Inversion Formulas for the Spherical Radon-Dunkl Transform

The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of $R_\kappa$ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms

Boundedness of operators on the Bergman spaces associated with a class of generalized analytic functions

The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{\lambda,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the $\lambda$-analytic functions, and with a class of radial weight functions $w$. For $\lambda\ge0$, a $C^2$ function $f$ on ${{\mathbb D}}$ is said to be $\lambda$-analytic if $D_{\bar{z}}f=0$, where $D_{\bar{z}}$ is the (complex) Dunkl operator given by $D_{\bar{z}}f=\partial_{\bar{z}}f-\lambda(f(z)-f(\bar{z}))/(z-\bar{z})$. It is shown that, for $2\lambda/(2\lambda+1)\le p\le1$, the boundedness of an operator from $A^{p}_{\lambda,w}({\mathbb{D}})$ into a Banach space depends only upon the norm estimate of a single vector-valued $\lambda$-analytic function. As applications, we obtain a necessary and sufficient conditions of sequence multipliers on the spaces $A^{p}_{\lambda,w}({\mathbb{D}})$ for general weights $w$, and characterize the dual space of $A^{p}_{\lambda,w}({\mathbb{D}})$ for the power weight $w=(1-|z|^2)^{\alpha-1}$ with $\alpha>0$, and also give a sufficient condition of Carleson type for boundedness of multiplication operators on $A^{p}_{\lambda,w}({\mathbb{D}})$.Comment: 42 page

Bond relaxation, electronic and magnetic behavior of 2D metals structures Y on Li(110) surface

We investigated the bond, electronic and magnetic behavior of adsorption Yttrium atoms on Lithium (110) surface using a combination of Bond-order-length-strength(BOLS) correlation and density-functional theory(DFT). We found that adsorption Y atoms on Li(110) surfaces form two-dimensional (2D) geometric structures of hexagon, nonagon, solid hexagonal, quadrangle and triangle. The consistent with the magnetic moment are 6.66{\mu}B, 5.54{\mu}B, 0.28{\mu}B, 1.04{\mu}B, 2.81{\mu}B, respectively. In addition, this work could pave the way for design new 2D metals electronic and magnetic properties

Product platform two-stage quality optimization design based on multiobjective genetic algorithm

AbstractProduct platform design (PFD) has been recognized as an effective means to satisfy diverse market niches while maintaining the economies of scale and scope. Numerous optimization-based approaches have been proposed to help resolve the tradeoff between platform commonality and the ability to achieve distinct performance targets for each variant. In this study, we propose a two-stage multiobjective optimization-based platform design methodology (TMOPDM) for solving the product family problem using a multiobjective genetic algorithm. In the first stage, the common product platform is identified using a nondominated sorting genetic algorithm II (NSGA-II); In the second stage, each individual product is designed around the common platform such that the functional requirements of the product are best satisfied. The design of a family of traction machine is used as an example to benchmark the effectiveness of the proposed approach against previous approachs

Numerical simulation of aerodynamic characteristics of windmill based on computer graphics display technology

Abstract This paper proposed research on wind computation fluid dynamics(CFD) analysis and visualization in scientific computing facing to OSG in order to obtain numerical result of aerodynamic characteristics stimulated by windmill and to display vivid and direct 3-D effect for easy observation experiment. This paper applied CFX module in ANSYS Workbench software to conduct CFD analysis and calculation of windmill through computer graphic display technology based on CFD principle and realize numerical stimulation of aerodynamic characteristics of windmill. Then the research on visualization in scientific computing of aerodynamic characteristics of windmill was realized combining with OSG software that face to virtual display technolog

Inversion Formulas for the Spherical Radon-Dunkl Transform

The spherical Radon-Dunkl transform Rκ, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of h-harmonics. Several inversion formulas of Rκ are given with the aid of spherical Riesz-Dunkl potentials, the Dunkl operators, and some appropriate wavelet transforms

Don’t Forget Your Supplier When Remanufacturing

A popular assumption in the current literature on remanufacturing is that the whole new product is produced by an integrated manufacturer, which is inconsistent with most industries. In this paper, we model a decentralised closed-loop supply chain consisting of a key component supplier and a non-integrated manufacturer, and demonstrate that the interaction between these players significantly impacts the economic and environmental implications of remanufacturing. In our model, the non-integrated manufacturer can purchase new components from the supplier to produce new products, and remanufacture used components to produce remanufactured products. Thus, the non-integrated manufacturer is not only a buyer but also a rival to the supplier. In a steady state period, we analyse the performances of an integrated manufacturer and the decentralised supply chain. We find that, although the integrated manufacturer always benefits from remanufacturing, the remanufacturing opportunity may constitute a lose-lose situation to the supplier and the non-integrated manufacturer, making their profits be lower than in an identical supply chain without remanufacturing. In addition, the non-integrated manufacturer may be worse off with a lower remanufacturing cost or a larger return rate of used products due to the interaction with the supplier. We further demonstrate that the government-subsidised remanufacturing in the non-integrated (integrated) manufacturer is detrimental (beneficial) to the environment

Equivariant Energy-Guided SDE for Inverse Molecular Design

Inverse molecular design is critical in material science and drug discovery, where the generated molecules should satisfy certain desirable properties. In this paper, we propose equivariant energy-guided stochastic differential equations (EEGSDE), a flexible framework for controllable 3D molecule generation under the guidance of an energy function in diffusion models. Formally, we show that EEGSDE naturally exploits the geometric symmetry in 3D molecular conformation, as long as the energy function is invariant to orthogonal transformations. Empirically, under the guidance of designed energy functions, EEGSDE significantly improves the baseline on QM9, in inverse molecular design targeted to quantum properties and molecular structures. Furthermore, EEGSDE is able to generate molecules with multiple target properties by combining the corresponding energy functions linearly