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.

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.

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.

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。

The Urban Singularity-Envisioning the Future of Cities

This paper is a hypothetical exploration of the connections between teleological evolution,the Omega Singularity,and the future of cities,weaving together insights from a diverse array of disciplines.Our investigation delves into the possibility that cities are evolving towards a Singularity,a state characterized by infinite knowledge,intelligence,and adaptability,which would bring about a radical transformation of urban environments and their underlying dynamics in the 21st century and beyond.At the heart of this exploration lies the role of language and time as crucial dimensions of the Urban Singularity.Moreover,we examine how linguistic developments and cross-cultural exchanges can foster more inclusive,adaptable,and resilient urban environments,while also highlighting the need for advanced technologies and communication modalities that can support the dynamic needs of future cities.Furthermore,the paper investigates the profound implications and transformative potential of merging human consciousness with the urban Singularity.By examining the interplay between these concepts,we seek for a deeper understanding of the potential trajectories and implications of these concepts for the transformation of human society and our relationship with the built environment.

Local singularity and S–A methods for analyzing ore-producing anomalies in the Jianbiannongchang area of Heilongjiang,China

The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.

Discrete vortex bound states with a van Hove singularity in the vicinity of the Fermi level

A theoretical study on discrete vortex bound states is carried out near a vortex core in the presence of a van Hove singularity(VHS) near the Fermi level by solving Bogoliubov–de Gennes(Bd G) equations. When the VHS lies exactly at the Fermi level and also at the middle of the band, a zero-energy state and other higher-energy states whose energy ratios follow integer numbers emerge. These discrete vortex bound state peaks undergo a splitting behavior when the VHS or Fermi level moves away from the middle of the band. Such splitting behavior will eventually lead to a new arrangement of quantized vortex core states whose energy ratios follow half-odd-integer numbers.

Self-Awareness,a Singularity of AI

Self-awareness,or self-consciousness,refers to reflective recognition of the existence of“subjective-self”.Every person has a subjective-self from which the person observes and interacts with the world.In this article,we argue that self-consciousness is an enigmatic phenomenon unique in human intelligence.Unlike many other intelligent and conscious capabilities,self-consciousness is not possible to be achieved in electronic computers and robots.Self-consciousness is an odd-point of human intelligence and a singularity of artificial intelligence(AI).Man-made intelligence through software is not capable of self-consciousness;therefore,robots will never become a newly created species.Because of the lack of self-awareness,AI software,such as Watson,Alpha-zero,ChatGPT,and PaLM,will remain a tool of humans and will not dominate the human society no matter how smart it is.This singularity of AI makes us re-think humbly what the future AI is like,what kind of robots we are going to deal with,and the blessing and threat of AI on humanity.

Singularity Formation forthe General Poiseuille Flow of Nematic Liquid Crystals

We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.

Singularity of Two Kinds of Quadcyclic Peacock Graphs

Let G be a graph. G is singular if and only if the adjacency matrix of graph G is singular. The adjacency matrix of graph G is singular if and only if there is at least one zero eigenvalue. The study of the singularity of graphs is of great significance for better characterizing the properties of graphs. The following definitions are given. There are 4 paths, the starting points of the four paths are bonded into one point, and the ending point of each path is bonded to a cycle respectively, so this graph is called a kind of quadcyclic peacock graph. And in this kind of quadcyclic peacock graph assuming the number of points on the four cycles is a1, a2, a3, a4, and the number of points on the four paths is s1, s2, s3, s4, respectively. This type of graph is denoted by γ (a1, a2, a3, a4, s1, s2, s3, s4), called γ graph. And let γ (a1, a2, a3, a4, 1, 1, 1, 1) = δ (a1, a2, a3, a4), this type four cycles peacock graph called δ graph. In this paper, we give the necessary and sufficient conditions for the singularity of γ graph and δ graph.

Homo Faber Scapegoated, or Apocalyptic Artificial Intelligence: Rethinking the Technological Singularity Concept From the Synergetic Historicism Position

The article is focused on discussing a new methodological approach to the study on specifics of transferring human beings to the posthuman cyber society.The approach in question assists in rethinking interconnected problems both of human origins in the universe and mankind’s digital future.And,besides,such an approach allows to deal with self-organising interconversions between the poles of the cardinal dual opposition of the Global Noosphere Brain and the Artificial General Intelligence.Herewith such phenomena of digital social life as Global Digitalisation,Digital Immortality,Mindcloning,and Technological Zombification being the constituents of Technological Singularity Concept,are rethought as paving the way for oncoming Posthuman Digital Era.This concept is evidently exemplified by a bifurcation resulting in two alternatives to be chosen by human beings,to wit,either to be undergone Mindcloning and become digitally immortal or being destroyed by powerful intelligent machines.The investigation in question is based on such a progressive methodology as the Law of Self-Organizing Ideals,as well as on the Method of Dual Oppositions.Rethinking interrelationships between the problem of a sense of social history and the meaning-of-life of local societies members which any intelligent machine is devoid of permits to substantiate specific regularities of Self-Transforming Homo Faber into Homo Digitalis and Technological Zombies ready to be transferred to posthuman cyberspace.

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.

Traversing the singularity hypersurface by applying the input disturbances to 6-SPS parallel manipulator

The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion un- certainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-flee region to another with a desired configuration.

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.

Integral Representation of the Manifold Solution for New Class of the Volterra Type Integral Equation with a Boundary Singularity in the Case, When Kernel Contain Logarithmic Singularity and its Power

In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.

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.

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.

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.

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.

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.