Nontrivial Topological Phases in Ternary Borides M_(2)XB_(2)(M=W,Mo;X=Co,Ni)

The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics.

Flat Band and Z_(2)Topology of Kagome Metal CsTi_(3)Bi_(5)

The simple kagome-lattice band structure possesses Dirac cones,flat band,and saddle point with van Hove singularities in the electronic density of states,facilitating the emergence of various electronic orders.Here we report a titanium-based kagome metal CsTi_(3)Bi_(5)where titanium atoms form a kagome network,resembling its isostructural compound CsV_3Sb_5.Thermodynamic properties including the magnetization,resistance,and heat capacity reveal the conventional Fermi liquid behavior in the kagome metal CsTi_(3)Bi_(5)and no signature of superconducting or charge density wave(CDW)transition anomaly down to 85 m K.Systematic angle-resolved photoemission spectroscopy measurements reveal multiple bands crossing the Fermi level,consistent with the first-principles calculations.The flat band formed by the destructive interference of hopping in the kagome lattice is observed directly.Compared to Cs V_(3)Sb_(5),the van Hove singularities are pushed far away above the Fermi level in CsTi_(3)Bi_(5),in line with the absence of CDW.Furthermore,the first-principles calculations identify the nontrivial Z_(2)topological properties for those bands crossing the Fermi level,accompanied by several local band inversions.Our results suppose CsTi_(3)Bi_(5)as a complementary platform to explore the superconductivity and nontrivial band topology.

Multi-Pseudo Peakons in the b-Family Fifth-Order Camassa–Holm Model

The b-family fifth-order Camassa–Holm model is a nontrivial extension of the celebrated Camassa–Holm model. This work investigates single-pseudo and multi-pseudo peakon solutions of this model via analytical calculations and numerical simulations. Some intriguing phenomena of multi-pseudo peakon which do not appear in the classical Camassa–Holm model interactions are observed, such as two-pseudo peakon collapses, threepseudo peakon resonance, and multi-pseudo peakon inelastic collisions. The present work will inspire further studies on the higher-dimensional integrable Camassa–Holm systems which may have high value in investigating the related higher-dimensional physical problems.

Scientists Reveal the Band Topology and Orbital-selective Nematicity in a New Ti-based Kagome Superconductor

The kagome superconductor with a twodimensional corner-sharing triangular lattice has attracted tremendous attention due to the interplay between nontrivial band topology,anomalous Hall effect(AHE),charge density waves(CDW),pair density wave(PDW),electronic nematicity and unconventional superconductivity.All these exotic quantum phenomena are thought to originate from the unique electronic structure of the kagome lattice including flat bands,Dirac cones and van Hove singularities.

NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR BIHARMONIC EQUATION INVOLVING CRITICAL EXPONENTS

In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.

THE EXISTENCE OF NONTRIVIAL SOLUTIONS TO A SEMILINEAR ELLIPTIC SYSTEM ON R N WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION

In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS INVOLVING m CRITICAL HARDY-SOBOLEV EXPONENTS AND m SIGN-CHANGING WEIGHT FUNCTION

In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign- changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.

THE EXISTENCE OF NONTRIVIAL SOLUTIONS OF HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.

Pressure-Induced Topological and Structural Phase Transitions in an Antiferromagnetic Topological Insulator

Recently,natural van der Waals heterostructures of(MnBi2 Te4)m(Bi2 Te3)n have been theoretically predicted and experimentally shown to host tunable magnetic properties and topologically nontrivial surface states.We systematically investigate both the structural and electronic responses of MnBi2 Te4 and MnBi4 Te7 to external pressure.In addition to the suppression of antiferromagnetic order,MnBi2 Te4 is found to undergo a metalsemiconductor-metal transition upon compression.The resistivity of MnBi4 Te7 changes dramatically under high pressure and a non-monotonic evolution of p(T)is observed.The nontrivial topology is proved to persist before the structural phase transition observed in the high-pressure regime.We find that the bulk and surface states respond differently to pressure,which is consistent with the non-monotonic change of the resistivity.Interestingly,a pressure-induced amorphous state is observed in MnBi2 Te4,while two high-pressure phase transitions are revealed in MnBi4 Te7.Our combined theoretical and experimental research establishes MnBi2 Te4 and MnBi4 Te7 as highly tunable magnetic topological insulators,in which phase transitions and new ground states emerge upon compression.

A NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC EQUATION VIA DUAL APPROACH

In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in R^N which includes the so-called modified nonlinear Schrodinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.

MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

We study nonautonomonus second order periodic systems with a nonslnooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

Oscillations in Systems of Linear Neutral Differential Equations

Algebraic sufficient conditions are obtained for all nontrivial solutions of the linear system d d t[x(t)+cx(t-τ)]+A(t)x(t-σ(t))=0to be oscillatory.

Five Nontrivial Solutions of p-Laplacian Problems Involving Critical Exponents and Singular Cylindrical Potential

In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem

Disorder effects in topological states:Brief review of the recent developments

Disorder inevitably exists in realistic samples,manifesting itself in various exotic properties for the topological states.In this paper,we summarize and briefly review the work completed over the last few years,including our own,regarding recent developments in several topics about disorder effects in topological states.For weak disorder,the robustness of topological states is demonstrated,especially for both quantum spin Hall states with Z2 = 1 and size induced nontrivial topological insulators with Z2 = 0.For moderate disorder,by increasing the randomness of both the impurity distribution and the impurity induced potential,the topological insulator states can be created from normal metallic or insulating states.These phenomena and their mechanisms are summarized.For strong disorder,the disorder causes a metal-insulator transition.Due to their topological nature,the phase diagrams are much richer in topological state systems.Finally,the trends in these areas of disorder research are discussed.

一类三阶非线性系统的全局渐近稳定性

本文利用Liapanov函数讨论了一类菲线性系统的全局渐近稳定性态。在研究自动调节系统和实际运用中,以往都是运用BKL定理,本文利用改进了的BKL定理,得到了一类三阶非线性系统的全局渐近稳定性。包含了Lurpe、Rongelerff、徐兆、张献珍文献的结论作为特例,并削弱了上述文献中的一些条件。

EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

One parabolic p-Laplacian-like differential equation with mixed boundaries is au/at in the corresponding studies is replaced by a（au/at）, studied in this paper, where the item au/at which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2（O, T; L2 （Ω）） is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.

MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.

Quantum Oscillations in Noncentrosymmetric Weyl Semimetal SmAlSi

As a new type of quantum state of matter hosting low energy relativistic quasiparticles,Weyl semimetals(WSMs)have attracted significant attention for scientific community and potential quantum device applications.In this study,we present a comprehensive investigation of the structural,magnetic,and transport properties of noncentrosymmetric RAl Si(R=Sm,Ce),which have been predicted to be new magnetic WSM candidates.Both samples exhibit nonsaturated magnetoresistance,with about 900%and 80%for Sm Al Si and Ce Al Si,respectively,at temperature of 1.8 K and magnetic field of 9 T.The carrier densities of Sm Al Si and Ce Al Si exhibit remarkable change around magnetic transition temperatures,signifying that the electronic states are sensitive to the magnetic ordering of rare-earth elements.At low temperatures,Sm Al Si reveals prominent Shubnikov–de Haas oscillations associated with the nontrivial Berry phase.High-pressure experiments demonstrate that the magnetic order is robust and survival under high pressure.Our results would yield valuable insights into WSM physics and potentials in applications to next-generation spintronic devices in the RAl Si(R=Sm,Ce)family.