Related papers: A classification of nonzero skew immaculate functi…

We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…

Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…

In this article we introduce the notion of Floer function which has the property that the Hessian is a Fredholm operator of index zero in a scale of Hilbert spaces. Since the Hessian has a complicated transformation under chart transition,…

We first show that a continuous function f is nonnegative on a closed set $K\subseteq R^n$ if and only if (countably many) moment matrices of some signed measure $d\nu =fd\mu$ with support equal to K, are all positive semidefinite (if $K$…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

We consider estimation of a functional of the data distribution based on i.i.d. observations. We assume the target function can be defined as the minimizer of the expectation of a loss function over a class of $d$-variate real valued cadlag…

In this paper we determine a class of admissible matrices which are the Hilbert functions of some 0-dimensional schemes in $\mathbb P^1\times\mathbb P^1$.

We introduce a countable collection of positivity classes for Hermitian symmetric functions on a complex manifold, and establish their basic properties. We study a related notion of stability. The first main result shows that, if the…

Let $C$ be an affine plane curve. We consider additive functions $f: K\rightarrow K$ for which $f(x)f(y)=0$, whenever $(x,y)\in C$. We show that if $K=\mathbb{R}$ and $C$ is the hyperbola with defining equation $xy=1$, then there exist…

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the…

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…

We investigate questions of an arithmetic nature related to the Abel-Jacobi map. We give a criterion for the zero locus of a normal function to be defined over a number field, and we give some comparison theorems with the Abel-Jacobi map…

Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution defines a matrix transform that preserves positivity. Within…

We propose necessary and sufficient conditions for an integer matrix to be decomposable in terms of its Hermite normal form. Specifically, to each integer matrix of maximal row rank without columns of zeros, we associate a symmetric whole…

Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P…

We show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic.

For the Frechet space E=C^{\infty}(S^1) and for a smooth \phi: R to R, we prove that the associated map E to E given by x mapsto\phi\circ x satisfies the continuous B\Gamma--differentiability condition in Yamamuro's inverse function theorem…

In this paper we classify the multiplicity-free skew characters of the symmetric group. Furthermore we show that the Schubert calculus is equivalent to that of skew characters in the following sense: If we decompose the product of two…

In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz…

We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both…