This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-ana...This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previou...In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.展开更多
In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^...In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.展开更多
Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work t...Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.展开更多
This paper gives a new generalization of Hilbert＇s inequality with a best constant factor involving the β function. An applications, we consider the equivalent form and some particular results.
In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. T...The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.展开更多
This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption t...This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption that a PID controller has additive gain perturbations.An H-infinite robust PID controller can be obtained by solving a linear matrix inequality.This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances.The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.展开更多
基金Supported by Natural Science Foundation of Ningxia(2023AAC 03001)Natural Science Foundation of China(12261068)
文摘This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
文摘In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
基金the Foundation of Higher School of Ningxia(04M33)the NSF of Ningxia University(ZR0622)
文摘In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.
基金the National Natural Science Foundation of China(10671056)
文摘In this paper, it is shown that： if λ1 ,……λs axe nonzero real numbers, not all of the same sign, such that A1/A2 is irrational, then for any real number η and ε 〉 0 the inequality ｜λ1x1^2 ＋ λ2x2^2＋ λ3x3^4＋ λsx3^4＋……λsx8^4 ＋η〈 ε has infinitely many solutions in positive integers x1,... ,xs.
文摘Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.
基金Supported by the NSF of Guangdong Institutions of Higher Learning, College and University(0177).
文摘This paper gives a new generalization of Hilbert＇s inequality with a best constant factor involving the β function. An applications, we consider the equivalent form and some particular results.
文摘In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
文摘The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.
基金Supported by the National Natural Science Foundation of China（60604015） the Key Research Program of Education Department of Zhejiang Province（Z200803521）
文摘This job focuses on the stroke regulation of a class of high-precision metering pumps.A parametertuning method of robust non-fragile PID（proportional-integral-derivative）controllers is proposed with the assumption that a PID controller has additive gain perturbations.An H-infinite robust PID controller can be obtained by solving a linear matrix inequality.This approach can guarantee that the closed-loop control systems is asymptotically stable and the H-infinite norm of the transfer function from the disturbance to the output of a controlled system is less than a given constant to attenuate disturbances.The simulation case shows that the control performance of the proposed strategy is significantly better than the traditional PID approach in the situation with perturbations of controller parameters.
