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The local trace function introduced in \cite{Dut} is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of…

Let $F$ be a nonarchimedean local field with residue field of cardinality $q$, let $G$ be the $F$-points of a connected reductive group defined over $F$, let $P$ and $Q$ be two parabolic subgroups with the same Levi factor $M$. We construct…

This paper constructs a unified family of nonconforming finite element spaces for $H\Lambda^k$ in $\mathbb{R}^n$ ($0\leqslant k\leqslant n$, $n\geqslant 1$). The spaces employ piecewise Whitney forms as shape functions, and include the…

If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a…

Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase…

Given a multiplicatively closed subset $S$ of the integers, there exist Structure Theorems for $LC$ modules over the localization $\mathbb{Z}S^{-1}$ that are "similar" to those of $LCA$ groups. The most notable one is the 1st Theorem: Given…

We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…

We investigate the generalization properties of dense text embeddings when the embedding backbone is a large language model (LLM) versus when it is a non-LLM encoder, and we study the extent to which spherical linear interpolation (SLERP)…

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are…

In this article we study some spectral properties of the linear operator $\mathcal{L}\_{\Omega}+a$ defined on the space $C(\bar\Omega)$ by :$$ \mathcal{L}\_{\Omega}[\varphi] +a\varphi:=\int\_{\Omega}K(x,y)\varphi(y)\,dy+a(x)\varphi(x)$$…

In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which separate the orbits of multi-qubit density operators $\rho$ under the action of the local unitary group was presented. We consider this family of invariants for the…

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…

We extend our discrete uniformization theorems for planar, $m$-connected, Jordan domains [Journal f\"ur die reine und angewandte Mathematik 670 (2012), 65--92] to closed surfaces of non-positive genus.

Radially symmetric wavelets possessing multiresolution framework are found to be useful in different fields like Pattern recognition, Computed Tomography (CT) etc. The compactly supported wavelets are known to be useful for localized…

This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…

We develop a theory of local asymptotic normality in the quantum domain based on a noncommutative extension of the Lebesgue decomposition. This formulation gives a substantial generalization of the previous paper [Yamagata, Fujiwara, and…

In a general measure space $(X,\mathcal L,\lambda)$, a characterization of weakly null sequences in $L_\infty (X,\mathcal L,\lambda)$ ($u_k \rightharpoonup 0$) in terms of their pointwise behaviour almost everywhere is derived from the…

In this paper, we determine completely the Lyubeznik numbers $\lambda_{i,j}(A)$ of the local ring $A$ at the vertex of the affine cone over a nonsingular projective variety $V$, where $V$ is defined over a field of characteristic zero, in…

We construct three-dimensional non-semisimple topological field theories from the unrolled quantum group of the Lie superalgebra $\mathfrak{osp}(1 \vert 2)$. More precisely, the quantum group depends on a root of unity $q=e^{\frac{2 \pi…

Let $k$ be an arbitrary field, $\Lambda$ be a $k$-algebra and $V$ be a $\Lambda$-module. When it exists, the universal deformation ring $R(\Lambda,V)$ of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the lifts of $V$ up…