Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces

Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FC$FC$-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature.     

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense given by Grimmer in [R. Grimmer, Resolvent operators for integral equations in a Banach space, Transaction of American Mathematical Society 273 (1982) 333–349]. The delayed part is assumed to be locally Lipschitz. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions.     

Exact penalty functions method for mathematical programming problems involving invex functions

In this paper, some new results on the exact penalty function method are presented. Simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption. Furthermore, the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved.     

Phase diagrams of a spin-1 Ising superlattice

The three-dimensional spin-1 Ising superlattice consisting of two different ferromagnetic materials with two different crystal fields _Δ1${\Delta }_1$ and _Δ2${\Delta }_2$ is considered in the mean field approximation. The phase diagrams are considered in the (t,_d2$t,d_2$) plane for different ranges of variation of _d1(t=T/J,_d1=_Δ1/J$d_1(t=T/J,d_1={\Delta }_1/J$, _d2=_Δ2/J$d_2={\Delta }_2/J$ are the reduced temperature and crystal fields respectively). The phase diagrams exhibit a variety of multicritical points and reentrant and double reentrant behaviours. They are found to depend qualitatively and/or quantitatively on the thicknesses of the materials in a supercell. This has direct consequences on the nature of the magnetic states of superlattices with different thicknesses.     

Multicritical behaviors of the antiferromagnetic Blume–Emery–Griffiths model with the external magnetic field on the Bethe lattice

The antiferromagnetic Blume–Emery–Griffiths model in an external magnetic field is studied by using the exact recursion relations on the Bethe lattice for arbitrary values of biquadratic and for negative values of bilinear interactions. We have studied the thermal variations of two-sublattice magnetizations belonging to spin-1 BEG model to obtain the phase diagrams on the (H/|J|,kT/|J|)$(H/|J|,\mathit{kT}/|J|)$ plane. As a result, we have found that the system presents second- and first-order phase transitions, therefore, tricritical points for appropriate values of K/|J|$K/\left|J\right|$, D/|J|$D/\left|J\right|$ and q  . We have also found that the second-order phase transition lines exhibit reentrant phenomena in temperature, besides it also shows reentrant phenomena for the first-order phase lines in external magnetic field for q=4$q=4$ and 6.     

Coverage-dependent spin reorientation transition temperature of the Fe double-layer on W(1 1 0) observed by scanning tunneling microscopy

The magnetic domain structure of the Fe double-layer on W(1 1 0) is investigated using a variable-temperature scanning tunneling microscope. At low temperature the well-known periodic magnetic stripe domain structure is identified via the observation of domain walls. This is done with a non-spin-polarized tip by taking advantage of a spin–orbit coupling effect. At higher temperature a reorientation to an in-plane easy axis is observed. The spin reorientation temperature is found to be coverage-dependent and it is determined for samples with a coverage of 1.5–2.2 atomic layers of Fe on W(1 1 0).     

Temperature behavior of bound magnetic polarons in antiferromagnetic chain

The behavior of a one-dimensional antiferromagnetic (AF) chain doped by non-magnetic donor impurities is analyzed, in the limit of low impurity density n  . The doping leads to the formation of ferromagnetically correlated regions localized near impurities (bound magnetic polarons or ferrons). The temperature evolution of the chain is calculated using an approximate variational method, and a Monte Carlo simulation. Both these methods give the similar results. The analysis of correlation functions for neighboring local spins demonstrates that the ferromagnetic correlations inside a ferron are significant even at high temperatures. The AF correlations in the rest part of the chain decay much faster with temperature. So, the ferron is a stable object that does not disappear even above the Néel temperature _TN$T_{\mathrm{N}}$. At rather small values of the electron–impurity coupling energy V$V$ (for V$V$ lower then the electron hopping integral t  ), the bound ferron depins from impurity retaining its magnetic structure. Such a depinning occurs at T∼V$T\sim V$.     

化学气相沉积法制备Zn2GeO4纳米线及其发光性质的研究

利用化学气相沉积法（CVD）,气-液-固（VLS）生长法则在表面溅有金属Au催化剂层的1 cm×1 cm的Si片上制备三元Zn₂GeO₄纳米线。X射线衍射仪（XRD）测试结果表明,锌源与锗源质量比为8：1时可成功制备出Zn₂GeO₄纳米结构;扫描电子显微镜（SEM）测试结果表明,Zn₂GeO₄纳米线直径为100 nm,长度为10~11 μm;光致发光（PL）测试结果表明,Zn₂GeO₄纳米线在432和480 nm处具有两个发光峰,最后对其生长机理进行了分析。     

Trigonometrical sums connected with the chiral Potts model,Verlinde dimension formula,two-dimensional resistor network,and number theory

We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N$N$ edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2)$SU\left(2\right)$ and SO(3)$SO\left(3\right)$ WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N$2\times N$. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory.