Related papers: The Zero-Difference Properties of Functions and Th…

We prove that, for any closed semialgebraic subset $W$ of $\mathbb{R}^n$ and for any positive integer $p$, there exists a Nash function $f:\mathbb{R}^n\setminus W\longrightarrow (0, \infty)$ which is equivalent to the distance function from…

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this…

We apply the Schrodinger functional method to the Abelian gauge theory in three dimensions with Nf=2 four-component fermions. We find that the calculated beta function does not cross zero in the range of coupling we study. This implies that…

Let $0<\alpha<d$ and $1\leq p<d/\alpha$. We present a proof that for all $f\in W^{1,p}(\mathbb{R}^d)$ both the centered and the uncentered Hardy-Littlewood fractional maximal operator $\mathcal M_\alpha f$ are weakly differentiable and $…

Let $W_{\beta}(\alpha,\gamma)$, $\beta<1$, denote the class of all normalized analytic functions $f$ in the unit disc ${\mathbb{D}}=\{z\in {\mathbb{C}}: |z|<1\}$ such that \begin{align*} {\rm Re\,}…

Given Boolean functions \( f, g : \mathbb{F}_2^n \to \{-1,+1\} \), we say they are {\em linearly isomorphic} if there exists \( A \in \mathrm{GL}_n(\mathbb{F}_2) \) such that \( f(x)=g(Ax) \) for all \( x \). We study this problem in the…

Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of…

Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

For the family of analytic functions $f(z)$ in the open unit disk $\mathbb{D}$ with $f(0)=f'(0)-1=0$, satisfying the differential equation \begin{equation*} zf'(z) - f(z) = \dfrac{1}{2} z^2 \phi(z), \quad |\phi(z)| \leq 1, \end{equation*}…

Kochol introduced the assigning polynomial $F(G,\alpha;k)$ to count nowhere-zero $(A,b)$-flows of a graph $G$, where $A$ is a finite Abelian group and $\alpha$ is a $\{0,1\}$-assigning from a family $\Lambda(G)$ of certain nonempty vertex…

Control barrier functions provide a powerful means for synthesizing safety filters that ensure safety framed as forward set invariance. Key to CBFs' effectiveness is the simple inequality on the system dynamics: $\dot{h} \geq - \alpha(h)$.…

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…

De Bruijn and Newman introduced a deformation of the completed Riemann zeta function $\zeta$, and proved there is a real constant $\Lambda$ which encodes the movement of the nontrivial zeros of $\zeta$ under the deformation. The Riemann…

A Lie algebra $L$ over a field $\mathbb{F}$ is said to be zero product determined (zpd) if every bilinear map $f:L\times L\to \mathbb{F}$ with the property that $f(x,y)=0$ whenever $x$ and $y$ commute is a coboundary. The main goal of the…

An expansion in the number of spatial covariant derivatives is carried out to compute the $\zeta$-function regularized effective action of 2+1-dimensional fermions at finite temperature in an arbitrary non-Abelian background. The real and…

The generalised Gegenbauer functions of fractional degree (GGF-Fs), denoted by ${}^{r\!}G^{(\lambda)}_\nu(x)$ (right GGF-Fs) and ${}^{l}G^{(\lambda)}_\nu(x)$ (left GGF-Fs) with $x\in (-1,1),$ $\lambda>-1/2$ and real $\nu\ge 0,$ are special…

Let $G$ be an additive group of order $v$. A $k$-element subset $D$ of $G$ is called a $(v, k, \lambda, t)$-almost difference set if the expressions $gh^{-1}$, for $g$ and $h$ in $D$, represent $t$ of the non-identity elements in $G$…

We study the correctness of automatic differentiation (AD) in the context of a higher-order, Turing-complete language (PCF with real numbers), both in forward and reverse mode. Our main result is that, under mild hypotheses on the primitive…

The Feistel Boomerang Connectivity Table (FBCT) was proposed as the feistel counterpart of the Boomerang Connectivity Table. The entries of the FBCT are actually related to the second-order zero differential spectrum. Recently, several…