In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic s...In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.展开更多
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y）...We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.展开更多
A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is po...A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem.展开更多
In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness...In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.展开更多
In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented...In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.展开更多
This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is g...Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.展开更多
In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by ...In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.展开更多
The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Ta...The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .展开更多
In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theo...In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on [f＇（z）] and sRf＇（z）. As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when p= 1, our results reduce to that of Liu and Minda.展开更多
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend ...The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu（r）/N（r）, where N（r） is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.展开更多
La Abe point separating uiatal subalgebra. of C(T) where T is a compact metric space. For each bounded function f:T which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of element...La Abe point separating uiatal subalgebra. of C(T) where T is a compact metric space. For each bounded function f:T which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of elements of the algebra A such that the sequence (w) converges uniformly to the function f on each compact subset of the interior of the continuity points of the function f.展开更多
In this investigation, we obtain some applications of first order differential subordination and superordination results involving an extended multiplier transformation and other linear operators for certain normalize...In this investigation, we obtain some applications of first order differential subordination and superordination results involving an extended multiplier transformation and other linear operators for certain normalized analytic functions. Some of our results improve previous results.展开更多
In this paper,with the idea of weighted sharing values,we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values.We obtain some theorems which improve the results of H X Yi and W R ...In this paper,with the idea of weighted sharing values,we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values.We obtain some theorems which improve the results of H X Yi and W R L.展开更多
A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems...A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.展开更多
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
文摘In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.
文摘We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.
基金The Project is Supported by National Nature Science Foundation of China
文摘A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘In this context, we mainly study the behavior in the neighborhood of finite singular points for k-regular functions in R1^n with values in R0、n. We get a Laurent expansion of them in an open set, prove its uniqueness, give the definitions of k-poles, isolated and essential singular points and removable singularity, discuss some properties, and further obtain the residue theorems.
基金Supported by the National Nature Science Foundation of China (Grant No. 11101014)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101103120016)+4 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No. PHR20110822)Training Programme Foundation for the Beijing Municipal Excellent Talents (Grant No. 2010D005015000002)the Fundamental Research Foundation of Beijing University of Technology (Grant No. X4006013201101)Education Department Science Project of Hebei Province (Grant No. Z2010297)Science Project of Shijiazhuang University of Economics (Grant No. XN0912)
文摘In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
文摘Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11126327)the Natural Science Foundation of Guangdong Province(Nos.2016A030313002+1 种基金2015A030313644)the Training Plan for the Outstanding Young Teachers in Higher Education of Guangdong Province(Grant No.Yq2013159)
文摘In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.
文摘The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .
基金Supported by the National Natural Science Foundation of China(Grant No.11001246)Natural Science Foundation of Zhejiang Province(Nos.D7080080Y6090694)
文摘In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on [f＇（z）] and sRf＇（z）. As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when p= 1, our results reduce to that of Liu and Minda.
基金Sponsored by HUST Foundation(0125011017)the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
文摘The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros has been recently generalized onto subharmonic functions with the Riesz measure on a half-line in Rn, n≥3. Here we extend the Drasin complement to the Valiron-Titchmarsh theorem and show that if u is a subharmonic function of this class and of order 0〈ρ〈1, then the existence of the limit limr→∞logu（r）/N（r）, where N（r） is the integrated counting function of the masses of u, implies the regular asymptotic behavior for both u and its associated measure.
文摘La Abe point separating uiatal subalgebra. of C(T) where T is a compact metric space. For each bounded function f:T which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of elements of the algebra A such that the sequence (w) converges uniformly to the function f on each compact subset of the interior of the continuity points of the function f.
文摘In this investigation, we obtain some applications of first order differential subordination and superordination results involving an extended multiplier transformation and other linear operators for certain normalized analytic functions. Some of our results improve previous results.
文摘In this paper,with the idea of weighted sharing values,we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values.We obtain some theorems which improve the results of H X Yi and W R L.
文摘A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
