GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.

The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4

The present paper proved that if λ1, λ2, λ3 are positive real numbers, λ1/λ2 is irrational. Then, the integer parts of λ1x12＋ λ2x22＋ λ3x34 are prime infinitely often for natural numbers x1, x2, x3.

An extension of the modified Sawada-Kotera equation and conservation laws

Based on the modified Sawad^Kotera equation, we introduce a 3 ~ 3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawad-Kotera equation, by which a Lax pair of the modified Sawada-Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawad-Kotera equation, the Kaup-Kupershmidt equation, and the modified Sawad-Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada-Kotera equation are constructed with the aid of their Lax pairs.

GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution.

Diophantine Approximation with Two Primes and One Square of Prime

We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .

Electronic structures and thermoelectric properties of solid solutions CuGa_(1-x) In_xTe_2 : A first-principles study

The electronic structures of solid solutions CuGal_xlnxTe2 are systematically investigated using the full-potential all-electron linearized augmented plane wave method. The calculated lattice parameters almost linearly increase with the increase of the In composition, which are in good agreement with the available experimental results. The calculated band structures with the modified Becke-Johnson potential show that all solid solutions are direct gap conductors. The band gap decreases linearly with In composition increasing. Based on the electronic structure calculated, we investigate the thermoelectric properties by the semi-classical Boltzmann transport theory. The results suggest that when Ga is replaced by In, the bipolar effect of Seebeck coefficient S becomes very obvious. The Seebeck coefficient even changes its sign from positive to negative for p-type doping at low carrier concentrations. The optimal p-type doping concentrations have been estimated based on the predicted maximum values of the power factor divided by the scattering time.

A New Algorithm for Computing the Determinant and the Inverse of a Pentadiagonal Toeplitz Matrix

An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.

Existence and asymptotic behavior for systems of nonlinear hyperbolic equations

The initial-boundary value problem for a class of nonlinear hyperbolic equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the asymptotic stability of global solutions by means of a difference inequality.

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^＊ which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if ｜r｜≥ r^＊; while they appear as damped oscillatory waves if ｜r｜ 〈 r^＊. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u（ξ） in the global phase portraits, and then obtain the approximate solutions （u（ξ）, H（ξ））. Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.

Electronic structure and optical properties of the red and yellow mercuric iodides

With the help of the ab initio full-potential linearized augmented plane wave （FPLAPW） method, calculations of the electronic structure and linear optical properties are carried out for red HgI2 and yellow HgI2. It is found that the red HgI2 has a direct gap of 1.22834 eV and the yellow HgI2 has an indirect gap of 2.11222 eV. For the red HgI2, the calculated optical spectra are qualitatively in agreement with the experimental data. Furthermore, the origins of the different peaks of ε2（ω） are discussed. Our calculated anisotropic dielectric function of the red HgI2 is a nice match with the experimental results. Our calculated results are able to reproduce the overall trend of the experimental reflectivity spectra. Although no comparable experimental and theoretical results are available, clearly, the above proves the reliability of our calculations, suggesting that our calculations should be convincing for the yellow HgI2. Finally, the different optical properties are discussed.

Preparation and characterization of barium strontium titanate/silicon nanoporous pillar array composite thin films by a sol-gel method

Barium strontium titanate （Ba0.5Sr0.5TiO3, BST）/silicon nanoporous pillar array （Si-NPA） thin films were prepared by a spin-coating/annealing technique based on Si-NPA with micro/nano-structure. Both the isomer conversion of acetylacetone and the network structure combined by enol and Ti-alkoxide facilitate the formation of the BST sol and the subsequent crystallization. Before the perovskite BST begins to form, the intermediate phase （Ba, Sr）Ti2OsCO3 is found. The boundary between BST and Si-NPA is of clarity and little interface diffusion, disclosing that Si-NPA is an ideal template substrate in the preparation of multifunctional composite films.

Two-dimensional models of threshold voltage and subthreshold current for symmetrical double-material double-gate strained Si MOSFETs

The two-dimensional models for symmetrical double-material double-gate （DM-DG） strained Si （s-Si） metal-oxide semiconductor field effect transistors （MOSFETs） are presented. The surface potential and the surface electric field ex- pressions have been obtained by solving Poisson＇s equation. The models of threshold voltage and subthreshold current are obtained based on the surface potential expression. The surface potential and the surface electric field are compared with those of single-material double-gate （SM-DG） MOSFETs. The effects of different device parameters on the threshold voltage and the subthreshold current are demonstrated. The analytical models give deep insight into the device parameters design. The analytical results obtained from the proposed models show good matching with the simulation results using DESSIS.

Partial Order and Extremes of Multivariate Extreme Value Distributions

This paper studies the dependence order among multivariate extreme value dis- tributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN

In this paper, we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian. We obtain some extem sion of results of Weissler who considered the case α = 1, and h ≡ 1.

Effect of Copper-vacancy on the Electrical,Optical and Thermoelectric Properties of CuInTe2 by the First-principles Study

The effects of copper-vacancy on the electrical, optical and thermoelectric properties of CuInTe2 have been investigated by the first-principles calculations and semi-classical Boltzmann theory. The estimated results of copper vacancy formation energies for Cu1-xn Te2(x = 0,1/16, 1/8 and 1/4) showed it is more difficult to prepare the sample with higher copper vacancy concentration. From the calculated energy band structures with MBJ-GGA, it can be seen that they are p-type semiconductors and the energy gap values increase with the vacancy concentration increasing. The wavelength is smaller than 460 nm, and the high copper vacancy concentration(x =1/4) is helpful to the values of absorption coefficient, while above 460 nm, the lower copper vacancy concentration(x = 1/16) is able to enhance the absorption coefficient. The lower copper vacancy concentration(x = 1/16) is more favorable to improve the power factor in low or middle temperature. However, the high copper vacancy concentration(x = 1/4) is better in high temperature. These results give hints for the design of CuInTe2 as the good photovoltaic and thermoelectric materials.

Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay

This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delay-dependent stability condition is derived by using the novel augmented Lyapunov-Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.

On the Metaheuristics Approach to the Problem of Genetic Sequence Comparison and Its Parallel Implementation

We describe parallel implementation of the metaheuristic approach to the problem of comparing strings representing DNA sequence. By this approach, one can define a whole new class of metrics on a set of strings;some of this metrics can lead to interesting results when used for string comparison. We propose several heuristics;compare results achieved when using those heuristics and compare parallel and sequential implementation of proposed approach.

Synthesis,Structure and Optical Properties of CdO Nanocrystals Directly Grown on Cd Foil

Semiconductor nanocrystals directly grown on the conducting metal can lower the contact resistance and can benefit the electron transfer between the semiconductor and the metal. In the present work, CdO nanocrystals are directly synthesized on the conducting Cd foil through a simple solvothermal method. Cd foil is used as the Cd2＋ source and the substrate. The average size of CdO nanocrystals is -23.1 nm by analyzing the XRD data. Moreover the growth mechanism is discussed. A hierarchic structure characterized by the nano rods and nano particles in the top and bottom layers, respectively, can be observed. From the UV-vis absorption analyzed by Taucs relation, the two different optical band gaps are obtained. The photoluminescence spectrum is obtained and studied.

Generation of Fabry–Pérot oscillations and Dirac state in two-dimensional topological insulators by gate voltage

We investigate electron transport through Hg Te ribbons embedded by strip-shape gate voltage through using a nonequilibrium Green function technique. The numerical calculations show that as the gate voltage is increased, an edgerelated state in the valence band structure of the system shifts upwards, then hangs inside the band gap and merges into the conduction band finally. It is interesting that as the gate voltage is increased continuously, another edge-related state in the valence band also shifts upwards in the small-k region and contacts the previous one to form a Dirac cone in the band structure. Meanwhile in this process, the conductance spectrum displays as multiple resonance peaks characterized by some strong antiresonance valleys in the band gap, then behaves as Fabry–P＇erot oscillations and finally develops into a nearly perfect quantum plateau with a value of 2e^2/h. These results give a physical picture to understand the formation process of the Dirac state driven by the gate voltage and provide a route to achieving particular quantum oscillations of the electronic transport in nanodevices.