L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is prove...L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is proved to hold for very general measures.展开更多
If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalize...If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalized inverse of A. In general,A^+ is a closed operator,but since R(B) R(A1/2),B~* A^+ B is bounded yet.展开更多
Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results f...Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results for positive operators on Hilbert lattice are also obtained.展开更多
The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information theory.Mathematically,a quantum state is a trace-class positive operator with tr...The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information theory.Mathematically,a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert space.In this paper,in more general frame,the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert spaces.However,not like the quantum state case,there are different kinds of separability for positive operators with different operator topologies.Four types of such separability are discussed;several criteria such as the finite rank entanglement witness criterion,the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established;some methods to construct separable positive operators by operator matrices are provided.These may also make us to understand the separability and entanglement of quantum states better,and may be applied to find new separable quantum states.展开更多
The classical Young’s inequality and its refinements are applied to positive operators on a Hilbert space at first. Based on the classical Poisson integral formula of relevant operators, some new inequalities on unit...The classical Young’s inequality and its refinements are applied to positive operators on a Hilbert space at first. Based on the classical Poisson integral formula of relevant operators, some new inequalities on unitarily invariant norm of A1-p XB1-q - A1-q Y B1-p are obtained with effective calculation, where A, B, X, Y ∈ B（H） with A, B 0 and 1 p, q ∞ with the conjugate exponent q = p/（p - 1）.展开更多
Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for...Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.展开更多
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh...In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).展开更多
In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the a...In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.展开更多
The conditions for the positive operation of water conservancy projects are described in this paper. A scientific and effective evaluation index system was established based on frequency analysis, theoretical analysis...The conditions for the positive operation of water conservancy projects are described in this paper. A scientific and effective evaluation index system was established based on frequency analysis, theoretical analysis, and expert consultation. This evaluation index system can be divided into six first-level indices： the degree to which facilities are intact and functionality standards are reached, the status of operation and management funds, the rationality and degree of advancement of the management team structure, the adaptability and rationality of the water conservancy project management system, the degree of automatization and informationization of the management techniques, and the conduciveness of the exterior environment. The weights for evaluation indices were obtained through the analytic hierarchy process method with consideration of the difference between public welfare and profit-oriented water conservancy projects. This study provides a scientific method for evaluating the positive operation of water conservancy projects.展开更多
By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solut...By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.展开更多
Furuta showed that if A≥B≥0,then for each r≥0,f（p）=（A^r/2 B^p A^r/2）^t＋r/p＋r is decreasing for p≥t≥0.Using this result,the following inequality（C^r/2（AB^2A）^δC^ r/2）^ p-1＋r/4δ＋r ≤C^p-1＋r is obtain...Furuta showed that if A≥B≥0,then for each r≥0,f（p）=（A^r/2 B^p A^r/2）^t＋r/p＋r is decreasing for p≥t≥0.Using this result,the following inequality（C^r/2（AB^2A）^δC^ r/2）^ p-1＋r/4δ＋r ≤C^p-1＋r is obtained for 0〈p ≤1,r≥1,1/4≤δ≤1 and three positive operators A, B, C satisfy（A^1/2BA^1/2）^p/2≤A^p,（B^1/2AB^1/2）^p/2≥B^p,（C^1/2AC^1/2）^p/2≤C^p,（A^1/2CA^1/2）^p/2≥A^p.展开更多
We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There a...To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.展开更多
In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a re...In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation and the Voronovskaya asymptotic formula.展开更多
In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed poi...In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.展开更多
In this paper,we give out a further extension of the relations between two famous inequalities(B r 2 A p B r 2) r p+r≥B r and Ap≥(A p 2 B r A p 2) p p+r,which can yield the result of Yamazaki and Yanagida's.
In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about a...In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about asymptotic formula and error estimation in terms of modules of continuity.展开更多
This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability ...This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.展开更多
BACKGROUND Bariatric surgery is one of the most effective ways to treat morbid obesity,and postoperative nausea and vomiting(PONV)is one of the common complications after bariatric surgery.At present,the mechanism of ...BACKGROUND Bariatric surgery is one of the most effective ways to treat morbid obesity,and postoperative nausea and vomiting(PONV)is one of the common complications after bariatric surgery.At present,the mechanism of the high incidence of PONV after weight-loss surgery has not been clearly explained,and this study aims to investigate the effect of surgical position on PONV in patients undergoing bariatric surgery.AIM To explore the effect of the operative position during bariatric surgery on PONV.METHODS Data from obese patients,who underwent laparoscopic sleeve gastrectomy(LSG)in the authors’hospital between June 2020 and February 2022 were divided into 2 groups and retrospectively analyzed.Multivariable logistic regression analysis and the t-test were used to study the influence of operative position on PONV.RESULTS There were 15 cases of PONV in the supine split-leg group(incidence rate,50%)and 11 in the supine group(incidence rate,36.7%)(P=0.297).The mean operative duration in the supine split-leg group was 168.23±46.24 minutes and 140.60±32.256 minutes in the supine group(P<0.05).Multivariate analysis revealed that operative position was not an independent risk factor for PONV(odds ratio=1.192,95%confidence interval:0.376-3.778,P=0.766).CONCLUSION Operative position during LSG may affect PONV;however,the difference in the incidence of PONV was not statistically significant.Operative position should be carefully considered for obese patients before surgery.展开更多
文摘L'convergence with 0<p<infinity of the positive operators F.(da,f) and G.(da,f), introduced by Nevai P. [3], and Qn,8(da,f), introduced by Hermann T. and Vertesi P. [1] to f is an element of C[-1,1] is proved to hold for very general measures.
文摘If a 3-tuple (A:H_1→H_1,B:H_2→H_1,C:H_2→H_2) of operators on Hilbert spaces is given,we proved that the operator A:= on H=H_1⊕H_2 is≥0 if and only if A≥0,R(B) R(A1/2)and C≥B~* A^+ B, where A^+ is the generalized inverse of A. In general,A^+ is a closed operator,but since R(B) R(A1/2),B~* A^+ B is bounded yet.
基金Supported by the National Natural Science Foundation of China(19771056,10571113)
文摘Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results for positive operators on Hilbert lattice are also obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11171249)。
文摘The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information theory.Mathematically,a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert space.In this paper,in more general frame,the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert spaces.However,not like the quantum state case,there are different kinds of separability for positive operators with different operator topologies.Four types of such separability are discussed;several criteria such as the finite rank entanglement witness criterion,the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established;some methods to construct separable positive operators by operator matrices are provided.These may also make us to understand the separability and entanglement of quantum states better,and may be applied to find new separable quantum states.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1087122411026134)the Special Research Project of Educational Department of Shaanxi Province (Grant No. 09JK741)
文摘The classical Young’s inequality and its refinements are applied to positive operators on a Hilbert space at first. Based on the classical Poisson integral formula of relevant operators, some new inequalities on unitarily invariant norm of A1-p XB1-q - A1-q Y B1-p are obtained with effective calculation, where A, B, X, Y ∈ B（H） with A, B 0 and 1 p, q ∞ with the conjugate exponent q = p/（p - 1）.
文摘Recently in [4], the Jessen＇s type inequality for normalized positive C0-semigroups is obtained. In this note, we present few results of this inequality, yielding Holder＇s Type and Minkowski＇s type inequalities for corresponding semigroup. Moreover, a Dresher＇s type inequality for two-parameter family of means, is also proved.
文摘In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).
基金The project supported by NNSF of China(10071080)
文摘In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.
文摘The conditions for the positive operation of water conservancy projects are described in this paper. A scientific and effective evaluation index system was established based on frequency analysis, theoretical analysis, and expert consultation. This evaluation index system can be divided into six first-level indices： the degree to which facilities are intact and functionality standards are reached, the status of operation and management funds, the rationality and degree of advancement of the management team structure, the adaptability and rationality of the water conservancy project management system, the degree of automatization and informationization of the management techniques, and the conduciveness of the exterior environment. The weights for evaluation indices were obtained through the analytic hierarchy process method with consideration of the difference between public welfare and profit-oriented water conservancy projects. This study provides a scientific method for evaluating the positive operation of water conservancy projects.
基金. This work is supported by the WNSFC(60304003, 10371066) the NSF of Shandong Province(Z2003A01, Y02P01) and the doctoral Foundation of Shandong Province(03B5092)
文摘By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.
基金Science Foundation of Ministry of Education of China(208081)
文摘Furuta showed that if A≥B≥0,then for each r≥0,f（p）=（A^r/2 B^p A^r/2）^t＋r/p＋r is decreasing for p≥t≥0.Using this result,the following inequality（C^r/2（AB^2A）^δC^ r/2）^ p-1＋r/4δ＋r ≤C^p-1＋r is obtained for 0〈p ≤1,r≥1,1/4≤δ≤1 and three positive operators A, B, C satisfy（A^1/2BA^1/2）^p/2≤A^p,（B^1/2AB^1/2）^p/2≥B^p,（C^1/2AC^1/2）^p/2≤C^p,（A^1/2CA^1/2）^p/2≥A^p.
基金Supported by Education Foundation of Henan Province(200510463024)Supported by the Foundation of Henan University of Technology(20050206)
文摘We shall give some results on generalized aluthge transformation for phyponormal and log-hyponormal operators. We shall also discuss the best possibility of these results.
文摘To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.
文摘In the present manuscript, we propose the modification of Jain operators which the generalization of Szasz-Mirakyan operators. These new class operators are linear positive operators of discrete type depending on a real parameters. We give theorem of degree of approximation and the Voronovskaya asymptotic formula.
基金Supported by the Youth Science Foundation of China（l1201272） Supported by the Youth Science Foundatioa of Shanxi Province（2010021002-1）
文摘In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（2011A110009）
文摘In this paper,we give out a further extension of the relations between two famous inequalities(B r 2 A p B r 2) r p+r≥B r and Ap≥(A p 2 B r A p 2) p p+r,which can yield the result of Yamazaki and Yanagida's.
文摘In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about asymptotic formula and error estimation in terms of modules of continuity.
基金supported by the National Natural Science Foundation of China under Grant No.11201007
文摘This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.
文摘BACKGROUND Bariatric surgery is one of the most effective ways to treat morbid obesity,and postoperative nausea and vomiting(PONV)is one of the common complications after bariatric surgery.At present,the mechanism of the high incidence of PONV after weight-loss surgery has not been clearly explained,and this study aims to investigate the effect of surgical position on PONV in patients undergoing bariatric surgery.AIM To explore the effect of the operative position during bariatric surgery on PONV.METHODS Data from obese patients,who underwent laparoscopic sleeve gastrectomy(LSG)in the authors’hospital between June 2020 and February 2022 were divided into 2 groups and retrospectively analyzed.Multivariable logistic regression analysis and the t-test were used to study the influence of operative position on PONV.RESULTS There were 15 cases of PONV in the supine split-leg group(incidence rate,50%)and 11 in the supine group(incidence rate,36.7%)(P=0.297).The mean operative duration in the supine split-leg group was 168.23±46.24 minutes and 140.60±32.256 minutes in the supine group(P<0.05).Multivariate analysis revealed that operative position was not an independent risk factor for PONV(odds ratio=1.192,95%confidence interval:0.376-3.778,P=0.766).CONCLUSION Operative position during LSG may affect PONV;however,the difference in the incidence of PONV was not statistically significant.Operative position should be carefully considered for obese patients before surgery.
