The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss t...The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss the special cases and application for double conditional expectation.展开更多
Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）...Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）n≥1 and prove that ε（x｜Mn）Lp→ε（x｜N） for any x ∈ Lp（M） （1 ≤ p 〈 ∞） if and only if （Mn）n≥1 τ-approaches and orthogonally approaches N.展开更多
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function...The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved ...In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.展开更多
By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships bet...The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.展开更多
Let be a filtration on some probability space and let denote the class of all -adapted -valued stochastic processes M such that for all t>s≥0 and the process is continuous (the conditional expectations are extende...Let be a filtration on some probability space and let denote the class of all -adapted -valued stochastic processes M such that for all t>s≥0 and the process is continuous (the conditional expectations are extended, so we do not demand that . It is shown that each is a locally square integrable martingale w. r. t. . Let X be the strong solution of the equation where , t is a continuous increasing process with -measurable values at all times, and Q is an -valued random function on , continuous in and -progressive at fixed x. Suppose also that there exists an -measurable in nonnegative random process Ψ such that, for all Then展开更多
The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regressi...The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.展开更多
Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmit...Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the <span style="font-family:Verdana;">main </span><span style="font-family:Verdana;">effects of genes and gene-covariate interaction</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""><span style="font-family:Verdana;">. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results </span><span style="font-family:Verdana;">showed M235T is associat</span></span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female</span><span style="font-family:Verdana;">.</span>展开更多
Let(Ω, J, P) be a probability space and э be a sub a-algebra of J. It is well known that for any non-negative J-measurable function X one can define the conditional expectation E[X[(?)] of X given (?). Therefore it ...Let(Ω, J, P) be a probability space and э be a sub a-algebra of J. It is well known that for any non-negative J-measurable function X one can define the conditional expectation E[X[(?)] of X given (?). Therefore it is natural to pose the following general definition of the conditional expectation.展开更多
Some characterizations of the conditional expectation operators on Lebesgue-Bochnerspaces L_p(μ,X)are given,where 1≤p【∞,p≠2.Also an example is given to show thatthe characterizations of the conditional expectatio...Some characterizations of the conditional expectation operators on Lebesgue-Bochnerspaces L_p(μ,X)are given,where 1≤p【∞,p≠2.Also an example is given to show thatthe characterizations of the conditional expectation operators on L_p(μ,X)are differentfrom that on L_p(μ)_z Finally,a representation of the constant-preserving contractiveprojection on spaces L_p(μ,X)is got when 0【p【1.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
Increase in requirement of hydrosulphuric water for improvement of the population set the task of identification of places of their possible congestion for hydrogeological service. Earlier detection of such congestion...Increase in requirement of hydrosulphuric water for improvement of the population set the task of identification of places of their possible congestion for hydrogeological service. Earlier detection of such congestions was accidental at well-drilling of different function. Therefore, development of new methodical approaches of search and allocation of perspective zones of their formation was required. It was for this purpose necessary to study in what conditions and what factors have an impact on formation of underground hydrosulphuric water. So far, definition of communication attempts only with separate geochemical signs was known. Results of studying of influence on formations of hydrosulphuric water of such factors as lithologic and facial in combination with oil-and-gas content, the geological and structural and hydrodynamic mode are given in this work. It is established that the main sign for formation of hydrosulphuric water is existence of evaporite thickness and hydrocarbon congestions. Besides, it is shown that small depth (up to 2 km) of their bedding has to be an indispensable condition and existence of explosive violation on which there has to be a water infiltration (a geological and structural factor). In the Surkhandarya region, the hydrodynamic mode caused by inclined bedding of aquifers was also one of essential factors. Active water is an exchange process with washing away (oxidation) sulfate of the containing thicknesses and subsequently, its restoration in interaction with hydrocarbons with formation of hydrosulphuric water is described. The technique is developed and the expected card of perspective zones of formation of hydrosulphuric water is constructed.展开更多
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epideriva...In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.展开更多
In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlike...This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.展开更多
基金Supported by the National Natural Science Foundation of China(10371092)the Foundation of Wuhan University
文摘The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss the special cases and application for double conditional expectation.
基金supported by National Natural Science Foundation of China(11271293,11471251)the Research Fund for the Doctoral Program of Higher Education of China(2014201020205)
文摘Let （M,τ） be a noncommutative probability space, （Mn）n≥l a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions of It-approach and orthogonal approach for （Mn）n≥1 and prove that ε（x｜Mn）Lp→ε（x｜N） for any x ∈ Lp（M） （1 ≤ p 〈 ∞） if and only if （Mn）n≥1 τ-approaches and orthogonally approaches N.
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
基金Project supported by the National Natural Science Foundation of China (No. 10371024) the Natural Science Foundation of Zhejiang Province (No.Y604003)
文摘The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
基金National Natural Science Foundation of China(1 9971 0 72 )
文摘In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.
基金Supported by the National Natural Science Foundation of China (10571035)
文摘By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
文摘The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.
文摘Let be a filtration on some probability space and let denote the class of all -adapted -valued stochastic processes M such that for all t>s≥0 and the process is continuous (the conditional expectations are extended, so we do not demand that . It is shown that each is a locally square integrable martingale w. r. t. . Let X be the strong solution of the equation where , t is a continuous increasing process with -measurable values at all times, and Q is an -valued random function on , continuous in and -progressive at fixed x. Suppose also that there exists an -measurable in nonnegative random process Ψ such that, for all Then
基金supported in part by the National Key Research and Development Program of China(2019YFB1503700)the Hunan Natural Science Foundation-Science and Education Joint Project(2019JJ70063)。
文摘The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.
文摘Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the <span style="font-family:Verdana;">main </span><span style="font-family:Verdana;">effects of genes and gene-covariate interaction</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""><span style="font-family:Verdana;">. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results </span><span style="font-family:Verdana;">showed M235T is associat</span></span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female</span><span style="font-family:Verdana;">.</span>
基金Project supported by the National Natural Science Foundation of China
文摘Let(Ω, J, P) be a probability space and э be a sub a-algebra of J. It is well known that for any non-negative J-measurable function X one can define the conditional expectation E[X[(?)] of X given (?). Therefore it is natural to pose the following general definition of the conditional expectation.
文摘Some characterizations of the conditional expectation operators on Lebesgue-Bochnerspaces L_p(μ,X)are given,where 1≤p【∞,p≠2.Also an example is given to show thatthe characterizations of the conditional expectation operators on L_p(μ,X)are differentfrom that on L_p(μ)_z Finally,a representation of the constant-preserving contractiveprojection on spaces L_p(μ,X)is got when 0【p【1.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
文摘Increase in requirement of hydrosulphuric water for improvement of the population set the task of identification of places of their possible congestion for hydrogeological service. Earlier detection of such congestions was accidental at well-drilling of different function. Therefore, development of new methodical approaches of search and allocation of perspective zones of their formation was required. It was for this purpose necessary to study in what conditions and what factors have an impact on formation of underground hydrosulphuric water. So far, definition of communication attempts only with separate geochemical signs was known. Results of studying of influence on formations of hydrosulphuric water of such factors as lithologic and facial in combination with oil-and-gas content, the geological and structural and hydrodynamic mode are given in this work. It is established that the main sign for formation of hydrosulphuric water is existence of evaporite thickness and hydrocarbon congestions. Besides, it is shown that small depth (up to 2 km) of their bedding has to be an indispensable condition and existence of explosive violation on which there has to be a water infiltration (a geological and structural factor). In the Surkhandarya region, the hydrodynamic mode caused by inclined bedding of aquifers was also one of essential factors. Active water is an exchange process with washing away (oxidation) sulfate of the containing thicknesses and subsequently, its restoration in interaction with hydrocarbons with formation of hydrosulphuric water is described. The technique is developed and the expected card of perspective zones of formation of hydrosulphuric water is constructed.
基金supported by the National Nature Science Foundation of China(11431004,11471291)the General Project of Chongqing Frontier and Applied Foundation Research(cstc2015jcyj A00050)the Key Project of Chongqing Frontier and Applied Foundation Research(cstc2017jcyj BX0055,cstc2015jcyj BX0113)
文摘In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
基金Supported by the National Natural Science Foundation of China !(19971072)
文摘In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
基金supported by Natural Science Foundation of China government under Grant No.11861002Natural Science Foundation of Ningxia under Grant No.NZ17112+3 种基金First-Class Disciplines Foundation of Ningxia under Grant No.NXYLXK2017B09The Key Project of North Minzu University under Grant No.ZDZX201804Graduate Innovation Project of North Minzu University No.YCX19122Nonlinear analysis and financial optimization research center of North Minzu University
文摘This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.
