More Compactification for Differential Systems

This article is a review and promotion of the study of solutions of differential equations in the “neighborhood of infinity” via a non traditional compactification. We define and compute critical points at infinity of polynomial autonomuos differential systems and develop an explicit formula for the leading asymptotic term of diverging solutions to critical points at infinity. Applications to problems of completeness and incompleteness (the existence and nonexistence respectively of global solutions) of dynamical systems are provided. In particular a quadratic competing species model and the Lorentz equations are being used as arenas where our technique is applied. The study is also relevant to the Painlevé property and to questions of integrability of dynamical systems.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor

The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension Φ where Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ2 . To be wave and a particle simultaneously intersection theory leads us to?(Φ) (Φ)2= Φ3 which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the M&#246bius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional M&#246bius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordinary energy density of spacetime E(O)=(Φ5/2) mc2 we now have P (Casimir) = (Φ3/2)(ch/d2) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc2 which can be written as E = E (O) + E (D)?where the exact rational approximation is E (O)=mc2/22 is?the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc2/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc2/(5/22)?+mc2/(16/22)??where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □?22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D=?4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.

The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

In this short survey, we give a complete list of the most important results obtained by El Naschie’s E-infinity Cantorian space-time theory in the realm of quantum physics and cosmology. Special attention is paid to his recent result on dark energy and revising Einstein’s famous formula .

From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos

Starting from well established results in pure mathematics, mainly transfinite set theory, E-infinity algebra over operads, fuzzy manifolds and fuzzy Lie symmetry groups, we construct an exact Weyl scaling for the highly structured E-infinity rings corresponding to E-infinity theory of high energy physics. The final result is an exact expression for the energy density of the cosmos which agrees with previous analysis as well as accurate cosmological measurements and observations, such as COBE, WMAP and Planck. The paper is partially intended as a vivid demonstration of the power of pure mathematics in physics and cosmology.

E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment

Using powerful concepts and tools borrowed from the seminal arsenal connecting physics fundamentals with esoteric set theoretical operations developed in recent years by Alexandria E-infinity theoretician M. S. El Naschie, this paper explores the deep implications of some of the dualities Dr El Naschie has identified and analyzed in his exposes, connecting them with our own Xonic Quantum Physics (XQP) which places dynamical action rather than spacetime and energy at the core of the System of the World.

区块链游戏生态的角色动态识别与演化分析——以Axie Infinity为例

针对区块链游戏生态的复杂性,提出一种基于时序有向加权网络的新型角色识别方法。该方法首先设计了节点投票算法ChainVoteRank以识别出关键基础角色,然后结合多特征融合的层次聚类算法挖掘潜在的隐蔽角色。以play-to-earn(P2E)模式区块链游戏Axie Infinity为对象进行研究,结果表明该P2E模式区块链游戏生态中存在6种基本角色:劳工、正常玩家、经理、繁育商、交易商和机构组织。相较于传统角色识别方法,该方法不仅可以更好地识别出区块链游戏生态中的主要用户角色,而且还揭示了P2E模式区块链游戏生态的角色演化过程、不同阶段中各角色发挥的作用,以及P2E生态日益严重的贫富差距。

From a Dual Einstein-Kaluza Spacetime to ‘tHooft Renormalon and the Reality of Accelerated Cosmic Expansion

We use a dual Einstein-Kaluza spacetime to calculate the exact energy density of dark energy and dark matter using a novel topological computation method. Starting from the said spacetime and ‘tHooft’s topological renormalon as well as the corresponding symmetry group, we show how the zero set quantum particle and the empty set quantum wave interact with the vacuum and give rise to pure dark energy and pure dark matter all along with ordinary energy density of the cosmos. The consistency of the exact calculation and the accurate observations attests to the reality of ‘tHooft’s renormalon dark matter, pure dark energy and accelerated cosmic expansion.

Reciprocity as an Ever-Present Dual Property of Everything

Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.

A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion

The well known finite elements Regge calculus is transformed to a triangulation in the hyperbolic plane using fractal Rindler wedges as tiling elements. The final result is an expanding de Sitter hyperbolic, i.e. Gauss-Bolyai-Lobachevsky universe with dark energy and ordinary energy densities in full agreement with cosmic observations and measurements. In the course of obtaining this vital result, the work addresses fundamental points connected to a host of subjects, namely Hardy’s quantum entanglement, an extension of Turing’s machine to a transfinite version, the phenomenon of measure concentration in the context of Banach-like spaces with high dimensionality as well as the pioneering work on the relation between quantum entanglement and computational efficiency.

EVG6200 Infinity掩模对准曝光机

总部设在奥地利的EV集团针对晶圆凸点和芯片级封装、MEMS、化合物半导体、功率器件及纳米技术设计的EVG6200 Infinity掩模对准曝光机，可以近距离对很厚的阻光层近距离曝光，能够通过升级、安装底部显微镜进行MEMS的双面曝光。

EVG展出最新掩模对准曝光机EV6200 INFINITY

在晶圆键合光刻设备领域领先的EVG近日在SEMICON China 2005展出了其最新的EVG6200 Infinity掩模对准曝光机，该机可以在近距离对很厚的整个阻光层近距离曝光，是针对先进的封装市场而设计的，它可以通过升级安装底部显微镜，用于MEMS的双面曝光。在市场上所有200mm掩模对准曝光机中，这种新的曝光机是而积最小、产量最高的，光刻间隙的设定也是最精确的。

医科达Infinity医用电子直线加速器多例维修案例分析探讨

医科达Infinity医用电子直线加速器是一种精密的放射治疗设备,用于肿瘤等疾病的治疗。然而,由于设备的复杂性和使用频率,设备在运行过程中可能会出现包括硬件故障、软件故障和系统设置故障等。对于这些故障,需要进行详细的故障分析,找出故障点并进行修复或更换。同时,需要对Infinity加速器进行定期的保养,以确保其能正常稳定工作并尽可能延长设备使用寿命和降低故障发生率。本文将对医科达Infinity医用电子直线加速器的多例故障维修进行详细的介绍,包括设备维护、故障排除、维修技巧等并详细介绍Infinity加速器的具体维护保养方法,以便同行进行查阅探讨。

QED Cosmic Dark Energy Density Using Schwinger-Fredkin and E-Infinity Theory

The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark energy via a golden mean scaling-super quantization of the electromagnetic field.

The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures

This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.

An Exact Mathematical Picture of Quantum Spacetime

Using von Neumann’s continuous geometry in conjunction with A. Connes’ noncommutative geometry an exact mathematical-topological picture of quantum spacetime is developed ab initio. The final result coincides with the general conclusion of E-infinity theory and previous results obtained in the realm of high energy physics. In particular it is concluded that the quantum particle and the quantum wave spans quantum spacetime and conversely quantum particles and waves mutates from quantum spacetime.

Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology

Using Dvoretzky’s theorem in conjunction with Bohm’s picture of a quantum particle inside a guiding quantum wave akin to De Broglie-Bohm pilot wave we derive Einstein’s famous formula E = mc2 as the sum of two parts E(O) = mc2/22 of the quantum particle and E(D) = m c2 (21/22) of the quantum wave where m is the mass, c is the speed of light and E is the energy. In addition we look at the problem of black holes information in the presence of extra dimensions where it seems initially that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. Again this surprising result is a consequence of the same well known theorem on measure concentration due to I. Dvoretzky. We conclude that there are only two real applications of the theorem and we expect that many more applications in physics and cosmology will be found in due course.

<i>E</i>Infinity, the Zero Set, Absolute Space and the Photon Spin

As defined and used in General Relativity calculations, spacetime is a strictly classical construct which does not incorporate in any way, shape or form the concept of quantum. While reviewing the efforts that Alexandria theoretician M. S. El Naschie has made to resolve the dichotomy, we discovered that his E infinity theory contains a Cantor set which has characteristics specified by Isaac Newton for Absolute space. We show that this unexpected connection leads to an understanding of the mysterious origin of the one and only attribute that all particles listed in the Standard Model of Elementary Particles possess—including notably the photon—and which has remained unexplained hitherto: spin. This most rewarding result reinforces our belief in the relevance of the E infinity basic concepts in relation to our own Xonic Quantum Physics (XQP) which places dynamical action rather spacetime and energy at the core of the System of the World.

基于自适应H_(∞)观测器的锂电池SOC与容量联合估计

为了提高锂电池SOC的估计精度,提出了一种基于自适应H_(∞)观测器的锂电池SOC与容量联合估计方法。基于锂电池的二阶RC等效电路模型,并考虑SOC和容量的耦合关系,将容量也作为系统的状态变量进行观测。设计了一种自适应H_(∞)观测器,其参数可随锂电池状态的变化自适应调整。由于在SOC估算时考虑了容量的影响,实现了SOC和容量的同时准确估计。实验结果表明:自适应H_(∞)观测器的估计精度高且鲁棒性强,电池的SOC平均估计误差始终保持在±0.43%以内,相比于EKF和H_(∞)观测器有更高的估计精度与稳定性。

Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy

The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.