The Hyperspace of the Regions Below of Continuous Maps from the Converging Sequence

Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0（S） = {↓f∈↓C（S） ： f（0） = 0}. ↓USC（S） endowed with the Vietoris topology is a topological space. A pair of topological spaces （X, Y） means that X is a topological space and Y is its subspace. Two pairs of topological spaces （X, Y） and （A, B） are called pair-homeomorphic （≈） if there exists a homeomorphism h ： X→A from X onto A such that h（Y） = B. It is proved that, （↓USC（S）,↓C0（S）） ≈（Q, s） and （↓USC（S）,↓C（S）／ ↓C0（S））≈（Q, c0）, where Q = [-1,1]^ω is the Hilbert cube and s = （-1,1）^ω,c0= {（xn）∈Q ： limn→∞= 0}. But we do not know what （↓USC（S）,↓C（S））is.

Numerical investigation of particle deposition on converging slot-hole film-cooled wall

Numerical research on the dilute particles movement and deposition characteristics in the vicinity of converging slot-hole(console) was carried out, and the effect of hole shape on the particle deposition characteristics was investigated. The EI-Batsh deposition model was used to predict the particle deposition characteristics. The results show that the console hole has an obvious advantage in reducing particle deposition in comparison with cylindrical hole, especially under higher blowing ratio. The coolant jet from console holes can cover the wall well. Furthermore, the rotation direction of vortices near console hole is contrary to that near cylindrical hole. For console holes, particle deposition mainly takes place in the upstream area of the holes.

Fast Converging Series for Riemann Zeta Function

Riemann zeta function has a key role in number theory and in its applications. In this paper we present a new fast converging series for . Applications of the series include the computation of the and recursive computation of , and generally . We discuss on the production of irrational number sequences e.g. for encryption coding and zeta function maps for analysis and synthesis of log-time sampled signals.

Converging spherical and cylindrical elastic–plastic waves of small amplitude

Converging spherical and cylindrical elastic-plastic waves in an isotropic work-hardening medium is investigated on the basis of a finite difference method. The small amplitude pressure is applied instantaneously and maintained on the outer surface of a spherical or a cylindrical medium. It is found that for undercritical loading, the induced wave structure is an elastic front followed in turn by an expanding plastic region and an expanding elastic region. For supercritical loading, the elastic front is followed in turn by an expanding plastic region, a narrowing elastic region and an expanding plastic region. After yielding is initiated, the strength of the elastic front is constant and equal to the critical loading pressure. The motion of the continuous elastic-plastic interface is discussed in detail. Spatial distributions of pressure near the axis show the strength of the converging wave is nearly doubled in the reflecting stage.

Depicting the role of gas–solid interactions on the hydrodynamics of converging pneumatic riser

The understanding of the flow characteristics and effect of gas–solid interactions in pneumatic risers is fundamental to investigate to ensure effective design cost-effective operation.Thus,to understand the effect of gas–solid interactions on the hydrodynamics of newly proposed conversing risers,this study mainly focused on predicting pressure drop in the dilute phase pneumatic conveying system.The experiments were conducted in a converging riser having a convergence angle of 0.2693°.Various solid particles such as sago,black mustard,and alumina have been considered to study the effect of particle sizes and density on the pressure drop.The experimental outcomes indicate that the total pressure drop increases with an increase in the solid density and gas mass flow rate.Moreover,smaller particle sizes are also increased the pressure drop.An empirical correlation is developed for the prediction of total pressure dropΔPTin converging pneumatic riser via dimensional analysis.All dependent variables such as particle and air density,drag force,acceleration due to gravity,the mass flow rate of air and particle,the diameter of particle and converging riser,the height of converging riser were considered to develop the empirical correlation.The established relationship is tested,and experimental data have been fitted for its validation.The estimated relative error of less than 0.05 proved the significance of the developed correlation.Hence,it can be stated that the established relationship is useful in studying the effects of various parameters on the pressure drop across the length of the conversing riser.

Turbulent flow in converging nozzles,part one:boundary layer solution

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer as- sumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.

Wave Propagation in A Converging Channel of Arbitrary Configuration

A numerical solution was derived to determine wave field in a converging channel bounded by rubble-mound jetties. The solution was achieved by applying boundary element method. The model was applied to analyze the effect of channel convergence, the cross-section of the jetties and their physical and damping properties on wave field in the channel. The study reveals numerous non-intuitive results specific for jetted and convergent channels. The analysis shows that wave reflection is usually low and is of secondary practical importance. Wave transmission strongly depends on the channel geometry and transmitted waves may be higher than incident waves, despite reflection and damping processes. Moreover, wave transmission depends on physical and damping properties of rubble jetties and the results show that wave transmission may increase with the increasing damping properties of jetties, which is a non-intuitive feature of wave fields in jetted channels. The analysis reveals several novel results of practical importance. It is shown that the rubble-mound jetties should be constructed from the material of high porosity, which ensures low transmission. More attention should be devoted to hydraulic properties of porous materials. It is recommended to use the material of moderate damping properties. The material of high damping properties often increases the wave transmission. It is possible, by a selection of rubble-mound material, to obtain lower transmission level for steep waves than for waves of moderate steepness. A series of laboratory experiments were conducted in the wave flume to verify the theoretical results. The comparisons show that theoretical results are in fairly good agreement with experimental data.

NOVEL COMPOSITE CVT SYSTEMS WITH DIVERGING AND DUAL-MODE CONVERGING POWER FLOW

A new type of composite CVT(continuously variable transmission) systemsfeatured by power flow divergence and dual-mode convergence, capable of improving CVT's efficiencyand power capacity or making AMTs(automated manual transmissions) become continuously variable, isstudied. With specific mechano-mechanical and electromechanical composite CVT systems as detailedexamples, its basic working principles are expatiated. General methods and key points in designingand realizing such systems are also analyzed and discussed.

Fusion of Multi-Pinched Plasma Beams Converging with Spatial Symmetry

Fusion reactions can be achieved by using deuterium from sea water as the fuel.The amount of deuterium in one gallon of sea water contains energy equivalent to three hundred gallons of gasoline.Satisfactory conditions of plasma temperature and density necessary to initiate fusion have been achieved in various research facilities.However,the confinement time is not sufficient for ignition due to plasma instabilities.Here we show that fatal plasma instabilities could be suppressed by the ingenious arrangement of multi-pinched plasma beams converging symmetrically in space based on the minimization principle of plasma potential energy.Confirmation tests are proposed using tiny wires containing deuterium.If successful,the results could lead to a feasible approach to obtaining commercial fusion power from sea water,hence without the need to use expensive and radioactive tritium as the fuel.

Are China and Europe converging?

This analysis aims at giving a flavour of what is happening between the European and Chinese markets with reference to selected energy indicators and economic variables. More precisely the analysis is concerned with the convergence between European countries (EU15 + Norway) and China in terms of both per capita GDP and "sustainability indicators". The variables we refer to as "sustainability indicators" are two: energy intensity (EI) and carbon intensity (CI). The paths of such variables will be investigated both looking at the economy as a whole and by analysing what is happening in three sectors of economic activity, namely industry, agriculture and services. It finds strong evidence of convergence in energy intensity and carbon intensity between the EU and China, with rates fast enough to achieve 90% convergence in a matter of two decades.

Using Converging Strategies to Reduce Divergence in Intercultural User Interface Design

This chapter starts with an introduction illuminating the theoretical back-ground necessary for taking culture into account in HCI design. Definitions of concepts used are provided followed by a historical overview on taking culture into account in HCI design. Subsequently, a glimpse of the current state of research in culture-centered HCI design is derived from secondary literature providing the gist of the structures, processes, methods, models and theoretic approaches concerning the relationship between culture and HCI design (“converging” strategies). After presenting controversies and challenges, a short discussion of results from empirical studies and design recommendations for culture-centered HCI design lead to implications and trends in future intercultural user interface design research to close the knowledge gap (the “divergence”) regarding the relationship between culture and Human-Computer Interaction (HCI), i.e. converging the divergence to reach the convergent divergence.

废气入射管道参数对缸内EGR分层的影响

为了在某款摩托车汽油机缸内实现废气再循环(exhaust gas recirculation,EGR)分层以减少泵气损失,降低NOx排放,将原有的进气旁通系统改造为EGR系统,使用GT-POWER模型求解出3000 r/min、60 mg进气量工况下废气入射管道以及进排气道的边界条件和初始条件,并将这些条件导入发动机的CONVERGE模型中进行计算,通过对比不同废气入射管径、不同安装角度、不同安装距离条件下的缸内流动特性、缸内速度场以及缸内废气质量分数分布,确定了最佳废气入射管道参数。结果表明:在3000 r/min、60 mg进气量工况下,当废气入射管径为5 mm,入射角度为17.5°,安装距离为22 mm时,气缸内能实现EGR分层。

Numerical study on Rayleigh-Taylor effect on cylindrically converging Richtmyer-Meshkov instability

Evolution of a two-dimensional air/SF6 single-mode interface is numerically investigated by an upwind CE/SE method under a cylindrically converging circumstance. The Rayleigh-Taylor effect caused by the flow deceleration on the phase inversion(RTPI)is highlighted. The RTPI was firstly observed in our previous experiment, but the related mechanism remains unclear. By isolating the three-dimensional effect, it is found here that the initial amplitude(a0), the azimuthal mode number(k0) and the re-shocking moment are the three major parameters which determine the RTPI occurrence. In the variable space of(k0, a0), a critical a0 for the RTPI occurrence is solved for each k0, and there exists a threshold value of k0 below which the RTPI will not occur no matter what a0 is. There exists a special k0 corresponding to the largest critical a0, and the reduction rule of critical a0 with k0 can be well described by an exponential decay function. The results show that the occurrence of the RTPI requires a small a0 which should be less than a critical value, a large k0 which should exceed a threshold, and a right impinging moment of the re-shock which should be later than the RTPI occurrence. Finally, the effects of the incident shock strength, the density ratio and the initial position of the interface on the threshold value of k0 and on the maximum critical a0 are examined. These new findings would facilitate the understanding of the converging Richtmyer-Meshkov instability and would be helpful for designing an optimal structure of the inertia confinement fusion capsule.

Gasdynamic characteristics of toroidal shock and detonation wave converging

The modified CCW relation is applied to analyzing the shock, detonation wave converging and the role of chemical reactions in the process. Results indicate that the shock wave is strengthened faster than the detonation wave in the converging at the same initial Mach number. Euler equations implemented with a detailed chemical reaction model are solved to simulate toroidal shock and detonation wave converging. Gasdynamic characteristics of the converging are investigated, including wave interaction patterns, observable discrepancies and physical phenomena behind them. By comparing wave diffractions, converging processes and pressure evolutions in the focusing area, the different effects of chemical reactions on diffracting and converging processes are discussed and the analytic conclusion is demonstrated through the observation of numerical simulations.

基于PISO算法的汽车喷油器优化仿真研究

通过三维数值模拟软件Converge结合PISO算法,针对重型直喷柴油机,研究喷油器的不同孔径、孔深和喷油倾角对发动机燃烧和排放性能的影响,得到柴油发动机最佳热效率的喷油器参数设置方案。结果表明:相较于喷孔深度和喷孔倾角,喷孔直径的改变对发动机热效率的影响更大,且可有效改善发动机的NO_(x)和碳烟排放。当喷孔直径为0.179 mm、0.219 mm及0.259 mm时,分别能实现1.4%、3.4%、和2.8%的增幅,热效率提升较为显著。

Mode coupling in converging Richtmyer-Meshkov instability of dual-mode interface

The converging Richtmyer-Meshkov(RM)instability on single-and dual-mode N2/SF6 interfaces is studied by an upwind conservation element and solution element solver.An unperturbed case is first considered,and it is found that the shocked interface undergoes a long-term deceleration after a period of uniform motion.The evolution of single-mode interface at the early stage exhibits an evident nonlinearity,which can be reasonably predicted by the nonlinear model of Wang et al.(Phys Plasmas 22:082702,2015).During the deceleration stage,the perturbation amplitude drops quickly and even becomes a negative(phase inversion)before the reshock due to the Rayleigh-Taylor(RT)stabilization.After the reshock,the interface experiences a phase inversion again or does not,depending on the reshock time.The growth of the second-order harmonic in the deceleration stage clearly reveals the competition between the RT effect and the nonlinearity.For dual-mode interfaces,the growth of the first mode(wavenumber k1)relies heavily on the second mode(wavenumber k2)due to the mode coupling effect.Specifically,for cases where k2 is an even or odd multiple of k1,the growth of the first mode is inhibited or promoted depending on its initial amplitude sign and the phase difference between two basic waves,while for cases where k2 is a non-integer multiple of k1,the second mode has negligible influence on the first mode.Through a systematic study,signs of perturbation amplitudes of the generated k2−k1 and k2+k1 waves are obtained for all possible dual-mode configurations,which are reasonably predicted by a modified Haan model(Phys Fluids B 3:2349-2355,1991).

Comparative transcriptomic evidence of physiological changes and potential relationships in vertebrates under different dormancy states

Dormancy represents a fascinating adaptive strategy for organisms to survive in unforgiving environments.After a period of dormancy,organisms often exhibit exceptional resilience.This period is typically divided into hibernation and aestivation based on seasonal patterns.However,the mechanisms by which organisms adapt to their environments during dormancy,as well as the potential relationships between different states of dormancy,deserve further exploration.Here,we selected Perccottus glenii and Protopterus annectens as the primary subjects to study hibernation and aestivation,respectively.Based on histological and transcriptomic analysis of multiple organs,we discovered that dormancy involved a coordinated functional response across organs.Enrichment analyses revealed noteworthy disparities between the two dormant species in their responses to extreme temperatures.Notably,similarities in gene expression patterns pertaining to energy metabolism,neural activity,and biosynthesis were noted during hibernation,suggesting a potential correlation between hibernation and aestivation.To further explore the relationship between these two phenomena,we analyzed other dormancy-capable species using data from publicly available databases.This comparative analysis revealed that most orthologous genes involved in metabolism,cell proliferation,and neural function exhibited consistent expression patterns during dormancy,indicating that the observed similarity between hibernation and aestivation may be attributable to convergent evolution.In conclusion,this study enhances our comprehension of the dormancy phenomenon and offers new insights into the molecular mechanisms underpinning vertebrate dormancy.

Valence Bands Convergence in p-Type CoSb_(3) through Electronegative Fluorine Filling

Band convergence is considered to be a strategy with clear benefits for thermoelectric performance,generally favoring the co-optimization of conductivity and Seebeck coefficients,and the conventional means include elemental filling to regulate the band.However,the influence of the most electronegative fluorine on the CoSb_(3) band remains unclear.We carry out density-functional-theory calculations and show that the valence band maximum gradually shifts downward with the increase of fluorine filling,lastly the valence band maximum converges to the highly degenerated secondary valence bands in fluorine-filled skutterudites.

A Finite-Time Convergent Analysis of Continuous Action Iterated Dilemma

Dear Editor,In this letter, a finite-time convergent analysis of continuous action iterated dilemma(CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary(cooperation or defection), which limits the number of strategies a player can choose from.

Prescribed-Time Nash Equilibrium Seeking for Pursuit-Evasion Game

Dear Editor,This letter is concerned with prescribed-time Nash equilibrium(PTNE)seeking problem in a pursuit-evasion game(PEG)involving agents with second-order dynamics.In order to achieve the prior-given and user-defined convergence time for the PEG,a PTNE seeking algorithm has been developed to facilitate collaboration among multiple pursuers for capturing the evader without the need for any global information.Then,it is theoretically proved that the prescribedtime convergence of the designed algorithm for achieving Nash equilibrium of PEG.Eventually,the effectiveness of the PTNE method was validated by numerical simulation results.A PEG consists of two groups of agents:evaders and pursuers.The pursuers aim to capture the evaders through cooperative efforts,while the evaders strive to evade capture.PEG is a classic noncooperative game.It has attracted plenty of attention due to its wide application scenarios,such as smart grids[1],formation control[2],[3],and spacecraft rendezvous[4].It is noteworthy that most previous research on seeking the Nash equilibrium of the game,where no agent has an incentive to change its actions,has focused on asymptotic and exponential convergence[5]-[7].