Reconstructing Equation of State for Dark Energy in Double Complex Symmetric Gravitational Theory

We propose to study the accelerating expansion of the universe in the double complex symmetric gravitational theory （DCSGT）. The universe we live in is taken as the real part of the whole spacetime MC^4（J）, which is double complex. By introducing the spatially flat FRW metric, not only the double Friedmann equations but also the two constraint conditions py = 0 and J^2 = 1 are obtained. Farthermore, using parametric DL（z） ansatz, we reconstruct the ω/（z） and V（Ф） for dark energy from real observational data. We find that in the two cases of J = i, pJ = 0, and J = ε, pJ≠0, the corresponding equations of state ω＇（z） remain close to -1 at present （z = 0） and change from below -1 to above -1. The results illustrate that the whole spacetime, i.e. the double complex spacetime MC^4（J）, may be either ordinary complex （J = i, pJ = 0） or hyperbolic complex （J = ε, pJ≠ 0）. And the fate of the universe would be Big Rip in the future.

Structural,electronic,and magnetic behaviors of 5d transition metal atom substituted divacancy graphene：A first-principles study

Structural, electronic, and magnetic behaviors of 5d transition metal（TM） atom substituted divacancy（DV） graphene are investigated using first-principles calculations. Different 5d TM atoms（Hf, Ta, W, Re, Os, Ir, and Pt） are embedded in graphene, these impurity atoms replace 2 carbon atoms in the graphene sheet. It is revealed that the charge transfer occurs from 5d TM atoms to the graphene layer. Hf, Ta, and W substituted graphene structures exhibit a finite band gap at high symmetric K-point in their spin up and spin down channels with 0.783 μB, 1.65 μB, and 1.78 μB magnetic moments,respectively. Ir and Pt substituted graphene structures display indirect band gap semiconductor behavior. Interestingly, Os substituted graphene shows direct band gap semiconductor behavior having a band gap of approximately 0.4 e V in their spin up channel with 1.5 μB magnetic moment. Through density of states（DOS） analysis, we can predict that d orbitals of 5d TM atoms could be responsible for introducing ferromagnetism in the graphene layer. We believe that our obtained results provide a new route for potential applications of dilute magnetic semiconductors and half-metals in spintronic devices by employing 5d transition metal atom-doped graphene complexes.

Invariance of Conjugate Normality Under Similarity

An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.

ON STRUCTURED VARIANTS OF MODIFIED HSS ITERATION METHODS FOR COMPLEX TOEPLITZ LINEAR SYSTEMS

The Modified Hermitian and skew-Hermitian splitting （MHSS） iteration method was presented and studied by Bai, Benzi and Chen （Computing, 87（2010）, 93-111） for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical ex- periments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear system.

Kernel Function-Based Primal-Dual Interior-Point Methods for Symmetric Cones Optimization

In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.