The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

There exist many di erent lossy compression meth ods and most of these methods have several tunable parameters In di erent situations di erent methods lead to di erent quality reconstruction so it is impor tant to select in each situation the best compression method A natural idea is to select the compression method for which the average value of some metric d I e I is the smallest possible The...

The natural gradient is a powerful method to improve the transient dynamics of learning by considering the geometric structure of the parameter space. Many natural gradient methods have been developed with regards to Kullback-Leibler (KL) divergence and its Fisher metric, but the framework of natural gradient can be essentially extended to other divergences. In this study, we focus on score mat...

Proposition 1.2 (Splitting Principle). Let E → M be a complex vector bundle of rank n over a manifold X. Then there is a manifold F (E) and a smooth fibration π : F (E) → M such that • The homomorphism π∗ : H∗(M, Z) → H∗(F (E), Z) is injective. • The bundle π∗E splits into a direct sum of complex line bundles, i.e. π∗E = l1 ⊕ · · ·⊕ ln Proof. Consider the projectivisation p : PC(E) → M and the ...

We study the boundedness of Riesz transforms in L for p > 2 on a doubling metric measure space endowed with a gradient operator and an injective, ω-accretive operator L satisfying Davies-Gaffney estimates. If L is non-negative self-adjoint, we show that under a reverse Hölder inequality, the Riesz transform is always bounded on L for p in some interval [2, 2 + ε), and that L gradient estimates ...

In this paper we establish approximate properties of Cesàro (C,−α)-means with α ∈ (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ−α n (f, x) to f (x) in the L p-metric. We also show that this condition cannot be improved in the case p = 1.

This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple impli...

Heterogeneous face recognition deals with matching face images from different modalities or sources. The main challenge lies in cross-modal differences and variations and the goal is to make cross-modality separation among subjects. A margin-based cross-modality metric learning (MCM²L) method is proposed to address the problem. A cross-modality metric is defined in a common subspace where sampl...

The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and...