Introduction to Ann-categories

In this paper, we present new concepts of Ann-categories, Ann-functors, and a transmission of the structure of categories based on Ann-equivalences. We build Ann-category of Pic-funtors and prove that each Ann-category can be faithfully embedded into an almost strictly Ann-category.Comment: 11 page

Density-Dependent Squeezing of Excitons in Highly Excited Semiconductors

The time evolution from coherent states to squeezed states of high density excitons is studied theoretically based on the boson formalism and within the Random Phase Approximation. Both the mutual interaction between excitons and the anharmonic exciton-photon interaction due to phase-space filling of excitons are included in consideration. It is shown that the exciton squeezing depends strongly on the exciton density in semiconductors and becomes smaller with increasing the latter.Comment: 6 pages, Two figures (ps) available from author upon reques

Group Extensions of the Co-type of a Crossed Module and Strict Categorical Groups

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of monoidal functors.Comment: 14 page

Structure of Ann-categories and Mac Lane - Shukla cohomology

In this paper we study the structure of a class of categories having two operations which satisfy axioms analoguos to that of rings. Such categories are called "Ann - categories". We obtain the classification theorems for regular Ann - categories and Ann - functors by using Mac Lane - Shukla cohomology of rings. These results give new interpretations of the cohomology groups and of the ringsComment: 14 page

Forward-Backward Splitting with Bregman Distances

We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained

ISIC 2017 Skin Lesion Segmentation Using Deep Encoder-Decoder Network

This paper summarizes our method and validation results for part 1 of the ISBI Challenge 2018. Our algorithm makes use of deep encoder-decoder network and novel skin lesion data augmentation to segment the challenge objective. Besides, we also propose an effective testing strategy by applying multi-model comparison.Comment: ISIC 201

Variable Quasi-Bregman Monotone Sequences

We introduce a notion of variable quasi-Bregman monotone sequence which unifies the notion of variable metric quasi-Fej\'er monotone sequences and that of Bregman monotone sequences. The results are applied to analyze the asymptotic behavior of proximal iterations based on variable Bregman distance and of algorithms for solving convex feasibility problems in reflexive real Banach spaces

Hadamard well-posedness of the gravity water waves system

We consider in this article the system of (pure) gravity water waves in any dimension and in fluid domains with general bottoms. The unique solvability of the problem was established by Alazard-Burq-Zuily [Invent. Math, 198 (2014), no. 1, 71--163] at a low regularity level where the initial surface is $C^{\frac{3}{2}+}$ in terms of Sobolev embeddings, which allows the existence of free surfaces with unbounded curvature. Our result states that the solutions obtained above depend continuously on initial data in the strong topology where they are constructed. This completes a well-posedness result in the sense of Hadamard.Comment: Explanation of the strategy expanded, some typos fixed. To appear in Journal of Hyperbolic Differential Equation

A pseudo-local property of gravity water waves system

By proving a weighted contraction estimate in uniformly local Sobolev spaces for the flow of gravity water waves, we show that this nonlocal system is in fact pseudo-local in the following sense: locally in time, the dynamic far away from a given bounded region has a small effect on that region (again, in a sense that we will make precise in the article). Our estimate on the flow also implies a new spatial decay property of the waves. To prove this result, we establish a paradifferential calculus theory in uniformly local Sobolev spaces with weights.Comment: We improved the main results and the paradifferential calculus for a general class of weights. Typos fixed, explanations and details adde

The factor set of Gr-categories of the type (Π,A)(\Pi,A)

Any $\Gamma$-graded categorical group is determined by a factor set of a categorical group. This paper studies the factor set of the group $\Gamma$ with coefficients in the categorical group of the type $(\Pi,A).$ Then, an interpretation of the notion of $\Gamma-$operator $3-$cocycle is presented and the proof of cohomological classification theorem for the a $\Gamma-$graded Gr-category is also presented.Comment: 12 page