Dirichlet分布统计性质汇总

Dirichlet分布是一种重要的多维连续概率分布族,广泛应用于贝叶斯统计,是成分数据和比例数据建模中变量分布类型的自然选择.本文对其所具有的优良统计性质进行了汇总证明.

Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

一类半线性双曲型微分不等式非齐次Dirichlet外问题解的存在性与非存在性

该文研究在高维外区域中(N≥2)的一类半线性双曲型微分不等式非齐次Dirichlet外问题.利用适当选取试验函数的方法及反证技巧,在依赖于时空变量的非齐次Dirichlet边界条件下建立问题解的非存在性定理且导出一些解的存在性结论.

WEIGHTED A PRIORI ESTIMATES FOR SOLUTION OF （-△）^mu = f WITH HOMOGENEOUS DIRICHLET CONDITIONS

Let u be a weak solution of （-△）mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω C Rn. Then, the main goal of this paper is to prove the following a priori estimate：｜｜u｜｜w2m/ω·p（Ω）≤C｜｜f｜｜L^pω（Ω）,where ω is a weight in the Muckenhoupt class Ap.

An extended iterative direct-forcing immersed boundary method in thermo-fluid problems with Dirichlet or Neumann boundary conditions

An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.

一种利用远场数据恢复Dirichlet特征值的神经网络方案

探讨了声场中利用远场数据重构具有Dirichlet边界条件的障碍物的特征值反问题,提出了一种基于数据驱动的神经网络方案。首先针对具有Dirichlet边界条件的障碍物建立内特征值问题和外散射问题的数学模型,然后构建一个具有序列对序列结构的多层前馈神经网络,该网络采用反向传播误差和自学习的方式更新网络中的超参数,最后在散射体信息未知的前提下,利用远场数据重构障碍物的Dirichlet特征值。数值实验表明该方法可以有效地重构障碍物的Dirichlet特征值。

POSITIVE SOLUTIONS FOR CRITICAL QUASILINEAR ELLIPTIC EQUATIONS WITH MIXED DIRICHLET-NEUMANN BOUNDARY CONDITIONS

The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.

Genesis of LCT Pegmatites during Early Paleozoic Orogeny of the North Qinling Orogenic Belt,China:Emplacement Conditions and Structural Control

The Guanpo pegmatite field in the North Qinling orogenic belt(NQB),China,hosts the most abundant LCT pegmatites.However,their emplacement conditions and structural control remain unexplored.In this contribution,we investigated it combining pegmatite orientation measurement with oxygen isotope geothermometry and fluid inclusion study.The orientations of type A1 pegmatites(P_(f)<σ_(2))are predominantly influenced by P-and T-fractures due to simple shearing in Shiziping dextral thrust shear zone during D_(2)deformation,whereas type A2 pegmatites(contemporaneous with D_(4))are governed by hydraulic fractures aligned with S_(0)and S_(0+1)stemming from fluid pressure(P_(f)<σ_(2)).Additionally,type B pegmatites(P_(f)≤σ_(2))exhibit orientations shaped by en echelon extensional fractures in local ductile shear zones(contemporaneous with D_(3)).The albite-quartz oxygen isotope geothermometry and microthermometric analysis of fluid inclusions in elbaites from the latest pegmatites(including types B and A2)suggest that the crystallization P-T for late magmatic and hydrothermal stages are 527.5-559.2℃,320℃,3.1-3.6 kbar and 2.0 kbar,respectively.Our observations along with previous studies suggest that the genesis of the LCT pegmatites was a long-term,multi-stage event during early Paleozoic orogeny(including the collision stage)of the NQB,and was facilitated by various local fractures.

Dirichlet空间上拟齐次符号H-Toeplitz算子的交换性

文章刻画了拟齐次符号的H-Toeplitz算子在Dirichlet空间上的交换性.当不同次拟齐次符号H-Toeplitz算子满足交换性,则必有一符号函数在1点的取值为0;相同次拟齐次符号H-Toeplitz算子必满足交换性.这与Bergman空间上具有相同符号的H-Toeplitz算子的交换性不同.

多项Caputo分数阶微分方程Dirichlet问题Lyapunov型不等式

该文探讨了一类含参数的多项分数阶微分方程在Dirichlet边值条件下的Lyapunov型不等式.首先将分数阶微分方程边值问题等价转化为带Green函数的积分方程,再证明出Green函数的相关性质,最后结合先验估计方法得出相应的Lyapunov型不等式.多项分数阶微分方程属于非局部方程类别,其复杂性超越了单项分数阶微分方程.研究多项分数阶微分方程边值问题的Lyapunov型不等式,对定性分析多项分数阶非线性微分方程边值问题具有重要意义.

Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method

An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.

Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results.

Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions

In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.

Role of outdoor trees on pedestrian wind and thermal conditions around a pre-education building for sustainable energy management

Finding sustainable energy resources is essential to face the increasing energy demand.Trees are an important part of ancient architecture but are becoming rare in urban areas.Trees can control and tune the pedestrian-level wind velocity and thermal condition.In this study,a numerical investigation is employed to assess the role of trees planted in the windward direction of the building complex on the thermal and pedestrian wind velocity conditions around/inside a pre-education building located in the center of the complex.Compared to the previous studies(which considered only outside buildings),this work considers the effects of trees on microclimate change both inside/outside buildings.Effects of different parameters including the leaf area density and number of trees,number of rows,far-field velocity magnitude,and thermal condition around the main building are assessed.The results show that the flow velocity in the spacing between the first-row buildings is reduced by 30%-40% when the one-row trees with 2 m height are planted 15 m farther than the buildings.Furthermore,two rows of trees are more effective in higher velocities and reduce the maximum velocity by about 50%.The investigation shows that trees also could reduce the temperature by about 1℃around the building.

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

Effects of Initial and Boundary Conditions on Heavy Rainfall Simulation over the Yellow Sea and the Korean Peninsula:Comparison of ECMWF and NCEP Analysis Data Effects and Verification with Dropsonde Observation

This study evaluated the simulation performance of mesoscale convective system(MCS)-induced precipitation,focusing on three selected cases that originated from the Yellow Sea and propagated toward the Korean Peninsula.The evaluation was conducted for the European Centre for Medium-Range Weather Forecasts(ECMWF)and National Centers for Environmental Prediction(NCEP)analysis data,as well as the simulation result using them as initial and lateral boundary conditions for the Weather Research and Forecasting model.Particularly,temperature and humidity profiles from 3D dropsonde observations from the National Center for Meteorological Science of the Korea Meteorological Administration served as validation data.Results showed that the ECMWF analysis consistently had smaller errors compared to the NCEP analysis,which exhibited a cold and dry bias in the lower levels below 850 hPa.The model,in terms of the precipitation simulations,particularly for high-intensity precipitation over the Yellow Sea,demonstrated higher accuracy when applying ECMWF analysis data as the initial condition.This advantage also positively influenced the simulation of rainfall events on the Korean Peninsula by reasonably inducing convective-favorable thermodynamic features(i.e.,warm and humid lower-level atmosphere)over the Yellow Sea.In conclusion,this study provides specific information about two global analysis datasets and their impacts on MCS-induced heavy rainfall simulation by employing dropsonde observation data.Furthermore,it suggests the need to enhance the initial field for MCS-induced heavy rainfall simulation and the applicability of assimilating dropsonde data for this purpose in the future.

Evaluation of Mechanical Properties and Surface Quality of Wood from Bosnia and Herzegovina Exposed to Outdoor Conditions

This study investigated the mechanical properties of beech(Fagus sylvatica L.)and fir(Abies alba)wood from Bosnia and Herzegovina under outdoor exposure.Samples were exposed for 3-month exposure to assess bending strength,color changes,and surface quality.Results showed outdoor exposure negatively affected mechanical properties,particularly in samples with extended finger joints,causing significant surface cracks in uncoated samples.Beech wood exhibited notable color changes under exposure,with approximately 50%darkening without coating compared to 25%under covered conditions.Coated samples displayed minimal color changes,affirming the efficacy of surface treatment.Fir wood exhibited a roughness of 8.264μm,while beechwood average roughness increased from 6.767 to 13.916μm after exposure,with micro-pore development affecting water performance.Microscopic analysis identified prevalent fungal colonies,including Penicillium,Aureobasidium,Sclerophoma,and Chaetomium,underscoring their role in organic matter decomposition.This study highlights the importance of wood exposure and treatment selection for various applications.

A new approach for pseudo hyperbolic partial differential equations with nonLocal conditions using Laplace Adomian decomposition method

This paper provides a nonlinear pseudo-hyperbolic partial differential equation with non-local conditions.Despite the importance of this problem,the exact solution to this problem is rare in the literature.Therefore,the Laplace-Adomian Decomposition Method(LADM)is used to provide a new approach to solving this problem.Additionally,we give a comparison between the exact and approximate solutions at various points with absolute error.The obtained result showed that the proposed method is effective and accurate for this problem and can be used for many other evolution of nonlinear equations in mathematical physics.

Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger(SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop.These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Influence of tectonic preservation conditions on the nanopore structure of shale reservoir:A case study of Wufeng-Longmaxi Formation shale in western Hubei area,south China

Tectonism is one of the dominant factors affecting the shale pore structure.However,the control of shale pore structure by tectonic movements is still controversial,which limits the research progress of shale gas accumulation mechanism in the complex tectonic region of southern China.In this study,34 samples were collected from two exploratory wells located in different tectonic locations.Diverse experiments,e.g.,organic geochemistry,XRD analysis,FE-SEM,low-pressure gas adsorption,and high-pressure mercury intrusion,were conducted to fully characterize the shale reservoir.The TOC,Ro,and mineral composition of the shale samples between the two wells are similar,which reflects that the shale samples of the two wells have proximate pores-generating capacity and pores-supporting capacity.However,the pore characteristics of shale samples from two wells are significantly different.Compared with the stabilized zone shale,the porosity,pore volume,and specific surface area of the deformed zone shale were reduced by 60.61%,64.85%,and 27.81%,respectively.Moreover,the macroscopic and fine pores were reduced by 54.01%and 84.95%,respectively.Fault activity and uplift denudation are not conducive to pore preservation,and the rigid basement of Huangling uplift can promote pore preservation.These three factors are important reasons for controlling the difference in pore structure between two wells shales.We established a conceptual model of shale pores evolution under different tectonic preservation conditions.This study is significant to clarify the scale of shale gas formation and enrichment in complex tectonic regions,and helps in the selection of shale sweet spots.