional products as special cases. We prove that every such product satisfies a sharp nonzero lower...
We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori error estimation purposes. Our numerical lower bound is...
We study nonlinear determination problems in Hilbert spaces in which inner products are observed up to prescribed rotations in the complex plane. Given a Hilbert space $H$ and a subset $Θ$ of the unit circle $\mathbb{T}$, we say that a system $\mathbf{G}\subseteq H$ does $Θ$-phase retrieval ($Θ$-PR) if for all $f,h\in H$ the condition...