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Extra Time Dimension: Deriving Relativistic Space-Time Transformations, Kinematics, and Example of Dimensional Compactification Using Time-Dependent Non-Relativistic Quantum Mechanics
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作者 Sajjad Zahir 《Journal of Modern Physics》 2023年第10期1333-1354,共22页
We consider a five-dimensional Minkowski space with two time dimensions characterized by distinct speeds of causality and three space dimensions. Formulas for relativistic coordinate and velocity transformations are d... We consider a five-dimensional Minkowski space with two time dimensions characterized by distinct speeds of causality and three space dimensions. Formulas for relativistic coordinate and velocity transformations are derived, leading to a new expression for the speed limit. Extending the ideas of Einstein’s Theory of Special Relativity, concepts of five-velocity and five-momenta are introduced. We get a new formula for the rest energy of a massive object. Based on a non-relativistic limit, a two-time dependent Schrödinger-like equation for infinite square-well potential is developed and solved. The extra time dimension is compactified on a closed loop topology with a period matching the Planck time. It generates interference of additional quantum states with an ultra-small period of oscillation. Some cosmological implications of the concept of four-dimensional versus five-dimensional masses are briefly discussed, too. 展开更多
关键词 Two-Time Physics Special Theory of Relativity Kaluza-Klein Theory Time-Dependent Schrödinger Equation compactification
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Effects of Compactification on Free Massive Scalar Fields in Five-Dimensional Space-Time with an Extra Time Dimension: Analysing Some Results
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作者 Sajjad Zahir 《Journal of Modern Physics》 2023年第12期1600-1616,共17页
This paper deals with some aspects of two-time physics (i.e., 2T + 3S five-dimensional space) for a Minkowski-like space with distinct speeds of causality for the time dimensions. Detailed calculations are provided to... This paper deals with some aspects of two-time physics (i.e., 2T + 3S five-dimensional space) for a Minkowski-like space with distinct speeds of causality for the time dimensions. Detailed calculations are provided to obtain results of Kaluza-Klein type compactification for free massive scalar fields and abelian free gauge fields. As already indicated in the literature, a tower of massive fields results from the compactification with mass terms having signs opposite to those of the ones appearing in other five-dimensional theories with an extra space dimension. We perform elaborate numerical calculations to highlight the magnitude of the imaginary masses and ask if we need to explore alternative compactification techniques. 展开更多
关键词 Two-Time Physics Theory of Special Relativity Kaluza-Klein Theory compactification Klein-Gordon Equation TACHYONS Abelian Gauge Theory
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On the Inverse Limit of Higson Compactifications 被引量:1
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作者 曹阳 孙以丰 《Northeastern Mathematical Journal》 CSCD 2002年第2期95-98,共4页
Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) ... Higson have introduced the conception of "Higson’s corona" (see [1]). For a given metric space X, it is a kind of compactification of X related to the metric d on it. Denote by BR(X) the set {y ∈ X\d(x,y) < R}. Recall that a slowly oscillating function on X is a function f G C*(X) satisfying the following condition: 展开更多
关键词 Stone-Cech corapactification Higson compactification coarse equivalent
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Resolvable Spaces and Compactifications
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作者 Monerah Al-Hajri Karim Belaid 《Advances in Pure Mathematics》 2013年第3期365-367,共3页
This paper deals with spaces such that their compactification is a resolvable space. A characterization of space such that its one point compactification (resp. Wallman compactification) is a resolvable space is given.
关键词 RESOLVABLE SPACE Alexandroff compactification Wallman compactification
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A&zeta;x- and Open <i>C<sub>D</sub><sup>*</sup></i>-Filters Process of Compactifications and Any Hausdorff Compactification
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作者 Hueytzen J. Wu Wan-Hong Wu 《Advances in Pure Mathematics》 2012年第4期296-300,共5页
By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding... By means of a characterization of compact spaces in terms of open CD*-filters induced by a , a - and open CD*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , YS = {ε |ε is an open CD*-filter that does not converge in Y}, YT = {A|A is a basic open CD*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Ysw (or YTw)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X?can be obtained from a by the?similar process in Sec.3. 展开更多
关键词 Net OPEN FILTER OPEN CD*-Filter Base Basic OPEN CD*-Filter OPEN CD*-Filter -Filter x-Filter Tychonoff Space Normal T1-Space Compact Space compactificationS Stone-Cech compactification Wallman compactification
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Proof That Spatial Transitions Release/Absorb Energy That Compactification Necessarily Leads to Changes in Volume, Energy and Entropy
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作者 Christopher Pilot 《Journal of High Energy Physics, Gravitation and Cosmology》 2019年第2期310-320,共11页
Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasi... Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasing spatial dimension for a given number of particles costs energy while decreasing dimensions supplies energy, which can be quantified, using a generalized version of the Clausius-Clapyeron relation. We show this explicitly for massive particles trapped in a box. Compactification from N -dimensional space to (N - 1) spatial dimensions is also simply demonstrated and the correct limit to achieve a lower energy result is to take the limit, Lw → 0, where Lw is the compactification length parameter. Higher dimensional space has more energy and more entropy, all other things being equal, for a given cutoff in energy. 展开更多
关键词 SPATIAL TRANSITIONS Box Quantization compactification
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An Expository on Some Nonstandard Compactifications
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作者 Alagu Somasundaram Rukhmoni Kala 《Advances in Pure Mathematics》 2021年第10期807-815,共9页
Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The gen... Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup><em>X </em>of the space <em>X</em> which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every <em>f</em> in <em>C</em>(<em>X</em>,<em>R</em>) (the space of bounded continuous real valued functions on <em>X</em>) or <em>Cc</em>(<em>X</em>,<em>R</em>) (the space of continuous real valued functions on <em>X</em> with compact support) or the dual group <span style="white-space:nowrap;">&#915; </span>of the locally compact Abelian group <em>G</em> is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of <em>f</em>. Then <em>X</em> is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />. 展开更多
关键词 Non-Standard compactification Completely Regular Space Locally Compact Hausdorff Space Locally Compact Abelian Group
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QUOTIENT SPACE OF LMC-COMPACTIFICATION AS A SPACE OF z-FILTERS
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作者 Mohammad Akbari Tootkaboni 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期2010-2020,共11页
The left multiplicative continuous compactification is the universal semigroup compactification of a semitopological semigroup.In this paper an internal construction of a quotient space of the left multiplicative cont... The left multiplicative continuous compactification is the universal semigroup compactification of a semitopological semigroup.In this paper an internal construction of a quotient space of the left multiplicative continuous compactification of a semitopological semigroup is constructed as a space of z-filters 展开更多
关键词 LMC-compactification z-filters quotient space
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More Compactification for Differential Systems
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作者 Harry Gingold Daniel Solomon 《Advances in Pure Mathematics》 2013年第1期190-203,共14页
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 ... 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. 展开更多
关键词 Nonlinear Polynomial compactification Ultra Extended Euclidean Space CRITICAL POINT Equilibrium POINT CRITICAL POINT at INFINITY CRITICAL Direction at INFINITY BASIN of Divergence BASIN of Convergence Ideal Solutions Asymptotic Stability Global Globally Asymptotically Stable Jacobian Painleve Analysis Competing Species Model Lorenz Equations Periodic Surface Differential Geometry Attractor REPELLER
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A Modified Wallman Method of Compactification
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作者 Hueytzen J.Wu Wan-Hong Wu 《Advances in Pure Mathematics》 2013年第6期590-597,共8页
Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(... Closed and basic closed C*D-filters are used in a process similar to Wallman method for compactifications of the topological spaces Y, of which, there is a subset of C*(Y) containing a non-constant function, where C*(Y) is the set of bounded real continuous functions on Y. An arbitrary Hausdorff compactification (Z,h) of a Tychonoff space X can be obtained by using basic closed C*D-filters from in a similar way, where C(Z) is the set of real continuous functions on Z. 展开更多
关键词 Closed █_(x)-Filter Open and Closed C^(*)_(D)-Filter Bases Basic Open and Closed C^(*)_(D)-Filters compactification Stone-Cech and Wallman compactifications
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A Inherent Characterization of L-fuzzy Compactification
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作者 孟培源 周武能 《湖北科技学院学报》 1994年第1期1-9,共9页
AInherentCharacterizationofL-fuzzyCompactification¥Mengpeiyuan(XianningTeachers'College,Hubei,China)Zhouwune... AInherentCharacterizationofL-fuzzyCompactification¥Mengpeiyuan(XianningTeachers'College,Hubei,China)Zhouwuneng(YunyangTeacher... 展开更多
关键词 α-ultra-closed filter Nice-compactness T_(1)-seperation L-fuzzy topological space compactification
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最小Q-过程的Martin流入边界与Ray-Knight紧化 被引量:4
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作者 徐长伟 阎国军 郝淑双 《应用概率统计》 CSCD 北大核心 2011年第6期633-641,共9页
郝淑双(黄河科技学院信息工程学院,郑州,450063)本文讨论了在最小Q-过程不中断的条件下Martin流入边界与Ray-Knight紧化之间的关系,即在Martin流入边界有限的条件下,Martin流入边界中的点与Ray-Knight紧化所添加的点之间具有一一对应关系.
关键词 最小Q-过程 Martin流入边界 ray-knight紧化 右过程
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最小Q-过程的Ray-Knight紧化与Martin边界关系的实例分析
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作者 郝淑双 徐长伟 《通化师范学院学报》 2014年第6期28-30,共3页
文中在极小转移函数Pminij(t)诚实的条件下讨论最小Q-过程的Martin流出边界与Ray-Knight紧化的关系,并实例分析Martin流入边界与Ray-Knight紧化所添加的点之间具有一一对应关系.
关键词 最小Q-过程 ray-knight紧化 Martin流出边界 Martin流入边界
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NO<sub>2</sub>Excited State Properties Revisited: An Effect of Extra Compactified Dimensions
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作者 Hans-Georg Weber 《Journal of Modern Physics》 2017年第11期1749-1761,共13页
Experiments on NO2 reveal a substructure underlying the optically excited isolated hyperfine structure (hfs) levels of the molecule. This substructure is seen in a change of the symmetry of the excited molecule and is... Experiments on NO2 reveal a substructure underlying the optically excited isolated hyperfine structure (hfs) levels of the molecule. This substructure is seen in a change of the symmetry of the excited molecule and is represented by the two “states” and of a hfs-level. Optical excitation induces a transition from the ground state of the molecule to the excited state . However, the molecule evolves from to in a time τ0 ≈ 3 μs. Both and have the radiative lifetime τR ≈ 40 μs, but and differ in the degree of polarization of the fluorescence light. Zeeman coherence in the magnetic sublevels is conserved in the transition &rarr;, and optical coherence of and is able to affect (inversion effect) the transition &rarr;. This substructure, which is not caused by collisions with baryonic matter or by intramolecular dynamics in the molecule, contradicts our knowledge on an isolated hfs-level. We describe the experimental results using the assumption of extra dimensions with a compactification space of the size of the molecule, in which dark matter affects the nuclei by gravity. In , all nuclei of NO2 are confined in a single compactification space, and in , the two O nuclei of NO2 are in two different compactification spaces. Whereas and represent stable configurations of the nuclei,represents an unstable configuration because the vibrational motion in shifts one of the two O nuclei periodically off the common compactification space, enabling dark matter interaction to stimulate the transition &rarr;with the rate (τ0)&minus;1. We revisit experimental results, which were not understood before, and we give a consistent description of these results based on the above assumption. 展开更多
关键词 EXTRA DIMENSIONS compactification Space DARK Matter Molecular Physics
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Equivariant R-Test Configurations and Semistable Limits of Q-Fano Group Compactifications
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作者 Yan Li Zhenye Li 《Peking Mathematical Journal》 CSCD 2023年第2期559-607,共49页
Let G be a connected,complex reductive group.In this paper,we classify G×G equivariant normal R-test configurations of a polarized G-compactification.Then,for Q-Fano G-compactifications,we express the H-invariant... Let G be a connected,complex reductive group.In this paper,we classify G×G equivariant normal R-test configurations of a polarized G-compactification.Then,for Q-Fano G-compactifications,we express the H-invariants of their equivariant normal R-test configurations in terms of the combinatory data.Based onHan and Li“Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties”,we compute the semistable limit of aK-unstable FanoG-compactification.As an application,we show that for the two smooth K-unstable Fano SO4(C)-compactifications,the corresponding semistable limits are indeed the limit spaces of the normalized Kähler-Ricci flow. 展开更多
关键词 Kähler-Ricci solitons Kähler-Ricci flow Q-Fano compactifications K-stability
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An infinite-dimensional representation of the Ray-Knight theorems
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作者 Elie Aidékon Yueyun Hu Zhan Shi 《Science China Mathematics》 SCIE CSCD 2024年第1期149-162,共14页
The classical Ray-Knight theorems for the Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin,or at the first hitting time of... The classical Ray-Knight theorems for the Brownian motion determine the law of its local time process either at the first hitting time of a given value a by the local time at the origin,or at the first hitting time of a given position b by the Brownian motion.We extend these results by describing the local time process jointly for all a and b,by means of the stochastic integral with respect to an appropriate white noise.Our result applies toμ-processes,and has an immediate application:aμ-process is the height process of a Feller continuous-state branching process(CSBP)with immigration(Lambert(2002)),whereas a Feller CSBP with immigration satisfies a stochastic differential equation(SDE)driven by a white noise(Dawson and Li(2012));our result gives an explicit relation between these two descriptions and shows that the SDE in question is a reformulation of Tanaka’s formula. 展开更多
关键词 ray-knight theorem μ-process white noise Tanaka's formula
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双边生灭过程的轨道结构与构造理论 被引量:4
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作者 陈丽 薛玲霞 +1 位作者 兰社云 刘利敏 《河南大学学报(自然科学版)》 CAS 北大核心 2012年第4期337-342,共6页
给出了双边生灭过程的轨道结构,用Markov链的Ray-Knight方法得到了强Markov过程X=(Ω,F,Ft,Xt,θt,Px),它克服了在Markov链通常构造的典范链的只具有右下半连续性及仅保持部分强Markov性的缺陷,并从∞是流入的、∞是流出的、∞是自然的... 给出了双边生灭过程的轨道结构,用Markov链的Ray-Knight方法得到了强Markov过程X=(Ω,F,Ft,Xt,θt,Px),它克服了在Markov链通常构造的典范链的只具有右下半连续性及仅保持部分强Markov性的缺陷,并从∞是流入的、∞是流出的、∞是自然的、∞是正则的等几个方面指出双边生灭轨道结构与构造理论之间的对应关系. 展开更多
关键词 双边生灭过程 Martin流出边界 ray-knight紧化 右过程 正则点
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生灭过程的轨道结构 被引量:3
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作者 赵晓晶 阎国军 《应用概率统计》 CSCD 北大核心 2013年第1期10-22,共13页
本文中我们给出了生灭过程的轨道结构,指出轨道结构与构造理论之间的一一对应关系,并且利用Ito游程理论说明构造理论中各个参数的概率含义.
关键词 生灭过程 Martin流出边界 ray-knight紧化 右过程 正则点 Ito游程理论
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双边生灭过程的轨道结构与构造理论(Ⅱ) 被引量:2
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作者 陈丽 薛玲霞 《河南大学学报(自然科学版)》 CAS 北大核心 2013年第1期5-10,共6页
利用Markov链的Ray-Knight方法继续给出双边生灭过程的轨道结构和构造理论,指出轨道结构与构造理论之间的对应关系,并且说明构造理论中各个参数的概率含义.
关键词 双边生灭过程 Martin流出边界 ray-knight紧化 右过程
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双边生灭过程的轨道结构与Motoo理论 被引量:1
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作者 陈丽 薛玲霞 《郑州大学学报(理学版)》 CAS 北大核心 2014年第1期42-46,共5页
主要研究双边生灭过程的轨道结构和构造理论中的生灭过程与Motoo理论之间的对应关系,并且说明了构造理论中各个参数的概率含义.
关键词 双边生灭过程 ray-knight紧化 右过程 Motoo理论
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