GENERAL ALGEBROID FUNCTION AND ITS APPLICATION

In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.

Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives,when emergencies occur,rumors will spread widely on the internet.However,it is quite difficult for the netizens to distinguish the truth of the information.The main reasons are the uncertainty of netizens’behavior and attitude,which make the transmission rates of these information among social network groups be not fixed.In this paper,we propose a stochastic rumor propagation model with general incidence function.The model can be described by a stochastic differential equation.Applying the Khasminskii method via a suitable construction of Lyapunov function,we first prove the existence of a unique solution for the stochastic model with probability one.Then we show the existence of a unique ergodic stationary distribution of the rumor model,which exhibits the ergodicity.We also provide some numerical simulations to support our theoretical results.The numerical results give us some possible methods to control rumor propagation.Firstly,increasing noise intensity can effectively reduce rumor propagation when R_(0)>1That is,after rumors spread widely on social network platforms,government intervention and authoritative media coverage will interfere with netizens’opinions,thus reducing the degree of rumor propagation.Secondly,speed up the rumor refutation,intensify efforts to refute rumors,and improve the scientific quality of netizen(i.e.,increase the value ofβand decrease the value ofαandγ),which can effectively curb the rumor propagation.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

Mathematical Analysis on a General Delayed HBV Model with Capsids and Two Infection Routes

Considering that HBV belongs to the DNA virus family and is hepatotropic,we model the HBV DNA-containing capsids as a compartment.In this paper,a delayed HBV infection model is established,where the general incidence function and two infection routes including cell-virus infection and cell-cell infection are introduced.According to some preliminaries,including well-posedness,basic reproduction number and existence of two equilibria,we obtain the threshold dynamics for the model.We illustrate numerical simulations to verify the above theoretical results,and furthermore explore the impacts of intracellular delay and cell-cell infection on the global dynamics of the model.

Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

The Weibull distribution is regarded as among the finest in the family of failure distributions.One of the most commonly used parameters of the Weibull distribution(WD)is the ordinary least squares(OLS)technique,which is useful in reliability and lifetime modeling.In this study,we propose an approach based on the ordinary least squares and the multilayer perceptron(MLP)neural network called the OLSMLP that is based on the resilience of the OLS method.The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers,and eases the difficulty of determining weights in case of the weighted least square(WLS).Another method is proposed by incorporating a weight into the general entropy(GE)loss function to estimate the parameters of the WD to obtain a modified loss function(WGE).Furthermore,a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation(BLWGE)by using a weighted GE loss function.The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes.In addition,the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods,in terms of the mean squared error and requirements related to time.

GLEASON'S PROBLEM ON THE SPACE F^(p,q,s)(B) IN C^(n)

Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).

Wind Power Potential in Interior Alaska from a Micrometeorological Perspective

The wind power potential in Interior Alaska is evaluated from a micrometeorological perspective. Based on the local balance equation of momentum and the equation of continuity we derive the local balance equation of kinetic energy for macroscopic and turbulent systems, and in a further step, Bernoulli’s equation and integral equations that customarily serve as the key equations in momentum theory and blade-element analysis, where the Lanchester-Betz-Joukowsky limit, Glauert’s optimum actuator disk, and the results of the blade-element analysis by Okulov and Sorensen are exemplarily illustrated. The wind power potential at three different sites in Interior Alaska (Delta Junction, Eva Creek, and Poker Flat) is assessed by considering the results of wind field predictions for the winter period from October 1, 2008, to April 1, 2009 provided by the Weather Research and Forecasting (WRF) model to avoid time-consuming and expensive tall-tower observations in Interior Alaska which is characterized by a relatively low degree of infrastructure outside of the city of Fairbanks. To predict the average power output we use the Weibull distributions derived from the predicted wind fields for these three different sites and the power curves of five different propeller-type wind turbines with rated powers ranging from 2 MW to 2.5 MW. These power curves are represented by general logistic functions. The predicted power capacity for the Eva Creek site is compared with that of the Eva Creek wind farm established in 2012. The results of our predictions for the winter period 2008/2009 are nearly 20 percent lower than those of the Eva Creek wind farm for the period from January to September 2013.

Multiplicity results for the unstirred chemostat model with general response functions

We investigate the multiplicity of positive steady state solutions to the unstirred chemostat model with general response functions. It turns out that all positive steady state solutions to this model lie on a single smooth solution curve, whose properties determine the multiplicity of positive steady state solutions. The key point of our analysis is to study the ＂turning points＂ on this positive steady state solution curve, and to prove that any nontrivial solution to the associated linearized problem is one of sign by constructing a suitable test function. The main tools used here include bifurcation theory, monotone method, mountain passing lemma and Sturm comnarison theorem.

General relative error criterion and M-estimation

Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.

A Class of General Transformation of Characteristic Functions in Dynamic Games

The transformation of characteristic functions is an effective way to avoid time-inconsistency of cooperative solutions in dynamic games.There are several forms on the transformation of characteristic functions.In this paper,a class of general transformation of characteristic functions is proposed.It can lead to the time-consistency of cooperative solutions and guarantee that the irrational-behaviorproof conditions hold true.To illustrate the theory,an example of dynamic game on a tree is given.

Global dynamics of an age-structured viral infection model with general incidence function and absorption

In this paper, we propose an age-structured viral infection model with general incidence function that takes account of the loss of viral particles due to their absorption into susceptible cells. The proposed model is described by partial differential and ordinary differential equations. We first show that the model is mathematically and biologically well-posed. Furthermore, the uniform persistence and the global behavior of the model are investigated. Moreover, the age-structured models and results presented in many previous studies are improved and generalized.

General Decay Synchronization for Recurrent Neural Networks with Mixed Time Delays

This paper studies the general decay synchronization(GDS)of a class of recurrent neural networks(RNNs)with general activation functions and mixed time delays.By constructing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques,some sufficient conditions on the GDS of considered RNNs are established via a type of nonlinear control.In addition,one example with numerical simulations is presented to illustrate the obtained theoretical results.

Analysis of within-host CHIKV dynamics models with general incidence rate

In this paper we study the stability analysis of two within-host Chikungunya virus （CHIKV） dynamics models. The incidence rate between the CHIKV and the uninfected mouocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes （i） latently infected monocytes which do not generate CHIKV and （ii） actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

An Empirical Analysis on the Relationship betweenExports and Economic Growth in China

This paper investigates the relationship between exports and economic growth in Chinafor the reform and open-door period 1978-1996. The estimations presented indicate a positive andsignificant relation between the two variables. Also, the statistical adequacy of the models used issupported by several diagnostic test. The results provide support for the export-led growth (ELG)hypothesis.

A FRAMEWORK FOR REAL-VALUED CIPHER SYSTEMS

Most cipher systems designed thus far are binary-valued or integer-valued cipher systems. Their security relies on the assumption that one-way functions exist. Though the existence of one-way functions has not been proved yet, most cryptographic researchers believe that one-way functions exist. In addition, many candidates for one-way functions have been proposed. Therefore, the key step for developing real-valued cipher systems is to define real one-way functions and to propose candidates for them. In this paper, based on computational complexity theory over the real field, we give two definitions of real one-way functions; one is for digital one-way functions and the other is for general one-way functions. Candidates for these two classes of one-way functions are also proposed. Moreover, we present two examples to demonstrate that the candidates for both digital one-way functions and general one-way functions can be applied to construct secure real-valued cipher systems.

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in with a global monopole in f（R） gravity. The exact background is obtained and is given in terms of the Heun functions to study the Hawking radiation and the gravitational field produced by a Schwarzschild black hole solution of the radial part of the Klein-Gordon equation in this general Heun functions. We apply the properties of the general the resonant frequencies of scalar particles.

Definite Condition of the Evolutionary p(x)−Laplacian Equation

For the nonlinear degenerate parabolic equations,how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been an interesting and challenging problem.In this paper,we develop the general characteristic function method to study the stability of weak solutions based on a partial boundary value condition.

Robust Estimation of Variance Components Model

The classical least-squares methods may only solve LS β when the variance-covariance (matrix ∑(σ2 ∑)) is known (σ2 is unknown and ∑ is known) in linear model. The author thinks that maximum likelihood type estimation (M-estimation) should replace LS estimation. The paper discusses robust estimations of parameter vector and variance components for corresponding error model based on the principle of maximum likelihood type estimations (M-estimations). The influence functions are given respectively.

Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values

Based on lower record values,we first derive the exact explicit expressions as well as recurrence relations for the single and product moments of record values and then use these results to compute the means,variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution(EMED),a new extension of moment exponential distribution,recently introduced by Hasnain(Exponentiated moment exponential distribution.Ph.D.Thesis,2013).Next we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the EMED.Finally,we consider Bayes estimation under the symmetric and asymmetric loss functions using gamma priors for both shape and scale parameters.We have also derived the Bayes interval of this distribution and discussed both frequentist and the Bayesian prediction intervals of the future record values based on the observed record values.Monte Carlo simulations are performed to compare the performances of the proposed methods,and a data set has been analyzed for illustrative purposes.

ROLE OF DISEASE PROPAGATION IN MIGRATORY BIRD POPULATION

Chatterjee considered a predator prey model with avian migration in the migration prey population IS. Chatterjee, Alternative prey source coupled with prey recovery enhance stability between migratory prey and their predator in the presence of disease, Nonlinear Anal. Real World Appl. 11 （2010） 4415-4430]. In this paper, we modify and analyze the model by taking time dependent parameters and the general flmctional response into consideration. The conditions for the persistence of the system and the extinction of the disease are obtained. The global attractivity of the system is also studied. By numerical simulations, we find that the qualitative behavior of the system independent on the choice of the functional response. Moreover, it is observed that the infection rate, recruitment rate and the predation rate play a vital role in predicting the behavior of the dynamics.