WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

WEAK CONVERGENCE THEOREMS FOR GENERAL EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS IN BANACH SPACES

In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.

Weak Convergence Theorems for Nonself Mappings

Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.

ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

The author shows a characterization of a （unbounded） weakly filter convergent sequence which is parallel to that every weakly null sequence （xn） in a Banach space admits a norm null sequence （yn） with yn ∈ co（xk）k≥n for all n ∈ N. A version of the Radon-Riesz type theorem is also proved within the frame of the filter convergence.

WEAK CONVERGENCE OF SOME SERIES

This paper contillues the study of [1] on weak functions. The weak convergence theory is investigated in complex analysis, Fourier transform and Mellin transform. A Mobius inverse formula of weak functions is obtained.

UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON- AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION

In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Valence Bands Convergence in p-Type CoSb_(3) through Electronegative Fluorine Filling

Band convergence is considered to be a strategy with clear benefits for thermoelectric performance,generally favoring the co-optimization of conductivity and Seebeck coefficients,and the conventional means include elemental filling to regulate the band.However,the influence of the most electronegative fluorine on the CoSb_(3) band remains unclear.We carry out density-functional-theory calculations and show that the valence band maximum gradually shifts downward with the increase of fluorine filling,lastly the valence band maximum converges to the highly degenerated secondary valence bands in fluorine-filled skutterudites.

Call for Papers——Feature Topic Vol.22,No.3,2025 Special Issue of China Communications:Convergence of 6G empowered Edge Intelligence and Generative AI:Theories,Algorithms,and Applications

Generative artificial intelligence(AI),as an emerging paradigm in content generation,has demonstrated its great potentials in creating high-fidelity data including images,texts,and videos.Nowadays wireless networks and applications have been rapidly evolving from achieving“connected things”to embracing“connected intelligence”.Generative AI has been recognized as a fundamentally innovative technology to drive the advancement of intelligent wireless communications and networks.

QUASI-WEAK CONVERGENCE WITH APPLICATIONS IN ORDERED BANACH SPACE

In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.

Diagnostic values of questionnaires of Convergence Insufficiency Symptom Survey and College of Optometrists Vision Development Quality of Life in the screening of convergence insufficiency

AIM:To compare and analyse the diagnostic efficacy of the College of Optometrists Vision Development Quality of Life Questionnaire(COVD-QOL)and the Convergence Insufficiency Symptom Survey(CISS)in detecting convergence insufficiency and to compare their diagnostic value in clinical applications.METHODS:Using the diagnostic test method,62 adult patients with convergence insufficiency(age:24.74±3.75y)and 62 normal participants(age:23.61±3.13y)who visited the Optometry Clinic of West China Hospital of Sichuan University from April 2021 to January 2023 were included.All subjects completed the CISS and COVD-QOL.Statistical analysis of the sensitivity and specificity of the CISS and COVD-QOL and comparison and joint experimental analysis of their diagnostic efficacy were performed.RESULTS:The sensitivity of the CISS and COVD-QOL for convergence insufficiency was 64.5%and 71.0%,respectively,while the specificity was 96.8%and 67.7%,respectively.Compared to the CISS alone,the combination of the CISS and COVD-QOL demonstrated lower sensitivity and specificity.The areas under the receiver operating characteristic curve of CISS,COVD-QOL and CISS combined with COVD-QOL were 0.806,0.694 and 0.782,respectively.CONCLUSION:Considering the low sensitivity of the CISS and the low specificity of the COVD-QOL,it is recommended to supplement these questionnaires with other screening tests for the detection of convergence insufficiency.

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

Quantitative analysis and prediction of the sound field convergence zone in mesoscale eddy environment based on data mining methods

The mesoscale eddy(ME)has a significant influence on the convergence effect in deep-sea acoustic propagation.This paper use statistical approaches to express quantitative relationships between the ME conditions and convergence zone(CZ)characteristics.Based on the Gaussian vortex model,we construct various sound propagation scenarios under different eddy conditions,and carry out sound propagation experiments to obtain simulation samples.With a large number of samples,we first adopt the unified regression to set up analytic relationships between eddy conditions and CZ parameters.The sensitivity of eddy indicators to the CZ is quantitatively analyzed.Then,we adopt the machine learning(ML)algorithms to establish prediction models of CZ parameters by exploring the nonlinear relationships between multiple ME indicators and CZ parameters.Through the research,we can express the influence of ME on the CZ quantitatively,and achieve the rapid prediction of CZ parameters in ocean eddies.The prediction accuracy(R)of the CZ distance(mean R:0.9815)is obviously better than that of the CZ width(mean R:0.8728).Among the three ML algorithms,Gradient Boosting Decision Tree has the best prediction ability(root mean square error(RMSE):0.136),followed by Random Forest(RMSE:0.441)and Extreme Learning Machine(RMSE:0.518).

On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

Multi-modal knowledge graph inference via media convergence and logic rule

Media convergence works by processing information from different modalities and applying them to different domains.It is difficult for the conventional knowledge graph to utilise multi-media features because the introduction of a large amount of information from other modalities reduces the effectiveness of representation learning and makes knowledge graph inference less effective.To address the issue,an inference method based on Media Convergence and Rule-guided Joint Inference model(MCRJI)has been pro-posed.The authors not only converge multi-media features of entities but also introduce logic rules to improve the accuracy and interpretability of link prediction.First,a multi-headed self-attention approach is used to obtain the attention of different media features of entities during semantic synthesis.Second,logic rules of different lengths are mined from knowledge graph to learn new entity representations.Finally,knowledge graph inference is performed based on representing entities that converge multi-media features.Numerous experimental results show that MCRJI outperforms other advanced baselines in using multi-media features and knowledge graph inference,demonstrating that MCRJI provides an excellent approach for knowledge graph inference with converged multi-media features.

Spatial Differentiation and Convergence Trend of High-quality Development Level of China’s Tourism Economy

This paper aims to interpret the connotation of high-quality development of tourism economy(HQTE)from the perspective of the new development concepts of innovation,coordination,green,openness and sharing,and then to evaluate the spatial differenti-ation of China’s HQTE based on provincial panel data from 2009 to 2018.Specifically,we employ the spatial convergence model to ex-plore the absolute and conditionalβconvergence trends of HQTE in the whole country and the eastern,central and western regions of China.Our empirical results reveal that:1)within the decade,from 2009 to 2018,regions of China with the highest HQTE index is its eastern region followed by the central region and then the western region,but the fastest growing one is the western region of China fol-lowed by the central region and then the eastern region.2)Whether or not the spatial effect is included,there are absolute and condition-alβconvergence in HQTE in the whole country and aforementioned three regions.3)The degree of government attention as well as the level of economic development and location accessibility are the positive driving factors for the convergence of HQTE in the whole country and the three regions.The degree of marketization and human capital have not passed the significance test either in the whole country or in the three regions.The above conclusions could deepen the understanding of the regional imbalance and spatial conver-gence characteristics of HQTE,clarify the primary development objects,and accomplish the goal of China’s HQTE.

Exploring the Dynamics of Industrial Convergence Among RCEP Member Countries: An Empirical Study

The evolving dynamics of industrial convergence among the member countries of the Regional Comprehensive Economic Partnership(RCEP)framework have emerged as a significant subject that merits in-depth consideration and analysis.This study initially employs multi-regional input-output(MRIO)data and the social network analysis(SNA)method to delineate the levels and variation trends of this industrial convergence across the RCEP member countries.It then delves into the positive effects of this convergence phenomenon on the trade and investment fields of the member countries.The research findings indicate:(a)In 2006 and 2015,before the implementation of the RCEP,the RCEP member countries displayed a relatively close industrial convergence.The convergence levels exhibited a general upward trend on both the supply and the demand sides,but there were significant disparities in the levels of industrial convergence among the member countries.Furthermore,while the convergence in the three economic sectors showed an increasing trend,the development was uneven across the board.(b)Since the implementation of the RCEP,the trade ties among the member countries within the region have strengthened significantly,and the interplay between the countries’industrial and supply chains has been characterized by high-quality collaboration and demonstrated remarkable resilience.In addition,the convergence in the investment fields of the RCEP member countries and their respective industries has unleashed a wave of positive synergies.These findings offer valuable insights that can serve as a robust foundation for formulating effective policies to advance the growth and prosperity of the RCEP region.

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.