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It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…

In this paper, we propose binary sparse convolutional networks called BSC-Net for efficient point cloud analysis. We empirically observe that sparse convolution operation causes larger quantization errors than standard convolution. However,…

We study conformal boundary conditions and corresponding one-point functions of the N=2 super-Liouville theory using both conformal and modular bootstrap methods. We have found both continuous (`FZZT-branes') and discrete (`ZZ-branes')…

We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…

Close binary stars are binary stars where the component stars are close enough such that they can exchange mass and/or energy. They are subdivided into semi-detached, overcontact or ellipsoidal binary stars. A challenging problem in the…

Given a commutative ring with identity $R$, many different and interesting operations can be defined over the set $H_R$ of sequences of elements in $R$. These operations can also give $H_R$ the structure of a ring. We study some of these…

We define the notion of a 2-operad relative to an operad, and prove that the 2-associahedra form a 2-operad relative to the associahedra. Using this structure, we define the notions of an $(A_\infty,2)$-category and $(A_\infty,2)$-algebra…

Building upon specific compatibility conditions, we establish fundamental structural results concerning ordering relations for triangular fuzzy numbers. We demonstrate that orders satisfying compatibility with arithmetic operations, MIN-MAX…

We revisit and extend known bounds on operator-valued functions of the type $$ T_1^{-z} S T_2^{-1+z}, \quad z \in \ol \Sigma = \{z\in\bbC\,|\, \Re(z) \in [0,1]\}, $$ under various hypotheses on the linear operators $S$ and $T_j$, $j=1,2$.…

We define a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. We study commutativity, cancellativity and associativity of this operation. We focus on rigid irreducible components and discuss…

In this notes unbounded regular operators on Hilbert $C^*$-modules over arbitrary $C^*$-algebras are discussed. A densely defined operator $t$ possesses an adjoint operator if the graph of $t$ is an orthogonal summand. Moreover, for a…

In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…

Let $U:[0,\infty)^2 \to [0,\infty)$ be a~measurable kernel satisfying: (i) $U(x,y)$ is nonincreasing in $x$ and nondecreasing in $y$; (ii) there exists a~constant $\theta>0$ such that $U(x,z) \le \theta\left( U(x,y)+U(y,z) \right)$ for all…

Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some…

The goal of binary classification is to estimate a discriminant function $\gamma$ from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available…

We study a family of unbounded solutions to the Korteweg-de Vries equation which can be constructed as log-derivatives of deformed Airy kernel Fredholm determinants, and which are connected to an integro-differential version of the second…

Let $D$ be an integral domain with quotient field $K$. A star-operation $\star$ on $D$ is a closure operation $A \longmapsto A^\star$ on the set of nonzero fractional ideals, $F(D)$, of $D$ satisfying the properties: $(xD)^\star = xD$ and…

This paper discusses the convexity of the range of the Berezin transform. For a bounded operator $T$ acting on a reproducing kernel Hilbert space $H$ (on a set $X$), this is the set $B(T) : = \{ < Tk_x, k_x >_H : x \in X \}$, where $k_x$ is…

A Conway semiring is a semiring $S$ equipped with a unary operation $^*:S \to S$, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally…

Let $A$ be a closed densely defined operator on a separable Hilbert space $\mathcal{H}$. Assume the resolvent set $\rho(A)$ is non-empty. For $z,z'\in\rho(A)$ let $[z,z']$ denote the straight line segment from $z$ to $z'$. For each…