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New Quantum Color Codes Based on hyperbolic geometry

Journal of Quantum Computing 2022年第2期4卷 113-120页

作者： Avaz Naghipour Duc Manh Nguyen Department of Computer Engineering University College of Nabi AkramTabrizIran CIT Lab University of UlsanUlsan44610Korea

In this paper,hyperbolic geometry is used to constructing new quantum color *** use hyperbolic tessellations and hyperbolic polygons to obtain them by pairing the edges on compact *** codes have minimum distance of at least 4 and the encoding rate near to 1,which are not mentioned in other ***,a comparison table with quantum codes recently proposed by the authors is provided.

关键词： Color codes compact surfaces hyperbolic geometry tessellations

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Quantum Dark Energy from the hyperbolic Transfinite Cantorian geometry of the Cosmos

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Natural Science 2016年第3期8卷 152-159页

作者： Mohamed S. El Naschie Department of Physics University of Alexandria Alexandria Egypt

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

关键词： Dark Energy Accelerated Cosmic Expansion hyperbolic geometry Fractal geometry Transfinite set Theory ‘tHooft Dimensional Regularization Hardy’s Quantum Entanglement Davis hyperbolic Manifold Compactified Klein Modular Curve Fractal Counting Lie Symmetry Groups Stein Spaces

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Uniqueness of PL Minimal Surfaces

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Acta Mathematica Sinica,English Series 2007年第6期23卷 961-964页

作者： Yi NI Department of Mathematics Princeton University Princeton New Jersey 08544

Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to clarify some ambiguity, we sharpen the definition of PL minimal surfaces, and prove a technical lemma on the Plateau problem in the hyperbolic space.

关键词： PL minimal surface hyperbolic geometry Plateau problem

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On the Volume Formulas of Cones and Orthogonal Multi-cones in S^n(1) and H^n(-1)

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Chinese Annals of Mathematics,Series B 2006年第1期27卷 1-30页

作者： Wu-Yi HSIANG Dedicated to the memory of Shiing-Shen Chern Department of Mathematics The Hong Kong University of Science ＆ Technology Hong Kong China School of Mathematical Sciences Peking University Beijing 100871. China.

Abstract In the study of n-dimensional spherical or hyperbolic geometry, n≥3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in S^n（1） and H^n（-1）.

关键词： hyperbolic geometry Volume

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On a Quantum Gravity Fractal Spacetime Equation: QRG ≃HD + FG and Its Application to Dark Energy—Accelerated Cosmic Expansion

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Journal of Modern Physics 2016年第8期7卷 729-736页

作者： Mohamed S. El Naschie Department of Physics University of Alexandria Alexandria Egypt

The paper suggests that quantum relativistic gravity (QRG) is basically a higher dimensionality (HD) simulating relativity and non-classical effects plus a fractal Cantorian spacetime geometry (FG) simulating quantum mechanics. This more than just a conceptual equation is illustrated by integer approximation and an exact solution of the dark energy density behind cosmic expansion.

关键词： Fractal Cantorian Spacetime Quantum Relativity Superstrings Transfinite Set Theory Extra Spacetime Dimensions Quantum Physics Dark Energy Accelerated Cosmic Expansion Cosmic Topology hyperbolic geometry E-Infinity Theory Post Modernistic Physics

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A Sharper Parameter Bound for Belgian Chocolate Stabilization Problem

A Sharper Parameter Bound for Belgian Chocolate Stabilizatio...

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第26届中国控制与决策会议

作者： Wang Li Wensheng Yu Shanghai Key Laboratory of Trustworthy Computing East China Normal University

In this paper, we study the Belgian Chocolate Stabilization Problem. By using a complex analysis method,following Hempel and Smith’s technique, we compute the parameter bound of the stabilization problem ultimately. ... 详细信息

关键词： Belgian Chocolate Stabilization Problem complex analysis elliptic modular function hyperbolic geometry closed geodesic

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