Stability of a cubic functional equation in intuitionistic random normed spaces

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.

YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES

In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C（K）, then it can be equivalently renormed so that the set of norm- attaining functionals contains an infinite dimensional closed subspace of X＊ if and only if X＊ contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.

Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM

A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.

APPROXIMATION OF A CAUCHY-JENSEN ADDITIVE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

UBOM-4, a New Scale for Psychic Function and Energy: General Population Normative Values and Influencing Parameters

Objective: We introduce Utena’s Brief Objective Measures of 4 Axes for Psychic Function and Energy (UBOM-4), a new brief test battery for evaluating psychic function concerning intellect, emotion, volition, and imagination. To date, insufficient general population data on the UBOM have been collected. This study aimed to establish the normative values for the general population in UBOM-4 and examine the effects of age, sex, and mental health status on the values. Methods: The General Health Questionnaire, 12-item version (GHQ-12) and UBOM-4 were administered to 149 individuals working in or attending professional schools or universities (73 males, 76 females;age: 19 - 65 years). Participants were classified as healthy based on their GHQ-12 responses and psychiatrist interviews. Results: UBOM-4 measures (mean ± SD) were: pulse rate difference (PRD or UBOM-pulse), −0.72 ± 4.31 beats/min;ruler catching time (RCT or UBOM-ruler), 18.42 ± 3.73 cm;degree of randomness (DOR or UBOM-random), 0.94 ± 0.18;mean randomizing time (MRT or UBOM-time), 0.60 ± 0.31 sec. The Baum Test drawings were classified as usual (86%) and unusual patterns (14%). Sex effects were observed for RCT (UBOM-ruler) and DOR (UBOM-random), but not for PRD (UBOM-pulse) and MRT (UBOM-time). Therefore, the normative values for RCT (UBOM-ruler) (males: 17.37 ± 3.25 cm;females: 19.42 ± 3.90 cm) and DOR (UBOM-random) (males: 0.92 ± 0.18;females: 0.95 ± 0.18) should be differentiated by sex. The patterns of the Baum Test drawings were affected by age, with individuals over 51 years showing the unusual pattern more frequently (42%). Discussion: Compared to previous results for healthy individuals, the present results were similar for RCT (UBOM-ruler), DOR (UBOM-random), MRT (UBOM-time), and the drawing pattern, but different for PRD (UBOM-pulse). This difference is probably because PRD is sensitive to test situation habituation, sex of examiner, order of subtests, etc. Thus, PRD (UBOM-pulse) should be measured after the subject-examiner relationship stabilizes. Conclusion: Our results suggest that UBOM-4 can be widely used in clinical settings, utilizing the present results as a reference.

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

Solution and stability of mixed type functional equation in non-Archimedean random normed spaces

The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.

Supporting Functions and The Differentiabilities of the Norms on Banach Spaces

In this paper, we defined a new continuity of supporting function and studyed a new convexity, smoothness of Banach Space and from this we studyed the relations among such convexity, smoothness and differentiability of the norm of Banach Space.

ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS

The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n ＋ a ＋ b.

Improved theory of generalized meteo-ballistic weighting factor functions and their use

It follows from the analysis of artillery fire errors that approximately two-thirds of the inaccuracy of indirect artillery fire is caused by inaccuracies in the determination of the meteo parameters included in fire error budget model.Trajectories calculated under non-standard conditions are considered to be perturbed.The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs)which are a special kind of sensitivity functions.WFFs are used for calculation of meteo ballistic elements B(ballistic wind w B,densityρB,virtual temperatureτB,pressure p B)as well.We have found that the existing theory of WFF calculation has several significant shortcomings.The aim of the article is to present a new,improved theory of generalized WFFs that eliminates the deficiencies found.Using this theory will improve methods for designing firing tables,fire control systems algorithms,and meteo message generation algorithms.

RANDOM APPROXIMATION OF AN ADDITIVE FUNCTIONAL EQUATION OF m-APPOLLONIUS TYPE

In this paper,using the fixed-point and direct methods,we prove the HyersUlam stability of the following m-Appolonius type functional equation：∑mi=1 f（z-xi）=mf（z-1/m2∑mi=1xi）-1/m∑1≤i〈j≤mf（xi＋xj）,where m is a natural number greater than 1,in random normed spaces. 更多还原

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

行政复议规范性文件审查的困境及功能优化

行政复议法规定了规范性文件审查制度,但该制度在实践中呈现出当事人申请意愿低、复议机关抵触情绪大、对规范性文件的监督效果差等诸多问题。上述问题产生的直接原因包括审查主体定位不当、审查标准与行政诉讼趋同、审查机制与审查后果不匹配等,而根本原因则在于该制度的功能定位偏离了行政复议制度的功能定位。根据行政复议法,复议规范性文件审查的首要功能是预防和纠正不合法、不适当的规范性文件,而不是辅助行政争议的解决;同时,该制度还需兼顾保护当事人合法权益和保障行政机关依法行使职权的目标。这与行政诉讼中的规范性文件审查制度以及备案审查制度的功能定位存在明显差异。复议规范性文件审查制度的功能应当与复议制度的整体功能保持协同。以此为指引,复议规范性文件审查主体应被限缩解释为对规范性文件有监督权的上级机关,审查标准应被扩张解释为广义合法性审查标准,审查程序应在考虑有效监督规范性文件的基础上作平衡性设计。

“双碳”背景下减污降碳协同治理的法治保障研究——结构功能主义的分析视角

实现碳达峰碳中和是一场广泛而深刻的经济社会系统性变革,同时也对中国国家治理体系和治理能力提出了新要求。综合考量中国当下生态环境和经济发展的现实情况,温室气体和环境污染物的产生具有一定的同源性,“以实现减污降碳协同增效为总抓手”具有合理性和科学性。从结构功能主义视角看,减污降碳协同治理的法治保障关涉价值理念、立法、法律实施以及多元参与四个维度。从法律的规范逻辑出发,以结构功能主义分析方法为进路,强调系统思维,借助AGIL图式分析,从纵向分化与横向交换两个维度全面检视减污降碳协同治理存在的架构缺失、功能离散、动力不足等问题;整合减污降碳协同治理中相互分离的社会实体,在明确绿色低碳原则、效能原则、综合调整原则的基础上,构建减污降碳协同治理的法律和政策体系,健全刚柔兼济的法律实施机制,推进建立网格化多元共治格局,以期为减污降碳协同增效的实现提供法治保障。

DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF R^n

Let H（B） be the set of all harmonic functions f on the unit ball B of Rn. For 0 p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ（B） consists of all functions f in H（B） for which the mixed norm p,q, φ ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ（B）. The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

THE EXTENSION THEOREM OF LINEAR RANDOM FUNCTIONALS AND ITS APPLICATIONS

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气候司法本土化的三重逻辑:规范、价值和功能

在全球气候治理司法化转型的背景下,中国司法系统在应对气候变化中呈现出全面积极的态度。气候司法作为环境司法专门化的新领域,亟须形成体系性的本土化方案。气候司法本土化的核心要义在于彰显主体性,需要将气候司法的概念体系、功能定位、审判机制、裁判体系与规则等置于中国法治现代化特定背景和社会结构条件之中予以把握,其内在逻辑是涵括规范体系、价值序列和功能定位的动态体系。当前,中国气候司法规范体系中的多层次立法呈现间接、倡导属性,且多元化司法规范创制不足,体系化任务尚未完成,继而诱导出气候司法规范的周延性困境和融贯性难题。在此情形下,气候司法所保护法益的识别和核心价值尚未被清晰地析出,且科学上的不确定性、政策权衡、经济诱因等诸多外部因素限制着对气候变化案件的价值判断。这些都深刻地影响气候司法作为公益型司法与治理型司法的双重功能定位和发展方向。为此,气候司法本土化的方式与进路需要基于规范、价值和功能三重逻辑及其呈现的问题或要求展开。首先,强化多重规范秩序的塑造,从公私法协同出发推动气候变化立法体系化,通过强化次级气候司法规范凝聚共识,借助多元法律解释方法提升气候司法规范体系的融通性。其次,以利益为核心建构法律论证的权威,通过涉碳利益的衡量强化裁判的实质理由,通过气候环境利益的多维保护强化裁判的开放性,通过外在因素与法律因素的平衡强化裁判的权威理由。最后,精准塑造气候司法的双重功能,以风险预防原则构建预防性公益型气候司法,以政策的司法化构建服务于“双碳”目标的治理型气候司法。