Related papers: The weak n-inner product space
In this paper, authors prove that if $X$ is a weak Asplund space, then the space $X\times R$ is a weak Asplund space. Thus the author definitely answered an open problem raised by D.G. Larman and R.R. Phelps for 45 years ago (J. London.…
This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…
We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the…
We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples…
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…
We offer a rationalization of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a…
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and…
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on…
Following W.T.Gan and S.Takeda, we obtain a weak second term identity of the regularized Siegel-Weil formula for the unitary dual pair $(U(n,n),U(V))$, where $V$ is a split hermitian space of dimension $2r$ with $r+1 \leq n \leq 2r-1$. As…
In this paper we provide a systematic exposition of basic properties of integrated distribution and quantile functions. We define these transforms in such a way that they characterize any probability distribution on the real line and are…
I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible…
Products of random matrix products of $\mathrm{SL}(2,\mathbb{R})$, corresponding to transfer matrices for the one-dimensional Schr\"odinger equation with a random potential $V$, are studied. I consider both the case where the potential has…
The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…
We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…
Weak-to-strong generalization is a phenomenon in post-training whereby a strong student model, when finetuned solely with feedback from a weaker teacher, can not only surpass the teacher, but can improve upon its own capabilities. Recent…
Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…
Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…
Weak-to-strong generalization, where weakly supervised strong models outperform their weaker teachers, offers a promising approach to aligning superhuman models with human values. To deepen the understanding of this approach, we provide…
In this paper, we detail and complete the existing characterizations of the decimation of the Ising model on $\Z^2$ in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…