The distribution of square-full integers

Let , wheref(n) is the characteristic function of square-full integers. A formula is proved that can be used to obtain better upper bound estimate for (x). We get (x)=O(x ^5/33+), which improves the exponent 11/72 obtained by R. Blasubramania and K. Ramachandra.     

A transmission problem in the calculus of variations

We study hölder regularity of minimizers of the functional , wherep(x) takes only two values and jumps across a Lipschitz surface. No restriction on the two values is imposed.This article was processed by the author using the Springer-Verlag T_EX PJourlg macro package 1991.     

Right distributive quasigroups on algebraic varieties

In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x ^–1 ax, fora , is an automorphism of (as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups.     

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

光谱法研究水溶性杯[8]芳烃对伊红的分子识别作用

采用荧光光谱法和紫外-可见光谱法研究了水溶性对-二甲氨甲基-杯[8]芳烃(简称杯[8]胺)对伊红的分子识别作用。研究发现,对-二甲氨甲基-杯[8]芳烃与伊红存在较强的静电作用,两者之间形成了2:1型的络合物,络合常数为2.1×109Lmol-1,小牛胸腺DNA对杯[8]胺-伊红络合物的稳定性有较大影响,DNA能夺取杯[8]胺-伊红络合物中的杯[8]胺,导致伊红游离,预示着杯[8]胺是良好的药物载体分子。同时考察了β-环糊精、几种常见有机溶剂和溶液的pH值等对杯[8]胺与伊红相互作用的影响,初步探讨了两者相互作用的机理。     

Al2O3衬底无催化剂生长GaN纳米线及其光学性能

采用一种绿色的等离子增强化学气相沉积法,以Al2O3为衬底, Ga金属为镓源, N2为氮源,在不采用催化剂的情况下,成功制备获得了结晶质量良好的GaN纳米线.研究表明,生长温度可显著调控GaN纳米线的形貌,当反应温度为950℃时,生长出的GaN微米片为六边形;当反应温度为1000℃时,生长出了长度为10-20μm的超长GaN纳米线.随着反应时间增加, GaN纳米线的长度增加. GaN纳米线内部存在着压应力,应力大小为0.84 GPa.同时,也进一步讨论了GaN纳米线无催化剂生长机制. GaN纳米线光致发光结果显示, GaN纳米线缺陷较少,结晶质量良好,在360 nm处有一个较为尖锐的本征发光峰,可应用于紫外激光器等光电子器件.本研究结果将为新型光电器件低成本绿色制备提供一个可行的技术方案.     

Tuning the electronic properties of hydrogen passivated C3N nanoribbons through van der Waals stacking

The two-dimensional (2D) C₃N has emerged as a material with promising applications in high performance device owing to its intrinsic bandgap and tunable electronic properties. Although there are several reports about the bandgap tuning of C₃N via stacking or forming nanoribbon, bandgap modulation of bilayer C₃N nanoribbons (C₃NNRs) with various edge structures is still far from well understood. Here, based on extensive first-principles calculations, we demonstrated the effective bandgap engineering of C₃N by cutting it into hydrogen passivated C₃NNRs and stacking them into bilayer heterostructures. It was found that armchair (AC) C₃NNRs with three types of edge structures are all semiconductors, while only zigzag (ZZ) C₃NNRs with edges composed of both C and N atoms (ZZCN/ CN) are semiconductors. The bandgaps of all semiconducting C₃NNRs are larger than that of C₃N nanosheet. More interestingly, AC-C₃NNRs with CN/CN edges (AC-CN/CN) possess direct bandgap while ZZ-CN/CN have indirect bandgap. Compared with the monolayer C₃NNR, the bandgaps of bilayer C₃NNRs can be greatly modulated via different stacking orders and edge structures, varying from 0.43 eV for ZZ-CN/CN with AB′-stacking to 0.04 eV for AC-CN/CN with AA-stacking. Particularly, transition from direct to indirect bandgap was observed in the bilayer AC-CN/CN heterostructure with AA′-stacking, and the indirect-to-direct transition was found in the bilayer ZZ-CN/CN with ABstacking. This work provides insights into the effective bandgap engineering of C₃N and offers a new opportunity for its applications in nano-electronics and optoelectronic devices.