Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential

Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin–orbit coupling quantum number κ. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy between members of the pseudospin doublet is removed by tensor interaction. Furthermore, the radial node structure of the Dirac spinor is discussed.     

Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods

We present effective linear programming based computational techniques for solving nonconvex quadratic programs with box constraints (BoxQP). We first observe that known cutting planes obtained from the Boolean Quadric Polytope (BQP) are computationally effective at reducing the optimality gap of BoxQP. We next show that the Chvátal–Gomory closure of the BQP is given by the odd-cycle inequalities even when the underlying graph is not complete. By using these cutting planes in a spatial branch-and-cut framework, together with a common integrality-based preprocessing technique and a particular convex quadratic relaxation, we develop a solver that can effectively solve a well-known family of test instances. Our linear programming based solver is competitive with SDP-based state of the art solvers on small instances and sparse instances. Most of our computational techniques have been implemented in the recent version of CPLEX and have led to significant performance improvements on nonconvex quadratic programs with linear constraints.     

Mingling: mixed-integer rounding with bounds

Mixed-integer rounding (MIR) is a simple, yet powerful procedure for generating valid inequalities for mixed-integer programs. When used as cutting planes, MIR inequalities are very effective for mixed-integer programming problems with unbounded integer variables. For problems with bounded integer variables, however, cutting planes based on lifting techniques appear to be more effective. This is not surprising as lifting techniques make explicit use of the bounds on variables, whereas the MIR procedure does not. In this paper we describe a simple procedure, which we call mingling, for incorporating variable bound information into MIR. By explicitly using the variable bounds, the mingling procedure leads to strong inequalities for mixed-integer sets with bounded variables. We show that facets of mixed-integer knapsack sets derived earlier by superadditive lifting techniques can be obtained by the mingling procedure. In particular, the mingling inequalities developed in this paper subsume the continuous cover and reverse continuous cover inequalities of Marchand and Wolsey (Math Program 85:15–33, 1999) as well as the continuous integer knapsack cover and pack inequalities of Atamtürk (Math Program 98:145–175, 2003; Ann Oper Res 139:21–38, 2005). In addition, mingling inequalities give a generalization of the two-step MIR inequalities of Dash and Günlük (Math Program 105:29–53, 2006) under some conditions.     

Singular approximation in polydiscs by summability process

In this paper, we approximate a continuous function in a polydisc by means of multivariate complex singular operators which preserve the analytic functions. In this singular approximation, we mainly use a regular summability method (process) from the summability theory. We show that our results are non-trivial generalizations of the classical approximations. At the end, we display an application verifying the singular approximation via summation process, but not the usual sense.     

Partial Geometric Difference Families

We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.     

CONTROLLING THE 3D NANOSCALE ORGANIZATION OF BULK HETEROJUNCTION POLYMER SOLAR CELLS

In this study,the three dimensional nanoscale organization in the photoactive layers of poly(3-hexylthiophene) (P3HT) and a methanofullerene derivative (PCBM) is revealed by transmission electron tomography.After annealing treatment,either at elevated temperature or during slow solvent evaporation,nanoscale interpenetrating networks are formed with high crystalline order and favorable concentration gradients of both components through the thickness of the photoactive layer.Such a tailored morphology acco...     

Irregular Boundary Value Problems with Discontinuous Coefficients and the Eigenvalue Parameter

In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(−1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.     

Room‐temperature terahertz emission from ZnSe‐based quantum cascade structures: A simulation study

We identified conditions for room‐temperature operation of terahertz quantum cascade lasers (THz QCLs) where variable barrier heights are used on ZnSe/Zn_1–xMg_x Se material systems. The THz QCL devices are based on three‐level two‐well design schemes. The THz QCL lasers with alternating quantum barriers with different heights were compared with THz QCL laser structures with fixed quantum barrier heights. It is found that the THz QCL device with novel design employing variable barrier heights achieved the terahertz emission of about 1.45 THz at room‐temperature (300 K), and has improved laser performance due to the suppression of thermally activated carrier leakage via higher‐energy parasitic levels. Thus, THz QCL devices employing the design with variable barrier heights may lead to future improvements of the operating temperature and performance of THz QCL lasers. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Synthesis,Characterization, Electronic and Gas‐Sensing Properties towards H2 and CO of Transparent,Large‐Area,Low‐Layer Graphene

Low‐layered, transparent graphene is accessible by a chemical vapor deposition (CVD) technique on a Ni‐catalyst layer, which is deposited on a <100> silicon substrate. The number of graphene layers on the substrate is controlled by the grain boundaries in the Ni‐catalyst layer and can be studied by micro Raman analysis. Electrical studies showed a sheet resistance (R_sheet) of approximately 1435 Ω per □, a contact resistance (R_c) of about 127 Ω, and a specific contact resistance (R_sc) of approximately 2.8×10^?4 Ω cm² for the CVD graphene samples. Transistor output characteristics for the graphene sample demonstrated linear current/voltage behavior. A current versus voltage (I_ds–V_ds) plot clearly indicates a p‐conducting characteristic of the synthesized graphene. Gas‐sensor measurements revealed a high sensor activity of the low‐layer graphene material towards H₂ and CO. At 300 °C, a sensor response of approximately 29 towards low H₂ concentrations (1 vol %) was observed, which is by a factor of four higher than recently reported.     

q-Shock soliton evolution

By generating function based on Jackson’s q-exponential function and the standard exponential function, we introduce a new q-analogue of Hermite and Kampe-de Feriet polynomials. In contrast to q-Hermite polynomials with triple recurrence relations similar to [1], our polynomials satisfy multiple term recurrence relations, which are derived by the q-logarithmic function. It allows us to introduce the q-Heat equation with standard time evolution and the q-deformed space derivative. We find solution of this equation in terms of q-Kampe-de Feriet polynomials with arbitrary number of moving zeros, and solved the initial value problem in operator form. By q-analog of the Cole–Hopf transformation we obtain a new q-deformed Burgers type nonlinear equation with cubic nonlinearity. Regular everywhere, single and multiple q-shock soliton solutions and their time evolution are studied. A novel, self-similarity property of the q-shock solitons is found. Their evolution shows regular character free of any singularities. The results are extended to the linear time dependent q-Schrödinger equation and its nonlinear q-Madelung fluid type representation.