Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

航空器供油问题中完全逆序类中的多项式时间可解类

航空器供油问题是一类非线性组合优化问题,其目标函数为分式形式,该问题目前不存在多项式时间算法,也未被证明是NP完全问题。一般可以用置换来刻画n架飞机的一个供油顺序。该问题中有一类实例被称为“完全逆序类”,“完全逆序类”用动态规划算法求解计算时间为O(n2ⁿ),具有指数时间复杂度。本文通过对该“完全逆序类”问题做进一步分析,发现在“完全逆序类”中也存在着多项式时间可解的情况。定理1研究一类一次可解的情况,若问题满足定理1的条件,则求解一次即可找到其最优解;定理2研究一类多项式时间可解的情况,当问题满足定理2的条件时,其最优解可在多项式时间内获得。     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

Radical Addition Reactions of α-Substituted β,β-Difluorovinyl Sulfones

The radical addition reactions of α-substituted β,β-difluorovinyl sulfones 1 with α-oxy and acyl radical species, such as 1,3-dioxolane, tetrahydrofuran, 1,4-dioxane, butanal and hexanal, afforded radical addition products 2--16 in good yields.     

The Synthesis of 1,3-Bis(Phenylseleno)-2-Propanol

A general and efficient synthetic method of 1,3-bis(phenylseleno)-2-propanol by reducing diphenyl diselenides with sodium borohydride in basic environment and then reacting with epichlorohydrin are described.     

Efficient Method of Synthesis of N,N′-Disubstituted Ureas/Thioureas by a Zinc Chloride Catalyzed Thermal Reaction

Symmetrically N,N′-disubstituted ureas/thioureas were synthesized by heating amines or phenyl hydrazine and urea/thiourea on a preheated hot plate at 80–85°C under solvent-free conditions in the presence of a catalytic amount of ZnCl₂ as a catalyst. The protocol has the advantages of not using toxic phosgene and other hazardous substrates or organic solvents. Increased reaction rate, good yield, and a simple workup procedure are involved.     

Synthesis of New 2-Aryl Substituted 2,3-Dihydroquinazoline-4(1H)-ones Under Solvent-Free Conditions,Using Molecular Iodine as a Mild and Efficient Catalyst

A simple, inexpensive, and efficient one-pot synthesis of 2,3-dihydroquinazoline-4(1H)-one derivatives under solvent-free conditions using a catalytic amount of iodine with excellent product yields is reported. This methodology provides easy, quantitative access to various 2,3-dihydroquinazoline-4(1H)-one derivatives, using commercially available iodine as a catalyst.     

Synthesis of Isobenzofuran-1(3H)-ones with the Aid of Silica-Supported Preyssler Nanoparticles

Silica-supported Preyssler nanoparticles appear to be a new and efficient solid acid catalyst for an economical, and environmentally benign one-pot synthesis of 3-substituted phthalides.