Haussler＇s convolution kernel provides an effective framework for engineering positive semidefinite kernels, and has a wide range of applications.On the other hand,the mapping kernel that we introduce in this paper i...Haussler＇s convolution kernel provides an effective framework for engineering positive semidefinite kernels, and has a wide range of applications.On the other hand,the mapping kernel that we introduce in this paper is its natural generalization,and will enlarge the range of application significantly.Our main theorem with respect to positive semidefiniteness of the mapping kernel（1） implies Haussler＇s theorem as a corollary,（2） exhibits an easy-to-check necessary and sufficient condition for mapping kernels to be positive semidefinite,and（3） formalizes the mapping kernel so that significant flexibility is provided in engineering new kernels.As an evidence of the effectiveness of our results,we present a framework to engineer tree kernels.The tree is a data structure widely used in many applications,and tree kernels provide an effective method to analyze tree-type data.Thus,not only is the framework important as an example but also as a practical research tool.The description of the framework accompanies a survey of the tree kernels in the literature,where we see that 18 out of the 19 surveyed tree kernels of different types are instances of the mapping kernel,and examples of novel interesting tree kernels.展开更多
Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation...Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation of G, the Artin pattern , which consists of families , resp. , of transfer targets, resp. transfer kernels, is defined for the vertices of any descendant tree T of finite p-groups. It is endowed with partial order relations and , which are compatible with the parent-descendant relation of the edges of the tree T. The partial order enables termination criteria for the p-group generation algorithm which can be used for searching and identifying a finite p-group G, whose Artin pattern is known completely or at least partially, by constructing the descendant tree with the abelianization of G as its root. An appendix summarizes details concerning induced homomorphisms between quotient groups, which play a crucial role in establishing the natural partial order on Artin patterns and explaining the stabilization, resp. polarization, of their components in descendant trees T of finite p-groups.展开更多
In this work we determine the physical and mechanical properties of local composites reinforced with papaya trunk fibers (FTP) on one hand and particles of the hulls of the kernels of the garlic (PCNFA) in the other h...In this work we determine the physical and mechanical properties of local composites reinforced with papaya trunk fibers (FTP) on one hand and particles of the hulls of the kernels of the garlic (PCNFA) in the other hand. The samples are produced according to BSI 2782 standards;by combining fibers and untreated to polyester matrix following the contact molding method. We notice that the long fibers of papaya trunks improve the tensile/compression characteristics of composites by 45.44% compared to pure polyester;while the short fibers improve the flexural strength of composites by 62.30% compared to pure polyester. Furthermore, adding fibers decreases the density of the final composite material and the rate of water absorption increases with the size of the fibers. As regards composite materials with particle reinforcement from the cores of the winged fruits, the particle size (fine ≤ 800 μm and large ≤ 1.6 mm) has no influence on the Young’s modulus and on the rate of water absorption. On the other hand, fine particles improve the flexural strength of composite materials by 53.08% compared to pure polyester;fine particles increase the density by 19% compared to the density of pure polyester.展开更多
文摘Haussler＇s convolution kernel provides an effective framework for engineering positive semidefinite kernels, and has a wide range of applications.On the other hand,the mapping kernel that we introduce in this paper is its natural generalization,and will enlarge the range of application significantly.Our main theorem with respect to positive semidefiniteness of the mapping kernel（1） implies Haussler＇s theorem as a corollary,（2） exhibits an easy-to-check necessary and sufficient condition for mapping kernels to be positive semidefinite,and（3） formalizes the mapping kernel so that significant flexibility is provided in engineering new kernels.As an evidence of the effectiveness of our results,we present a framework to engineer tree kernels.The tree is a data structure widely used in many applications,and tree kernels provide an effective method to analyze tree-type data.Thus,not only is the framework important as an example but also as a practical research tool.The description of the framework accompanies a survey of the tree kernels in the literature,where we see that 18 out of the 19 surveyed tree kernels of different types are instances of the mapping kernel,and examples of novel interesting tree kernels.
文摘Based on a thorough theory of the Artin transfer homomorphism from a group G to the abelianization of a subgroup of finite index , and its connection with the permutation representation and the monomial representation of G, the Artin pattern , which consists of families , resp. , of transfer targets, resp. transfer kernels, is defined for the vertices of any descendant tree T of finite p-groups. It is endowed with partial order relations and , which are compatible with the parent-descendant relation of the edges of the tree T. The partial order enables termination criteria for the p-group generation algorithm which can be used for searching and identifying a finite p-group G, whose Artin pattern is known completely or at least partially, by constructing the descendant tree with the abelianization of G as its root. An appendix summarizes details concerning induced homomorphisms between quotient groups, which play a crucial role in establishing the natural partial order on Artin patterns and explaining the stabilization, resp. polarization, of their components in descendant trees T of finite p-groups.
文摘In this work we determine the physical and mechanical properties of local composites reinforced with papaya trunk fibers (FTP) on one hand and particles of the hulls of the kernels of the garlic (PCNFA) in the other hand. The samples are produced according to BSI 2782 standards;by combining fibers and untreated to polyester matrix following the contact molding method. We notice that the long fibers of papaya trunks improve the tensile/compression characteristics of composites by 45.44% compared to pure polyester;while the short fibers improve the flexural strength of composites by 62.30% compared to pure polyester. Furthermore, adding fibers decreases the density of the final composite material and the rate of water absorption increases with the size of the fibers. As regards composite materials with particle reinforcement from the cores of the winged fruits, the particle size (fine ≤ 800 μm and large ≤ 1.6 mm) has no influence on the Young’s modulus and on the rate of water absorption. On the other hand, fine particles improve the flexural strength of composite materials by 53.08% compared to pure polyester;fine particles increase the density by 19% compared to the density of pure polyester.
