Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

Journal of Nonlinear Science - We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $$L^2$$ weak...     

Strong convergence theorem for nonexpansive semigroups in Hilbert space

The purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in Hilbert space.     

A linear wave equation with a nonlinear boundary condition of viscoelastic type

The paper is devoted to the study of a linear wave equation with a nonlinear boundary condition of viscoelastic type. The existence of a weak solution is proved by using the Faedo–Galerkin method. The uniqueness, regularity and asymptotic expansion of the solution are also discussed.     

Regularization inertial proximal point algorithm for common solutions of a finite family of inverse-strongly monotone equations

The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.     

An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and Earth science in which the sphere is taken as a model for the Earth. Spherical radial basis functions provide a convenient tool for constructing the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner for accelerating the solution process. An estimate for the condition number of the preconditioned system will be discussed. Numerical experiments using MAGSAT satellite data will be presented.     

Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches

In this paper, we consider a task allocation model that consists of assigning a set of m unmanned aerial vehicles (UAVs) to a set of n tasks in an optimal way. The optimality is quantified by target scores. The mission is to maximize the target score while satisfying capacity constraints of both the UAVs and the tasks. This problem is known to be NP-hard. Existing algorithms are not suitable for the large scale setting. Scalability and robustness are recognized as two main issues. We deal with these issues by two optimization approaches. The first approach is the Cross-Entropy (CE) method, a generic and practical tool of stochastic optimization for solving NP-hard problem. The second one is Branch and Bound algorithm, an efficient classical tool of global deterministic optimization. The numerical results show the efficiency of our approaches, in particular the CE method for very large scale setting.     

Gold-Catalyzed Amine Cascade Addition to Diyne-Ene: Enantioselective Synthesis of 1,2-Dihydropyridines

With the well-documented chemical and biological applications, piperidine and pyridine are among the most important N-heterocycles, and a new synthetic strategy, especially one with an alternative bond-forming design, is of general interest. Using the gold-catalyzed intermolecular condensation of amine and diyne-ene, we report herein the first example of enantioselective 1,2-dihydropyridine synthesis through a formal [3+2+1] fashion (up to 95 % yield, up to 99 % e.e.).     

Hemin-Promoted Direct C−H Thiolation in the Synthesis of Diaryl Sulfides

Diaryl sulfides are a class of important synthetic chemical units. Herein, we report a new method for direct preparation of diphenyl sulfides using P-toluenesulfonyl chloride as an effective thiophenyl radical precursor with assistance from Hemin. Various substituted anisoles and benzenesulfonyl chlorides are well tolerated, resulting in moderate to good yields of diaryl sulfides. The potential of the proposed method is validated by good yields obtained in gram scale reactions.     

Proof of Modulational Instability of Stokes Waves in Deep Water

It is proven that small-amplitude steady periodic water waves with infinite depth are unstable with respect to long-wave perturbations. This modulational instability was first observed more than half a century ago by Benjamin and Feir. It has been proven rigorously only in the case of finite depth. We provide a completely different and self-contained approach to prove the spectral modulational instability for water waves in both the finite and infinite depth cases. © 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.     

Synthesis,Structure and Electrochemical Property of a New Copper(II) Complex Based on Benzene-1,2,4,5-tetracarboxylate and 2,5-Bis(3-pyridyl)-1,3,4-oxadiazole Ligands

Abstract  

A new three-dimensional (3-D) supramolecular complex, [Cu₂(btec)(bpo)₂(H₂O)₂]·8H₂O (1), has been synthesized by hydrothermal reaction with the mixed ligands benzene-1,2,4,5-tetracarboxylate (btec) and bent dipyridyl based ligand 2,5-bis(3-pyridyl)-1,3,4-oxadiazole (bpo), and structurally characterized by elemental analysis, IR, TG, powder-XRD and single-crystal X-ray diffraction analysis. The results reveal that each Cu(II) ion is bridged by two different ligands (btec and bpo) to form a 2-D polymer layer in complex 1. The adjacent layers are further linked by 1-D H-bonded water chains simultaneously containing (H₂O)₆ rings and (H₂O)₈ rings to form a 3-D supramolecular framework. Moreover, the electrochemical behavior of complex 1 bulk-modified carbon paste electrode (1-CPE) has been reported.