HB-Continuous Mappings in L-Topological Space

In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.

A Note on Topological Entropy of Continuous Self-Maps

Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.

Continuous Selections and Fixed Points forφ-maps with Their Applications to Section Problems

The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as applications of the above fixed point theorems, some section problems are discussed. The results generalize and improve many corresponding conclusions.

Characteristics of glucose change in diabetes mellitus generalized through continuous wavelet transform processing:A preliminary study

BACKGROUND The continuous glucose monitoring(CGM)system has become a popular evaluation tool for glucose fluctuation,providing a detailed description of glucose change patterns.We hypothesized that glucose fluctuations may contain specific information on differences in glucose change between type 1 diabetes mellitus(T1DM)and type 2 diabetes mellitus(T2DM),despite similarities in change patterns,because of different etiologies.Unlike Fourier transform,continuous wavelet transform(CWT)is able to simultaneously analyze the time and frequency domains of oscillating data.AIM To investigate whether CWT can detect glucose fluctuations in T1DM.METHODS The 60-d and 296-d glucose fluctuation data of patients with T1DM(n=5)and T2DM(n=25)were evaluated respectively.Glucose data obtained every 15 min for 356 d were analyzed.Data were assessed by CWT with Morlet form(n=7)as the mother wavelet.This methodology was employed to search for limited frequency glucose fluctuation in the daily glucose change.The frequency and enclosed area(0.02625 scalogram value)of 18 emerged signals were compared.The specificity for T1DM was evaluated through multiple regression analysis using items that demonstrated significant differences between them as explanatory variables.RESULTS The high frequency at midnight(median:75 Hz,cycle time:19 min)and middle frequency at noon(median:45.5 Hz,cycle time:32 min)were higher in T1DM vs T2DM(median:73 and 44 Hz;P=0.006 and 0.005,respectively).The area of the>100 Hz zone at midnight to forenoon was more frequent and larger in T1DM vs T2DM.In a day,the lower frequency zone(15-35 Hz)was more frequent and the area was larger in T2DM than in T1DM.The threedimensional scatter diagrams,which consist of the time of day,frequency,and area of each signal after CWT,revealed that high frequency signals belonging to T1DM at midnight had a loose distribution of wave cycles that were 17-24 min.Multivariate analysis revealed that the high frequency signal at midnight could characterize T1DM(odds ratio:1.33,95%confidence interval:1.08-1.62;P=0.006).CONCLUSION CWT might be a novel tool for differentiate glucose fluctuation of each type of diabetes mellitus using CGM data.

Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

CONTINUOUS SELECTION THEOREMS FOR FAN-BROWDER MAPPINGS IN TOPOLOGICAL SPACES AND THEIR APPLICATIONS

The concept of Fan-Browder mappings was first introduced in topological spaces without any convex structure. Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological space without any convex structure and noncompact domain. As applications, some fixed point theorems, coincidence theorems and a nonempty intersection theorem were given. Both the new concepts and results unify and extend many known results in recent literature.

Block and parallel modelling of broad domain nonlinear continuous mapping based on NN

The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.

On Some Properties of Neutrosophic Semi Continuous and Almost Continuous Mapping

The neutrality’s origin,character,and extent are studied in the Neutrosophic set.The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applications.The neutrosophic set can find its spot to research because the universe is filled with indeterminacy.Neutrosophic set is currently being developed to express uncertain,imprecise,partial,and inconsistent data.Truth membership function,indeterminacymembership function,and falsitymembership function are used to express a neutrosophic set in order to address uncertainty.The neutrosophic set producesmore rational conclusions in a variety of practical problems.The neutrosophic set displays inconsistencies in data and can solve real-world problems.We are directed to do our work in semi-continuous and almost continuous mapping on the basis of the neutrosophic set by observing these.Since we are going to study the properties of semi continuous and almost continuous mapping,we present the meaning of N-semi-open set,N-semi-closed set,N-regularly open set,N-regularly closed set,N-continuous mapping,N-open mapping,N-closed mapping,Nsemi-continuous mapping,N-semi-open mapping,N-semi-closed mapping.Additionally,we attempt to demonstrate a portion of their properties and furthermore referred to some examples.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

Logistic映射下N-continuous OFDM加密方案

针对信号传输安全问题,提出利用混沌随机性和初值敏感性相结合的数据传输加密方案.该方案首先利用混沌产生随机混沌序列,然后用该序列改变传输数据的相位以及系统子载波的映射规则,最后利用密钥恢复信号.仿真结果表明该方案能有效对系统进行数据加密,加密效果良好,在保证高频谱利用率和较强分配灵活性的同时,能增强旁瓣抑制效果.因此,该方案能确保数据传输安全.

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.

ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

ON THE SPECTRAL CHARACTERIZATION OF A STRONGLY CONTINUOUS PERTURBED SEMIGROUP

In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.

Necessary Conditions for a Fixed Point of Maps in Non-Metric Spaces

The main purpose of the present work is to introduce necessary conditions for a map on a non-metric space, defined by using a map on a metric space, to have a fixed point.

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.

p-order Feigenbaum's Maps

A continuous map f from the unit closed interval into itself is called a p-order Feigenbaum's map if fp(λx) = λf(x),f(O)=1 and f|[λ,1] is univallecular. In this paper, some characterizations of p order Feigenbaum's maps are discussed and the existence for both types of such maps is proven.

An Efficient PRBG Based on Chaotic Map and Engel Continued Fractions

In recent years, a variety of chaos-based cryptosystems have been proposed. Some of these systems are used in designing a pseudo random bit generator (PRBG) for stream cipher applications. Most of the chaotic systems used in cryptography have good chaotic properties like ergodicity, sensitivity to initial values and sensitivity to control parameters. However, some of them are not very suitable for use in cryptography because of their non-uniform density function, and their relatively small key space. To be used in cryptography, a PRBG may need to meet stronger requirements than for other applications. In particular, various statistical tests can be applied to the outputs of such generators to conclude whether the generator produces a truly random sequence or not. In this paper, we propose a PRBG based on the use of the standard chaotic map with large key space and the Engle Continued Fractions (ECF) map. The outputs of the standard map are used as the inputs of ECF-map. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. The numerical simulation analysis indicates that our PRBG produces bit sequences possessing excellent statistical and cryptographic properties.

On Common Fixed Point Theorem of Four Self Maps in a Fuzzy Metric Space

In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically commuting.

Analysis of the ITIL Mapping with COBIT over the Business Process Continuity Management

Planning and implementation as well as increased control over the Business Continuity Management （BCM） is a complex task in the company requiring adequate resources. BCM aims to reduce risks and develops plans for restoring business activities if they are interrupted by a disaster. The purpose of the paper is to analyze and describe two standards, Information Technology Infrastructure Library （ITIL） and Control Objectives for Information and Related Technology （COBIT）, especially their mapping for the improved planning and implementation of the BCM as well as the increased control over the BCM activities. COBIT is used more as a management framework, providing management tools, such as control objectives, metrics and maturity models in order to complement the control framework. ITIL includes process steps and tasks because it is more oriented towards IT processes （process framework）, defining the best practice for IT service management. Within this mapping, ITIL processes may be used to achieve and demonstrate compliance with COBIT control objectives for BCM process.

节点拓扑变量非耦合映射的ICM方法

文章提出了节点拓扑变量一种非耦合映射的ICM方法,对于结构拓扑优化问题予以建模和求解:首先将基结构划分为由较小单元组成的网格,取节点独立、连续的拓扑变量,建立了一种双线性形函数插值的变量非耦合映射,替代了单元独立连续拓扑变量,使单元的“有”或“无”连续化近似,实现了节点拓扑变量过滤识别与物理量的单元内插值,推导建立了节点拓扑设计变量的优化模型,采用基于变量可分离的二阶对偶规划算法求解,并且改进了最优拓扑构型的圆整技术.接着以常见的位移约束下结构重量(或体积)极小拓扑优化问题为例,演示了上述建模及求解过程.最后分别给出了单载荷工况和多载荷工况下的位移约束拓扑优化的算例,数值计算结果验证了本方法的有效性.研究有如下优点:克服了以往基于单元拓扑变量研究的缺陷,即最优结构边界为锯齿形,得到的最优结构的拓扑边界光滑清晰;给出了节点拓扑变量和单元拓扑函数场定义,提炼出构造该场必须遵循的5点准则,克服了节点拓扑ICM方法有关研究中存在的不足;得到节点设计变量不再是耦合关系,可以方便地求出结构物理量的二阶导数,从而利用变量可分离对偶优化算法进行高效的寻优;研究成果不仅丰富了ICM方法的内涵,推动了其发展,而且对变密度的节点拓扑方法也有参考的裨益.