Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field *

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglemententropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field .The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum hase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge $c=1$ is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.     

k-途径正则有向图

In this paper, we define a class of strongly connected digraph, called the k-walk- regular digraph, study some properties of it, provide its some algebraic characterization and point out that the 0-walk-regular digraph is the same as the walk-regular digraph discussed by Liu and Lin in 2010 and the D-walk-regular digraph is identical with the weakly distance-regular digraph defined by Comellas et al in 2004.     

A dual band CMOS VCO with a balanced duty cycle buffer

This paper proposes a dual band VCO with a standard 0.35 μm CMOS process to generate 1.07 and 2.07 GHz. The proposed VCO architecture with 50% duty cycle circuit and a half adder (HA) is able to produce a frequency two times higher than that of the conventional VCOs. The measurement results demonstrate that the gain of VCO and power dissipation are 561 MHz/V and 14.6 mW, respectively. The phase noises of the dual band VCO are measured to be −102.55 and −95.88 dBc/Hz at 2 MHz offset from 1.07 and 2.07 GHz, respectively.     

Mechanosynthesis and mechanical activation processes to the preparation of the Sr2[Srn−1TinO3n+1] Ruddlesden–Popper family

A novel mechanochemical activation route has been applied in order to obtain the n=1–4 and ∞ members of the Sr₂[Sr_n−1Ti_nO_3n+1] Ruddlesden–Popper series. The evolution of the (n+1)SrO:nTiO₂ powder mixtures during mechanical treatment was followed by X-ray powder diffraction in all cases. Except for the 2SrO:TiO₂ composition, SrTiO₃ was always mechanosynthesized. High-energy milling of 2SrO:TiO₂ sample resulted in the formation of nanosized Sr₂TiO₄, which is the only K₂NiF₄-type oxide prepared by mechanical treatment until now.The mechanical treatment was followed by annealing at different temperatures to establish the optimized protocol for synthesis of each member of the series. SrTiO₃, Sr₂TiO₄ and Sr₃Ti₂O₇ were obtained with very important decreases in the formation temperatures and reaction times as compared with the traditional ceramic method. Final and milled products were studied by X-ray powder diffraction at room and increasing temperatures, and by thermal analysis and scanning and high resolution transmission electron microscopy.     

Constructions of uniform designs by using resolvable packings and coverings

Uniform designs have been widely used in computer experiments, as well as in industrial experiments when the underlying model is unknown. Based on the discrete discrepancy, the link between uniform designs, and resolvable packings and coverings in combinatorial theory is developed. Through resolvable packings and coverings without identical parallel classes, many infinite classes of new uniform designs are then produced.     

Existence of nonlinear boundary layer to the Boltzmann equation with reverse reflection boundary condition

Many physical models have boundaries. When the Boltzmann equation is used to study a physical problem with boundary, there usually exists a layer of width of the order of the Knudsen number along the boundary. Hence, the research on the boundary layer problem is important both in mathematics and physics. Based on the previous work, in this paper, we consider the existence of boundary layer solution to the Boltzmann equation for hard sphere model with positive Mach number. The boundary condition is imposed on incoming particles of reverse reflection type, and the solution is assumed to approach to a global Maxwellian in the far field. Similar to the problem with Dirichlet boundary condition studied in [S. Ukai, T. Yang, S.H. Yu, Nonlinear boundary layers of the Boltzmann equation: I. Existence, Comm. Math. Phys. 3 (2003) 373-393], the existence of a solution is shown to depend on the Mach number of the far field Maxwellian. Moreover, there is an implicit solvability condition on the boundary data. According to the solvability condition, the co-dimension of the boundary data related to the number of the positive characteristic speeds is obtained.     

Ekeland's variational principle in locally convex spaces and the density of extremal points

In this paper, we prove a general version of Ekeland's variational principle in locally convex spaces, where perturbations contain subadditive functions of topology generating seminorms and nonincreasing functions of the objective function. From this, we obtain a number of special versions of Ekeland's principle, which include all the known extensions of the principle in locally convex spaces. Moreover, we give a general criterion for judging the density of extremal points in the general Ekeland's principle, which extends and improves the related known results.     

Covering arrays of strength 3 and 4 from holey difference matrices

A covering array CA(N; t, k, v) is an N × k array with entries from a set X of v symbols such that every N × t sub-array contains all t-tuples over X at least once, where t is the strength of the array. The minimum size N for which a CA(N; t, k, v) exists is called the covering array number and denoted by CAN(t, k, v). Covering arrays are used in experiments to screen for interactions among t-subsets of k components. One of the main problems on covering arrays is to construct a CA(N; t, k, v) for given parameters (t, k, v) so that N is as small as possible. In this paper, we present some constructions of covering arrays of strengths 3 and 4 via holey difference matrices with prescribed properties. As a consequence, some of known bounds on covering array number are improved. In particular, it is proved that (1) CAN(3, 5, 2v) ≤ 2v ²(4v + 1) for any odd positive integer v with gcd(v, 9) ≠ 3; (2) CAN(3, 6, 6p) ≤ 216p ³ + 42p ² for any prime p > 5; and (3) CAN(4, 6, 2p) ≤ 16p ⁴ + 5p ³ for any prime p ≡ 1 (mod 4) greater than 5.