HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

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.

Hypersphere World-Universe Model. Tribute to Classical Physics

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.

Bipartite Threshold Multi-Secret Sharing Scheme Based on Hypersphere

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.

Mathematical Overview of Hypersphere World-Universe Model

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].

A NEW HYPERSPHERE SUPPORT VECTOR MACHINE ALGORITHM

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.

Overview of Hypersphere World-Universe Model

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.

Hypersphere World-Universe Model: Basic Ideas

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.

Hypersphere World-Universe Model

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: “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” [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.

Hypersphere World-Universe Model: Evolution of the World

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: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Missing Baryon problem related to the fact that the observed amount of baryonic matter did not match theoretical predictions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters 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. “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (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: “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”.

ABOUT THE FOURIER TRANSFORMS OF NON-SMOOTH MEASURES ON HYPERSPHERES

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.

On the Physics inside a Closed,Static,Rotating Einsteinian Hypersphere in Due Consideration of the Galaxy

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.

基于混合高斯先验变分自编码器的深度多球支持向量数据描述

随着数据维度和规模的不断增加,基于深度学习的异常检测方法取得了优异的检测性能,其中深度支持向量数据描述(Deep SVDD)得到了广泛应用。然而,要缓解超球崩溃问题,就需要对Deep SVDD中映射网络的各种参数施加约束。为了进一步提高Deep SVDD中映射网络的特征学习能力,同时解决超球崩溃问题,提出了基于混合高斯先验变分自编码器的深度多球支持向量数据描述(Deep Multiple-Sphere Support Vector Data Description Based on Variational Autoencoder with Mixture-of-Gaussians Prior,DMSVDD-VAE-MoG)。首先,通过预训练初始化网络参数和多个超球中心;其次,利用映射网络获得训练数据的潜在特征,对VAE损失、多个超球的平均半径和潜在特征到所对应超球中心的平均距离进行联合优化,以获得最优网络连接权重和多个最小超球。实验结果表明,所提DMSVDD-VAE-MoG在MNIST,Fashion-MNIST和CIFAR-10上均取得了优于其他8种相关方法的检测性能。

基于超球面三元组编码的干扰模式开集识别

干扰模式识别是现代军事通信对抗中必不可少的一环,随着复杂电磁环境当中各种新型恶意干扰样式层出不穷,对于未知型干扰的判决也变得愈发重要。因此,要求干扰模式识别算法保持对于已知型干扰高精度识别的同时,也能够完成对于未知型干扰的判决,以排除未知型恶意干扰的影响。基于此,该文将未知型干扰存在时的干扰模式识别问题建模为开集识别问题,并提出一种基于超球面3元组编码的干扰模式开集识别方法。所提方法基于超球面3元组对输入的时频图像进行降维编码以提高识别精度,然后采用元识别分类器准确地完成干扰模式开集识别任务。通过仿真试验证明该算法在干信比大于–2 dB时能够高效地完成开放空间中的干扰模式识别任务。

氦原子的超球绝热势

利用B样条技术和两粒子角函数,对氦原子的超球绝热哈密顿方程进行数值计算.获得了氦原子1 S和1 P态的超球势曲线和绝热道函数.计算结果与文献中的结果一致.文中计算方法可以处理三体系统的高角动量问题.

煤矿运输系统多元异常图像检测研究

煤矿运输系统的异常险情种类繁多、场景多样,煤矿现场异常事故的发生具有偶然性,异常样本的获取其数量远小于正常样本,造成正负样本不平衡。针对上述问题,提出一种基于超球重构数据描述(HRDD)的煤矿运输系统多元异常图像检测方法。在全卷积数据描述(FCDD)基础上引入图像重构辅助任务,选用均方差损失函数作为图像重构辅助任务的目标函数,将异常图像检测和定位量化为一个不等式约束优化问题。采用无缝融合技术将辅助数据集、异常样本融合到正常样本中,以缩小异常融合样本与正常样本的差异,扩大异常样本总量,平衡异常样本、正常样本的比例。通过多组噪声模拟实验和现场实验证明,以一定概率在抵抗区添加高斯噪声进行增强训练,可提高HRDD模型的抗噪效能、泛化能力、检测准确率等。消融实验结果表明:辅助数据集有效地改善了样本不平衡问题,准确率提高了36.5%;引入图像重构辅助任务可保证深层特征能够准确映射到异常位置,交并比(IoU)提升了33.4%;辅助数据集与图像重构辅助任务之间存在强耦合作用,二者组合使用能进一步激发HRDD算法的性能潜力;添加无缝融合样本、高斯噪声增强等在一定程度上提高了HRDD模型的泛化能力。对照实验结果表明,HRDD算法准确率及IoU均优于其他主流算法,相比FCDD算法,HRDD算法准确率、IoU分别提高了4.6%,7.0%,更适用于煤矿现场。

基于DBN实现QSSVM模型的WSN数据异常检测

无线传感器网络(Wireless Sensor Network,WSN)数据异常处理效率保障了现在智能的高效率运行。在分析1/4超球面支持向量机(Quarter-Sphere support vector machines,QSSVM)测试模型的基础上,进行深度信念网络(Deep Belief Network,DBN)构建实现,设计了一种可以实现在线测试功能的异常检测算法。研究结果表明:随着窗口大小的增加,所需要的计算时间增多。QSSVM在窗口开始扩大时便产生变化,主要表现在准确度的持续提高。QSSVM检测性能随着样本维度不断升高得到较大提升,相反K-means的检测性能却有降低趋势。采用QSSVM算法处理560维HAR数据时,测试结果显示检测率高达94.16%。该研究能够满足大规模高维传感器的数据处理需求,具有很高的应用价值。

Performance of Hyperspherical Harmonic Expansionon the Low-lying P and D States of Helium Atom

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.

ON THE HYPERSPHERICAL HARMONIC METHODTO THREE AND FOUR BODY NUCLEAR PROBLEMS

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.

Some Features of Hyperspherical Functins

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基于支持向量数据描述的往复式注水泵健康度评价方法

往复式注水泵作为油田注水作业的关键装备,由于恶劣的工作环境,易导致轴瓦、缸体和电机等部件故障,对其进行健康监测及健康度评价,以及时发现异常状态,保障安全可靠的注水作业十分必要。本文提出了一种基于支持向量数据描述的往复式注水泵健康度量化评价方法。首先,考虑到注水泵振动信号非线性、非平稳的特点,在有限条件下提取注水泵振动信号中的特征信息。针对注水泵核心部件多且间距小的问题分析振动信号的测点位置,以搭建数据采集系统。针对振动信号频率成分复杂的特点,利用变分模态分解提取振动数据的变分模态分量,在所有模态分量排列熵的基础上构建高维多域特征集,以描述注水泵的健康状态。其次,针对注水泵实际采集数据过程中,大多数设备处于健康工作状态,故障数据较少,容易造成样本不均衡的问题,利用单值分类方法支持向量数据描述在单值分类问题上的优势,仅使用健康状态运行下注水泵数据样本的特征向量进行支持向量数据描述的超球体模型构建,并引入粒子群优化算法对模型参数进行优化;通过计算注水泵不同健康状态的数据到超球体球心的距离,参考隶属度函数进行公式拟合,实现注水泵的健康度定量评价。最终,为验证该评价方法的适用性,对长庆油田现场注水泵的振动数据进行健康度评价计算,粒子群优化后模型准确率能达到95%,本文所提出的方法具有较好的准确性。