相关论文: Introduction to Tensor Variational Inequalities

A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution…

In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are…

This work explores the tensor and combinatorial constructs underlying the linearised higher-order variational equations of a generic autonomous system along a particular solution. The main result of this paper is a compact yet explicit and…

A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…

This work contains the teleparallel version of the stationary axisymmetric solutions. We obtain the tetrad and the torsion fields representing these solutions. The tensor, vector and axial-vector parts of the torsion tensor are evaluated.…

Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…

Parsimonious games are a subset of constant sum homogeneous weighted majority games unequivocally described by their free type representation vector. We show that the minimal winning quota of parsimonious games satisfies a second order,…

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function…

The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing…

In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…

With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $\mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $\mathfrak{gl}(n)$-module $V$, and the set $S$, we…

The conventional definition of a depth function is vector-based. In this paper, a novel projection depth (PD) technique directly based on tensors, such as matrices, is instead proposed. Tensor projection depth (TPD) is still an ideal depth…

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…

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the…

An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.

This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…