Application of η-expansion technique to the φ3-theory in arbitrary dimension

2018 ◽  
Vol 33 (35) ◽  
pp. 1850209
Author(s):  
A. L. Pismensky
Keyword(s):  
Euclidean Space ◽  
Critical Exponent ◽  
Space Dimension ◽  
Arbitrary Dimension ◽  
Approximate Equation ◽  
Conformal Bootstrap ◽  
Expansion Technique ◽  
The Given

The [Formula: see text]-theory in the Euclidean space of arbitrary dimension is considered in the present paper. The method of [Formula: see text]-expansion in frames of conformal bootstrap equations is used. As one knows, there is an [Formula: see text]-expansion technique that allows one to calculate the critical exponent in the form of a series in [Formula: see text], the deviation of the space dimension from the logarithmic one. However, the given series in [Formula: see text] is divergent, and it is not possible to extend it analytically to arbitrary dimension. To solve the problem, we propose using the [Formula: see text]-expansion: we construct series in powers of the Fisher’s exponent [Formula: see text] or a parameter [Formula: see text] expressed through the Fisher’s exponent and we obtain some approximate equation for [Formula: see text] or [Formula: see text].

scholarly journals On the induced distribution of the shape of the projection of a randomly rotated configuration

2010 ◽  
Vol 42 (02) ◽  
pp. 331-346
Author(s):  
H. Le ◽  
D. Barden
Keyword(s):  
Euclidean Space ◽  
Arbitrary Dimension ◽  
Shape Space ◽  
Size And Shape ◽  
The Given

Using the geometry of the Kendall shape space, in this paper we study the shape, as well as the size-and-shape, of the projection of a configuration after it has been rotated and, when the given configuration lies in a Euclidean space of an arbitrary dimension, we obtain expressions for the induced distributions of such shapes when the rotation is uniformly distributed.

scholarly journals On the induced distribution of the shape of the projection of a randomly rotated configuration

2010 ◽  
Vol 42 (2) ◽  
pp. 331-346
Author(s):  
H. Le ◽  
D. Barden
Keyword(s):  
Euclidean Space ◽  
Arbitrary Dimension ◽  
Shape Space ◽  
Size And Shape ◽  
The Given

Using the geometry of the Kendall shape space, in this paper we study the shape, as well as the size-and-shape, of the projection of a configuration after it has been rotated and, when the given configuration lies in a Euclidean space of an arbitrary dimension, we obtain expressions for the induced distributions of such shapes when the rotation is uniformly distributed.

Circles on the Complex Plane

2021 ◽  
pp. 3-12
Author(s):  
A. Girsh
Keyword(s):  
Euclidean Space ◽  
Complex Plane ◽  
Euclidean Plane ◽  
Complex Space ◽  
Radical Center ◽  
Special Cases ◽  
Different Types ◽  
Different Dimensions ◽  
The Given ◽  
Made In

The Euclidean plane and Euclidean space themselves do not contain imaginary elements by definition, but are inextricably linked with them through special cases, and this leads to the need to propagate geometry into the area of imaginary values. Such propagation, that is adding a plane or space, a field of imaginary coordinates to the field of real coordinates leads to various variants of spaces of different dimensions, depending on the given axiomatics. Earlier, in a number of papers, were shown examples for solving some urgent problems of geometry using imaginary geometric images [2, 9, 11, 13, 15]. In this paper are considered constructions of orthogonal and diametrical positions of circles on a complex plane. A generalization has been made of the proposition about a circle on the complex plane orthogonally intersecting three given spheres on the proposition about a sphere in the complex space orthogonally intersecting four given spheres. Studies have shown that the diametrical position of circles on the Euclidean E-plane is an attribute of the orthogonal position of the circles’ imaginary components on the pseudo-Euclidean M-plane. Real, imaginary and degenerated to a point circles have been involved in structures and considered, have been demonstrated these circles’ forms, properties and attributes of their orthogonal position. Has been presented the construction of radical axes and a radical center for circles of the same and different types. A propagation of 2D mutual orthogonal position of circles on 3D spheres has been made. In figures, dashed lines indicate imaginary elements.

HIERARCHY IN HOŘAVA-LIKE GRAVITY

2011 ◽  
Vol 26 (16) ◽  
pp. 2795-2805 ◽  
Author(s):  
YU-LEI FENG ◽  
LI-XIN XU ◽  
YU-TING WANG
Keyword(s):  
Critical Exponent ◽  
Gravity Model ◽  
Space Dimension ◽  
Dimensional Space ◽  
Space Time ◽  
Mass Hierarchy ◽  
Factor Solution ◽  
Exponential Factor ◽  
Extra Space ◽  
Dimensional Space Time

We investigate a Hořava-like gravity model in (4+1)-dimensional space–time. Differing from the original one, we put a critical exponent z to the extra space dimension, which preserves the 4-dimensional diffeomorphism. Surprisingly, we obtain a mass hierarchy [Formula: see text] in a way completely different from the Randall–Sundrum model, we also obtain an exponential factor solution with the use of Ricci-like flow. More interesting relations with AdS5/CFT4 are further demonstrated. Since AdS/CFT is a realization of holography, we conclude that the Hořava-like gravity may be also a realization of holography.

scholarly journals SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH PRESCRIBED EIGENCURVES

2010 ◽  
Vol 07 (02) ◽  
pp. 211-254 ◽  
Author(s):  
HELGE KRISTIAN JENSSEN ◽  
IRINA A. KOGAN
Keyword(s):  
Conservation Laws ◽  
Gas Dynamics ◽  
Hyperbolic Conservation Laws ◽  
Space Dimension ◽  
Euler System ◽  
Complete Analysis ◽  
Overdetermined System ◽  
Hyperbolic Conservation ◽  
Algebraic Differential Equations ◽  
The Given

We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and Cartan–Kähler). We give a complete analysis of the possible scenarios, including examples, for systems of three equations. As an application we characterize conservative systems with the same eigencurves as the Euler system for 1-dimensional compressible gas dynamics. The case of general rich systems of any size (i.e. when the given eigenvector fields are pairwise in involution; this includes all systems of two equations) is completely resolved and we consider various examples in this class.

scholarly journals Parabolic Stein Manifolds

2014 ◽  
Vol 114 (1) ◽  
pp. 86 ◽  
Author(s):  
A. Aytuna ◽  
A. Sadullaev
Keyword(s):  
Riemann Surface ◽  
Subharmonic Function ◽  
Arbitrary Dimension ◽  
Topological Type ◽  
Zero Set ◽  
Space Of Analytic Functions ◽  
Exhaustion Function ◽  
Stein Manifolds ◽  
Open Riemann Surface ◽  
The Given

An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among these different definitions. In section 3 we relate some of these notions to the linear topological type of the Fréchet space of analytic functions on the given manifold. In section 4 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.

Deiktiskās, prospektīvās un retrospektīvās frāzes zinātnes valodā

2021 ◽  
pp. 63-70
Author(s):  
Iveta Kopankina ◽  
◽  
Artūrs Viļums ◽  
Keyword(s):  
Content Analysis ◽  
Corpus Linguistics ◽  
Space Dimension ◽  
Time Dimension ◽  
Space And Time ◽  
Language Of Science ◽  
Research Material ◽  
Demonstrative Pronouns ◽  
The Given ◽  
Dimensions Of Space

The article focuses on the dimensions of space and time in the Latvian language of science. The space dimension is expressed by the deictic constructions of place (demonstrative pronouns and adverbs), and the time dimension is expressed by prospective and retrospective constructions (adverbs and adjectives). The research material consists of the texts of scientific articles included in the project “The Latvian Language of Science in the Intralingual Aspect”. The aim of the present study is to explore research articles written in Latvian and to single out the most frequently used wording expressing the mentioned dimensions. In the present research, content analysis has been carried out to establish the knowledge gap present in the given field. It was found out that very few publications so far exist pertaining to space and time deixis in the Latvian language. The respective wording in the research material has been singled out with the help of AntConc; therefore, the present study is a study in Latvian Linguistics, with the elements of Corpus Linguistics. The content analysis and the study revealed that the deictic space and prospective and retrospective time constructions are present throughout the articles written in the Latvian language of science, i.e. in the introductory parts, in the main bodies, and the conclusions of the mentioned texts and serve the function of creating the joint psychological space of the author and the audience. They facilitate the process of communication between the author and the reader of the given texts.

THE BOSONIC STRING REPRESENTED AS Φ3 GRAPHS: NEW MONTE-CARLO SIMULATIONS

1990 ◽  
Vol 05 (10) ◽  
pp. 771-785 ◽  
Author(s):  
J. AMBJØRN ◽  
D. BOULATOV ◽  
V. A. KAZAKOV
Keyword(s):  
Monte Carlo ◽  
Partition Function ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Space Dimension ◽  
Asymptotic Form ◽  
Bosonic String ◽  
Target Space ◽  
Logarithmic Corrections

We discuss a new method for measuring the critical exponent γ for the partition function of the bosonic string. The statistics seems very good and the fit to γconsistent with the assumed asymptotic form for the partition function for dimensions d=1–6. The results are in agreement with analytical results when the target space dimension is d=0, but disagree when d=1. We conjecture that this is due to the appearance of logarithmic corrections to the asymptotic form of the partition function. These corrections might persist for d>1 and might render the determination of γquite difficult.

scholarly journals Diophantine approximation on polynomial curves

2017 ◽  
Vol 163 (3) ◽  
pp. 533-546 ◽  
Author(s):  
JOHANNES SCHLEISCHITZ
Keyword(s):  
Euclidean Space ◽  
Number Field ◽  
Rational Approximation ◽  
Diophantine Approximation ◽  
Rational Number ◽  
Linear Dependence ◽  
Arbitrary Dimension ◽  
Approximation Properties ◽  
Polynomial Curves

AbstractIn a paper from 2010, Budarina, Dickinson and Levesley studied the rational approximation properties of curves parametrised by polynomials with integral coefficients in Euclidean space of arbitrary dimension. Assuming the dimension is at least three and excluding the case of linear dependence of the polynomials together with P(X) ≡ 1 over the rational number field, we establish proper generalisations of their main result.

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