Research
Research
Research
Research
443+ open-access research outputs.
The spectral kernel field equation R[k] = T[k] lacks a conservation-law analog. We prove (i) the fixed-point flow is strictly volume-expanding (tr DF > 0), precluding automatic conservation, and (ii) …
We compare two classes of polynomial automorphisms, strongly nilpotent and Pascal finite. We conclude that every strongly nilpotent automorphism is a Pascal finite one, but not vice versa. We observe …
In this paper, we extend the concept of a Lascar generic automorphism in the setting of models of Peano arithmetic ($\mathrm{PA}$) to the subgroup of the automorphism group of a countable recursively …
We discuss spacetime singularities of a solution to the Schr\"odinger equation with a metric perturbation and a sublinear potential. The quasi-homogeneous wave front set, due to Lascar (1977), of a so…
The main purpose of this note is to provide an elementary discussion of some simple triangles of integer numbers in particular through their connections with representation theory of $sl_2$. The trian…
Decorated cospans provide a categorical framework for composing open systems along shared interfaces. This paper is a computational proof of concept: we show that the framework produces a working coup…
We compare the classifying anima of two natural condensed $\infty$-categories associated to a coherent $\infty$-topos. One from our work with Barwick and Glasman on exit-path categories in algebraic g…
This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boole…
Rainfall is associated with the outbreak of certain waterborne faecal-oral diseases, driving the implementation of various human interventions for their control and prevention. Taking into account hum…
We discuss propagation of space-time singularities for the quantum harmonic oscillator with time-dependent metric and potential perturbations. Reformulating the quasi-homogeneous wave front set accord…
We study the Pascal determinantal arrays $\PD_k$, whose entries $\PD_k(i,j)$ are the $k\times k$ minors of the lower-triangular Pascal matrix $P=( \binom{a}{b} )_{a,b\ge 0}$. We prove an exact facto…
We investigate the dimension dependence of Bramble--Pasciak--Xu (BPX) preconditioners for high-dimensional partial differential equations and establish that the condition numbers of BPX-preconditioned…
Various spaces of symmetries of a structure are naturally endowed with both an algebraic and a topological structure. For example, the automorphism group of a structure is, on top of being a group, a …
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares tensors, the CPB tenso…
For an $(n\ge 2)$-dimensional real Banach space $E$ with unit ball $E_{\le 1}$ and a topological space $X$ arbitrary elements in $C(X,E_{\le 1})$ are always expressible as linear combinations of at mo…
This work investigates the vertical quantum cohomology and quantum spectra of flag bundles, uncovering new links between the Gromov-Witten theory of homogeneous fibrations and analytic number theory. …
We say a sequence $f_0, f_1, f_2, \ldots$ of symmetric functions is Schur log-concave if $f_n^2 - f_{n-1}f_{n+1}$ is Schur positive for all $n\ge1$. We conjecture that a very general class of sequence…
We establish a local $\mathcal{O}(k^{-2})$ rate for the gradient update $x^{k+1}=x^k-\nabla f(x^k)/\sqrt{H\|\nabla f(x^k)\|}$ under a $2H$-Hessian--Lipschitz assumption. Regime detection relies on Hes…
A nonempty set $F$ is Schreier if $\min F\ge |F|$. Bird observed that counting Schreier sets in a certain way produces the Fibonacci sequence. Since then, various connections between variants of Schre…
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