Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

Distribution law and susceptibility of geohazards across a gradient belt of the Western Sichuan Plateau

Across a gradient belt of the Western Sichuan Plateau,geohazards have seriously limited economic and social development.According to incomplete statistics,15,673 geohazards have been recorded in the study area.In order to mitigate the threat of geohazards to human engineering activities in the region,an overall understanding of the distribution pattern of geohazards and susceptibility assessment are necessary.In this paper,a gradient belt of the Western Sichuan Plateau and its zoning criteria were defined.Subsequently,on the basis of relief amplitude,distance to faults,rainfall,and human activities,three indicators of endogenic process were introduced:Bouguer gravity anomaly gradient,vertical deformation gradient,and horizontal deformation gradient.Thereafter,the distribution patterns of geohazards were investigated through mathematical statistics and ArcGIS software.By randomly selecting 10,449 hazards,a geohazard susceptibility map was generated using the Information Value(IV)model.Finally,the IV model was validated against 5224 hazards using the Area Under Curve(AUC)method.The results show that 47.6%of the geohazards were distributed in the zone of steep slope.Geohazards showed strong responses to distance to faults,human activities,and annual rainfall.The distribution of geohazards in the gradient belt of the Western Sichuan Plateau is more sensitive to vertical internal dynamics factors(such as vertical deformation gradient and Bouguer gravity anomaly gradient)without any apparent sensitivity to horizontal internal dynamics factors.The areas of high and very-high risk account for up to 32.22%,mainly distributed in the Longmenshan and Anning River faults.According to the AUC plot,the success rate of the IV model for generating the susceptibility map is 76%.This susceptibility map and geohazard distribution pattern can provide a reference for geological disaster monitoring,preparation of post-disaster emergency measures,and town planning.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.

Two innovative equivalent statements of the third law of thermodynamics

It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.

The Rule of Law is the Most Important Means of Human Rights Protection

Today,we are here to commemorate the 75^(th) anniversary of the adoption of the Universal Declaration of Human Rights.In this Declaration,which consists of only30 articles,seven articles are related to the constitution,law,court,and the rule of law,making it a declaration filled with the rule of law.Coincidentally,today is also the 10^(th) National Constitution Day of China.Nineteen years ago,“the state respects and protects human rights”was enshrined in the Constitution,becoming a constitutional principle.Since then,human rights protection in China has been based on fundamental law.

Analysis of the Characterization of the Old Man in“The Law of Life”from the Narrative Perspective

“The Law of Life”is one of Jack London’s representative works,depicting the story of an elderly Native American abandoned by his family,alone and waiting for life to fade away.This paper,based on narrative theory,aims to explore how the author employs narrative techniques to present the image of the old man in the short story.The narrative techniques of dual focalization and dual narrative timelines in the text demonstrate the abandonment of the old man’s homeland and his inescapable death under a naturalistic view of life and reflect a desolate life picture of resignation towards death under naturalistic determinism,depicting a grim elderly world under the naturalistic concept of“survival of the fittest.”Studying this short story helps us reflect on the living conditions of the elderly and provides insights into how to better care for the elderly population amid the global trend of aging.

Malawi Opens Tourism Doors No visa’s needed for Chinese tourists and others,as Malawi makes visits more convenient

When Malawian President Lazarus Chakwera delivered a State of the Nation Address at the 50th Parliamentary Session and Budget Meeting in February,tourism was top of mind.

Experimental Study on the Influence of Fracturing Fluid Retention on Shale Gas Diffusion Law

Shale gas reservoirs have poor physical properties and a large number of micro-nano pores have been developed.Shale gas wells have no natural productivity and need fracturing reconstruction measures to put into production.However,the fracturing fluid will enter the reservoir space of shale matrix after fracturing and affect the production of shale gas.At present,there is no consensus on the influence of fracturing fluid retention on gas well production.Based on this,the paper adopts gas molecular transport analyzer to carry out experimental research on the influence of fracturing fluid on shale gas diffusion law after entering matrix pores.The results show that:(1)Compared with the diffusion capacity of single-phase shale gas,the diffusion capacity of shale gas decreases significantly when fracturing fluid is present in the reservoir;(2)In the process of fracturing fluid flowback,when the water saturation in the reservoir decreases from 50%to 0,the gas well productivity increases by about 60%.(3)When fracturing fluid exists in the reservoir,the pore diameter has an exponential relationship with the shale gas diffusion coefficient,and the diffusion coefficient increases exponentially with the increase of pore diameter.The research of this paper provides theoretical basis for guiding the efficient development of shale gas wells.

Smart all-time vision:The battery-free video communication for urban administration and law enforcement

The Chinese government is dedicated to enhancing the level of informatization in administrative law enforcement to ensure fairness and increase credibility.Currently,law enforcement has exposed such problems as insufficient force,difficulties in collecting evidence,and low evidential power.These problems contradict the principles of rule of law and standardization.Many local governments have implemented advanced information technologies for urban administration and law enforcement,including big data,artificial intelligence,and IoT.Among these technologies,IoT is the core communication infrastructure for innovative law enforcement platforms.However,traditional video communications rely on batteries or dedicated power sources,leading to maintenance challenges and high power consumption.In this paper,we propose AT-Eye,a new video communication paradigm for all-time law enforcement video monitoring,which is battery-free and high-throughput.The key enabler of AT-Eye is ambient backscatter technology,which enables energy harvesting and video communication simultaneously.Unlike previous methods,our proposal introduces a novel CCK-based modulation for tag cameras and achieves 4-way concurrency.The modulation is simple because it uses phase difference and it is energyefficient because generating square waves is adequate.Moreover,to ensure full compatibility with COTS WiFi,we modulate the physical service data unit.Therefore,data recovery is possible using only commercial NICs.We conduct comprehensive experiments to examine our proposal and experiment results show that AT-Eye achieves a throughput of 10.8 Mbps with COTS radios.We also simulate a 16-way battery-free tag camera system,demonstrating AT-Eye’s feasibility of high-definition video communication.

Research on the Application of Juvenile Psychological Development and Sports Acquisition Law System in Physical Education Teaching

Adolescents’physical and mental development has obvious age-stage characteristics.Therefore,before the implementation of physical education teaching,it is necessary to fully analyze the laws of adolescents’psychological development and fully understand the laws of adolescents’physical development and exercise acquisition.The purpose of this study is to start from the actual needs of physical education teaching and to fully understand the laws of psychological development of adolescent groups.After the review and analysis,the law of adolescents’sports acquisition is summarized and summarized,so as to form the system of adolescents’psychological development and sports acquisition law in physical education teaching,lay a good foundation for physical education teachers to implement teaching on the teaching objects of adolescent students in a targeted and efficient manner,and ultimately promote the benign development of school sports.

Comprehensive use of the Gutenberg–Richter law and geotomography for improving seismic hazard evaluation in hard coal mines

Mining-induced seismicity occurs in numerous underground mines worldwide where extraction is conducted at great depths or in areas characterised by complex tectonic structure.It is accompanied by rock bursts,which result in the loss of working functionality and the possibility of accidents among personnel.The issue of a constant and reliable seismic hazard evaluation is of key signifcance for both the safety of miners and the stability of production.Research on its improvement is directed at developing new interpretive solutions and methods.The nature of the presented solution is the complex interpretation of seismological data that characterise rock mass seismicity and of underground measurement results in the form of a map presenting the longitudinal wave propagation velocity distribution in the rock surrounding the mined coal seam.The solution was tested in hard coal mines located in the Upper Silesian Coal Basin.The mines are equipped with a modern seismological system enabling the constant monitoring of seismicity together with hazard level evaluation as well as with seismic apparatus for conducting periodic measurements of the seismic wave propagation velocity before the mining face.Comprehensive seismic hazard evaluation criteria were determined based on the obtained results,involving the anomaly of the Gutenberg–Richter law“b”value and the maximum longitudinal seismic wave propagation velocity in the roof rock.The obtained experience and the result validation of this new comprehensive hazard evaluation method confrm its practical usefulness and indicate the directions of improvement for the solution in question.

Black Holes and the Third Law of Thermodynamics Revisited

Black holes contradict the Nernst-Planck (N/P) version of the 3rd law of thermodynamics, but agree with its unattainability (U) version. This happens without contradiction, because the N/P and U versions are not equivalent, namely, N/P implies U but U does not imply N/P. So, black holes obey the weaker version of the 3rd law, but not the stronger one.

A modified generalized scaling law for the similitude of dynamic strain in centrifuge modeling

Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s generalized scaling law(GSL),a modified scaling law was proposed based on Iai′s GSL to secure the same dynamic shear strain between the centrifuge model and the prototype by modulating the amplitude and frequency of the input motion at the base.A suite of dynamic centrifuge model tests of dry sand level ground was conducted with the same overall scaling factor(λ=200)under different centrifugal accelerations by using the technique of“modeling of models”to validate the modified GSL.The test results show that the modified GSL could achieve the same dynamic strain in model as that of the prototype,leading to better modeling for geotechnical problems where dynamic strain dominates the response or failure of soils.Finally,the applicability of the proposed scaling law and possible constraints on geometry scaling due to the capability limits of existing centrifuge shaking tables are discussed.

Relationship between the Three Laws of Dialectics of Nature and Agricultural Development

Based on the three laws of dialectics of nature-the law of unity of opposites, the law of mutual change of quality and the law of negation of negation, this paper analyzes the relationship between the three laws and agricultural development, and proposes making good use of the three laws to promote the better development of agriculture and realize agricultural modernization.

Simulation of the Behaviour Laws in the Thermal Affected Zones of the 13Cr-4Ni Martensitic Stainless Steel

During the welding, many phenomena occur. The materials deform under the action of residual stresses. This tendency is due to the high gradients of temperature during the process. These deformations are really difficult for many professionals operating in the area. In the goal to predict these variations, one has established the behaviour laws which will be applied to evaluate residual stresses and strains. This research is focused on the study of the Thermal Affected Zone (TAZ) during the welding of the 13Cr-4Ni martensitic stainless steel. The TAZ does not know any change of state (solid/liquid). It only knows the metallurgical phase change (austenite/martensite). There are three types of behaviour laws in this study: thermal, mechanical and metallurgical behaviour laws. The thermal behaviour law serves to evaluate the temperature field which induces the mechanical strains. The mechanical behaviour law serves to evaluate spherical stress (pressure) and deviatoric stress which compose the residual stress. It also helps to measure the total strain. The metallurgical behaviour law serves for the evaluation of the metallurgical phase proportions. To validate the modelling developed in this study, one has made the simulations to compare the results obtained with the analytical and experimental data.

CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW

In this paper,we justify the convergence from the two-species Vlasov-PoissonBoltzmann(VPB,for short)system to the two-fluid incompressible Navier-Stokes-FourierPoisson(NSFP,for short)system with Ohm’s law in the context of classical solutions.We prove the uniform estimates with respect to the Knudsen numberεfor the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions.Consequently,we prove the convergence to the two-fluid incompressible NSFP asεgoes to 0.

THE LAW OF THE ITERATED LOGARITHM FOR SPATIAL AVERAGES OF THE STOCHASTIC HEAT EQUATION

Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.

Cooperative game theory-based steering law design of a CMG system

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

Effect of particle gradation on pore structure and seepage law of solution in weathered crust elution-deposited rare earth ores

Both CT and Avizo software were used to explore the effect of particle gradation on the evolution characteristics of pore structure and seepage paths in weathered crust elution-deposited rare earth ores during leaching.The results showed that the pore areas in four kinds of ore samples before leaching were mainly concentrated in 10^(4)–10^(7)μm^(2),whose pore quantities accounted for 96.89%,94.94%,90.48%,and 89.45%,respectively,while the corresponding pore volume only accounted for 30.74%,14.55%,7.58%,and 2.84%of the total pore volume.With the decrease of fractal dimension,the average pore throat length increased,but pore throat quantities,the average pore throat radius and coordination number decreased.Compared with that before leaching,the change degree of pore structure during leaching increased with the fractal dimension decreasing.For example,the reduction rate of the average coordination number of ore samples was 14.36%,21.30%,28.00%,and 32.90%,respectively.Seepage simulation results indicated that seepage paths were uniformly distributed before leaching while the streamline density and seepage velocity increased with the fractal dimension decreasing.Besides,the phenomenon of the streamline interruption gradually reduced during leaching while preferential seepage got more obvious with the decrease of the fractal dimension.