Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

A Unified Bit-to-Symbol Mapping for Generalized Constellation Modulation

Gray mapping is a well-known way to improve the performance of regular constellation modulation,but it is challenging to be applied directly for irregular alternative.To address this issue,in this paper,a unified bit-to-symbol mapping method is designed for generalized constellation modulation(i.e.,regular and irregular shaping).The objective of the proposed approach is to minimize the average bit error probability by reducing the hamming distance(HD)of symbols with larger values of pairwise error probability.Simulation results show that the conventional constellation modulation(i.e.,phase shift keying and quadrature amplitude modulation(QAM)with the proposed mapping rule yield the same performance as that of classical gray mapping.Moreover,the recently developed golden angle modulation(GAM)with the proposed mapping method is capable of providing around1 d B gain over the conventional mapping counterpart and offers comparable performance to QAM with Gray mapping.

The Generalized Roper-Suffridge Extension Operator for Locally Biholomorphic Mappings

In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

CONFORMAL AND GENERALIZED CONCIRCULAR MAPPINGS OF EINSTEIN-WEYL MANIFOLDS

In this article, after giving a necessary and sufficient condition for two Einstein- Weyl manifolds to be in conformal correspondence, we prove that any conformal mapping between such manifolds is generalized concircular if and only if the covector field of the conformal mapping is locally a gradient. Using this fact we deduce that any conformal mapping between two isotropic Weyl manifolds is a generalized concircular mapping. Moreover, it is shown that a generalized concircularly flat Weyl manifold is generalized concircular to an Einstein manifold and that its scalar curvature is prolonged covariant constant.

A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

Suppose f is an almost starlike function of order α on the unit disk D. In this paper, we will prove that Фn,β2,γ2,…βn,γn（f）（z）=（f（z1）,（f（z1）/z1）^β2（f＇（z1））^γ2 z2,…,（f（z1）/z1）^βn（f＇（z1））^γnzn）1 preserves almost starlikeness of order α on Ωn,p2,…,pn={z=（z1,z2,…,zn）＇∈Cn：∑^n j=1｜zj｜^pj〈1},where 0〈p1≤2,pj≥1,j=2,…,n,are real numbers.

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z（G） be the center of G. Suppose that F, T ：G→G are two co-commuting R-linear mappings, i.e., F（x）x = xT（x） for all x ∈ G. In this note, we study the question of when co-commuting mappings on G are proper.

On Products and Diagonals of Mappings in Generalized Topological Spaces

Based on the theory of products of generalized topologies,we introduce the product mappings and the diagonal mappings in generalized topological spaces in this paper.We investigate some basic properties(especially,the continuity,openness and closedness)of the product mappings and the diagonal mappings in generalized topological spaces.Some applications are given to answer two questions raised in[3].

COMMON FIXED POINT THEOREM FOR NONCOMMUTING MAPPINGS SATISFYING A GENERALIZED ASYMPTOTICALLY NONEXPANSIVE CONDITION

We present a common fixed point theorem for generalized asymptotically non- expansive and noncommuting mappings in normed linear spaces.

Common Fixed Point Iterations of Generalized Asymptotically Quasi-Nonexpansive Mappings in Hyperbolic Spaces

We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

Demonstration of a small‐scale power generator using supercritical CO_(2)

The supercritical CO_(2)(sCO_(2))power cycle could improve efficiencies for a wide range of thermal power plants.The sCO_(2)turbine generator plays an important role in the sCO_(2)power cycle by directly converting thermal energy into mechanical work and electric power.The operation of the generator encounters challenges,including high temperature,high pressure,high rotational speed,and other engineering problems,such as leakage.Experimental studies of sCO_(2)turbines are insufficient because of the significant difficulties in turbine manufacturing and system construction.Unlike most experimental investigations that primarily focus on 100 kW‐or MW‐scale power generation systems,we consider,for the first time,a small‐scale power generator using sCO_(2).A partial admission axial turbine was designed and manufactured with a rated rotational speed of 40,000 rpm,and a CO_(2)transcritical power cycle test loop was constructed to validate the performance of our manufactured generator.A resistant gas was proposed in the constructed turbine expander to solve the leakage issue.Both dynamic and steady performances were investigated.The results indicated that a peak electric power of 11.55 kW was achieved at 29,369 rpm.The maximum total efficiency of the turbo‐generator was 58.98%,which was affected by both the turbine rotational speed and pressure ratio,according to the proposed performance map.

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

Generalized synchronization between different chaotic maps via dead-beat control

This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.

Predictive Vegetation Mapping Approach Based on Spectral Data, DEM and Generalized Additive Models

This study aims to provide a predictive vegetation mapping approach based on the spectral data, DEM and Generalized Additive Models (GAMs). GAMs were used as a prediction tool to describe the relationship between vegetation and environmental variables, as well as spectral variables. Based on the fitted GAMs model, probability map of species occurrence was generated and then vegetation type of each grid was defined according to the probability of species occurrence. Deviance analysis was employed to test the goodness of curve fitting and drop contribution calculation was used to evaluate the contribution of each predictor in the fitted GAMs models. Area under curve (AUC) of Receiver Operating Characteristic (ROC) curve was employed to assess the results maps of probability. The results showed that: 1) AUC values of the fitted GAMs models are very high which proves that integrating spectral data and environmental variables based on the GAMs is a feasible way to map the vegetation. 2) Prediction accuracy varies with plant community, and community with dense cover is better predicted than sparse plant community. 3) Both spectral variables and environmental variables play an important role in mapping the vegetation. However, the contribution of the same predictor in the GAMs models for different plant communities is different. 4) Insufficient resolution of spectral data, environmental data and confounding effects of land use and other variables which are not closely related to the environmental conditions are the major causes of imprecision.

Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion

Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.

基于MAP准则的无线信道密钥量化算法

在物理层安全领域中,基于无线信道的密钥生成技术包括信道探测、量化、密钥协商和保密增强等4个步骤。针对传统量化方案仅关注量化端点值设计、初始密钥不一致率(Key Disagreement Rate,KDR)偏高的问题,通过搭建对合作方量化结果进行概率推算的数学模型,获取其量化符号信息和比特软信息,提出了基于最大后验判决准则(Maximum a Posteriori,MAP)的量化算法。仿真结果表明,所提算法能取得更低的KDR,在信噪比为10 dB环境下,该算法的KDR比等概量化降低了43%,比信道交互量化(Channel Quantization Alternating,CQA)降低了35%;采用2比特量化,该算法的可生成密钥长度较CQA提高了2倍。