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.     

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$T\sim V$.     

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.     

Probing Planckian physics in de Sitter space with quantum correlations

We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α$\alpha$-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we construct proper Unruh modes admitting general α$\alpha$-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α$\alpha$. Moreover, an one-to-one correspondence between convergent points H_c$H_c$ of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved.     

Effects of oxygen-containing defect complex on the electronic structures and transport properties of single-walled carbon nanotubes

The electronic structures and transport properties of (10,0)$(10,0)$ single-walled carbon nanotube ((10,0)$(10,0)$ (SWNT)) with oxygen-containing defect complex are investigated using density functional theory in combination with nonequilibrium Green?s function method. The complex delocalizes the local states of (10,0)$(10,0)$ SWNT induced by mono- and di-vacancy but strengthens the localization of the states induced by the Stone–Wales defect. As a result, the complex partially restores the transport properties of (10,0)$(10,0)$ SWNT with vacancies, but reduces the transmission of (10,0)$(10,0)$ SWNT with Stone–Wales defect. However, the oxygen-containing defect complex only slightly influences the transmission gap and threshold voltage of the system.