اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPlaceholder Substructures III: A Bit-String-Driven Recipe Theory for Infinite-Dimensional Zero-Divisor Spaces
46
0
0.0
(
0
)
تأليف
Robert P. C. de Marrais
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any integer greater than 8 and not a power of 2 generates a meta-fractal or Sky when it is interpreted as the strut constant (S) of an ensemble of octahedral vertex figures called Box-Kites (the fundamental building blocks of ZDs). Remarkably simple bit-manipulation rules or recipes provide tools for transforming one fractal genus into others within the context of Wolframs Class 4 complexity.
قيم البحث
اقرأ أيضاً
Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent singularities and, as N approaches infinite, fractals -- and thereby,scale-free networks. Any integer great
er than 8 and not a power of 2 generates a meta-fractal or Sky when it is interpreted as the strut constant (S) of an ensemble of octahedral vertex figures called Box-Kites (the fundamental building blocks of ZDs). Remarkably simple bit-manipulation rules or recipes provide tools for transforming one fractal genus into others within the context of Wolframs Class 4 complexity.
In this paper, the Teichm{u}ller spaces of surfaces appear from two points of views: the conformal category and the hyperbolic category. In contrast to the case of surfaces of topologically finite type, the Teichm{u}ller spaces associated to surfaces
of topologically infinite type depend on the choice of a base structure. In the setting of surfaces of infinite type, the Teichm{u}ller spaces can be endowed with different distance functions such as the length-spectrum distance, the bi-Lipschitz distance, the Fenchel-Nielsen distance, the Teichm{u}ller distance and there are other distance functions. Unlike the case of surfaces of topologically finite type, these distance functions are not equivalent. We introduce the finitely supported Teichm{u}ller space T f s H 0 associated to a base hyperbolic structure H 0 on a surface $Sigma$, provide its characterization by Fenchel-Nielsen coordinates and study its relation to the other Teichm{u}ller spaces. This paper also involves a study of the Teichm{u}ller space T 0 ls H 0 of asymptotically isometric hyperbolic structures and its Fenchel-Nielsen parameterization. We show that T f s H 0 is dense in T 0 ls H 0 , where both spaces are considered to be subspaces of the length-spectrum Teichm{u}ller space T ls H 0. Another result we present here is that asymptotically length-spectrum bounded Teichm{u}ller space A T ls H 0 is contractible. We also prove that if the base surface admits short curves then the orbit of every finitely supported hyperbolic surface is non-discrete under the action of the finitely supported mapping class group MCG f s $Sigma$ .
From a commutative associative algebra $A$, the infinite dimensional unital 3-Lie Poisson algebra~$mathfrak{L}$~is constructed, which is also a canonical Nambu 3-Lie algebra, and the structure of $mathfrak{L}$ is discussed. It is proved that: (1) the
re is a minimal set of generators $S$ consisting of six vectors; (2) the quotient algebra $mathfrak{L}/mathbb{F}L_{0, 0}^0$ is a simple 3-Lie Poisson algebra; (3) four important infinite dimensional 3-Lie algebras: 3-Virasoro-Witt algebra $mathcal{W}_3$, $A_omega^delta$, $A_{omega}$ and the 3-$W_{infty}$ algebra can be embedded in $mathfrak{L}$.
In this paper, we introduce a new graph whose vertices are the nonzero zero-divisors of commutative ring $R$ and for distincts elements $x$ and $y$ in the set $Z(R)^{star}$ of the nonzero zero-divisors of $R$, $x$ and $y$ are adjacent if and only if
$xy=0$ or $x+yin Z(R)$. we present some properties and examples of this graph and we study his relation with the zero-divisor graph and with a subgraph of total graph of a commutative ring.
In string bit models, the superstring emerges as a very long chain of bits, in which s fermionic degrees of freedom contribute positively to the ground state energy in a way to exactly cancel the destabilizing negative contributions of d=s bosonic de
grees of freedom. We propose that the physics of string formation be studied nonperturbatively in the class of string bit models in which s>d, so that a long chain is stable, in contrast to the marginally stable (s=d=8) superstring chain. We focus on the simplest of these models with s=1 and d=0, in which the string bits live in zero space dimensions. The string bit creation operators are N X N matrices. We choose a Hamiltonian such that the large N limit produces string moving in one space dimension, with excitations corresponding to one Grassmann lightcone worldsheet field (s=1) and no bosonic worldsheet field (d=0). We study this model at finite N to assess the role of the large N limit in the emergence of the spatial dimension. Our results suggest that string-like states with large bit number M may not exist for N<(M-1)/2. If this is correct, one can have finite chains of string bits, but not continuous string, at finite N. Only for extremely large N can such chains behave approximately like continuous string, in which case there will also be the (approximate) emergence of a new spatial dimension. In string bit models designed to produce critical superstring at N=infinity, we can then expect only approximate Lorentz invariance at finite N, with violations of order 1/N^2.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
