Research
Research
Research
Research
3,759+ open-access research outputs.
We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ exhibits long-range checkerboard order at sufficiently high temperature. The model ha…
The reciprocality means a duality in Kirchberg algebras between K-theory groups and strong extension groups. In the paper, we will find a certain class of unital simple Exel--Laca algebras for which t…
We develop a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly i…
Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of c…
This paper presents various transcendence results in the ring of integers modulo infinitely large primes $\mathcal{A}$. In the ring $\mathcal{A}$, one can consider two notions of transcendence. One is…
We present a uniform framework for constructing $3$-designs from $\mathrm{GL}_2(\mathbb F_q)$-invariant subspaces of $\mathbb F_q[X,Y]_k$, the space of homogeneous polynomials of degree $k$. Given suc…
We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant …
Let $U$ be a Lucas sequence, $p$ be prime, and $\rho_U(p)$ be the rank of appearance of $p$ in $U$. We derive closed-form formulas for the Dirichlet density of primes $p$ for which $d\mid \rho_U(p)$, …
This study presents a mathematical optimization framework and preliminary analysis for long-term investment planning in Puerto Rico's electric power system. We develop a high-resolution capacity expan…
We study the set $S(q)$ of residue classes $r$ modulo the Pisano period $\pi(q)$ for which $q \mid \varphi(F_m)$ for every $m \equiv r \pmod{\pi(q)}$. We prove that if $q$ is a Sophie Germain prime an…
Oriented cohomology theories provide a general framework to perform intersection-theory-type calculus. The Chow ring, algebraic $K$-theory, and Levine--Morel's algebraic cobordism are all instances of…
Here we report the spectroscopic and geometric confirmation of an extremely bright ($i=14.77$) and compact (Einstein radius of $\sim0.45''$) quadruply-lensed quasar at $z=2.22$, J1330$-$0905, which we…
The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dyna…
In our paper [Tak6], we constructed eight families of quasi-smooth prime $\mathbb{Q}$-Fano threefolds, anticanonically embedded in codimension four, using weighted projectivizations of the $14$-dimens…
Large Foundation Model (LFM) inference is both memory- and compute-intensive, traditionally relying on GPUs. However, the limited availability and high cost have motivated the adoption of high-perform…
Non-commutative crepant resolutions (NCCRs) are non-commutative versions of classical crepant resolutions in algebraic geometry. For 3-dimensional terminal Gorenstein singularities Iyama and Wemyss pr…
In this work we develop exact formulas to the number of solutions of $ax+by+cz=n$ in some special cases. In 2020, Binner gave a formula for the number of non negative integer solutions, $N(a,b,c;n)$ i…
The use of free energy perturbation (FEP) methods to study protein-ligand complexes is one of the most important tools in structure-based drug design. Because FEP methods typically rely on force field…
In this paper, we prove that for any weak Del Pezzo surface $S$ of degree at least $4$, the tangent bundle $T_S$ is almost nef. For the proof, we use total dual VMRTs induced by conic bundle structure…
The Lucas sequences are integers defined by a homogeneous recurrence relation. They include the well-known Fibonacci numbers, which appear abundantly in nature. The complementary Lucas numbers, define…
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