Volume 71, Issue 4

This article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

Korteweg–de Vries (KdV)-type equations can describe the nonlinear phenomena in shallow water waves, stratified internal waves, and ion-acoustic waves in plasmas. In this article, the two-dimensional generalization of the Sawada–Kotera equation, one of the KdV-type equations, is discussed by virtue of the Bell polynomials and Hirota method. The results show that there exist multi-soliton solutions for such an equation. Relations between the direction of the soliton propagation and coordinate axes are shown. Elastic interaction with the multi-soliton solutions are analysed.

We predict that a given transition-metal salt as, for example, a K 2 CuCl 4 ·2H 2 O–type compound, can behave as an electrical conductor in the paramagnetic case. In fact, we determine the electrical conductance in a salt of this type. This conductance is found to be quantised in agreement with previous well-known results. Related mathematical expressions in the context of superexchange interaction are obtained. In addition, we determine the corresponding (macroscopically viewed) current density and the associated electron wave functions.

Effects of the size of the unit cell on energy, atomic charges, and phonon frequencies of graphene at the Γ point of the Brillouin zone are studied in the absence and presence of an electric field using density functional theory (DFT) methods (LDA and DFT-PBE functionals with Goedecker–Teter–Hutter (GTH) and Troullier–Martins (TM) norm-conserving pseudopotentials). Two types of unit cells containing n C =4–28 carbon atoms are considered. Results show that stability of graphene increases with increasing size of the unit cell. Energy, atomic charges, and phonon frequencies all converge above n C =24 for all functional-pseudopotentials used. Except for the LDA-GTH calculations, application of an electric field of 0.4 and 0.9 V/nm strengths does not change the trends with the size of the unit cell but instead slightly decreases the binding energy of graphene. Results of this study show that the choice of unit cell size and type is critical for calculation of reliable characteristics of graphene.

A condensing potential (CP) model was established for predicting the geometric structure of two-dimensional (2D) atomic islands on crystal surfaces. To further verify the CP model, statistical molecular dynamics simulations are performed to investigate the trapping adatom process of atomic island steps on Pt (111). According to the detailed analysis on the adatom trapping process, the CP model should be a universal theory to understand the shape of the 2D atomic islands on crystal surfaces.

The aim of this article is to calculate the thermodynamic functions of a neutron star in curved space. We obtained equation of state (EOS) and the excess free energy for a neutron star in curved space up to order n 4 , where n is the density of particles.

The Union Jack lattice UJL ( n , m ) with toroidal boundary condition can be obtained from an n × m square lattice with toroidal boundary condition by inserting a new vertex v f to each face f and adding four edges ( v f , u i ( f )), where u 1 ( f ), u 2 ( f ), u 3 ( f ), and u 4 ( f ) are four vertices on the boundary of f . The Union Jack lattice has been studied extensively by statistical physicists. In this article, we consider the problem of enumeration of spanning trees of the so-called generalised Union Jack lattice UD n , which is obtained from the Aztec diamond ADnt$AD_n^t$ of order n with toroidal boundary condition by inserting a new vertex v f to each face f and adding four edges ( v f , u i ( f )), where u 1 ( f ), u 2 ( f ), u 3 ( f ) and u 4 ( f ) are four vertices on the boundary of f .

In this article, the prolongation structure technique is applied to a generalised inhomogeneous Gardner equation, which can be used to describe certain physical situations, such as the stratified shear flows in ocean and atmosphere, ion acoustic waves in plasmas with a negative ion, interfacial solitary waves over slowly varying topographies, and wave motion in a non-linear elastic structural element with large deflection. The Lax pairs, which are derived via the prolongation structure, are more general than the Lax pairs published before. Under the Painlevé conditions, the linear-damping coefficient equals to zero, the quadratic non-linear coefficient is proportional to the dispersive coefficient c ( t ), the cubic non-linear coefficient is proportional to c ( t ), leaving no constraints on c ( t ) and the dissipative coefficient d ( t ). We establish the prolongation structure through constructing the exterior differential system. We introduce two methods to obtain the Lax pairs: (a) based on the prolongation structure, the Lax pairs are obtained, and (b) via the Lie algebra, we can derive the Pfaffian forms and Lax pairs when certain parameters are chosen. We set d ( t ) as a constant to discuss the influence of c ( t ) on the Pfaffian forms and Lax pairs, and to discuss the influence of d ( t ) on the Pfaffian forms and Lax pairs, we set c ( t ) as another constant. Then, we get different prolongation structure, Pfaffian forms and Lax pairs.

It is easy to check that both algebraic equation Det(p^ − m) = 0$Det(\hat p\, - \,m)\, = \,0$ and Det(p^ + m) = 0$Det(\hat p\, + \,m)\, = \,0$ for u – and v – 4-spinors have solutions with p0 = ±Ep = ± p2 + m2.${p_0}\, = \, \pm {E_p}\, = \, \pm \,\sqrt {{{\bf{p}}^2}\, + \,{m^2}} .$ The same is true for higher-spin equations. Meanwhile, every book considers the equality p 0 = E p for both u – and v – spinors of the (1/2, 0)⊕(0, 1/2) representation only, thus applying the Dirac–Feynman–Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We reconsider this possibility on the quantum field level for both s =1/2 and higher-spin particles.

The truncated Painlevé method is developed to obtain the nonlocal residual symmetry and the Bäcklund transformation for the (2+1)-dimensional KdV–mKdV equation. The residual symmetry is localised after embedding the (2+1)-dimensional KdV–mKdV equation to an enlarged one. The symmetry group transformation of the enlarged system is computed. Furthermore, the (2+1)-dimensional KdV–mKdV equation is proved to be consistent Riccati expansion (CRE) solvable. The soliton–cnoidal wave interaction solution in terms of the Jacobi elliptic functions and the third type of incomplete elliptic integral is obtained by using the consistent tanh expansion (CTE) method, which is a special form of CRE.

With the extended logarithmic flow equations and some extended Vertex operators in generalized Hirota bilinear equations, extended bigraded Toda hierarchy (EBTH) was proved to govern the Gromov-Witten theory of orbiford c NM in literature. The generating function of these Gromov-Witten invariants is one special solution of the EBTH. In this article, the multifold Darboux transformations and their determinant representations of the EBTH are given with two different gauge transformation operators. The two Darboux transformations in different directions are used to generate new solutions from known solutions which include soliton solutions of ( N , N )-EBTH, i.e. the EBTH when N = M . From the generation of new solutions, we can find the big difference between the EBTH and the extended Toda hierarchy (ETH). Also, we plotted the soliton graphs of the ( N , N )-EBTH from which some approximation analysis is given. From the analysis on velocities of soliton solutions, the difference between the extended flows and other flows are shown. The two different Darboux transformations constructed by us might be useful in Gromov-Witten theory of orbiford c NM .

Graphene plasmon has been attracting interests from both theoretical and experimental research due to its gate tunability and potential applications in the terahertz frequency range. Here, we propose an effective scheme to unidirectionally excite the graphene plasmon by exploiting magneto-optical materials in the famous attenuated total reflection (ATR) configuration. We show that the graphene plasmon dispersion relation in such a device is asymmetric in different exciting directions, thus making it possible to couple the incident light unidirectionally to the propagating plasmon. The split of absorption spectrum of graphene clearly indicates that under a magnetic field for one single frequency, graphene plasmon can only be excited in one direction. The possible gate tunablity of excitation direction and the further application of the proposed scheme, such as optical isolator, also are discussed.

In this study we applied the fuzzy logic approach in order to model the energy depending on the two torsion angles for the threonine (C 4 H 9 NO 3 ) molecule. The model is set up according to theoretical results obtained by the density functional theory (B3LYP) with a 6-31 G(d) basic set on a Gausian program. We aimed to determine the best torsion angle values providing the energy of the molecule minimum by a fuzzy logic approach and to compare them with the density functional theory results. It was concluded that the fuzzy logic approach gives information about the untested data and its best value which are expensive and time-consuming to obtain by other methods and experimentation.