相关论文: The primal framework. II. Smoothness
Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…
We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and…
In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity, temperature, and specific humidity. The main difficulty…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We introduce a new topological invariant of a rigidly-compactly generated tensor-triangulated category and two new notions of support. The first is based on smashing subcategories: it is unknown whether the frame of smashing subcategories…
Abstract grammatical knowledge - of parts of speech and grammatical patterns - is key to the capacity for linguistic generalization in humans. But how abstract is grammatical knowledge in large language models? In the human literature,…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved.…
In part I of this paper we studied additive decomposability of the set $\F_y$ of th $y$-smooth numbers and the multiplicative decomposability of the shifted set $\g_y=\F_y+\{1\}$. In this paper, focusing on the case of 'large' functions…
This is a part of an ongoing research project, with the aim of finding the connections between properties related to theory combination in Satisfiability Modulo Theories. In previous work, 7 properties were analyzed: convexity, stable…
To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
The paper is intended to be a survey on some topics within the framework of automorphisms of a relatively free groups of infinite rank. We discuss such properties as tameness, primitivity, small index, Bergman property, and so on.
In the first part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and super-rosy theories. Then we try to develop analogous theory for arbitrary dependent theories.
We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will…
We consider a class of smooth mixing flows $T^{\alpha,\gamma}$ on $\mathbb{T}^2$ with one degenerated fixed point $x_0\in \mathbb{T}^2$ of power type $\gamma\in (-1,0)$. We prove that for a $G_\delta$ dense set of $\alpha\in \mathbb{T}$, a…
In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…
On a compact, oriented, Riemannian manifold, the Hodge decomposition theorem associates a smooth primitive to any exact smooth form omega. In this paper, we show that given a smooth family of exact smooth forms omega(t), the family of…
In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.