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. .

医科达INFINITY直线加速器机架旋转系统简析

目前,临床上的医用电子直线加速器主要是用于肿瘤疾病放射治疗的一种微波电子直线加速器,是临床上放射治疗中较为常用的设备之一,用于放射治疗的原理在于通过运用高能电子打靶进而产生韧致X射线,照射病灶区后,进而达到抑制和控制肿瘤发展的目的。而医科达INFINITY直线加速器机架旋转系统,能够帮助患者在照射治疗的过程中稳定运转设备,减少故障发生,为患者后续治疗提供更优质的保障。

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.

Hilbert’s First Problem and the New Progress of Infinity Theory

In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.

Uniqueness of Viscosity Solutions to the Dirichlet Problem Involving Infinity Laplacian

In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution.

Lipschitz Regularity of Viscosity Solutions to the Infinity Laplace Equation

In this paper, we study the viscosity solutions of the Neumann problem in a bounded C2 domain Ω, where ΔN∞ is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .

Infinity HE高清恒染系统在病理常规染色中的应用

在日常病理工作中,为保证HE染色的质量,一般染片1 500~1 800张需更换染液。由于苏木精氧化持续等因素的存在,每张切片进行染色时试剂所处的状态不一致,也无法做到每张切片着色均一。在相对固定的染色程序中寻找稳定性较高的染液,保证在一定染片数量范围内每张切片着色均一,成为病理工作者致力解决的问题之一。本文就Infinity高清恒染系统在常规病理染色的稳定性进行评价。

Infinity高清恒染系统在常规HE自动化染色中的应用及染色持续能力的对比观察

目前我国常规病理诊断中使用最多的HE染色方法为传统的手工染色。手工HE染色过程繁琐、工作效率低、随意性强,不同的人操作会出现明显的波动,HE染色效果不稳定。试剂的配置和染色过程也费时、费力,要占用技术员大量的时间和精力,也不利于常规病理的质量控制,尤其在工作量大的综合性医院中,此缺点尤为突出。

H-infinity鲁棒滤波增益研究

基于Krein空间状态模型,深入分析H-infinity滤波增益,提出了广义滤波增益、增益失调因子等相关概念,并给出了H-infinity滤波器鲁棒性机理及H-infinity滤波器发散原因等相关结论。在此基础上,建立了一套结构化算法,清晰地描述了H-infinity滤波的两个计算回路和两个更新过程。仿真结果证明了相关结论的正确性。

An Analytical Study of Leibniz’s Secant and Tangent on the Logical Basis of Mathematical Infinity

Refs 1 and 2 provide the definition of the concepts of‘potential infinity’(poi)and actual infinity(aci);Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate(p,-p).The second part of this paper,i.e.,§2,further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that,in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A).Finally,on the basis of this conclusion,we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions.

Mathematical Infinity and Medium Logic （I） --Logical-mathematical Interpretation of Leibniz＇s Secant and Tangent Lines Problem in Medium Logic

From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in 'unmediated opposition' (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz's secant and tangent lines in the medium logic system from the perspective of logical mathematics.

安捷伦科技公司推出用于1290 Infinity Ⅱ液相色谱系统的新型自动进样器

本刊讯（记者申海鹏）7月6日,安捷伦科技公司推出了第二款适用于超高效1290 Infinity II液相色谱系统的自动进样器。新型1290 Infinity II样品瓶进样器能够缩短进样周期、减少交叉污染并提高样品容量,同时压力范围最高可达到1300bar。此款全新模块在瑞士日内瓦举办的高效液相色谱分离及相关技术的国际研讨会HPLC 2015上首次亮相。安捷伦科技公司副总裁兼液相色谱产品事业部总经理Stefan Schuette博士表示：＂借助这款新产品,

H infinity Control for Sandwiched Maglev Stage with Dynamic Damping

An H infinity(H∞)controller for a sandwiched maglev positioning stage is proposed.The maglev positioning stage has a special structure:a sandwiched maglev stage,consisting of repulsive linear motors and attractive linear motors,which have better levitation performance.Forces on the sandwiched maglev stage are analyzed and modeled.The positioning controller is designed based on the feedback linearized model with a dynamic damping system.The design of the H infinity controller for stage positioning is derived as a series of linear matrix inequalities(LMIs)which are efficiently solved in Matlab.The proposed controller and its effectiveness is demonstrated compared to PID method.

医科达Infinity直线加速器X线容积成像系统故障分析与维修四例

图像引导放疗技术为肿瘤疾病的精确治疗提供了强有力的技术保障。X线容积成像(X-ray volumetric images,XVI)系统是图像引导放疗技术的成像系统,主要由kV级X线球管、探测器及图像处理工作站组成。在机架旋转过程中,球管发出锥形束X线,采集患者不同角度的影像数据并传输到工作站重建成三维图像,通过与定位图像配准后得到X、Y、Z轴3个方向的位移误差,治疗师可在线校准误差,以实现精准治疗[1-2]。

THE HYPERMEDIA DATA MODEL BASED ON THE INFINITY IMAGE

This paper presents the hypermedia data model based on the infinity RS image information system we have developed.The hypermedia data model consists of different semantic units called nodes,and the associations between nodes are called links.This paper proposes three kinds of nodes (interior node,physical node and complex node) and two kinds of links (plane network structure link,hyper_cube network structure links).The hypermedia information system,based on the model and the basic data layer (the infiniy RS image),represents a digital globe.An approach to the “Getting Lost in the Hyper_space” problem is presented.The approach using the hypermedia data model is an efficient way of handling a large number of RS images in various geographical information systems.

安捷伦科技公司推出全新1200 Infinity液相色谱系列产品

北京一安捷伦科技公司于2010年6月21日推出1200Infinity系列产品。该系列产品包括新的Agilent 1220Infinity LC、Agilent 1260 Infinity LC以及增强型Agilent 1290 Infinity LC，采用最新的1200系列快速高分离度液相色谱（RRLC）和1290 Infinity LC技术，是色谱柱技术、仪器以及软件的完美结合。她的推出为液相色谱技术的发展翻开了新的一页。

任无穷幻变 自稳固于心 全新Agilent 1260 Infinity Ⅱ液相色谱仪

日复一日持续稳定运行的液相色谱平台值得您的信赖.Agilent 1260 Infinity II液相色谱系统为您提供更广泛的仪器选择,更佳的操作,使您对结果更有信心-任无穷幻变,自稳固于心.

INFINITY——船舶通信解决方案介绍

INFINITY是一个专门为海上业务设计的全带宽管理及优化的船舶通信解决方案,适用于所有基于IP的通信业务。INFINITY包含一个适合于安装在船上的工业级的PC或服务器,一个云实例、船方和岸方INFINITY软件及一个友好的IT管理员可以集中管理所有的INFINITY组件和产品的用户网页界面,支持船员通信业务,客户可以和船员共享套餐包内的数据量。