The paper is related to the error analysis of Multicategory Support Vector Machine （MSVM） classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernel as Mercer kernel and give the error e...The paper is related to the error analysis of Multicategory Support Vector Machine （MSVM） classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernel as Mercer kernel and give the error estimate with De La Vall6e Poussin means. We also introduce the standard estimation of sample error, and derive the explicit learning rate.展开更多
In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of al...In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to <em>T</em><em>c</em> in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition <em>T</em><em>c</em> upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schr<span style="white-space:nowrap;">ö</span>dinger to most recently Geesink.展开更多
Let E and F be Banach spaces over the same field K which is either the field R or the field C.The character of continuous mappings in P a(E;F) which is a vector space of all polynomials from E into F is discussed.In ...Let E and F be Banach spaces over the same field K which is either the field R or the field C.The character of continuous mappings in P a(E;F) which is a vector space of all polynomials from E into F is discussed.In particular,some equivalent conditions for a mapping P in P a(E;F) to be continuous are established.This is very important and useful to determine a mapping P in P a(E;F) to be either continuous or not in theory or practice.展开更多
本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间...本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.展开更多
文摘The paper is related to the error analysis of Multicategory Support Vector Machine （MSVM） classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernel as Mercer kernel and give the error estimate with De La Vall6e Poussin means. We also introduce the standard estimation of sample error, and derive the explicit learning rate.
文摘In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to <em>T</em><em>c</em> in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition <em>T</em><em>c</em> upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schr<span style="white-space:nowrap;">ö</span>dinger to most recently Geesink.
文摘Let E and F be Banach spaces over the same field K which is either the field R or the field C.The character of continuous mappings in P a(E;F) which is a vector space of all polynomials from E into F is discussed.In particular,some equivalent conditions for a mapping P in P a(E;F) to be continuous are established.This is very important and useful to determine a mapping P in P a(E;F) to be either continuous or not in theory or practice.
基金the NNSF(10671094 )the Specialized Research Fund for the Doctor Program of Higher Education of China(20060319001)the NSF for the Higher Education of Anhui(KJ2008B242).
文摘本文的目标是在一般的p-线性空间和局部p-凸空间框架下建立针对单值和拟上半连续集值映射的不动点定理、最佳逼近定理、和对应的Leray-Schauder非线性(二择一)选择原理,这里p∈(0,1].我们建立的不动点定理是在p-线性空间和局部p-凸空间对Schauder猜想的肯定答复,对应的最佳逼近定理和Leray-Schauder选择原理也是非线性泛函分析的核心工具.这些新结果统一和推广了目前在数学文献中存在的理论成果,也是对作者最近工作([Fixed Point Theory Algorithms Sci.Eng.,2022,2022:Paper Nos.20,26])的继续和深度发展.
