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We consider conditional distribution and conditional density functionals in the space of generalized functions. The approach follows Phillips (1985, 1991, 1995) who employed generalized functions to overcome non-differentiability in order to develop expansions. We obtain the limit of the kernel estimators for weakly dependent data, even under non-differentiability of the distribution function; the limit Gaussian process is characterized as a stochastic random functional (random generalized function) on the suitable function space. An alternative simple to compute estimator based on the empirical distribution function is proposed for the generalized random functional. For test statistics based on this estimator, limit properties are established. A Monte Carlo experiment demonstrates good finite sample performance of the statistics for testing logit and probit specification in binary choice models.

The purpose of this paper is to state new formulation of the programme‐styled framework of pansystems research and related expansions.

Pansystems‐generalized extremum principle (0**: (dy/dx=0)**) is presented with recognitions to various logoi of philosophy, mathematics, technology, systems, cybernetics, informatics, relativity, biology, society, resource, communications and related topics: logic, history, humanities, aesthetics, journalism, IT, AI, TGBZ* <truth*goodness*beauty*Zen*>, etc. including recent rediscoveries of 50 or so pansystems logoi.

A keynote of the paper is to develop the deep logoi of the analytic mathematics, analytic mechanics, variational principles, Hilbert's sixth/23rd problems, pan‐axiomatization to encyclopedic principles and various applications. The 0**‐universal connections embody the transfield internet‐styled academic tendency of pansystems exploration.

The paper includes topics: history megawave, pansystems sublation‐modes, pan‐metaphysics, pansystems dialogs with logoi of 100 thinkers or so, and pansystems‐sublation for a series of logoi concerning the substructure of encyclopedic dialogs such as systems, derivative, extremum, quantification, variational principle, equation, symmetry, OR, optimization, approximation, yinyang, combination, normality‐abnormality, framework, modeling, simulation, relativity, recognition, practice, methodology, mathematics, operations and transformations, quotientization, product, clustering, Banach completeness theorem, Weierstrass approximation theorem, Jackson approximation theorem, Taylor theorem, approximation transformation theorems due to Walsh‐Sewell mathematical school, Hilbert problems, Cauchy theorem, theorems of equation stability, function theory, logic, paradox, axiomatization, cybernetics, dialectics, multistep decision, computer, synergy, vitality and the basic logoi for history, ethics, economics, society OR, aesthetics, journalism, institution, resource and traffics, AI, IT, etc.

Financial performance has been paid attention at an unprecedented level, which can be confirmed as a fact that the quantitative expansion of financial performance evaluation work. The purpose of this study is to propose a more appropriate model for financial performance evaluation under the unbalanced development.

This paper introduces the differentiation criteria to eliminate the deviation caused by the same principle for multiple performance evaluation objects whose development are unbalanced; Then the generalized grey number is adopted to describe the value of performance evaluation index; and the information entropy weight is used to obtain the index weight to reduce the artificial judgment error; Finally, the generalized grey information entropy weight TOPSIS evaluation model is constructed.

Empirical research shows that in the new evaluation model, the differentiated possibility function effectively eliminates the deviation caused by the same principle, the application of information entropy weight reduces the human judgment error, and the value of generalized grey number further enhances the closeness of the results. Moreover, it is also found that in different scenarios, an adaptive performance evaluation model should be selected to match scientifically reasonable results.

The proposed model offers a solution for financial performance evaluation considering unbalanced development among cities. It can be realized by determining the differentiation possibility function matrix, and then the information entropy weight TOPSIS evaluation model can be constructed. This model reflects the actual situation, improves the performance evaluation accuracy, and can be used under similar conditions.

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

The framework, panorama, related applications and development of pansystems thinking are introduced and some problems concerning generalized systems, derivatives, symmetry and quantification are investigated, a sort of difference‐identity theory within the framework of pansystems thinking is cultivated, and a new type of clustering method with many intertransformations among some important pansystems concepts is presented. Related contents include: pansystems combination of mathematics, systems, dialectics and poetry thinking, methodology to comprehend laws by pansymmetries or by moving networks, the pansystems views of generalized order, quotientization and series‐parallel relations, control‐reachability, duality transformation, discoupling principle, communication theorems, general parental relations, etc.

The framework, methodology and development of pansystems cybernetics are introduced. Related contents include: the postmodernizational systems thought, the epitome of pansystems methods, hi‐tech mechanism, social cybernetics, pansystems views of value, labor, management and economics, pedagogy, history and futurology, systems mathematics, general clustering analysis, observocontrollability, generalized living systems, information metascience, regret information, general fuzzy control, generalized gray systems, entropy, large scale dynamical supercomplicated Shengke systems, function simulations, transformation theory, simplification, strengthening, forming substance of subsystems of living systems of Miller’s theory, etc.

This paper aims to improve the mathematical justification of certain analog signal theory concepts and offer a rigorous framework for it.

The framework relies on functional analysis, namely theory of distributions and the concept of weak limit. Its notation is adjusted to resemble the notation usually used in engineering signal theory. It can be used to prove in a rigorous manner already established results in signal theory, but also to establish new ones.

Examples have shown the lack of rigour caused by using ordinary calculus in proving fundamental signal theoretic results. On that basis, concepts of limit, Fourier transform and derivative are revisited in the spirit of functional analysis. A new useful formula for weak limit computation is proved.

Functional analysis is efficiently used in signal theory in a manner approachable by engineers. An original and efficient formula for weak limit computation is presented and proved.

This paper aims to open the gateway of methodological abstraction and its application in an Islamic perspective in a way that has not been carried out before in Islamic literature. That is because of the absence of ontological and epistemological inquiry in Islamic erudition for a long time now. In the case of the Shari’ah and its induction of socioeconomic studies, the span of intellection and application ought to be premised on the ontological, epistemological, phenomenological and continuity attributes derived from the monotheistic law. This takes the formalism of organic inter-causal unity of being and becoming between the complementary good choices of life. The ontological monotheistic law of unity of knowledge is referred to as Tawhid in the Qur’an. Empirical work is done in support of the argument presented in this paper.

This paper is a formal contribution in the direction of developing a model of well-being based on the methodology of unity of knowledge arising from the Tawhidi epistemic foundation. In this regard, a methodologically interrelated theoretical and empirically applied study is accomplished to test the argumentation and hypothesis of endogenous systemic embedding of inter-variable causality between Shari’ah and economic and financial issues.

In spite of the epistemic approach to explain the embedding model of interrelationship between Islamic law and details of the socioeconomic field, Islamic scholarship and practice in all fields have remained oblivious to its epistemic roots. Consequently, as presently understood, Shari’ah and economics and the various socio-scientific specifics, as of Islamic finance and financial and religious institutions in these areas, could not make a generalized model of social well-being, one that can be simulated by inter-variable causal relations.

The paper conveys a critical conceptual idea to debate the scope and approach of Islamic Law, Shari’ah, on economic matters. The system-oriented approach is used to formulate a systems theory of integration between Shari’ah and economics. The results of the approach implemented in this study constitute a major contribution of this paper to scholarship in general and acts as a critique of traditional Islamic thought with respect to Shari’ah and economics.

A concise introduction to the normalized quadratic expenditure or cost function is provided so that the interested reader will have the necessary information to understand and use this functional form. The normalized quadratic is an attractive functional form for use in empirical applications as correct curvature can be imposed in a parsimonious way without losing the desirable property of flexibility. We believe it is unique in this regard. Topics covered include the problem of cardinalizing utility, the modeling of nonhomothetic preferences, the use of spline functions to achieve greater flexibility, and the use of a “semiflexible” approach to make it feasible to estimate systems of equations with a large number of commodities.

The purpose of this paper is to present eight local elasto‐plastic beam element formulations incorporated into the corotational framework for two‐noded three‐dimensional beams. These formulations capture the warping torsional effects of open cross‐sections and are suitable for the analysis of the nonlinear buckling and post‐buckling of thin‐walled frames with generic cross‐sections. The paper highlights the similarities and discrepancies between the different local element formulations. The primary goal of this study is to compare all the local element formulations in terms of accuracy, efficiency and CPU‐running time.

The definition of the corotational framework for a two‐noded three‐dimensional beam element is presented, based upon the works of Battini .The definitions of the local element kinematics and displacements shape functions are developed based on both Timoshenko and Bernoulli assumptions, and considering low‐order as well as higher‐order terms in the second‐order approximation of the Green‐Lagrange strains. Element forces interpolations and generalized stress resultant vectors are then presented for both mixed‐based Timoshenko and Bernoulli formulations. Subsequently, the local internal force vector and tangent stiffness matrix are derived using the principle of virtual work for displacement‐based elements and the two‐field Hellinger‐Reissner assumed stress variational principle for mixed‐based formulations, respectively. A full comparison and assessment of the different local element models are performed by means of several numerical examples.

In this study, it is shown that the higher order elements are more accurate than the low‐order ones, and that the use of the higher order mixed‐based Bernoulli element seems to require the least number of FEs to accurately model the structural behavior, and therefore allows some reduction of the CPU time compared to the other converged solutions; where a larger number of elements are needed to efficiently discretize the structure.

The paper reports computation times for each model in order to assess their relative efficiency. The effect of the numbers of Gauss points along the element length and within the cross‐section are also investigated.