Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii–Moriya interaction

The quantum phase transition(QPT)and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii-Moriya(DM)interaction,which is interpreted as an electric field,are investigated,wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order.It is shown that the thermal Drude weight is a good quantity to characterize the gapped(D_(th)=0)and gapless(D_(th)>0)ground states.The continuous QPT is marked by a quantum critical point(QCP)associated with entropy accumulation,which is manifested by a characteristic Güneisen ratio(GR)with or without selfduality symmetry.It is shown that at a self-dual QCP,the GR keeps a finite value as T→0,while at a general QCP without self-duality symmetry,it displays a power-law temperature dependent divergence:Γ(T,r_(c))∼±T^(−1),which provides a novel thermodynamic means for probing QPT.

Massive self-duality solution associated with invariant one-forms

A massive self-duality solution associated with invariant 1-forms is presented. At the zero mass limit the massive self-dual theory of the SO（3） gauge group on 4 dimensions cannot be reduced to that of massless self-duality.In such a case the self-dual connection turns to the flat connection and one cannot obtain a massless theory in such an approach.

规范场论中自对偶磁单极子解的存在唯一性

Magnetic monopoles stand for the static solution arising from a(1 + 3)–dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity.

SELF-DUAL PERMUTATION CODES OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.

On Study of Solutions of Kac-van Moerbeke Lattice and Self-dual Network Equations

The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical computation of travelling wave solutions for differential difference equations, our method obtains exact solutions which have physical relevance.

Self-Dual Permutation Codes over Finite Chain Rings

Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given.

The Self-dual Codes over Formal Power Series Rings

The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.

Self-dual Codes Defined on Factor Graphs

A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.

ON SELF-DUAL PERMUTATION CODES

Permutation codes over finite fields are introduced, some conditions for existence or non-existence of self-dual permutation codes are obtained.

Fermionic Zero Modes in Self-dual Vortex Background on a Torus

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation.

Construction of Self-dual Codes over F_p+vF_p

In this paper, we give an explicit construction for self-dual codes over F_p+vF_p(v^2= v) and determine all the self-dual codes over F_p+ vF_p by using self-dual codes over finite field F_p, where p is a prime.

New MDS Euclidean and Hermitian Self-Dual Codes over Finite Fields

In this paper, we construct MDS Euclidean self-dual codes which are ex-tended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes.

Self-dual Vortices in Schrdinger-Chern-Simons Model

By making use of the U（1） gauge potential decomposition theory and the Ф-mapping topological current theory, we investigate the Schroedinger-Chern-Simons model in the thin-film superconductor system and obtain an exact Bogomolny self-dual equation with a topological term. It is revealed that there exist self-dual vortices in the system. We study the inner topological structure of the self-dual vortices and show that their topological charges are topologically quantized and labeled by Hopf indices and Brouwer degrees. Furthermore, the vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field Ф.

Self-dual Codes with Symplectic Inner Product

In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.

Fractional Breaking Soliton Equation Reduced from a Linear Spectral Problem Associated with Fractional Self-Dual Yang-Mills Equations

Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.

Deformation of Rigid Conjugate Self-dual Galois Representations

In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called rigid.Second,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

Novel Multisoliton Solutions of Some Soliton Equations

The novel multisoliton solutions for the nonlinear lumped self-dual network equations, Toda lattice and KP equation were obtained by using the Hirota direct method.

The Double Self—Dual Gravity with Cosmological Term and Constraints Under the Double Constant Conformal Transformation

The double constraint equations in the self-dual gravitational theory containing the cosmological term are derived in gravity. Furthermore, in order to deeply study the Lorentzian and Euclidean reality conditions for this theory, the relations between constraints are discussed by introducing the double constant conformal transformation and the double complex function method.

CONSTACYCLIC CODES OF ARBITRARY LENGTHS OVER RING Z_(p^m) +vZ_(p^m)

By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.