arXiv preprints from January 1, 2026 through July 21, 2026 — 21:08:30 EST
We consider the free-boundary relativistic Euler equations in Minkowski spacetime $\mathbb{M}^{1+3}$ equipped with a physical vacuum boundary, which models the motion of a relativistic gas. We concern ourselves with the family of isentropic, barotropic, and polytropic gas, with an equation of state $p = ρ^{1+κ}, κ\in (0,\frac23]$. We...
In this paper, we have found some features of $\ast$- Ricci Bourguignon Soliton on Kenmotsu manifold. We estimated the conditions for $\ast$-Ricci Bourguignon on Kenmotsu manifold to be compressing, balancing or enlarging accordingly. We have found some curvature properties of Kenmotsu manifold admitting $\ast$-Ricci Bourguignon...
We investigate the conditions under which pseudo-Riemannian inner products induce pseudo-Riemannian algebraic Ricci solitons on four-dimensional Lie algebras. By analyzing the algebraic Ricci soliton equation for each four-dimensional Lie algebra, we obtain a complete description of when such pseudo-Riemannian algebraic Ricci solitons...
We are interested in the multiplicity of solutions to the following scalar field equation $$ -Δu - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\}. $$ We establish the existence of infinitely many radial and non-radial solutions.
This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel definitions are introduced in this work which minimize the established definitions by reducing the...
The recent discovery of a family of aperiodic monotiles, which includes David Smith's famous Hat, has shaken the field of plane tessellations. Music composers have already utilised the visual representation of plane tilings in their artwork (Tom Johnson through his use of Vuza's canons, talea and color in isorhythmic motets...)....
In this paper, we study a combinatorial Ricci flow on closed pseudo $3$-manifolds $(M,\mathcal{T})$. We prove that if every edge in the triangulation $\mathcal{T}$ has valence at least $9$, then the combinatorial Ricci flow converges exponentially fast to a hyperbolic metric. As a consequence, for any compact $3$-manifold $N$ with...
We give two new upper bounds on the covering minima of convex bodies, depending on covering minima of certain projections and intersections with linear subspaces. We show one bound to be sharp for direct sums of two convex bodies, generalizing previous results on the covering radius and lattice width of direct sums. We apply our...
We consider infinite-dimensional Bayesian linear inverse problems governed by time-dependent partial differential equations (PDEs) and develop a mathematical and computational framework for optimal design of mobile sensor paths in this setting. The proposed path optimal experimental design (path-OED) framework is established...
The first non-zero Laplace eigenvalue of a hyperbolic surface, or its spectral gap, measures how well-connected the surface is: surfaces with a large spectral gap are hard to cut in pieces, have a small diameter and fast mixing times. For large hyperbolic surfaces (of large area or large genus $g$, equivalently), we know that the...
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
We prove that homological filling functions over a ring $R$ equipped with the discrete norm are quasi-isometry invariants for all groups of type $\mathrm{FP}_n$. This confirms a conjecture of Bader-Kropholler-Vankov in the case of discrete norms. The proof uses a technique of equipping free chain complexes with a geometric structure,...
In this paper we present, for any integers $0\leq ν\leq n$, a set of inequalities satisfied by the Chern classes of any minimal complex projective variety of dimension $n$ and numerical dimension $ν$. In the cases where $ν$ is either very small or very large compared with $n$, this recovers many previously known results. We...
We introduce a new measure of coarseness for characterizing phase separation processes such as those described by Cahn--Hilliard equations. An advantage of our measure is that it remains consistent throughout the evolution, including for solutions with no periodic structure. We use our measure to compare two previous models of...
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases. Each variety encodes a collection of matroids, whose flats capture algebraic dependencies among variables. Using this approach, we provide a systematic...
We frame the Painlevè mechanical system, which has been extensively studied because of the paradox it generates, within the class of Regular Geometric Impulsive Mechanical Systems (RGIMS), by modeling it as a mechanical system subject to a rough unilateral positional constraint $\cal{S}$, where friction is represented by an...
Continuing our previous study \cite{DJKZ} on the monostable reaction-diffusion-convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the reaction term $g$ has constant sign, thereby establishing both existence and nonexistence of bistable...
Cohomological equations appear frequently in dynamical systems. One of the most classical examples is the Livšic equation $$ v(x) = α\circ F(x) - α(x).$$ The existence and regularity of its solutions $α$ is well understood when $F$ is a hyperbolic dynamical system (for instance an expanding map of the circle) and $v$ is a Hölder...
In this work, we consider solutions to (fully nonlinear) parabolic integro-differential equations with integrable interaction kernels. A typical equation would be that obtained by starting with, for $s\in(0,1)$, the $s$-fractional heat equation, but replacing the interaction kernel in the integro-differential term with one which has...
In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in situations where the inner-level problem does not have a unique solution. This has led to the...
Carbon capture and storage or utilization (CCUS) will play an important role to achieve climate neutrality in many economies. Pipelines are widely regarded as the most efficient means of CO2 transport; however, they are currently non-existent. Policy-makers and companies need to develop large-scale infrastructure under substantial...
We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we give a new proof of the uniform boundedness of $\ell$-primary torsion points on fibers of an abelian scheme over a smooth curve, a result originally...
We compute the stable Faltings height of the hyperelliptic curve $X_n\colon y^2=x^{n}-1$ for every odd integer $n\ge 3$ in terms of special values of Euler's gamma function. In particular, we prove the bounds $$-0.975n< h_{\mathrm{Fal}}(X_n)-\tfrac{n}{8}\log n<\tfrac{9}{64}n\log\log n-0.263n.$$ As an application, we bound the Faltings...
Let $R = W(k)$ be the ring of Witt vectors over an algebraically closed field $k$ of characteristic $p > 2$. Let $M$ be a three-dimensional regular integral flat projective $R$-scheme such that $H^0(M,\mathcal{O}_M) = R$ and the anticanonical sheaf $ω_M^{-1}$ is ample. We show that $M$ is globally $+$-regular if the closed fiber $M_k$...
We show that for $\gg K^2$ of the half-integral weight Hecke cusp forms in the Kohnen plus subspaces with weight bounded by a large parameter $K$, the number of "real" zeroes grows at the expected rate. A key technical step in the proof is to obtain sharp bounds for the mollified first and second moments of quadratic twists of modular...