In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

Pitch, one of the primary auditory percepts, is related to the temporal regularity or periodicity of a sound. Previous functional brain imaging work in humans has shown that the level of population neural activity in centers throughout the auditory system is related to the temporal regularity of a sound, suggesting a possible relationship to pitch. In the current study, functional magnetic reso...

We study the regularity problem for sub-Riemannian geodesics, i.e., for those curves that minimize length among all curves joining two fixed endpoints and whose derivatives are tangent to a given, smooth distribution of planes with constant rank. We review necessary conditions for optimality and we introduce extremals and the Goh condition. The regularity problem is nontrivial due to the presen...

We establish regularity conditions for the 3D Navier-Stokes equation via two components of the vorticity vector. It is known that if a LerayHopf weak solution u satisfies ω̃ ∈ L2/(2−r)(0, T ;L(R)) with 0 < r < 1, where ω̃ form the two components of the vorticity, ω = curlu, then u becomes the classical solution on (0, T ] (see [5]). We prove the regularity of Leray-Hopf weak solution u under each...

The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions of the lemma. Williams [25] recently as...

We discuss local convergence of Newton’s method to a singular solution x∗ of the nonlinear equations F (x) = 0, for F : IR → IR. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x∗ from a starlike domain around x∗ for F twice Lipschitz continuously differentiable and x∗ satisfying a particular regularity condition, can be adapted to the case i...

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the uni…cation and re…nement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years ...

Abstract. This paper studies the regularity problem for the 3D incompressible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence [16] predicts that there exists a critical wavenumber above which the high frequency part is dominated by the dissipation term in the fluid equation. Inspired by this idea, we apply an approach of spl...

To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483–500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush–Kuhn– Tucker (KKT)-type necessary conditions of multiobjective optimiz...

Reenable function vectors are usually given in the form of an innnite product of their reenement (matrix) masks in the frequency domain and approximated by a cascade algorithm in both time and frequency domains. We provide necessary and suu-cient conditions for the convergence of the cascade algorithm. We also give necessary and suucient conditions for the stability and orthonormality of reenab...