A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
This manuscript summarizes the results of Classical Physics before Quantum Mechanics and Hypotheses proposed by classical physicists from the 17th until the beginning of 21st century. We then proceed to unify these re...This manuscript summarizes the results of Classical Physics before Quantum Mechanics and Hypotheses proposed by classical physicists from the 17th until the beginning of 21st century. We then proceed to unify these results into a single coherent picture in frames of the developed Hypersphere World-Universe Model (WUM). The Model proposes 5 types of Dark Matter particles and predicts their masses;models the origin, evolution, and structure of the World and Macroobjects;provides a mathematical framework that ties together a number of Fundamental constants and allows for direct calculation of their values.展开更多
To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (...To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.展开更多
The Hypersphere World-Universe Model (WUM) provides a mathematical framework that allows calculating the primary cosmological parameters of the World which are in good agreement with the most recent measurements and o...The Hypersphere World-Universe Model (WUM) provides a mathematical framework that allows calculating the primary cosmological parameters of the World which are in good agreement with the most recent measurements and observations. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the World and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;the concentration of intergalactic plasma and time delay of Fast Radio Bursts. Additionally, the model predicts masses of dark matter particles, photons, and neutrinos;proposes new types of particle interactions (Super Weak and Extremely Weak);shows inter-connectivity of primary cosmological parameters of the World. WUM proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values. This paper is the summary of the mathematical results obtained in [1]-[4].展开更多
The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between t...The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.展开更多
This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, ev...This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, evolution, structure, ultimate fate, and primary parameters of the World. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the world and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;gamma-ray background and cosmic neutrino background;macrostructure of the world and macroobjects structure. Additionally, the model makes predictions pertaining to masses of dark matter particles, photons, and neutrinos, proposes new types of particle interactions (Super Weak and Extremely Weak), and shows inter-connectivity of primary cosmological parameters of the world and the rise of the solar luminosity during the last 4.6 Byr. The model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values.展开更多
In this paper, we study the problems of geometric inequality for the radii of escribed hyperspheres of an n-dimensional simplex in Euclidean space En. Some new geometric inequalities for the radii of escribed hypersph...In this paper, we study the problems of geometric inequality for the radii of escribed hyperspheres of an n-dimensional simplex in Euclidean space En. Some new geometric inequalities for the radii of escribed hyperspheres of a simplex are established.展开更多
Hypersphere World-Universe Model (WUM) envisions Matter carried from the Universe into the World from the fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is a byproduct of Dark Matter (DM) se...Hypersphere World-Universe Model (WUM) envisions Matter carried from the Universe into the World from the fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is a byproduct of Dark Matter (DM) self-annihilation. WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) and Luminous Epoch (ever since for 13.77 billion years). Big Bang discussed in Standard Cosmology (SC) is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning DM Supercluster’s Cores and self-annihilation of DMPs. WUM solves a number of physical problems in SC and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Coronal Heating problem in solar physics—temperature of Sun’s corona exceeding that of photosphere by millions of degrees;Cores of Sun and Earth rotating faster than their surfaces;Diversity of Gravitationally-Rounded objects in Solar system and their Internal Heating. Model makes predictions pertaining to Rest Energies of DMPs, proposes New Type of their Interactions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.展开更多
This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the descr...This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of the training samples from one class and use this boundary to classify the test samples. The generalized multiplicative updates are applied to solving boundary optimization progranmning. Multiplicative updates available are suited for nonnegative quadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadratic programming in this paper. They provide an extremely straightforward way to implement support vector machines （SVMs） where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution of the maximum margin hyperplane. The experiments show the superiority of our new algorithm.展开更多
Dirac’s themes were the unity and beauty of Nature. He identified three revolutions in modern physics: Relativity, Quantum Mechanics and Cosmology. In his opinion: “<i>The new cosmology will probably turn out ...Dirac’s themes were the unity and beauty of Nature. He identified three revolutions in modern physics: Relativity, Quantum Mechanics and Cosmology. In his opinion: “<i>The new cosmology will probably turn out to be philosophically even more revolutionary than relativity or the quantum theory, perhaps looking forward to the current bonanza in cosmology, where precise observations on some of the most distant objects in the universe are shedding light on the nature of reality, on the nature of matter and on the most advanced quantum theories</i>” [Farmelo, G. (2009) The Strangest Man. The Hidden Life of Paul Dirac, Mystic of the Atom. Basic Books, Britain, 661 p]. In 1937, Paul Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”;and later added the notion of continuous creation of Matter in the World. The developed Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics and it can already serve as a basis for a New Cosmology proposed by Paul Dirac.展开更多
The main objective of this paper is to discuss the Evolution of a 3D Finite World (that is a Hypersphere of a 4D Nucleus of the World) from the Beginning up to the present Epoch in frames of World-Universe Model (WUM)...The main objective of this paper is to discuss the Evolution of a 3D Finite World (that is a Hypersphere of a 4D Nucleus of the World) from the Beginning up to the present Epoch in frames of World-Universe Model (WUM). WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) when only Dark Matter (DM) Macroobjects (MOs) existed, and Luminous Epoch (ever since for 13.77 billion years) when Luminous MOs emerged due to Rotational Fission of Overspinning DM Superclusters’ Cores and self-annihilation of Dark Matter Particles (DMPs). WUM envisions that DM is created by the Universe in the 4D Nucleus of the World. Dark Matter Particles (DMPs) carry new DM into the 3D Hypersphere World. Luminous Matter is a byproduct of DMPs self-annihilation. By analogy with 3D ball, which has two-dimensional sphere surface (that has surface energy), we can imagine that the 3D Hypersphere World has a “Surface Energy” of the 4D Nucleus. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: <b>Angular Momentum problem</b> in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;<b>Fermi Bubbles</b>—two large structures in gamma-rays and X-rays above and below Galactic center;<b>Missing Baryon problem</b> related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals <b>Inter-Connectivity of Primary Cosmological Parameters</b> and calculates their values, which are in good agreement with the latest results of their measurements. In 2013, WUM predicted the values of the following Cosmological parameters: gravitational, concentration of intergalactic plasma, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. “<i>The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy</i>” (Nobel Prize in Physics 2020) made by Prof. R. Genzel and A. Ghez is a confirmation of one of the most important predictions of WUM in 2013: “<i>Macroobjects of the World have cores made up of the discussed DM particles. Other particles, including DM and baryonic matter, form shells surrounding the cores</i>”.展开更多
If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show tha...If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.展开更多
Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but ev...Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but even identical, or to rephrase the main statement of this work: A gravitational force does not exist. Rather, gravity is a fictitious force, or, more pointedly: Gravity is the centrifugal force which acts upon material bodies within the rotating S3-hypersphere of the Universe. These in turn warp the adjacent space-fabric, shaping it to the well-known field geometry of general relativity.展开更多
The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic...The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic functions in the angle part and of generalized Laguerre functions in the radial part respectively, and are then augmented by the simplest type of Jastrow correlation factor to incorporate electron-nucleus cusp only. The excellent agreement between the present nonrelativistic eigen-energies and those from the sophisticated configuration interaction (CI) method for the examined states indicates that the hyperspherical harmonic method can also be applied to the P and the D excited states of the helium atom.展开更多
In this paper, the hyperspherical harmonics used for solving the three and four body problems in nuclear physics are given. The equations of the adiabatic approximation to hyperspherical harmonic method are derived. S...In this paper, the hyperspherical harmonics used for solving the three and four body problems in nuclear physics are given. The equations of the adiabatic approximation to hyperspherical harmonic method are derived. Some properties of the hypernuclous Heare given as the illustrative example of the application of this method.展开更多
Let P(a,a)n (z) be n-degree hyperspherical polinomials, Q(a,a)n (z) be the second stort of hyperspherical functions, Ea be an elipse on z-plane. In this paper, we found some inequalitys about P(a,a)n (z) and Q(a,a)n (...Let P(a,a)n (z) be n-degree hyperspherical polinomials, Q(a,a)n (z) be the second stort of hyperspherical functions, Ea be an elipse on z-plane. In this paper, we found some inequalitys about P(a,a)n (z) and Q(a,a)n (z) on z-plane, and gneralize inequality in paper [2] when a= 0 to when α≥0. In addition ,we also foundwo important expressions of the relation.展开更多
针对国际疾病分类(ICD)自动编码方法的长文本处理、编码的层次结构以及长尾分布等导致的模型泛化能力弱的问题,提出一种充分利用医学预训练语言模型的基于提示学习和超球原型的小样本ICD自动编码方法(hypersphere prototypical with pro...针对国际疾病分类(ICD)自动编码方法的长文本处理、编码的层次结构以及长尾分布等导致的模型泛化能力弱的问题,提出一种充分利用医学预训练语言模型的基于提示学习和超球原型的小样本ICD自动编码方法(hypersphere prototypical with prompt learning,PromptHP)。首先,将编码描述与临床文本融合进提示学习模型中的提示模板,使得模型能够更加深入地理解临床文本;然后,充分利用预训练语言模型的先验知识进行初始预测;接着,在预训练语言模型输出表示的基础上引入超球原型进行类别建模和度量分类,并在医学数据集上微调网络,充分纳入数据知识,提高模型在小样本ICD编码分配任务上的性能;最后,对以上两部分预测结果集成加权获得最终编码预测结果。在公开医学数据集MIMIC-Ⅲ上的实验结果表明,该模型优于最先进的基线方法,PromptHP将小样本编码的macro-AUC、micro-AUC、macro-F_(1)和micro-F_(1)分别提高了1.77%、1.54%、14.22%、15.01%。实验结果验证了该模型在小样本编码分类任务中的有效性。展开更多
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
文摘This manuscript summarizes the results of Classical Physics before Quantum Mechanics and Hypotheses proposed by classical physicists from the 17th until the beginning of 21st century. We then proceed to unify these results into a single coherent picture in frames of the developed Hypersphere World-Universe Model (WUM). The Model proposes 5 types of Dark Matter particles and predicts their masses;models the origin, evolution, and structure of the World and Macroobjects;provides a mathematical framework that ties together a number of Fundamental constants and allows for direct calculation of their values.
文摘To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.
文摘The Hypersphere World-Universe Model (WUM) provides a mathematical framework that allows calculating the primary cosmological parameters of the World which are in good agreement with the most recent measurements and observations. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the World and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;the concentration of intergalactic plasma and time delay of Fast Radio Bursts. Additionally, the model predicts masses of dark matter particles, photons, and neutrinos;proposes new types of particle interactions (Super Weak and Extremely Weak);shows inter-connectivity of primary cosmological parameters of the World. WUM proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values. This paper is the summary of the mathematical results obtained in [1]-[4].
基金Supported by the National Natural Science Foundation of China (No.60277101, No.60301003, No.60431020), Beijing Foundation (No.3052005), and Beijing Munici-pal Commission of Education Project (KM200410005030).
文摘The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.
文摘This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, evolution, structure, ultimate fate, and primary parameters of the World. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the world and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;gamma-ray background and cosmic neutrino background;macrostructure of the world and macroobjects structure. Additionally, the model makes predictions pertaining to masses of dark matter particles, photons, and neutrinos, proposes new types of particle interactions (Super Weak and Extremely Weak), and shows inter-connectivity of primary cosmological parameters of the world and the rise of the solar luminosity during the last 4.6 Byr. The model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values.
基金Supported by the Doctoral Programs Foundation of Education Ministry of China(20113401110009)Supported by the Universities Natural Science Foundation of Anhui Province(KJ2013A220)Supported by the Natural Science Research Project of Hefei Normal University(2012kj11)
文摘In this paper, we study the problems of geometric inequality for the radii of escribed hyperspheres of an n-dimensional simplex in Euclidean space En. Some new geometric inequalities for the radii of escribed hyperspheres of a simplex are established.
文摘Hypersphere World-Universe Model (WUM) envisions Matter carried from the Universe into the World from the fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is a byproduct of Dark Matter (DM) self-annihilation. WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) and Luminous Epoch (ever since for 13.77 billion years). Big Bang discussed in Standard Cosmology (SC) is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning DM Supercluster’s Cores and self-annihilation of DMPs. WUM solves a number of physical problems in SC and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Coronal Heating problem in solar physics—temperature of Sun’s corona exceeding that of photosphere by millions of degrees;Cores of Sun and Earth rotating faster than their surfaces;Diversity of Gravitationally-Rounded objects in Solar system and their Internal Heating. Model makes predictions pertaining to Rest Energies of DMPs, proposes New Type of their Interactions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.
基金Project supported by the National Natural Science Foundation of China (Grant No.60574075)
文摘This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of the training samples from one class and use this boundary to classify the test samples. The generalized multiplicative updates are applied to solving boundary optimization progranmning. Multiplicative updates available are suited for nonnegative quadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadratic programming in this paper. They provide an extremely straightforward way to implement support vector machines （SVMs） where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution of the maximum margin hyperplane. The experiments show the superiority of our new algorithm.
文摘Dirac’s themes were the unity and beauty of Nature. He identified three revolutions in modern physics: Relativity, Quantum Mechanics and Cosmology. In his opinion: “<i>The new cosmology will probably turn out to be philosophically even more revolutionary than relativity or the quantum theory, perhaps looking forward to the current bonanza in cosmology, where precise observations on some of the most distant objects in the universe are shedding light on the nature of reality, on the nature of matter and on the most advanced quantum theories</i>” [Farmelo, G. (2009) The Strangest Man. The Hidden Life of Paul Dirac, Mystic of the Atom. Basic Books, Britain, 661 p]. In 1937, Paul Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”;and later added the notion of continuous creation of Matter in the World. The developed Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics and it can already serve as a basis for a New Cosmology proposed by Paul Dirac.
文摘The main objective of this paper is to discuss the Evolution of a 3D Finite World (that is a Hypersphere of a 4D Nucleus of the World) from the Beginning up to the present Epoch in frames of World-Universe Model (WUM). WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM introduces Dark Epoch (spanning from the Beginning of the World for 0.45 billion years) when only Dark Matter (DM) Macroobjects (MOs) existed, and Luminous Epoch (ever since for 13.77 billion years) when Luminous MOs emerged due to Rotational Fission of Overspinning DM Superclusters’ Cores and self-annihilation of Dark Matter Particles (DMPs). WUM envisions that DM is created by the Universe in the 4D Nucleus of the World. Dark Matter Particles (DMPs) carry new DM into the 3D Hypersphere World. Luminous Matter is a byproduct of DMPs self-annihilation. By analogy with 3D ball, which has two-dimensional sphere surface (that has surface energy), we can imagine that the 3D Hypersphere World has a “Surface Energy” of the 4D Nucleus. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: <b>Angular Momentum problem</b> in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;<b>Fermi Bubbles</b>—two large structures in gamma-rays and X-rays above and below Galactic center;<b>Missing Baryon problem</b> related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals <b>Inter-Connectivity of Primary Cosmological Parameters</b> and calculates their values, which are in good agreement with the latest results of their measurements. In 2013, WUM predicted the values of the following Cosmological parameters: gravitational, concentration of intergalactic plasma, and the minimum energy of photons, which were experimentally confirmed in 2015-2018. “<i>The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy</i>” (Nobel Prize in Physics 2020) made by Prof. R. Genzel and A. Ghez is a confirmation of one of the most important predictions of WUM in 2013: “<i>Macroobjects of the World have cores made up of the discussed DM particles. Other particles, including DM and baryonic matter, form shells surrounding the cores</i>”.
基金This research is supported by a grant of NSF of P.R.China.
文摘If dμ is the Fourier transform of a smooth measure,dμ on the hypersphere Sn-1(n≥2)the there exists a constant C dependent only on n such that |dμ(y) |≤C(1+ |y |)-(n-1) /2 for all y∈Rn. In this paper, we show that the above statement is false for non-smooth measures. And we present the corresponding estimations far the Fourier transforms of certain non-smooth measures on Sn-1.
文摘Einstein’s weak equivalence principle suggests that gravity and acceleration (centrifugal force) are indistinguishable from each other and, therefore, equivalent. We maintain that they are not only equivalent, but even identical, or to rephrase the main statement of this work: A gravitational force does not exist. Rather, gravity is a fictitious force, or, more pointedly: Gravity is the centrifugal force which acts upon material bodies within the rotating S3-hypersphere of the Universe. These in turn warp the adjacent space-fabric, shaping it to the well-known field geometry of general relativity.
基金Supported by the National Natural Science Foundation of China(No. 29703003).
文摘The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic functions in the angle part and of generalized Laguerre functions in the radial part respectively, and are then augmented by the simplest type of Jastrow correlation factor to incorporate electron-nucleus cusp only. The excellent agreement between the present nonrelativistic eigen-energies and those from the sophisticated configuration interaction (CI) method for the examined states indicates that the hyperspherical harmonic method can also be applied to the P and the D excited states of the helium atom.
文摘In this paper, the hyperspherical harmonics used for solving the three and four body problems in nuclear physics are given. The equations of the adiabatic approximation to hyperspherical harmonic method are derived. Some properties of the hypernuclous Heare given as the illustrative example of the application of this method.
文摘Let P(a,a)n (z) be n-degree hyperspherical polinomials, Q(a,a)n (z) be the second stort of hyperspherical functions, Ea be an elipse on z-plane. In this paper, we found some inequalitys about P(a,a)n (z) and Q(a,a)n (z) on z-plane, and gneralize inequality in paper [2] when a= 0 to when α≥0. In addition ,we also foundwo important expressions of the relation.
文摘针对国际疾病分类(ICD)自动编码方法的长文本处理、编码的层次结构以及长尾分布等导致的模型泛化能力弱的问题,提出一种充分利用医学预训练语言模型的基于提示学习和超球原型的小样本ICD自动编码方法(hypersphere prototypical with prompt learning,PromptHP)。首先,将编码描述与临床文本融合进提示学习模型中的提示模板,使得模型能够更加深入地理解临床文本;然后,充分利用预训练语言模型的先验知识进行初始预测;接着,在预训练语言模型输出表示的基础上引入超球原型进行类别建模和度量分类,并在医学数据集上微调网络,充分纳入数据知识,提高模型在小样本ICD编码分配任务上的性能;最后,对以上两部分预测结果集成加权获得最终编码预测结果。在公开医学数据集MIMIC-Ⅲ上的实验结果表明,该模型优于最先进的基线方法,PromptHP将小样本编码的macro-AUC、micro-AUC、macro-F_(1)和micro-F_(1)分别提高了1.77%、1.54%、14.22%、15.01%。实验结果验证了该模型在小样本编码分类任务中的有效性。
