Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilit...Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilities.Among them,projection criterion proposed by one of the authors aimsdirectly at optimal generalization.The projection idea leads to three specific learning approaches,projection learning,partial projection learning,and averaged projection learning,and a framework of afamily of projection learning called S-L projection learning is established to discuss infinite kinds oflearning.S-L projection learning has a different form from the three methods,and it is not easy to analyzetheir relationship.This paper focuses on an equivalent form of S-L projection learning,which shows thatit is a transformed version of partial projection learning.展开更多
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution...The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.展开更多
A convenient synthetic approach leading to protected inositol was described based on regioselective O-alkylation using alkyl halide under solid-liquid PTC condition
Facile and rapid polycondensation reactions of N,N'-(pyromellitoyl)-bis-L-leucine diacid chloride 1 with eight different derivatives of hydantoin compounds 2a-h were developed by using a domestic microwave oven in...Facile and rapid polycondensation reactions of N,N'-(pyromellitoyl)-bis-L-leucine diacid chloride 1 with eight different derivatives of hydantoin compounds 2a-h were developed by using a domestic microwave oven in the presence of a small amount of polar organic medium such as o-cresol. The polycondensation reactions proceeded rapidly, compared with the conventional solution polycondensation, and was completed within 7-10 min, producing a series of novel optically active poly(amide-imide)s 3a-h with high yield and inherent viscosity of 0.35-0.65 dL/g. All of the above polymers were fully characterized by FT-IR, elemental analyses, inherent viscosity (η inh ), solubility test and specific rotation. Some structural characterization and physical properties of these optically active poly(amide-imide)s are reported.展开更多
文摘Learning a mapping between an input space and an output.space from training data canbe viewed as a problem of function approximation,which means that different criteria result in learningapproaches of different abilities.Among them,projection criterion proposed by one of the authors aimsdirectly at optimal generalization.The projection idea leads to three specific learning approaches,projection learning,partial projection learning,and averaged projection learning,and a framework of afamily of projection learning called S-L projection learning is established to discuss infinite kinds oflearning.S-L projection learning has a different form from the three methods,and it is not easy to analyzetheir relationship.This paper focuses on an equivalent form of S-L projection learning,which shows thatit is a transformed version of partial projection learning.
文摘The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.
文摘A convenient synthetic approach leading to protected inositol was described based on regioselective O-alkylation using alkyl halide under solid-liquid PTC condition
基金This project was supported by the Research Affairs Division of Arak University.
文摘Facile and rapid polycondensation reactions of N,N'-(pyromellitoyl)-bis-L-leucine diacid chloride 1 with eight different derivatives of hydantoin compounds 2a-h were developed by using a domestic microwave oven in the presence of a small amount of polar organic medium such as o-cresol. The polycondensation reactions proceeded rapidly, compared with the conventional solution polycondensation, and was completed within 7-10 min, producing a series of novel optically active poly(amide-imide)s 3a-h with high yield and inherent viscosity of 0.35-0.65 dL/g. All of the above polymers were fully characterized by FT-IR, elemental analyses, inherent viscosity (η inh ), solubility test and specific rotation. Some structural characterization and physical properties of these optically active poly(amide-imide)s are reported.
