Benefit allocation model of distributed photovoltaic power generation vehicle shed and energy storage charging pile based on integrated weighting-Shapley method

In this study,to develop a benefit-allocation model,in-depth analysis of a distributed photovoltaic-powergeneration carport and energy-storage charging-pile project was performed;the model was developed using Shapley integrated-empowerment benefit-distribution method.First,through literature survey and expert interview to identify the risk factors at various stages of the project,a dynamic risk-factor indicator system is developed.Second,to obtain a more meaningful risk-calculation result,the subjective and objective weights are combined,the weights of the risk factors at each stage are determined by the expert scoring method and entropy weight method,and the interest distribution model based on multi-dimensional risk factors is established.Finally,an example is used to verify the rationality of the method for the benefit distribution of the charging-pile project.The results of the example indicate that the limitations of the Shapley method can be reasonably avoided,and the applicability of the model for the benefit distribution of the charging-pile project is verified.

Transport path optimization algorithm based on fuzzy integrated weights

Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi- weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.

ON WEIGHTED L^p INTEGRABILITY AND APPROXIMATION OF TRIGONOMETRIC SERIES

We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series. Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series.

INTEGRAL INEQUALITIES WITH WEIGHTS FOR MAXIAMAL OPERATORS

Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) is the maximal function on R+n+1, which was introduced by Ruiz,F. and Torrea, J.

Weighted integral inequalities in Orlicz martingale classes

Under appropriate conditions on Young's functions Φ1 and Φ2,we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob's maximal operator M on martingale Orlicz setting.When Φ1 = tp and Φ2 = tq,the inequalities revert to the ones of strong or weak(p,q)-type on martingale space.

Weighted Norm Inequalities for Some Singular Integral Operators

In this paper,we consider the related weighted boundedness of the operators which were studied by J.Duoandikotxea and J.L.Ruhio de Francia.

Theta Function and Hilbert Modular Forms of Half Integral Weight

In this paper a kind of theta function is constructed by means of spherical function. And we also obtain some Hilbert modular forms of half integral weight.

An Integral Representation for the Weighted Geometric Mean and Its Applications

By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.

Probabilistic Tractable Models in Mixed Discrete-Continuou s Domains

We study the problem of the unsupervised learning of graphical models in mixed discrete-continuous domains.The problem of unsupervised learning of such models in discrete domains alone is notoriously challenging,compounded by the fact that inference is computationally demanding.The situation is generally believed to be significantly worse in discrete-continuous domains:estimating the unknown probability distribution of given samples is often limited in practice to a handful of parametric forms,and in addition to that,computing conditional queries need to carefully handle low-probability regions in safety-critical applications.In recent years,the regime of tractable learning has emerged,which attempts to learn a graphical model that permits efficient inference.Most of the results in this regime are based on arithmetic circuits,for which inference is linear in the size of the obtained circuit.In this work,we show how,with minimal modifications,such regimes can be generalized by leveraging efficient density estimation schemes based on piecewise polynomial approximations.Our framework is realized on a recent computational abstraction that permits efficient inference for a range of queries in the underlying language.Our empirical results show that our approach is effective,and allows a study of the trade-off between the granularity of the learned model and its predictive power.

A Class of Maximal Functions with Oscillating Kernels

The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. Lp estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted.