GENERALIZED VARIATIONAL DATA ASSIMILATION METHOD AND NUMERICAL EXPERIMENT FOR NON-DIFFERENTIAL SYSTEM

The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.

Test Method for Refractoriness Under Load of Refractory Products(Non-differential,with Rising Temperature)

This standard specifies the definitions, theory, apparatus, specimens, procedures, test results and disposal, test error and report of test method for refractoriness under load of refractory products （non-differential, with rising temperature）.

A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

This paper develops a fully distributed hybrid control framework for distributed constrained optimization problems.The individual cost functions are non-differentiable and convex.Based on hybrid dynamical systems,we present a distributed state-dependent hybrid design to improve the transient performance of distributed primal-dual first-order optimization methods.The proposed framework consists of a distributed constrained continuous-time mapping in the form of a differential inclusion and a distributed discrete-time mapping triggered by the satisfaction of local jump set.With the semistability theory of hybrid dynamical systems,the paper proves that the hybrid control algorithm converges to one optimal solution instead of oscillating among different solutions.Numerical simulations illustrate better transient performance of the proposed hybrid algorithm compared with the results of the existing continuous-time algorithms.

Holographic-Type Gravitation via Non-Differentiability in Weyl-Dirac Theory

In the Weyl-Dirac non-relativistic hydrodynamics approach, the non-linear interaction between sub-quantum level and particle gives non-differentiable properties to the space. Therefore, the movement trajectories are fractal curves, the dynamics are described by a complex speed field and the equation of motion is identified with the geodesics of a fractal space which corresponds to a Schrodinger non-linear equation. The real part of the complex speed field assures, through a quantification condition, the compatibility between the Weyl-Dirac non-elativistic hydrodynamic model and the wave mechanics. The mean value of the fractal speed potential, identifies with the Shanon informational energy, specifies, by a maximization principle, that the sub-quantum level “stores” and “transfers” the informational energy in the form of force. The wave-particle duality is achieved by means of cnoidal oscillations modes of the state density, the dominance of one of the characters, wave or particle, being put into correspondence with two flow regimes (non-quasi-autonomous and quasi-autonomous) of the Weyl-Dirac fluid. All these show a direct connection between the fractal structure of space and holographic principle.

具有随机扰动的三种群系统的持久性和非持久性

建立并分析了随机三种群模型,应用随机微分方程的比较原理得到该系统的持久性和非持久性.

A Preliminary Application of the Differential Evolution Algorithm to Calculate the CNOP

A projected skill is adopted by use of the differential evolution (DE) algorithm to calculate a conditional nonlinear optimal perturbation (CNOP). The CNOP is the maximal value of a constrained optimization problem with a constraint condition, such as a ball constraint. The success of the DE algorithm lies in its ability to handle a non-differentiable and nonlinear cost function. In this study, the DE algorithm and the traditional optimization algorithms used to obtain the CNOPs are compared by analyzing a theoretical grassland ecosystem model and a dynamic global vegetation model. This study shows that the CNOPs generated by the DE algorithm are similar to those by the sequential quadratic programming (SQP) algorithm and the spectral projected gradients (SPG2) algorithm. If the cost function is non-differentiable, the CNOPs could also be caught with the DE algorithm. The numerical results suggest the DE algorithm can be employed to calculate the CNOP, especially when the cost function is non-differentiable.

CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENT-IABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary dec-imal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.

Fixed Points and Asymptotic Properties of Neutral Stochastic Delay Differential Equations

This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.

Dynamic analysis of a predator-prey model of Gause type with Allee effect and non-Lipschitzian hyperbolic-type functional response

In this work,we study a predator-prey model of Gause type,in which the prey growth rate is subject to an Allee effect and the action of the predator over the prey is determined by a generalized hyperbolic-type functional response,which is neither differentiable nor locally Lipschitz at the predator axis.This kind of functional response is an extension of the so-called square root functional response,used to model systems in which the prey have a strong herd structure.We study the behavior of the solutions in the first quadrant and the existence of limit cycles.We prove that,for a wide choice of parameters,the solutions arrive at the predator axis in finite time.We also characterize the existence of an equilibrium point and,when it exists,we provide necessary and sufficient conditions for it to be a center-type equilibrium.In fact,we show that the set of parameters that yield a center-type equilibrium,is the graph of a function with an open domain.We also prove that any center-type equilibrium is stable and it always possesses a supercritical Hopf bifurcation.In particular,we guarantee the existence of a unique limit cycle,for small perturbations of the system.

Subgradient-based feedback neural networks for non-differentiable convex optimization problems

This paper developed the dynamic feedback neural network model to solve the convex nonlinear programming problem proposed by Leung et al. and introduced subgradient-based dynamic feedback neural networks to solve non-differentiable convex optimization problems. For unconstrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive, we proved that with arbitrarily given initial value, the trajectory of the feedback neural network constructed by a projection subgradient converges to an asymptotically stable equilibrium point which is also an optimal solution of the primal unconstrained problem. For constrained non-differentiable convex optimization problem, on the assumption that the objective function is convex coercive and the constraint functions are convex also, the energy functions sequence and corresponding dynamic feedback subneural network models based on a projection subgradient are successively constructed respectively, the convergence theorem is then obtained and the stopping condition is given. Furthermore, the effective algorithms are designed and some simulation experiments are illustrated.

Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process

Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.

HIGHER-ORDER DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED TYPE I AND RELATED FUNCTIONS

This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.