相关论文: A Generalization of Monotonicity Condition and App…

In the framework of Nelson stochastic quantization we derive exact non-stationary states for a class of time-dependent potentials. The wave-packets follow a classical motion with constant dispersion. The new states thus define a possible…

We show that for a system containing a set of general second class constraints which are linear in the phase space variables, the Abelian conversion can be obtained in a closed form and that the first class constraints generate a…

We quantise General Relativity for a class of energy-momentum-stress tensors.

A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with L\'evy process are investigated. We establish a comparison theorem which allows us to derive an…

In this paper, we improve the famous Reid Inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid and…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.

Various normalization layers have been proposed to help the training of neural networks. Group Normalization (GN) is one of the effective and attractive studies that achieved significant performances in the visual recognition task. Despite…

We give a multivariate generalization of Borell's noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.

This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…

The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…

Hofstadter's Q-sequence remains an enigma fifty years after its introduction. Initially, the terms of the sequence increase monotonically by 0 or 1 at a time. But, Q(12)=8 while Q(11)=6, and monotonicity fails shortly thereafter. In this…

A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…

We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems,…

In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length…

In this paper, we propose to obtain the skewed version of a unimodal symmetric density using a skewing mechanism that is not based on a cumulative distribution function. Then we disturb the unimodality of the resulting skewed density. In…

Regularization can mitigate the generalization gap between training and inference by introducing inductive bias. Existing works have already proposed various inductive biases from diverse perspectives. However, none of them explores…

Normalization methods are a central building block in the deep learning toolbox. They accelerate and stabilize training, while decreasing the dependence on manually tuned learning rate schedules. When learning from multi-modal…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…