Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural number...Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural numbers with no laws except that of chance. Questions about prime numbers have been perplexing mathematicians over centuries. How to efficiently predict greater prime numbers has been a great challenge for many. Most of the previous studies focus on how many prime numbers there are in certain ranges or patterns of the first or last digits of prime numbers. Honestly, although these patterns are true, they help little with accurately predicting new prime numbers, as a deviation at any digit is enough to annihilate the primality of a number. The author demonstrates the periodicity and inter-relationship underlying all prime numbers that makes the occurrence of all prime numbers predictable. This knowledge helps to fish all prime numbers within one net and will help to speed up the related research.展开更多
The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using the bases 2;3;5;7 whose two symmetric combinations explain the main lepton mass ratios. The corresponding Holic Principle induc...The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using the bases 2;3;5;7 whose two symmetric combinations explain the main lepton mass ratios. The corresponding Holic Principle induces a symmetry between the Newton and Planck constants which confirm the Permanent Sweeping Holography Bang Cosmology, with invariant baryon density 3/10, the dark baryons being dephased matter-antimatter oscillation. This implies the DNA bi-codon mean isotopic mass, confirming to 0.1 ppm the electron-based Topological Axis, whose terminal boson is the base 2 c-observable Universe in the base 3 Cosmos. The physical parameters involve the Euler idoneal numbers and the special Fermat primes of Wieferich (bases 2) and Mirimanoff (base 3). The prime numbers and crystallographic symmetries are related to the 4-fold structure of the DNA bi-codon. The forgotten Eddington’s proton-tau symmetry is rehabilitated, renewing the supersymmetry quest. This excludes the concepts of Multiverse, Continuum, Infinity, Locality and Zero-mass Particle, leading to stringent predictions in Cosmology, Particle Physics and Biology.展开更多
In this paper, we show a new theoretical procedure for calculating the nucleonic mass values. We develop this procedure on the geometric representation of (u, d) quarks, these seen as golden structures of coupled quan...In this paper, we show a new theoretical procedure for calculating the nucleonic mass values. We develop this procedure on the geometric representation of (u, d) quarks, these seen as golden structures of coupled quantum oscillators (Aureum Geometric Model or AGM). Using AGM, we also build the geometric structures of nucleons (p, n), determining their structure equations and spins. Thank AGM, coherent to QCD, new aspects of the Quantum Mechanics emerge, opening to anew descriptive paradigm in Particle Physics.展开更多
In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Fir...In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.展开更多
Flow distribution and the effects of different boundary conditions are achieved for a steady-state conjugate (Conduction & Convection) heat transfer process. A plate fin heat sink with horizontal fin orientation a...Flow distribution and the effects of different boundary conditions are achieved for a steady-state conjugate (Conduction & Convection) heat transfer process. A plate fin heat sink with horizontal fin orientation along with a computer chassis is numerically investigated and simulated using software ANSYS CFX. Fin orientation of a heat sink changes the direction of fluid flow inside the chassis. For predicting turbulence of the flow inside the domain, a two</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">equation based</span><span style="font-size:10pt;font-family:""><span style="font-family:Verdana;font-size:12px;"> <i></span><i><span style="font-family:Verdana;font-size:12px;">k</span></i><span style="font-family:Verdana;font-size:12px;">-</span><i><span style="font-family:Verdana;font-size:12px;">ε</span></i><span style="font-family:Verdana;font-size:12px;"></i> turbulence model is chosen. The</span></span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">Reynolds number based on inflow velocity and geometry is found 4.2</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">×</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">10<sup>3</sup> that indicates that the flow is turbulent inside the chassis. To get proper thermal cooling, the optimum velocity ratio of inlet/outlet, dimension of inlet/outlet and different positions of outlet on the back sidewall of the chassis are predicted.</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">Aspect</span><span style="font-family:Verdana;"> velocity ratio between the inlet airflow and the outlet airflow has an effect on the steadiness of the flow. Mass flow rate depends</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">on the dimension of the inlet/outlet. The horizontal fin orientation with 1:1.6 inlet-outlet airflow velocity ratio gives better thermal performance when outlet is located at the top corner of the chassis, near to the inner sidewall. Flow distribution and heat transfer characteristics are also analyzed to obtain the final model.展开更多
A nonincreasing sequenceπ=(d1,…,dn)of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.In this case,G is referred to as a realization ofπ.Given a graph H,a graphic se...A nonincreasing sequenceπ=(d1,…,dn)of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.In this case,G is referred to as a realization ofπ.Given a graph H,a graphic sequenceπis potentially H-graphic ifπhas a realization containing H as a subgraph.For graphs G1 and G2,the potential-Ramsey number rpot(G1,G2)is the smallest integer k such that for every k-term graphic sequenceπ,eitherπis potentially G1-graphic or the complementary sequenceπ=(k-1-dk,…,k-1-d1)is potentially G2-graphic.For 0≤k≤[t/2],denote Kt-k to be the graph obtained from Kt by deleting k independent edges.If k=0,Busch et al.(Graphs Combin.,30(2014)847-859)present a lower bound on rpot(G,Kt)by using the 1-dependence number of G.In this paper,we utilize i-dependence number of G for i≥1 to give a new lower bound on rpot(G,Kt-k)for any k with 0≤k≤[T/2].Moreover,we also determine the exact values of rpot(Kn,Kt-k)for 1≤k≤2.展开更多
Namibia’s Etosha National Park(ENP)is home to many different animals such as lions,jackals,hyenas,zebras,elephants,etc.Each year,grazing animals are infected and die from anthrax caused by the bacteria Bacillus anthr...Namibia’s Etosha National Park(ENP)is home to many different animals such as lions,jackals,hyenas,zebras,elephants,etc.Each year,grazing animals are infected and die from anthrax caused by the bacteria Bacillus anthracis.This increases the number of carcasses in the park,which serve as food for scavengers such as jackals.This study investigates the interplay between anthrax transmission in zebras and the scavenging of zebra carcasses in ENP,using a deterministic mathematical model to describe the population dynamics.We strive to answer the following research questions:Under what conditions can the presence of scavengers control anthrax outbreaks in zebra populations?Does carcass production by anthrax help or hurt scavengers in the long term?Standard qualitative analysis techniques distinguished outcomes(stable equilibria)using reproduction numbers as threshold quantities.We found that,when scavengers feed on anthrax-laden carcasses,the scavengers help the zebras,by eliminating potential infection zones for the zebras.In this way they reduce anthrax’s spread by orders of magnitude.We also identify conditions under which the presence of anthrax benefits the scavengers,in terms of death-to-birth ratios for zebras,scavengers and anthrax.展开更多
The novel coronavirus(COVID-19)pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world.It became the most important public health challenge facing man...The novel coronavirus(COVID-19)pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world.It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic.Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic.This study presents a primer for formulating,analysing and simulating mathematical models for understanding the dynamics of COVID-19.Specifically,we introduce simple compartmental,Kermack-McKendrick-type epidemic models with homogeneously-and heterogeneously-mixed populations,an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine.We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model.A brief overview of other kinds of models that have been used to study the dynamics of COVID-19,such as agent-based,network and statistical models,is also presented.Possible extensions of the basic model,as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics,are suggested.展开更多
One of the major difficulties with modelling an ongoing epidemic is that often data is limited or incomplete,making it hard to estimate key epidemic parameters and outcomes(e.g.attack rate,peak time,reporting rate,rep...One of the major difficulties with modelling an ongoing epidemic is that often data is limited or incomplete,making it hard to estimate key epidemic parameters and outcomes(e.g.attack rate,peak time,reporting rate,reproduction number).In the current study,we present a model for data-fitting limited infection case data which provides estimates for important epidemiological parameters and outcomes.The model can also provide reasonable short-term(one month)projections.We apply the model to the current and ongoing COVID-19 outbreak in Canada both at the national and provincial/territorial level.展开更多
The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically t...The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically through mathematical modelling.We conducted a systematic review of epidemic prediction models of COVID-19 and the public health intervention strategies by searching the Web of Science database.55 studies of the COVID-19 epidemic model were reviewed systematically.It was found that the COVID-19 epidemic models were different in the model type,acquisition method,hypothesis and distribution of key input parameters.Most studies used the gamma distribution to describe the key time period of COVID-19 infection,and some studies used the lognormal distribution,the Erlang distribution,and theWeibull distribution.The setting ranges of the incubation period,serial interval,infectious period and generation time were 4.9e7 days,4.41e8.4 days,2.3e10 days and 4.4e7.5 days,respectively,and more than half of the incubation periods were set to 5.1 or 5.2 days.Most models assumed that the latent period was consistent with the incubation period.Some models assumed that asymptomatic infections were infectious or pre-symptomatic transmission was possible,which overestimated the value of R0.For the prediction differences under different public health strategies,the most significant effect was in travel restrictions.There were different studies on the impact of contact tracking and social isolation,but it was considered that improving the quarantine rate and reporting rate,and the use of protective face mask were essential for epidemic prevention and control.The input epidemiological parameters of the prediction models had significant differences in the prediction of the severity of the epidemic spread.Therefore,prevention and control institutions should be cautious when formulating public health strategies by based on the prediction results of mathematical models.展开更多
The raging COVID-19 pandemic is arguably the most important threat to global health presently.Although there Although there is currently a a a vaccine,preventive measures have been proposed to reduce the spread of inf...The raging COVID-19 pandemic is arguably the most important threat to global health presently.Although there Although there is currently a a a vaccine,preventive measures have been proposed to reduce the spread of infection but the efficacy of these interventions,and their likely impact on the number of COVID-19 infections is unknown.In this study,we proposed the SEIQHRS model(susceptible-exposed-infectious-quarantinehospitalized-recovered-susceptible)model that predicts the trajectory of the epidemic to help plan an effective control strategy for COVID-19 in Ghana.We provided a short-term forecast of the early phase of the epidemic trajectory in Ghana using the generalized growth model.We estimated the effective basic Reproductive number Re in real-time using three different estimation procedures and simulated worse case epidemic scenarios and the impact of integrated individual and government interventions on the epidemic in the long term using compartmental models.The maximum likelihood estimates of Re and the corresponding 95%confidence interval was 2.04[95%CI:1.82-2.27;12th March-7th April 2020].The Re estimate using the exponential growth method was 2.11[95%CI:2.00-2.24]within the same period.The Re estimate using time-dependent(TD)method showed a gradual decline of the Effective Reproductive Number since March 12,2020 when the first 2 index cases were recorded but the rate of transmission remains high(TD:Re=2.52;95%CI:[1.87-3.49]).The current estimate of Re based on the TD method is 1.74[95%CI:1.41-2.10;(13th May 2020)]but with comprehensive integrated government and individual level interventions,the Re could reduce to 0.5 which is an indication of the epidemic dying out in the general population.Our results showed that enhanced government and individual-level interventions and the intensity of media coverage could have a substantial effect on suppressing transmission of new COVID-19 cases and reduced death rates in Ghana until such a time that a potent vaccine or drug is discovered.展开更多
Density currents are caused by a difference in density,though low,of an entering fluid with the ambient fluid.This type of current is two-phased and found on riverbeds or in reservoirs behind dams,and is nonlinear in ...Density currents are caused by a difference in density,though low,of an entering fluid with the ambient fluid.This type of current is two-phased and found on riverbeds or in reservoirs behind dams,and is nonlinear in nature,complex,and sensitive to initial conditions.Fractal geometry is used as a powerful tool for studying complex natural phenomena.Using experimental studies and changes in inlet current conditions,the fractal and multi-fractal analyses of the interface between the density current and the ambient fluid were done.In addition,a search was made to find a possible connection between the nonlinear patterns.According to the results,with an increase in the inlet discharge and inlet density of the current the fractal dimension decreased.Further,the smaller the range of the singularity spectrum diagram was,i.e.,the more it was less than 0.34,the lower the system's tendency was to be multi-fractal,and the system sensitive to large local changes.In the interface between the density current and the ambient fluid,using the fractal dimension-based Richardson number could improve experimental data by 12.4%.Moreover,with an increase in the Richardson number,the Reynolds number of the current decreased.Further,upon considering the fractal dimension,the Reynolds number improved by 23%and a good correlation with a coefficient of determination of 0.76.展开更多
The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed.Further,the effects of the viscou...The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed.Further,the effects of the viscous forces,Joule heating,heat source/sink,and radiation on the flow are taken into account.The non-dimensional transformations are used to solve the governing equations.Then,the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique.The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs.From the perspective of numerical results,it is recognized that the production of entropy can be improved with the Joule heating,viscous dissipation,and convective heating aspects.It is concluded that the production of entropy is the maximum with increases in the Casson parameter,the angle of inclination,and the Hartmann number.Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.展开更多
The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation.An irreversible process is a process in which the entropy of the system is increased.The second law of the...The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation.An irreversible process is a process in which the entropy of the system is increased.The second law of thermodynamics is used to define whether the given system is reversible or irreversible.Here,our focus is how to reduce the entropy of the system and maximize the capability of the system.There are many methods for maximizing the capacity of heat transport.The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy.The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel.For this,we choose two different fluid models,namely,the plane and generalized Couette flows.The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid.The present analysis shows the effects of the fluid parameters on the velocity,the temperature,the entropy generation,and the Bejan number.The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method.To validate the perturbation solution,a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0.The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters.It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number.Whenηi→0(i=1,2,3),the Eyring-Powell fluid is transformed into a Newtonian fluid.展开更多
For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(...For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(G;t)≤cn for p-arrangeable graphs with n vertices,where p≥1,c=c(p)and t=t(p)are positive constants.展开更多
Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modifica...Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.展开更多
To study the effects of the gamma reflection of multi-element materials,gamma ray transport models of single-element materials,such as iron and lead,and multielement materials,such as polyethylene and ordinary concret...To study the effects of the gamma reflection of multi-element materials,gamma ray transport models of single-element materials,such as iron and lead,and multielement materials,such as polyethylene and ordinary concrete,were established in this study.Relationships among the albedo factors of the gamma photons and energies and average energy of the reflected gamma rays by material type,material thickness,incident gamma energy,and incidence angle of gamma rays were obtained by Monte Carlo simulation.The results show that the albedo factors of single-element and multi-element materials increase rapidly with an increase in the material thickness.When the thickness of the material increases to a certain value,the albedo factors do not increase further but rather tend to the saturation value.The saturation values for the albedo factors of the gamma photons,and energies and the reflection thickness are related not only to the type of material but also to the incident gamma energy and incidence angle of the gamma rays.At a given incident gamma energy,which is between 0.2 and 2.5 MeV,the smaller the effective atomic number of the multi-element material is,the higher the saturation values of the albedo factors are.The larger the incidence angle of the gamma ray is,the greater the saturation value of the gamma albedo factor,saturation reflection thickness,and average saturation energy of the reflected gamma photons are.展开更多
In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setti...In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.展开更多
The work presented herein investigates the velocity, heat transfer, Nusselt number and skin friction profiles involved in boundary layer flow past a moving vertical porous plate. Similarity transformations are employe...The work presented herein investigates the velocity, heat transfer, Nusselt number and skin friction profiles involved in boundary layer flow past a moving vertical porous plate. Similarity transformations are employed to convert the governing nonlinear unsteady momentum and energy equations from their partial differential equation forms to boundary value ordinary differential equations. The resulting equations are then solved numerically by the Runge-Kutta fourth order method with the help of a shooting technique. Several features of the flow and heat transfer characteristics for different values of problem parameters are analyzed and discussed. These include the effects of the radiation parameter (R), suction and injection parameter (c), Grashof (Gr) and Prandtl (Pr) numbers on the flow and heat profiles. Numerical results show the impact of blowing and sucking as well as radation on boundary layer flows of this type. Both the skin frictions as well as the heat transfer rate are also significantly related to the radiation parameter. For all these cases;the numerical results are found to be in agreement with the physics of the problem.展开更多
This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only o...This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.展开更多
文摘Prime numbers are the integers that cannot be divided exactly by another integer other than one and itself. Prime numbers are notoriously disobedient to rules: they seem to be randomly distributed among natural numbers with no laws except that of chance. Questions about prime numbers have been perplexing mathematicians over centuries. How to efficiently predict greater prime numbers has been a great challenge for many. Most of the previous studies focus on how many prime numbers there are in certain ranges or patterns of the first or last digits of prime numbers. Honestly, although these patterns are true, they help little with accurately predicting new prime numbers, as a deviation at any digit is enough to annihilate the primality of a number. The author demonstrates the periodicity and inter-relationship underlying all prime numbers that makes the occurrence of all prime numbers predictable. This knowledge helps to fish all prime numbers within one net and will help to speed up the related research.
文摘The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using the bases 2;3;5;7 whose two symmetric combinations explain the main lepton mass ratios. The corresponding Holic Principle induces a symmetry between the Newton and Planck constants which confirm the Permanent Sweeping Holography Bang Cosmology, with invariant baryon density 3/10, the dark baryons being dephased matter-antimatter oscillation. This implies the DNA bi-codon mean isotopic mass, confirming to 0.1 ppm the electron-based Topological Axis, whose terminal boson is the base 2 c-observable Universe in the base 3 Cosmos. The physical parameters involve the Euler idoneal numbers and the special Fermat primes of Wieferich (bases 2) and Mirimanoff (base 3). The prime numbers and crystallographic symmetries are related to the 4-fold structure of the DNA bi-codon. The forgotten Eddington’s proton-tau symmetry is rehabilitated, renewing the supersymmetry quest. This excludes the concepts of Multiverse, Continuum, Infinity, Locality and Zero-mass Particle, leading to stringent predictions in Cosmology, Particle Physics and Biology.
文摘In this paper, we show a new theoretical procedure for calculating the nucleonic mass values. We develop this procedure on the geometric representation of (u, d) quarks, these seen as golden structures of coupled quantum oscillators (Aureum Geometric Model or AGM). Using AGM, we also build the geometric structures of nucleons (p, n), determining their structure equations and spins. Thank AGM, coherent to QCD, new aspects of the Quantum Mechanics emerge, opening to anew descriptive paradigm in Particle Physics.
文摘In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.
文摘Flow distribution and the effects of different boundary conditions are achieved for a steady-state conjugate (Conduction & Convection) heat transfer process. A plate fin heat sink with horizontal fin orientation along with a computer chassis is numerically investigated and simulated using software ANSYS CFX. Fin orientation of a heat sink changes the direction of fluid flow inside the chassis. For predicting turbulence of the flow inside the domain, a two</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">equation based</span><span style="font-size:10pt;font-family:""><span style="font-family:Verdana;font-size:12px;"> <i></span><i><span style="font-family:Verdana;font-size:12px;">k</span></i><span style="font-family:Verdana;font-size:12px;">-</span><i><span style="font-family:Verdana;font-size:12px;">ε</span></i><span style="font-family:Verdana;font-size:12px;"></i> turbulence model is chosen. The</span></span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">Reynolds number based on inflow velocity and geometry is found 4.2</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">×</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">10<sup>3</sup> that indicates that the flow is turbulent inside the chassis. To get proper thermal cooling, the optimum velocity ratio of inlet/outlet, dimension of inlet/outlet and different positions of outlet on the back sidewall of the chassis are predicted.</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">Aspect</span><span style="font-family:Verdana;"> velocity ratio between the inlet airflow and the outlet airflow has an effect on the steadiness of the flow. Mass flow rate depends</span><span style="font-size:10pt;font-family:""> </span><span style="font-family:Verdana;">on the dimension of the inlet/outlet. The horizontal fin orientation with 1:1.6 inlet-outlet airflow velocity ratio gives better thermal performance when outlet is located at the top corner of the chassis, near to the inner sidewall. Flow distribution and heat transfer characteristics are also analyzed to obtain the final model.
基金supported by the High-level Talent Project of Hainan Provincial Natural Science Foundation of China(No.2019RC085)by the National Natural Science Foundation of China(No.11961019)。
文摘A nonincreasing sequenceπ=(d1,…,dn)of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices.In this case,G is referred to as a realization ofπ.Given a graph H,a graphic sequenceπis potentially H-graphic ifπhas a realization containing H as a subgraph.For graphs G1 and G2,the potential-Ramsey number rpot(G1,G2)is the smallest integer k such that for every k-term graphic sequenceπ,eitherπis potentially G1-graphic or the complementary sequenceπ=(k-1-dk,…,k-1-d1)is potentially G2-graphic.For 0≤k≤[t/2],denote Kt-k to be the graph obtained from Kt by deleting k independent edges.If k=0,Busch et al.(Graphs Combin.,30(2014)847-859)present a lower bound on rpot(G,Kt)by using the 1-dependence number of G.In this paper,we utilize i-dependence number of G for i≥1 to give a new lower bound on rpot(G,Kt-k)for any k with 0≤k≤[T/2].Moreover,we also determine the exact values of rpot(Kn,Kt-k)for 1≤k≤2.
文摘Namibia’s Etosha National Park(ENP)is home to many different animals such as lions,jackals,hyenas,zebras,elephants,etc.Each year,grazing animals are infected and die from anthrax caused by the bacteria Bacillus anthracis.This increases the number of carcasses in the park,which serve as food for scavengers such as jackals.This study investigates the interplay between anthrax transmission in zebras and the scavenging of zebra carcasses in ENP,using a deterministic mathematical model to describe the population dynamics.We strive to answer the following research questions:Under what conditions can the presence of scavengers control anthrax outbreaks in zebra populations?Does carcass production by anthrax help or hurt scavengers in the long term?Standard qualitative analysis techniques distinguished outcomes(stable equilibria)using reproduction numbers as threshold quantities.We found that,when scavengers feed on anthrax-laden carcasses,the scavengers help the zebras,by eliminating potential infection zones for the zebras.In this way they reduce anthrax’s spread by orders of magnitude.We also identify conditions under which the presence of anthrax benefits the scavengers,in terms of death-to-birth ratios for zebras,scavengers and anthrax.
基金One of the authors(ABG)acknowledge the support,in part,of the Simons Foundation(Award#585022)the National Science Foundation(Award#1917512)CNN acknowledges the support of the Simons Foundation(Award#627346)。
文摘The novel coronavirus(COVID-19)pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world.It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic.Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic.This study presents a primer for formulating,analysing and simulating mathematical models for understanding the dynamics of COVID-19.Specifically,we introduce simple compartmental,Kermack-McKendrick-type epidemic models with homogeneously-and heterogeneously-mixed populations,an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine.We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model.A brief overview of other kinds of models that have been used to study the dynamics of COVID-19,such as agent-based,network and statistical models,is also presented.Possible extensions of the basic model,as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics,are suggested.
文摘One of the major difficulties with modelling an ongoing epidemic is that often data is limited or incomplete,making it hard to estimate key epidemic parameters and outcomes(e.g.attack rate,peak time,reporting rate,reproduction number).In the current study,we present a model for data-fitting limited infection case data which provides estimates for important epidemiological parameters and outcomes.The model can also provide reasonable short-term(one month)projections.We apply the model to the current and ongoing COVID-19 outbreak in Canada both at the national and provincial/territorial level.
基金This work was supported by the National Natural Science Foundation of China(51778382)the National Key R&D Program of China(2016YFC0700400).
文摘The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically through mathematical modelling.We conducted a systematic review of epidemic prediction models of COVID-19 and the public health intervention strategies by searching the Web of Science database.55 studies of the COVID-19 epidemic model were reviewed systematically.It was found that the COVID-19 epidemic models were different in the model type,acquisition method,hypothesis and distribution of key input parameters.Most studies used the gamma distribution to describe the key time period of COVID-19 infection,and some studies used the lognormal distribution,the Erlang distribution,and theWeibull distribution.The setting ranges of the incubation period,serial interval,infectious period and generation time were 4.9e7 days,4.41e8.4 days,2.3e10 days and 4.4e7.5 days,respectively,and more than half of the incubation periods were set to 5.1 or 5.2 days.Most models assumed that the latent period was consistent with the incubation period.Some models assumed that asymptomatic infections were infectious or pre-symptomatic transmission was possible,which overestimated the value of R0.For the prediction differences under different public health strategies,the most significant effect was in travel restrictions.There were different studies on the impact of contact tracking and social isolation,but it was considered that improving the quarantine rate and reporting rate,and the use of protective face mask were essential for epidemic prevention and control.The input epidemiological parameters of the prediction models had significant differences in the prediction of the severity of the epidemic spread.Therefore,prevention and control institutions should be cautious when formulating public health strategies by based on the prediction results of mathematical models.
文摘The raging COVID-19 pandemic is arguably the most important threat to global health presently.Although there Although there is currently a a a vaccine,preventive measures have been proposed to reduce the spread of infection but the efficacy of these interventions,and their likely impact on the number of COVID-19 infections is unknown.In this study,we proposed the SEIQHRS model(susceptible-exposed-infectious-quarantinehospitalized-recovered-susceptible)model that predicts the trajectory of the epidemic to help plan an effective control strategy for COVID-19 in Ghana.We provided a short-term forecast of the early phase of the epidemic trajectory in Ghana using the generalized growth model.We estimated the effective basic Reproductive number Re in real-time using three different estimation procedures and simulated worse case epidemic scenarios and the impact of integrated individual and government interventions on the epidemic in the long term using compartmental models.The maximum likelihood estimates of Re and the corresponding 95%confidence interval was 2.04[95%CI:1.82-2.27;12th March-7th April 2020].The Re estimate using the exponential growth method was 2.11[95%CI:2.00-2.24]within the same period.The Re estimate using time-dependent(TD)method showed a gradual decline of the Effective Reproductive Number since March 12,2020 when the first 2 index cases were recorded but the rate of transmission remains high(TD:Re=2.52;95%CI:[1.87-3.49]).The current estimate of Re based on the TD method is 1.74[95%CI:1.41-2.10;(13th May 2020)]but with comprehensive integrated government and individual level interventions,the Re could reduce to 0.5 which is an indication of the epidemic dying out in the general population.Our results showed that enhanced government and individual-level interventions and the intensity of media coverage could have a substantial effect on suppressing transmission of new COVID-19 cases and reduced death rates in Ghana until such a time that a potent vaccine or drug is discovered.
文摘Density currents are caused by a difference in density,though low,of an entering fluid with the ambient fluid.This type of current is two-phased and found on riverbeds or in reservoirs behind dams,and is nonlinear in nature,complex,and sensitive to initial conditions.Fractal geometry is used as a powerful tool for studying complex natural phenomena.Using experimental studies and changes in inlet current conditions,the fractal and multi-fractal analyses of the interface between the density current and the ambient fluid were done.In addition,a search was made to find a possible connection between the nonlinear patterns.According to the results,with an increase in the inlet discharge and inlet density of the current the fractal dimension decreased.Further,the smaller the range of the singularity spectrum diagram was,i.e.,the more it was less than 0.34,the lower the system's tendency was to be multi-fractal,and the system sensitive to large local changes.In the interface between the density current and the ambient fluid,using the fractal dimension-based Richardson number could improve experimental data by 12.4%.Moreover,with an increase in the Richardson number,the Reynolds number of the current decreased.Further,upon considering the fractal dimension,the Reynolds number improved by 23%and a good correlation with a coefficient of determination of 0.76.
文摘The heat transfer and entropy generation characteristics of the magnetohydrodynamic Casson fluid flow through an inclined microchannel with convective boundary conditions are analyzed.Further,the effects of the viscous forces,Joule heating,heat source/sink,and radiation on the flow are taken into account.The non-dimensional transformations are used to solve the governing equations.Then,the reduced system is resolved by the fourth-fifth order Runge-Kutta-Fehlberg method along with the shooting technique.The effects of different physical parameters on the heat transfer and entropy generation are discussed in detail through graphs.From the perspective of numerical results,it is recognized that the production of entropy can be improved with the Joule heating,viscous dissipation,and convective heating aspects.It is concluded that the production of entropy is the maximum with increases in the Casson parameter,the angle of inclination,and the Hartmann number.Both the Reynolds number and the radiation parameter cause the dual impact on entropy generation.
基金Project supported by the National Natural Science Foundation of China(Nos.11971142,11871202,61673169,11701176,11626101,and 11601485)。
文摘The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation.An irreversible process is a process in which the entropy of the system is increased.The second law of thermodynamics is used to define whether the given system is reversible or irreversible.Here,our focus is how to reduce the entropy of the system and maximize the capability of the system.There are many methods for maximizing the capacity of heat transport.The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy.The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel.For this,we choose two different fluid models,namely,the plane and generalized Couette flows.The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid.The present analysis shows the effects of the fluid parameters on the velocity,the temperature,the entropy generation,and the Bejan number.The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method.To validate the perturbation solution,a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0.The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters.It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number.Whenηi→0(i=1,2,3),the Eyring-Powell fluid is transformed into a Newtonian fluid.
基金supported by NSFC(No.11671088)“New century excellent talents support plan for institutions of higher learning in Fujian province”(SJ2017-29).
文摘For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(G;t)≤cn for p-arrangeable graphs with n vertices,where p≥1,c=c(p)and t=t(p)are positive constants.
基金supported by the National Natural Science Foundation of China(No.11901236)the Scientific Research Fund of Hunan Provincial Science and Technology Department(No.2019JJ50479)+2 种基金the Scientific Research Fund of Hunan Provincial Education Department(No.18B322)the Young Core Teacher Foundation of Hunan Province(No.202043)the Fundamental Research Fund of Xiangxi Autonomous Prefecture(No.2018SF5026)。
文摘Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.
基金This work was supported by the State Key Lab of Intense Pulsed Radiation Simulation and Effect Basic Research Foundation(No.SKLIPR1504).
文摘To study the effects of the gamma reflection of multi-element materials,gamma ray transport models of single-element materials,such as iron and lead,and multielement materials,such as polyethylene and ordinary concrete,were established in this study.Relationships among the albedo factors of the gamma photons and energies and average energy of the reflected gamma rays by material type,material thickness,incident gamma energy,and incidence angle of gamma rays were obtained by Monte Carlo simulation.The results show that the albedo factors of single-element and multi-element materials increase rapidly with an increase in the material thickness.When the thickness of the material increases to a certain value,the albedo factors do not increase further but rather tend to the saturation value.The saturation values for the albedo factors of the gamma photons,and energies and the reflection thickness are related not only to the type of material but also to the incident gamma energy and incidence angle of the gamma rays.At a given incident gamma energy,which is between 0.2 and 2.5 MeV,the smaller the effective atomic number of the multi-element material is,the higher the saturation values of the albedo factors are.The larger the incidence angle of the gamma ray is,the greater the saturation value of the gamma albedo factor,saturation reflection thickness,and average saturation energy of the reflected gamma photons are.
基金Supported by the National Natural Science Foundation of China(11671060).
文摘In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.
文摘The work presented herein investigates the velocity, heat transfer, Nusselt number and skin friction profiles involved in boundary layer flow past a moving vertical porous plate. Similarity transformations are employed to convert the governing nonlinear unsteady momentum and energy equations from their partial differential equation forms to boundary value ordinary differential equations. The resulting equations are then solved numerically by the Runge-Kutta fourth order method with the help of a shooting technique. Several features of the flow and heat transfer characteristics for different values of problem parameters are analyzed and discussed. These include the effects of the radiation parameter (R), suction and injection parameter (c), Grashof (Gr) and Prandtl (Pr) numbers on the flow and heat profiles. Numerical results show the impact of blowing and sucking as well as radation on boundary layer flows of this type. Both the skin frictions as well as the heat transfer rate are also significantly related to the radiation parameter. For all these cases;the numerical results are found to be in agreement with the physics of the problem.
文摘This article B is almost autonomous because it can be read independently from the first published article A [1] using only a few parts of the article A. Be-low are given instructions so to need the reader study only on few places of the article A. Also, in the part A of Introduction, here, you will find simple and useful definitions and the strategy we are going to follow as well useful new theorems (also and in Section 5, which have been produced in this solution). So the published solution of twin’s problem can now be easily understood. The inequalities (4.17), (4.18) of Article A are proved here in Section 4 by a new clear method, without the possible ambiguity of the text between the relations (4.14), (4.16) of the Article A. Also we complete the proof for the twin’s distri-bution which we use. At the end here are presented the Conclusions, the No-menclatures and the numerical control of the proof, which is probably useful as well in coding methods. For a general and convincing picture is sufficient, a study from the beginning of this article B until the end of the part A of the In-troduction here as well a general glance on the Section 5 and on the Conclu-sions below.