Non-commutative Chiral QCD2 Model

The effective action of chiral QCD₂ was studied in two-dimensional non-commutative space-time by using path integral approach. It is shown that vector boson has a mass generation and the effective Lagrangian contains a term corresponding to a Wess-Zumino-Witten-like term.     

Curriculum, Classroom Practices, and Tool Design in the Learning of Functions Through Technology-Aided Experimental Approaches

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a ‘transposition’ of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic geometry and spreadsheets. The paper focuses then on the potentialities of classroom use of computer algebra packages that could help to go beyond this shortcoming. It looks at a contradiction: while symbolic calculation is a basic tool for mathematicians, curricula and teachers are very cautious regarding their use by students. The rest of the paper considers the design and experiment of a computer environment Casyopée as means to contribute to an evolution of curricula and classroom practices to achieve the transposition in the domain of algebraic activities linked to functions.     

Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.     

On enumeration of polynomial equivalence classes

The isomorphism of polynomials(IP),one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials.Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem.In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX2qi when char(Fq) = 2,which implies that these polynomials are all weak IP instances.Moreover,we study the cardinality of an equivalence class containing the binomial aX 2q i + bX 2qj(i=j) over Fqn without the restriction that char(Fq) = 2,which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.     

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained.     

A meshless method based on the dual reciprocity method for one‐dimensional stochastic partial differential equations

This article describes a new meshless method based on the dual reciprocity method (DRM) for the numerical solution of one‐dimensional stochastic heat and advection–diffusion equations. First, the time derivative is approximated by the time–stepping method to transforming the original stochastic partial differential equations (SPDEs) into elliptic SPDEs. The resulting elliptic SPDEs have been approximated with the new method, which is a combination of radial basis functions (RBFs) method and the DRM method. We have used inverse multiquadrics (IMQ) and generalized IMQ (GIMQ) RBFs, to approximate functions in the presented method. The noise term has been approximated at the source points, at each time step. The developed formulation is verified in two test problems with investigating the convergence and accuracy of numerical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 292–306, 2016     

Dynamics of a general non-autonomous stochastic Lotka-Volterra model with delays

In this paper, a general non-autonomous n-species Lotka-Volterra model with delays and stochastic perturbation is investigated. For this model, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence are established. The influences of the stochastic noises to the properties of the stochastic model are discussed. The property permanence for the model is preserved with the sufficiently small noise and sufficiently large noise may cause extinction of the model. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.     

GJMS operators and Q-curvature for conformal Codazzi structures

The conformal Codazzi structure is an intrinsic geometric structure on strictly convex hypersurfaces in a locally flat projective manifold. We construct the GJMS operators and the Q-curvature for conformal Codazzi structures by using the ambient metric. We relate the total Q-curvature to the logarithmic coefficient in the volume expansion of the Blaschke metric, and derive the first and second variation formulas for a deformation of strictly convex domains.     

Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems

A smoothing method for solving stochastic linear complementarity problems is proposed. The expected residual minimization reformulation of the problem is considered, and it is approximated by the sample average approximation (SAA). The proposed method is based on sequential solving of a sequence of smoothing problems where each of the smoothing problems is defined with its own sample average approximation. A nonmonotone line search with a variant of the Barzilai–Borwein (BB) gradient direction is used for solving each of the smoothing problems. The BB search direction is efficient and low cost, particularly suitable for nonmonotone line search procedure. The variable sample size scheme allows the sample size to vary across the iterations and the method tends to use smaller sample size far away from the solution. The key point of this strategy is a good balance between the variable sample size strategy, the smoothing sequence and nonmonotonicity. Eventually, the maximal sample size is used and the SAA problem is solved. Presented numerical results indicate that the proposed strategy reduces the overall computational cost.