Structural Foundation and Geometry of the Material Singularity (and Its Quantum Entanglement)

In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.

New Raw Materials Ignite the Singularity of Cosmetic Innovation

As traced by the Big Bang theory,the starting point of the universe,is called the“Singularity”in Da Ci Hai,an unabridged,comprehensive dictionary.According to cosmological reasoning,the singularity has an infinite density of matter,an infinite curvature of space and time,and it is invisible and infinite.These characteristics are analogous to the human imagination at the level of innovation.For the innovation of cosmetic raw materials,there is also the possibility of infinite evolution.For example,in recent years,the scientific research in cosmetic industry the for promoting upgrade in raw materials is quite proactive.From the raw material enterprises,down to the brand company,the investment in raw material innovation is also strengthened at a visible rate.

On the Vacuum Hydrodynamics of Moving Bodies—The Theory of General Singularity

The Theory of General Singularity is presented, unifying quantum field theory, general relativity, and the standard model. This theory posits phonons as fundamental excitations in a quantum vacuum, modeled as a Bose-Einstein condensate. Through key equations, the role of phonons as intermediaries between matter, energy, and spacetime geometry is demonstrated. The theory expands Einsteins field equations to differentiate between visible and dark matter, and revises the standard model by incorporating phonons. It addresses dark matter, dark energy, gravity, and phase transitions, while making testable predictions. The theory proposes that singularities, the essence of particles and black holes, are quantum entities ubiquitous in nature, constituting the very essence of elementary particles, seen as micro black holes or quantum fractal structures of spacetime. As the theory is refined with increasing mathematical rigor, it builds upon the foundation of initial physical intuition, connecting the spacetime continuum of general relativity with the hydrodynamics of the quantum vacuum. Inspired by the insights of Tesla and Majorana, who believed that physical intuition justifies the infringement of mathematical rigor in the early stages of theory development, this work aims to advance the understanding of the fundamental laws of the universe and the perception of reality.

基于Singularity的超算资源容器化

深度学习往往伴随着大量的计算,属于典型的高性能计算(HPC)应用。基于Python的深度学习中往往使用PyTorch或者TensorFlow库,环境的配置与管理极为复杂,可重复性低,导致代码的升级、管理、测试、迁移成为大难题。为此,诞生了容器化技术。容器化技术以Docker为代表,通过在迁移代码的同时迁移代码运行环境,从而避免了代码在移植的时候存在繁杂的环境配置过程。但是超算服务器与普通的服务器又有很大的差别,如开发人员无root权限,测试代码时需要进行资源管理(内存,CPU)。这些问题都让Docker技术在HPC环境的应用受限,针对以上问题,使用Singularity代替Docker,在神威蓝光II型超级计算机上尝试生成了Python3.7+Numpy+Pandas+Scipy数据科学计算环境的Singularity镜像文件,在阿里云服务器上无root权限创建容器并成功运行了距离判别Python计算程序。结果表明,使用Singularity可以解决Docker在服务器上面的root权限问题,有助于深度学习环境在不同HPC服务器上面的部署。

Singularity-free Green's function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.

Singularity-free expression of magnetic field of cuboid under undulating terrain

Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. AT at all points in the source-flee space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.

Singularity theories and methods for characterizing mineralization processes and mapping geo-anomalies for mineral deposit prediction

In this paper, we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes. Associ- ating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods. This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral deposit prediction. Mineral deposits, as the products of singular mineralization processes caused by geo-anomalies, can be characterized by means of fractal or multifractal models. It has been shown that singularity can characterize the degree of geo-abnormality, and this has been demonstrated to be useful for mapping anomalies of undiscovered mineral deposits. The study of mineralization and mineral deposits from a nonlinear process point of view is a new but promising research direction. This study emphasizes the relationships between geo-anomalies and singularity, including singular processes resulting in singularity and geo-anomalies, the characterization of singularity and geo-anomalies and the identification of geo-anomalies for mineral deposit prediction. The concepts and methods are demon- strated using a case study of Sn mineral deposit prediction in the Gejiu mineral district in Yunnan, China.

Singularity Analysis of a 3-RPS Parallel Manipulator Using Geometric Algebra

Singular configurations must be avoided in path planning and control of a parallel manipulator. However, most studies rarely focus on an overall singularity loci distribution of lower-mobility parallel mechanisms. Geometric algebra is employed in analysis of singularity of a 3-RPS parallel manipulator. Twist and wrench in screw theory are represented in geometric algebra. Linear dependency of twists and wrenches are described by outer product in geometric algebra. Reciprocity between twists and constraint wrenches are reflected by duality. To compute the positions of the three spherical joints of the 3-RPS parallel manipulator, Tilt-and-Torsion angles are used to describe the orientation of the moving platform. The outer product of twists and constraint wrenches is used as an index for closeness to singularity（ICS） of the 3-RPS parallel manipulator. An overall and thorough perspective of the singularity loci distribution of the 3-RPS parallel manipulator is disclosed, which is helpful to design, trajectory planning and control of this kind of parallel manipulator.

Analysis and Application of the Singularity Locus of the Stewart Platform

The direct use of the determinant of Jacobian matrix being equal to zero for the singularity analysis is generally difficult which is due to complexity of the Jacobian matrix of 6-DOF parallel manipulators,especially for Stewart platform.Recently,several scholars make their great contribution to the effective solution of this problem,but neither of them find the right answer.This paper gives a brief analysis of the kinematics of the Stewart platform and derives the Jacobian matrices of the system through the velocity equation.On the basis of the traditional classification of singularities,the second type of singularity is investigated.An assumption of any three of the six variables of the Stewart platform as constant is made,then the analytical expression of singularity locus equation of the second type singularity which contains another three pose variables is obtained.The singularity locus is represented in the three-dimensional space through the derived equation.The correctness and validity of the proposed method are verified through examples.Finally,the singularity analysis of an electric Stewart platform in its desired workspace and reachable workspace is implemented.Thus,one can easily identify whether singularity exists in a given workspace of a Stewart platform and determine whether the existed singularity can be avoided through the proposed method.The proposed method also provides theoretical principle for the design and application of the Stewart platform and has great significance for the trajectory planning and control.

METH0D USED IN SINGULARITY RESEARCH BASED 0N KINEMATICS AND ITS EXAMPLE IN APPLICATION

First the kinematic principle of singularity is proved, that is theintersecting point of three normal planes of three velocities at three non-collinear points in arigid body lying in the plane determined by the three corresponding points. It is a sufficient andnecessary condition that the velocities of three non-collinear points in a rigid body can determinea screw motion of the body. Based on this principle, a simple and direct new method to distinguishthe singularity of the parallel manipulator is derived. With this new kinematic method, the 3-RPSparallel manipulator is studied. Its singularity loci are obtained for some orientations for thefirst time and verified with Grassmann line geometry and screw theory and the force Jacobian matrix.

COUPLING EFFECT OF FLEXIBLE JOINT AND FLEXIBLE LINK ON DYNAMIC SINGULARITY OF FLEXIBLE MANIPULATOR

The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived. Secondly, the relationship and property between the flexible joint and the flexible link are analyzed. It shows that the flexible joint＇s amplitude will increase abruptly, thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link. Finally, some numerical simulations which will verify the correctness of the theoretical analysis, are carded out. The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.

Reciprocal Screw Theory Based Singularity Analysis of a Novel 3-DOF Parallel Manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.

Variation of singularity of earthquake-size distribution with respect to tectonic regime

Frequency-size relation of earthquakes in a region can be approximated by the Gutenberg-Richter law(GR). This power-law model involves two parameters: a-value measuring seismic activity or earthquake productivity, and b-value describing the relation between frequencies of small and large earthquakes.The spatial and temporal variations of these two parameters, especially the b-value, have been substantially investigated. For example, it has been shown that b-value depends inversely on differential stress. The b-value has also been utilized as earthquake precursor in large earthquake prediction.However, the physical meaning and properties of b-value including its value range still remain as an open fundamental question. We explore the property of b-value from frequency-size GR model in a new form which relates average energy release and probability of large earthquakes. Based on this new form of GR relation the b-value can be related to the singularity index(1-2/3 b) of fractal energy-probability power-law model. This model as applied to the global database of earthquakes with size M ≥ 5 from 1964 to 2015 indicates a systematic increase of singularity from earthquakes occurring on mid-ocean ridges, to those in subduction zones and in collision zones.

Geometric Analysis of Singularity for Single-Gimbal Control Moment Gyro Systems

This research is focused on the singularity analysis for single-gimbal control moment gyros systems （SCMGs） which include two types, with constant speed （CSCMG） or variable speed （VSCMG） rotors. Through angular momentum hypersurfaces of singular states, the passable and impassable singular points are discriminated easily, meanwhile the information about how much the angular momentum workspace as well as the steering capability available is provided directly. It is obvious that the null motions of steering laws are more effective for the five pyramid configuration（FPC） than for the pyramid configuration（PC） from the singular plots. The possible degenerate hyperbolic singular points of the preceding configurations are calculated and the distinctness of them is denoted by the Gaussian curvature. Furthermore, failure problems to steer integrated power and attitude control system （IPACS） are also analyzed. A sufficient condition of choosing configurations of VSCMGs to guarantee the IPACS steering is given. The angular momentum envelops of VSCMGs, in a given energy and a limited range of rotor speeds, are plotted. The connection and distinctness between CSCMGs and VSCMGs are obtained from the point of view of envelops.

Solution with Singularity of Order One for Singular Integral Equation with Hilbert Kernal

The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.

PROPERTY IDENTIFICATION OF SINGULARITY LOCI OF GOUGHSTEWART MANIPULATOR

The problem of identifying the property of singularity loci of Gough-Stewart manipulators is addressed. After constructing the Jacobian matrix of the Gough-Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constantorientation singularity locus of the manipulator, is derived. Graphical representations of the singularity locus of the manipulator for different orientations are illustrated with examples. Further, the singularity locus of the manipulator in the principal-section, where the mobile platform lies, is analyzed. It shows that singularity loci of the ,manipulator in parallel principal-sections are all quadratic expressions including a parabola, four pairs of intersecting straight lines and infinite hwerbolas. Their geometric and kinematic properties are also researched as well.

Singularity analysis of Jeffcott rotor-magnetic bearing with time delays

A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center manifold reduction and normal form are employed to study the bifurcation from simple zero and zero-purely imaginary singularities. The results of this paper will help to understand the influence of the time delays in feedback loop on the dynamics of rotor-magnetic bearing system.

STUDY OF REGULARITY OF GENERAL-LINEAR-COMPLEX SINGULARITY OF 3/6-STEWART MECHANISM

The general-linear-complex singularity of Stewart mechanism is a veryimportant problem in the parallel manipulator. Its general regularity is not found yet during thepast two decades. St-Onge and Gosselin pointed Out that the singularity locus of the Stewartmechanism at some given orientations of the moving platform should be polynomial expressions withvaried degrees in 2000, but they didn't formulate the expression. Based on the kinematicssingularity principle and the geometry condition proposed by Huang Zhen in 1999, firstly thesingularity equation in degree two is derived. It is a hyperbola when the orientation of the movingplatform is given. This result is also proved using screw theory. Then some singularity surfaces aregotten in three-dimensional space. This result is of important significance.

On Generating Expected Kinetostatic Nonlinear Stiffness Characteristics by the Kinematic Limb-Singularity of a Crank-Slider Linkage with Springs

Being di erent from avoidance of singularity of closed-loop linkages, this paper employs the kinematic singularity to construct compliant mechanisms with expected nonlinear sti ness characteristics to enrich the methods of compliant mechanisms synthesis. The theory for generating kinetostatic nonlinear sti ness characteristic by the kinematic limb-singularity of a crank-slider linkage is developed. Based on the principle of virtual work, the kinetostatic model of the crank-linkage with springs is established. The influences of spring sti ness on the toque-position angle relation are analyzed. It indicates that corresponding spring sti ness may generate one of four types of nonlinear sti ness characteristics including the bi-stable, local negative-sti ness, zero-sti ness or positive-sti ness when the mechanism works around the kinematic limb-singularity position. Thus the compliant mechanism with an expected sti ness characteristic can be constructed by employing the pseudo rigid-body model of the mechanism whose joints or links are replaced by corresponding flexures. Finally, a tri-symmetrical constant-torque compliant mechanism is fabricated,where the curve of torque-position angle is obtained by an experimental testing. The measurement indicates that the compliant mechanism can generate a nearly constant-torque zone.

Stress singularity analysis of anisotropic multi-material wedges under antiplane shear deformation using the symplectic approach

Symplectic approach has emerged a popular tool in dealing with elasticity problems especially for those with stress singularities. However, anisotropic material problem under polar coordinate system is still a bottleneck. This paper presents a subfield method coupled with the symplectic approach to study the anisotropic material under antiplane shear deformation. Anisotropic material around wedge tip is considered to be consisted of many subfields with constant material properties which can be handled by the symplectic approach individually. In this way, approximate solutions of the stress and displacement can be obtained. Numerical examples show that the present method is very accurate and efficient for such wedge problems. Besides, this paper has extended the application of the symplectic approach and provides a new idea for wedge problems of anisotropic material.