In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k...In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].展开更多
In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient po...In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient point of set is established.展开更多
Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several...Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.展开更多
Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanc...Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanche criterion （SAC） is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction technique, two new methods to construct cheating immune secret sharing functions are proposed.展开更多
The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Fr...The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.展开更多
In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
The strict avalanche criterion(SAC)is one of the most important cryptographic criteria for substitution boxes(S-boxes)used in many symmetric encryption systems.However,there are few constructive methods for S-boxes fu...The strict avalanche criterion(SAC)is one of the most important cryptographic criteria for substitution boxes(S-boxes)used in many symmetric encryption systems.However,there are few constructive methods for S-boxes fulfilling the SAC until now.In this paper,to construct S-boxes satisfying the SAC directly,we generalize the concatenation techniques of Boolean functions to S-boxes.Using the idea of concatenating small variable S-boxes,we present a simple yet effective construction method of S-boxes satisfying the SAC.Finally,a simple example on how to construct SAC S-boxes with large input variables by small variables SAC S-boxes is given.展开更多
Two two-function minimax theorems are proved. The concavity-convexity conditions of the two functions involve strictly monotone transformations and mixing of the values of the two functions, and are described by the i...Two two-function minimax theorems are proved. The concavity-convexity conditions of the two functions involve strictly monotone transformations and mixing of the values of the two functions, and are described by the inequalities as upward and weakly downward conditions.展开更多
文摘In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].
文摘In this paper, the strictly weak major efficient point of set is introduced. A functional as a separate function is constructed, therefore, a necessary and sufficient condition for the strictly weak major efficient point of set is established.
文摘Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.
基金Supported by the National Nature Science Foundation of China（ No. 60773003,60970120）.
文摘Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanche criterion （SAC） is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction technique, two new methods to construct cheating immune secret sharing functions are proposed.
文摘The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.
文摘In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
基金Supported by the National Science Foundation of China(No.60773002,61072140)the 111 Project(No.B08038),the Doctoral Program Foundation of Institutions of Higher Education of China(No.20100203110003)+1 种基金the Fundamental Research Funds for the Central Universities(No.JY10000901034)the Anhui Provincial Natural Science Foundation(No.1208085QF119)
文摘The strict avalanche criterion(SAC)is one of the most important cryptographic criteria for substitution boxes(S-boxes)used in many symmetric encryption systems.However,there are few constructive methods for S-boxes fulfilling the SAC until now.In this paper,to construct S-boxes satisfying the SAC directly,we generalize the concatenation techniques of Boolean functions to S-boxes.Using the idea of concatenating small variable S-boxes,we present a simple yet effective construction method of S-boxes satisfying the SAC.Finally,a simple example on how to construct SAC S-boxes with large input variables by small variables SAC S-boxes is given.
文摘Two two-function minimax theorems are proved. The concavity-convexity conditions of the two functions involve strictly monotone transformations and mixing of the values of the two functions, and are described by the inequalities as upward and weakly downward conditions.
