Optimal confrontation position selecting games model and its application to one-on-one air combat

In the air combat process,confrontation position is the critical factor to determine the confrontation situation,attack effect and escape probability of UAVs.Therefore,selecting the optimal confrontation position becomes the primary goal of maneuver decision-making.By taking the position as the UAV’s maneuver strategy,this paper constructs the optimal confrontation position selecting games(OCPSGs)model.In the OCPSGs model,the payoff function of each UAV is defined by the difference between the comprehensive advantages of both sides,and the strategy space of each UAV at every step is defined by its accessible space determined by the maneuverability.Then we design the limit approximation of mixed strategy Nash equilibrium(LAMSNQ)algorithm,which provides a method to determine the optimal probability distribution of positions in the strategy space.In the simulation phase,we assume the motions on three directions are independent and the strategy space is a cuboid to simplify the model.Several simulations are performed to verify the feasibility,effectiveness and stability of the algorithm.

An adaptive ant colony system algorithm for continuous-space optimization problems

Ant colony algorithms comprise a novel category of evolutionary computation methods for optimization problems, especially for sequencing-type combinatorial optimization problems. An adaptive ant colony algorithm is proposed in this paper to tackle continuous-space optimization problems, using a new objective-function-based heuristic pheromone assignment approach for pheromone update to filtrate solution candidates.Global optimal solutions can be reached more rapidly by self-adjusting the path searching behaviors of the ants according to objective values. The performance of the proposed algorithm is compared with a basic ant colony algorithm and a Square Quadratic Programming approach in solving two benchmark problems with multiple extremes. The results indicated that the efficiency and reliability of the proposed algorithm were greatly improved.

Some New Fixed Point Theorems in Probabilistic Metric Spaces

In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.

Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.

Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces

The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.

Effect of Continuous Cooling Conditions on Microstructure and Mechanical Properties of High Carbon Steel Rod

The effect of cooling rate and austenitizing condition on the mechanical properties of high carbon steel (SWRH82B) has beeninvestigated. Specimens were made of high carbon steel rod and heat-treated by Gleeble-2000 to produce a wide variation in prior austenite size. Different cooling rates were carried out, and then pearlite interlaminar spacing and mechanical properties were measured andtested respectively. According to the results, it could be found that under the continuous cooling with the increase of cooling rate, tensilestrength greatly increases and reduction in area exhibits a slightly increase for an equivalent value of prior austenite grain size. Whenprior austenite size increases, reduction in area decreases, and tensile strength increases slightly for an equivalent value of pearlite interlaminar spacing. It is concluded that prior austenite size primarily controls ductility and pearlite interlaminar spacing controls tensilestrength. Mathematical formulae are given for these relations.

NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE MODIFIED CAMASSA-HOLM EQUATION ON THE LINE

In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt ＋ umx ＋ 2ux m = 0, m =（1- δx^2）^2u,u（x, 0） = u0（x） ∈ H^s（R）, x ∈ R, t 〉 0,and show that the solution map is not uniformly continuous in Sobolev spaces H^s（R） for s 〉 7/2. Compared with the periodic problem, the non-periodic problem is more difficult,e.g., it depends on the conservation law. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part.

Well-posedness of degenerate differential equations in Hiilder continuous function spaces

Using known operator-valued Fourier multiplier results on vectorvalued HSlder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations （Mu）＇（t） = Au（t） ＋ f（t） for t ∈ R in HSlder continuous function spaces C^α（R; X） by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D（A） D（M）.

Stochastic differential equation software reliability growth model with change-point

This paper presents software reliability growth models(SRGMs) with change-point based on the stochastic differential equation(SDE).Although SRGMs based on SDE have been developed in a large scale software system,considering the variation of failure distribution in the existing models during testing time is limited.These SDE SRGMs assume that failures have the same distribution.However,in practice,the fault detection rate can be affected by some factors and may be changed at certain point as time proceeds.With respect to this issue,in this paper,SDE SRGMs with changepoint are proposed to precisely reflect the variations of the failure distribution.A real data set is used to evaluate the new models.The experimental results show that the proposed models have a fairly accurate prediction capability.

Preliminary Study of Reconstruction of a Dynamic System Using an One－Dimensional Time Series

This paper concerns the reconstruction of a dynamic system based on phase space continuation of monthly meantemperature iD time series and the assumption that the equation for the time-varying evolution of phase space statevariables contains linear and nonlinear quadratic terms. followed by the fitting of the dataset subjected to continuation so as to get, by the least square method. the coefficients of the terms, of which those of greater variance contribution are retained for use. Results show that the obtained low-order system may be used to describe nonlinear properties of the short range climate variation shown by monthly mean temperature series.

A Nonlinear Time-lag Differential Equation Mdel for Predicting Monthly Precipitation

This paper investigates the nonlinear prediction of monthly rainfall time series which consists of phase space continuation of one-dimensional sequence, followed by least-square determination of the coefficients for the terms ofthe time-lag differential equation model and then fitting of the prognostic expression is made to 1951-1980 monthlyrainfall datasets from Changsha station. Results show that the model is likely to describe the nonlinearity of the allnual cycle of precipitation on a monthly basis and to provide a basis for flood prevention and drought combating forthe wet season.

Continuous selections for pseudo-lower semicontinuous set-valued mappings on convex structure spaces and hyperspace contractibility

SINCE 1956, Michael’s continuous selection theory has been applied to functional analysis,topology, approximation theory and other mathematical fields. In this letter, the concept ofthe pseudo-lower semicontinuity is introduced, and a convex structure of metric space is de-fined. A continuous selection theorem for pseudo-lower semicontinuity is given. This

On Ideal Convergence of Double Sequences in Probabilistic Normed Spaces

The notion of ideal convergence is a generalization of statistical convecgence which has been intensively investigated in last few years. For an admissible ideal ∮ C N × N, the aim of the present paper is to introduce the concepts of ∮-convergence and ：∮＊-convergence for double sequences on probabilistic normed spaces （PN spaces for short）. We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide. We also define ∮-Cauchy and ：∮＊- Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces. We establish example which shows that our method of convergence for double sequences on PN spaces is more general.

Characteristic conditions-for strongly continuous groups of linear operators on a Hilbert space

IN 1932, Stone [1] gave the first result concerning C0 semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C0 group of unitary operators on a Hilbert space if and only if it is skew-adjoint. This result has been applied extensively to linear partial differential equations （PDEs） with a law of conservation. Hille [2] then discovered the generation theorem of the Hille-Yosida type for a C0 group on a Banach space. There are also some conditions under which a C0 semigroup on a Banach space can be embedded in a C0 group. We refer the readers to ref. [3] for details of the results mentioned above.

A Novel Framework for Lim-inf Convergence in Posets

In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T_(0) enriched closure spaces.More precisely,we define and study Enr-convergence in T_(0) enriched closure spaces.Especially,we give a sufficient and necessary condition for Enr-convergence in T_(0) enriched closure spaces to be topological.

GRIP： A Group Recommender Based on Interactive Preference Model

Numerous applications of recommender systems can provide us a tool to understand users. A group recommender reflects the analysis of multiple users＇ behavior, and aims to provide each user of the group with the things they involve according to users＇ preferences. Currently, most of the existing group recommenders ignore the interaction among the users. However, in the course of group activities, the interactive preferences will dramatically affect the success of recommenders. The problem becomes even more challenging when some unknown preferences of users are partly influenced by other users in the group. An interaction-based method named GRIP （Group Recommender Based on Interactive Preference） is presented which can use group activity history information and recommender post-rating feedback mechanism to generate interactive preference parameters. To evaluate the performance of the proposed method, it is compared with traditional collaborative filtering on the MovieLens dataset. The results indicate the superiority of the GRIP recommender for multi-users regarding both validity and accuracy.

The Fine Spectra of the Difference Operator △ Over the Sequence Space bv_p,(1≤p<∞)

The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.

Generation of ultra-wide and flat optical frequency comb based on electro-absorption modulator and frequency modulator

An ultra-wide and flat optical frequency comb(OFC) generation scheme using multiple continuous wave(CW) light sources based on electro-absorption modulator(EAM) and frequency modulator(FM) is proposed. In the scheme, each CW light source is broadened and modulated by the first EAM and FM, respectively. The second EAM is introduced to flatten the ultra-wide OFC lines. By setting the wavelength spacing of light sources equal to the bandwidth of sub-OFC, an ultra-wide OFC can be obtained. Principle analysis and simulation for the scheme are performed. The results show that in the case of a single light source, a tunable and flat OFC is obtained. With the increase of light sources, the bandwidth of the generated ultra-wide OFC expands rapidly. In the case of 28 light sources, a 22 GHz ultra-wide OFC with bandwidth of 16.52 THz can be generated.

Design Methodology of the Structure of Postal Express Mail Networks of Aviation Channels in China

On the basis of the postal area center office system, the continuous space approximation is used to study the structure of postal express mail networks of aviation channels in China. Tradeoffs among sorting, handling, transportation, administrative and facilities costs are examined. The optimizing design methodology proposed in this paper can be used to analyze and design the postal express mail network. The objective is to minimize the total system cost.

A parallel scheduling algorithm for reinforcement learning in large state space

The main challenge in the area of reinforcement learning is scaling up to larger and more complex problems. Aiming at the scaling problem of reinforcement learning, a scalable reinforcement learning method, DCS-SRL, is proposed on the basis of divide-and-conquer strategy, and its convergence is proved. In this method, the learning problem in large state space or continuous state space is decomposed into multiple smaller subproblems. Given a specific learning algorithm, each subproblem can be solved independently with limited available resources. In the end, component solutions can be recombined to obtain the desired result. To ad- dress the question of prioritizing subproblems in the scheduler, a weighted priority scheduling algorithm is proposed. This scheduling algorithm ensures that computation is focused on regions of the problem space which are expected to be maximally productive. To expedite the learning process, a new parallel method, called DCS-SPRL, is derived from combining DCS-SRL with a parallel scheduling architecture. In the DCS-SPRL method, the subproblems will be distributed among processors that have the capacity to work in parallel. The experimental results show that learning based on DCS-SPRL has fast convergence speed and good scalability.