Random size trees on the one and two dimensional integer lattice

1969 ◽  
Vol 6 (2) ◽  
pp. 301-308
Author(s):  
A.M.V. Verhagen
Keyword(s):  
Stochastic Process ◽  
Continuous Distribution ◽  
Integer Lattice ◽  
Two Dimensional ◽  
Random Size ◽  
Integer Lattices ◽  
The One

A stochastic process in which any tree in a forest planted on an integer lattice eliminates its four neighbours when it exceeds their heights, is studied for the case when all heights are independent samples from a continuous distribution. The proportion of the trees of the forest eliminated in this manner is determined for both the one and the two dimensional integer lattices.

Random size trees on the one and two dimensional integer lattice

1969 ◽  
Vol 6 (02) ◽  
pp. 301-308
Author(s):  
A.M.V. Verhagen
Keyword(s):  
Stochastic Process ◽  
Continuous Distribution ◽  
Integer Lattice ◽  
Two Dimensional ◽  
Random Size ◽  
Integer Lattices ◽  
The One

A stochastic process in which any tree in a forest planted on an integer lattice eliminates its four neighbours when it exceeds their heights, is studied for the case when all heights are independent samples from a continuous distribution. The proportion of the trees of the forest eliminated in this manner is determined for both the one and the two dimensional integer lattices.

Ergodic theorems for graph interactions

1975 ◽  
Vol 7 (1) ◽  
pp. 179-194 ◽  
Author(s):  
David Griffeath
Keyword(s):  
Bethe Lattice ◽  
Ergodic Theorems ◽  
Two Dimensional ◽  
Integer Lattices ◽  
The One

A criterion for ergodicity of lattice interactions has been given by Dobrushin [2], and improved by Harris [3] and Holley [5]. In this paper we present a simplified derivation of these results, and obtain stronger conditions for interactions on the one- and two-dimensional integer lattices, and the 3–Bethe lattice.

Ergodic theorems for graph interactions

1975 ◽  
Vol 7 (01) ◽  
pp. 179-194 ◽  
Author(s):  
David Griffeath
Keyword(s):  
Bethe Lattice ◽  
Ergodic Theorems ◽  
Two Dimensional ◽  
Integer Lattices ◽  
The One

A criterion for ergodicity of lattice interactions has been given by Dobrushin [2], and improved by Harris [3] and Holley [5]. In this paper we present a simplified derivation of these results, and obtain stronger conditions for interactions on the one- and two-dimensional integer lattices, and the 3–Bethe lattice.

F.VIII R:Ag in Hepatitis

1979 ◽  
Author(s):  
R. Kotitschke ◽  
J. Scharrer
Keyword(s):  
Chronic Hepatitis ◽  
Blood Donors ◽  
Blood Donation ◽  
Normal Population ◽  
Rabbit Antiserum ◽  
Two Dimensional ◽  
Plastic Plate ◽  
Significant Difference ◽  
Acute Hepatitis B ◽  
The One

F.VIII R:Ag was determined by quantitative immunelectrophoresis (I.E.) with a prefabricated system. The prefabricated system consists of a monospecific f.VIII rabbit antiserum in agarose on a plastic plate for the one and two dimensional immunelectrophoresis. The lognormal distribution of the f.VIII R:Ag concentration in the normal population was confirmed (for n=70 the f.VIII R:Ag in % of normal is = 95.4 ± 31.9). Among the normal population there was no significant difference between blood donors (one blood donation in 8 weeks; for n=43 the f.VIII R:Ag in % of normal is = 95.9 ± 34.0) and non blood donors (n=27;f.VIII R:Ag = 94.6 ± 28.4 %). The f.VIII R:Ag concentration in acute hepatitis B ranged from normal to raised values (for n=10, a factor of 1.8 times of normal was found) and was normal again after health recovery (n=10, the factor was 1.0). in chronic hepatitis the f.VIII R:Ag concentration was raised in the majority of the cases (for n=10, the factor was 3.8). Out of 22 carrier sera 20 showed reduced, 2 elevated levels of the f.VIII R:Ag concentration. in 5 sera no f.VIII R:Ag could be demonstrated. The f.VIII R:Ag concentration was normal for n=10, reduced for n=20 and elevated for n=6 in non A-non B hepatitis (n=36). Contrary to results found in the literature no difference in the electrophoretic mobility of the f.VIII R:Ag was found between hepatitis patients sera and normal sera.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Studies of the neutral trisaccharides of goat (Capra hircus) colostrum and of the one- and two-dimensional 1H and 13C NMR spectra of 6′-N-acetylglucosaminyllactose

1994 ◽  
Vol 262 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Tadasu Urashima ◽  
William A. Bubb ◽  
Michael Messer ◽  
Yuhnagi Tsuji ◽  
Yasuko Taneda
Keyword(s):  
13C Nmr ◽  
Nmr Spectra ◽  
Capra Hircus ◽  
13C Nmr Spectra ◽  
Two Dimensional ◽  
1H And 13C Nmr ◽  
The One
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