On Torsion-free Connections in Finsler Geometry

We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. I: Deduction and geometric illustration

Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.

3D non-stationary geometry-based stochastic model for unmanned aerial vehicle air-to-ground multi-input multi-output channels

A three-dimensional non-stationary geometry-based stochastic model for unmanned aerial vehicle(UAV)air-to-ground multi-input multi-output(MIMO)channels is proposed.The scatterers surrounding the UAV and ground station are assumed to be distributed on the surface of two cylinders in the proposed model.The impact of UAV rotations and accelerated motion is considered to describe channel non-stationarity.The computational methods of the corresponding time-variant parameters,such as UAV antenna array angles,time delays,and maximum Doppler frequencies,are theoretically deduced.The model is then used to derive channel statistical properties such as space-time correlation functions and Doppler power spectral density.Finally,numerical simulations are run to validate the channel s statistical properties.The simulation results show that increasing the UAV and ground station accelerations can reduce the time correlation function and increase channel non-stationarity in the time domain.Furthermore,the UAV s rotation significantly influences the spatial correlation function,with rolling having a greater influence than pitching.Similarly,the different directions of UAV movement significantly impact the Doppler power spectral density.

Stochastic Geometric Analysis of the Uplink Throughput in Cognitive Radio Cellular Networks

This paper investigates the uplink throughput of Cognitive Radio Cellular Networks(CRCNs).As oppose to traditional performance evaluation schemes which mainly adopt complex system level simulations,we use the theoretical framework of stochastic geometry to provide a tractable and accurate analysis of the uplink throughput in the CRCN.By modelling the positions of User Equipments(UEs)and Base Stations(BSs)as Poisson Point Processes(PPPs),we analyse and derive expressions for the link rate and the cell throughput in the Primary(PR)and Secondary(SR)networks.The expressions show that the throughput of the CRCN is mainly affected by the density ratios between the UEs and the BSs in both the PR and SR networks.Besides,a comparative analysis of the link rate between random and regular BS deployments is concluded,and the results confirm the accuracy of our analysis.Furthermore,we define the cognitive throughput gain and derive an expression which is dominated by the traffic load in the PR network.

《道行般若经》疑难词句试释

主要用同经异译相互勘证的方法,兼参考梵本英译,对东汉《道行般若经》中的一些疑难词语和句子,例如自恣、何而、此所有、学成、无不、摩诃僧那僧涅等及其所在的句子,进行了阐释.

Constructing Measure by Repeated Infinite Subdivision

This paper generalizes the method of constructing measure by repeated finite subdivision in fractal geometry to that by infinite subdivision. Two conditions for the existing method are removed. A measure on the interval [0, 1] is constructed using this generalized method.

Mathematical Model and Simulation of Cutting Layer Geometry in Orthogonal Turn⁃Milling with Zero Eccentricity

Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.

Geometric and electronic effects on the performance of a bifunctional Ru2P catalyst in the hydrogenation and acceptorless dehydrogenation of N‐heteroarenes

The development of bifunctional catalysts for the efficient hydrogenation and acceptorless dehydrogenation of N‐heterocycles is a challenge.In this study,Ru_(2)P/AC effectively promoted reversible transformations between unsaturated and saturated N‐heterocycles affording yields of 98%and 99%,respectively.Moreover,a remarkable enhancement in the reusability of Ru_(2)P/AC was observed compared with other Ru‐based catalysts.According to density functional theory calculations,the superior performance of Ru_(2)P/AC was ascribed to specific synergistic factors,namely geometric and electronic effects induced by P.P greatly reduced the large Ru‐Ru ensembles and finely modified the electronic structures,leading to a low reaction barrier and high desorption ability of the catalyst,further boosting the hydrogenation and acceptorless dehydrogenation processes.

On the Computation of Noether Normalization

This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.

Infinitesimal Methods in the Works of Thabit ibn Qurra and L, Euler in Spherical Trigonometry

In one of his astronomical works the prominent arabic medieval scientists Thabit ibn Qurra （836-901） studied the visible motion of the Sun and found the points, where its velocity is maximum or minimum. He also lbund the points on the ecliptic, where this velocity is equal to the average velocity of the Sun over all the ecliptic. For this purpose he used the idea of infinitely small arcs and their ratios in different points of the circle. The great scientist Leonard Euler （1707-1783） introduced in his works on spherical trigonometry the line-element ds of the surface of the sphere, i.e. the differential of the arc length. He constructed the spherical trigonometry as an inner geometry on the surface of the sphere. He replaced the trigonometry lines, which were in use befbre him, by trigonometric functions.

Matrix-Geometric Method Based Unified Delay Analysis for Wireless Relay Networks

A lot of work has been focused on desig-ning and analyzing various cooperative diversity pro-tocols for wireless relay networks. To provide a uni-fied queuing analytic framework, we fonmlate an em-bedded Markov chain, which rams out to be a Quasi-Birth-and-Death （QBD） process. Using the Matrix-Ce-ometric method, we can analyze the average delay in a unified way. Theoretical analysis is validated by simu-lation results. We show that the delay performances of Amplify-and-Forward or Decode-and-Forwaxd （AF/ DF） and incremental AF/DF schemes can be analyzed in the unified way. Thus, we can always choose the best cooperative diversity scheme in different scenari-os for delay minimization.

Polarization Projection for 3D Geometry-Based Stochastic Channel Model

Comprehensive radiation characteristics of polarized antenna are crucial in creating practical channel coefficients for next generation wireless communication system designs.Being currently supported within3 D geometry-based stochastic channel models(GSCM),field patterns are technically obtained by chamber measurement(or by its best fitting).However,in some channel related performance analysis scenarios,design insight can be crystallized better by starting the derivations with theoretical co-polarization and cross-polarization components.Specifically,these two components are mathematically linked with field patterns through the proposed polarization projection algorithm.In this manuscript,we focus on revealing the transformation criterion of polarization states between the antenna plane and the propagation plane.In practice,it makes retrieving the field patterns by electromagnetic computation possible.Meanwhile,the impact imposed by distinct antenna orientations is geometrically illustrated and consequently incorporated into the proposed algorithm.This will further facilitate flexible performance evaluation of related radio transmission technologies.Our conclusions are verified by the closed-form expression of the dipole field pattern(via an analytical approach) and by chamber measurement results.Moreover,we find that its 2D degenerative case is aligned with the definitions in 3^(rd) generation partnership project(3GPP)technical report 25.996.The most obvious benefit of the proposed algorithm is to significantly reduce the cost on generating channel coefficients in GSCM simulation.

The lift-off effect analysis of flexible differential pick-up koch fractal eddy current probe

This study utilized finite element simulation and experimental methods to investigate the evolution of crack detection performanceof a flexible differential fractal Koch eddy current probe at different excitation frequencies as the lift-off distance increases.As the lift-off distanceincreased,the distribution shape of induced eddy currents changed,leading to reduced similarity in the shape of the excitation coil and an expandeddistribution range of induced eddy currents,ultimately resulting in weakened output signal strength.The experimental results showed that forexcitation frequencies of 10 kHz,20 kHz,50 kHz,100 kHz,200 kHz,500 kHz,and1000 kHz,the maximum lift distances of the real partof the output signal when cracks were detected were 5.0 mm,7.0 mm,8.0 mm,8.0 mm,8.0 mm,6.5 mm,and 4.0 mm,respectively.Theimaginary parts were 6.5 mm,6.5 mm,7.5 mm,5.5 mm,8.0 mm,6.5 mm,and 6.5 mm,respectively.

Accurate modelling of the crush behaviour of thin tubular columns using material point method

In this paper,we apply the material point method(MPM),also known as a meshfree method,to examine the crush behaviour of thin tubular columns.Unlike the finite element method,randomly-distributed-weak-particle triggers were used to account for the deformation behaviour of collapse modes.Both symmetric and asymmetric modes of deformation and their associated mean collapse loads are determined for an elasto-plastic constitutive law describing the tubular columns.Attention was devoted to the accuracy and the convergence of the MPM simulation,which is determined by the number of the particles and the size of the background cells used in our explicit solver.Furthermore,a novel contact approach was adopted to establish the crush behaviour of the tubular columns.Two aspects of the work were accordingly examined,including three different crush velocities(5,10 and 15 m/s) and varied geometrical features of the tube(t/d and l/d) based on the deformation history.The results of our model,which were compared with existing analytical predictions and experimental findings,identify the critical geometric features of the tubular columns that would dictate the deformation mode as being either progressive collapse or following Euler's buckling mode.

Detection of Supernova Neutrinos on the Earth for Large θ_(13)

Supernova （SN） neutrinos detected on the Earth are subject to the shock wave effects, the Mikheyev- Smirnov-Wolfenstein （MSW） effects, the neutrino collective effects and the Earth matter effects. Considering the recent experimental result about the large mixing angle 013 （-8.8°） provided by the Daya Bay Collaboration and applying the available knowledge for the neutrino conversion probability in the high resonance region of SN, PH , which is in the form of hypergeometric function in the case of large 813, we deduce the expression of PH taking into account the shock wave effects. It is found that PH is not zero in a certain range of time due to the shock wave effects. After considering all the four physical effects and scanning relevant parameters, we calculate the event numbers of SN neutrinos for the ＂Garehing＂ distribution of neutrino energy spectrum. From the numerical results, it is found that the behaviors of neutrino event numbers detected on the Earth depend on the neutrino mass hierarchy and neutrino spectrum parameters including the dimensionless pinching parameter βa （where a refers to neutrino flavor）, the average energy 〈Ea〉, and the SN neutrino luminosities La. Finally, we give the ranges of SN neutrino event numbers that will be detected at the Daya Bay experiment.

An engineering approach to improve the accuracy of one-step simulation for vehicle forming-to-crashworthiness integrated evaluation

To improve the accuracy of the vehicle crashworthiness simulation, it is necessary as well as important to integrate the valid forming effects of key parts. It has been agreed by many that one-step simulation results should be used only as a qualitative trend of the part but not as an engineering result for further structural analysis, especially for a relatively complex part. The study shows that it is inaccurate to analyze the forming effects with one-step simulation based on the geometry of the final part through comparison with the incremental simulation and verification with the actual part, whether in thickness or in plastic strain. However, incremental simulation is very time consuming and infeasible in the early stage of vehicle design due to lack- ing of forming tools and process parameters. An engineering approach is proposed to meet the requirement of accuracy as well as the time efficiency, where one-step simulation is conducted based on the geometry of the transformed part instead of the fi- nN part. The geometry of the transformed part is generated by simple die design engineering and proves to offer much more accuracy than the one-step simulation based on the final part geometry.

Dynamic Transition and Pattern Formation in Taylor Problem

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.