ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE p-LAPLACIAN DIFFUSION

We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.

Nondegenerate Soliton Solutions of(2+1)-Dimensional Multi-Component Maccari System

For a multi-component Maccari system with two spatial dimensions,nondegenerate one-soliton and two-soliton solutions are obtained with the bilinear method.It can be seen by drawing the spatial graphs of nondegenerate solitons that the real component of the system shows a cross-shaped structure,while the two solitons of the complex component show a multi-solitoff structure.At the same time,the asymptotic analysis of the interaction behavior of the two solitons is conducted,and it is found that under partially nondegenerate conditions,the real and complex components of the system experience elastic collision and inelastic collision,respectively.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

AN ALGEBRAIC APPROACH TO DEGENERATE APPELL POLYNOMIALS AND THEIR HYBRID FORMS VIA DETERMINANTS

It is remarkable that studying degenerate versions of polynomials from algebraic point of view is not limited to only special polynomials but can also be extended to their hybrid polynomials.Indeed for the first time,a closed determinant expression for the degenerate Appell polynomials is derived.The determinant forms for the degenerate Bernoulli and Euler polynomials are also investigated.A new class of the degenerate Hermite-Appell polynomials is investigated and some novel identities for these polynomials are established.The degenerate Hermite-Bernoulli and degenerate Hermite-Euler polynomials are considered as special cases of the degenerate Hermite-Appell polynomials.Further,by using Mathematica,we draw graphs of degenerate Hermite-Bernoulli polynomials for different values of indices.The zeros of these polynomials are also explored and their distribution is presented.

Ground State and Its Topological Properties of Three-Dimensional Spin-Orbit Coupled Degenerate Fermi Gases

Three-dimensional(3D)degenerate Fermi gases in the presence of spin-orbit coupling,inducing various kinds of physical findings and phenomena,have attracted tremendous attention in these years.We investigate the 3D spin-orbit coupled degenerate Fermi gases in theory and first present the analytic expression of their ground state.Our study provides an innovative perspective into understanding of the topological properties of 3D unconventional superconductors,and describes the topological phase transitions in trivial and topological phase areas.Further,such a system is provided with a richer set of Cooper pairings than traditional superconductors.The dual Cooper pairs with same spin directions emerge and exhibit peculiar behaviors,leading to topological phase transitions.Our study and discussion can be generalized to some other types of unconventional superconductors and areas of optical lattices.

Quantum degenerate Bose–Fermi atomic gas mixture of 23Na and 40K

We report a compact experimental setup for producing a quantum degenerate mixture of Bose23Na and Fermi40K gases. The atoms are collected in dual dark magneto–optical traps(MOT) with species timesharing loading to reduce the light-induced loss, and then further cooled using the gray molasses technique on the D2line for23Na and D1line for40K. The microwave evaporation cooling is used to cool23Na in |F = 2, mF= 2〉 in an optically plugged magnetic trap, meanwhile,40K in |F = 9/2, mF= 9/2〉 is sympathetically cooled. Then the mixture is loaded into a large volume optical dipole trap where23Na atoms are immediately transferred to |1, 1〉 for further effective cooling to avoid the strong three-body loss between23Na atoms in |2, 2〉 and40K atoms in |9/2, 9/2〉. At the end of the evaporation in optical trap, a degenerate Fermi gas of40K with 1.9 × 10^(5) atoms at T/TF= 0.5 in the |9/2, 9/2〉 hyperfine state coexists with a Bose–Einstein condensate(BEC) of23Na with 8 × 10^(4) atoms in the |1, 1〉 hyperfine state at 300 n K. We also can produce the two species mixture with the tunable population imbalance by adjusting the 23Na magneto–optical trap loading time.

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.

Some Identities of the Degenerate Poly-Cauchy and Unipoly Cauchy Polynomials of the Second Kind

In this paper,we introduce modified degenerate polyexponential Cauchy(or poly-Cauchy)polynomials and numbers of the second kind and investigate some identities of these polynomials.We derive recurrence relations and the relationship between special polynomials and numbers.Also,we introduce modified degenerate unipolyCauchy polynomials of the second kind and derive some fruitful properties of these polynomials.In addition,positive associated beautiful zeros and graphical representations are displayed with the help of Mathematica.

The Solvability of the Degenerate Differential Systems with Delay

In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.

Some Results on Type 2 Degenerate Poly-Fubini Polynomials and Numbers

In this paper,we introduce type 2 degenerate poly-Fubini polynomials and derive several interesting characteristics and properties.In addition,we define type 2 degenerate unipoly-Fubini polynomials and establish some certain identities.Furthermore,we give some relationships between degenerate unipoly polynomials and special numbers and polynomials.In the last section,certain beautiful zeros and graphical representations of type 2 degenerate poly-Fubini polynomials are shown.

STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION

Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.

Study of Degenerate Poly-Bernoulli Polynomials byλ-Umbral Calculus

Recently,degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee.The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed‘λ-umbral calculus.’In more detail,we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind,by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind,and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.

The Riemann problem for nonlinear degenerate wave equations

This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case.

Global existence and blow up of a degenerate parabolic system

This paper deals with positive solutions of a degenerate parabolic system: u t= Δ u m+ v p ln α(h+u), v t= Δ v n+u q ln β(h+v) with homogeneous Dirichlet boundary conditions and positive initial conditions. This system describes the processes of diffusion of heat and burning in two component continuous media with nonlinear conductivity and volume energy release. We obtain the global existence and blow up results of the solution relying on comparison with carefully constructed upper solutions and lower solutions.

Cloning of Thymidine Kinase Gene of Duck Plague Virus Using Degenerate PCR

The DNA of duck plague virus （DPV） thymidine kinase （TK） gene was cloned and sequenced from a vaccine virus in the study. Degenerate oligonucleotide primers for the consensus site of herpesvirus UL24, TK, and glycoprotein H（gH） gene were used in the polymerase chain reaction （PCR） to amplify DNA product with 3 741-base-pairs （bp） in size. DNA sequence analysis revealed a 1 077-base-pairs （bp） open reading frame （ORF） encoding a 358 amino acid polypeptide homologous to herpesvirus TK proteins. The predicted TK protein shared 31.2, 41.3, 35.7, 37.4, and 28.4% identity with herpes simplex virus typel, equine herpesvirus type 4, Marek＇s disease virus 2, herpesvirus turkey, and infectious laryngotracheitis virus, respectively. Comparison of the amino acid sequences of other herpesvirus TK proteins showed that these proteins were not conserved on the whole, otherwise the portion of the TK proteins corresponding to the nucleotide binding domain and the nucleoside binding site were highly conserved among herpesvirus. Comparison with the amino acid sequences of the conserved nucleotide and nucleoside binding domains of other eleven herpesvirus TK proteins to the predicted DPV peptide confirmed its identity as the DPV TK protein.

BLOW-UP AND GLOBAL EXISTENCE FOR A COUPLED SYSTEM OF DEGENERATE PARABOLIC EQUATIONS IN A BOUNDED DOMAIN

This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut= △u^l ＋ u^p1v^q1 and vt = △v ^m ＋ u^p2 v^q2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1 - （l -p1）（m- q2）, the initial data, and the domain Ω.

The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay

This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.

THE BLOW-UP PROPERTIES FOR A DEGENERATE SEMILINEAR PARABOL IC EQUATION WITH NONL OCAL SOURCE

This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.

Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations

We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.