scholarly journals Anti-self-dual Equation on 4-manifolds with Degenerate Metric

1998 ◽  
Vol 8 (3) ◽  
pp. 466-528 ◽  
Author(s):  
K. Fukaya
Keyword(s):  
Degenerate Metric ◽  
Dual Equation

scholarly journals Particles and strings in degenerate metric spaces

2000 ◽  
Vol 17 (7) ◽  
pp. 1577-1594 ◽  
Author(s):  
Luís A Cabral ◽  
Victor O Rivelles
Keyword(s):  
Metric Spaces ◽  
Degenerate Metric

On Almost Contingent Manifolds of Second Class with Applications in Relativity

1978 ◽  
Vol 21 (3) ◽  
pp. 289-295 ◽  
Author(s):  
K. L. Duggal
Keyword(s):  
General Relativity ◽  
Electromagnetic Fields ◽  
Vector Fields ◽  
Killing Vector ◽  
Positive Definite ◽  
Geometric Proof ◽  
Sasakian Manifolds ◽  
Killing Vector Fields ◽  
Degenerate Metric ◽  
Frame Work

D. E. Blair [1] has introduced the notion of K-manifolds as an analogue of the even dimensional Kähler manifolds and of the odd dimensional quasi-Sasakian manifolds. These manifolds have been studied with respect to a positive definite metric. In this paper, we study a more general case of if-manifolds carrying an arbitrary non-degenerate metric, in particular, a metric of Lorentz signature. This theory is then applied within the frame-work of general relativity. Using the Ruse-Synge classification [8, 9] of non-null electromagnetic fields with source, we develop a geometric proof for the existence of either two space like or one space like and one time like Killing vector fields on the space-time manifold.

scholarly journals DUAL EQUATION AND INVERSE PROBLEM FOR AN INDEFINITE STURM–LIOUVILLE PROBLEM WITH M TURNING POINTS OF EVEN ORDER

2012 ◽  
Vol 17 (5) ◽  
pp. 618-629
Author(s):  
Hamidreza Marasi ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Infinite Product ◽  
Turning Points ◽  
Liouville Problem ◽  
Product Representation ◽  
Dual Equation ◽  
Number Of Zeros ◽  
Even Order ◽  
Sturm Liouville ◽  
Infinite Product Representation

In this paper the differential equation y″ + (ρ 2 φ 2 (x) –q(x))y = 0 is considered on a finite interval I, say I = [0, 1], where q is a positive sufficiently smooth function and ρ 2 is a real parameter. Also, [0, 1] contains a finite number of zeros of φ 2 , the so called turning points, 0 < x 1 < x 2 < … < x m < 1. First we obtain the infinite product representation of the solution. The product representation, satisfies in the original equation. As a result the associated dual equation is derived and then we proceed with the solution of the inverse problem.

scholarly journals Some Bernstein processes similar to Cox–Ingersoll–Ross ones

2019 ◽  
Vol 19 (06) ◽  
pp. 1950047
Author(s):  
Mohamad Houda ◽  
Paul Lescot
Keyword(s):  
Quantum Mechanics ◽  
Heat Equation ◽  
Bessel Processes ◽  
Dual Equation ◽  
Phd Thesis

We present some results on Bernstein processes, which are Brownian diffusions that appear in Euclidean Quantum Mechanics. We express the distributions of these processes with the help of those of Bessel processes. We then determine two solutions of the dual equation of the heat equation with potential. These results first appeared in the first author’s PhD thesis (Rouen, 2013).

Demographic analysis of gummy shark (Mustelus antarcticus) and school shark (Galeorhinus galeus) off southern Australia by applying a generalized Lotka equation and its dual equation

2000 ◽  
Vol 57 (1) ◽  
pp. 214-222 ◽  
Author(s):  
Yongshun Xiao ◽  
Terence I Walker
Keyword(s):  
Total Mortality ◽  
Intrinsic Rate ◽  
Fish Population ◽  
Intrinsic Rate Of Increase ◽  
Demographic Analysis ◽  
Instantaneous Rate ◽  
Dual Equation ◽  
Population Dynamics Model ◽  
Rate Of Increase ◽  
Galeorhinus Galeus

Although Lotka's equation is commonly used for calculating the intrinsic rate of increase with time of a fish population in demographic analysis, its dual equation has never been derived. In this paper, we establish an explicit relationship between the intrinsic rate of increase with time of a fish population and its instantaneous rate of natural mortality from an age-dependent population dynamics model, derive a generalized Lotka equation for calculating the intrinsic rate of increase with time, and derive its dual equation for calculating the intrinsic rate of decrease with age. The virginal intrinsic rate of increase with time of the gummy shark (Mustelus antarcticus) population was calculated as 0.115957·year-1 and its intrinsic rate of decrease with age as -0.312957·year-1. The virginal intrinsic rate of increase with time of the school shark (Galeorhinus galeus) population was calculated as 0.109480·year-1 and its intrinsic rate of decrease with age as -0.216980·year-1. The generalized Lotka equation and its dual equation thus derived imply that both reproductive schedules of a population of animals and its instantaneous rate of total mortality determine its intrinsic rate of increase with time, whereas its reproductive schedules alone determine its intrinsic rate of decrease with age.

scholarly journals TOPOLOGICAL STRUCTURE OF THE MANY VORTICES SOLUTION IN JACKIW–PI MODEL

2008 ◽  
Vol 23 (14) ◽  
pp. 1055-1066 ◽  
Author(s):  
XI-GUO LEE ◽  
ZI-YU LIU ◽  
YONG-QING LI ◽  
PENG-MING ZHANG
Keyword(s):  
Topological Structure ◽  
The Self ◽  
Gauge Potential ◽  
Topological Properties ◽  
Dual Equation ◽  
The Many ◽  
Chern Simons ◽  
Topological Number

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw–Pi model. We obtain a new concrete self-dual equation and find relationship between Chern–Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Ψ-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw–Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

Sign in / Sign up

Export Citation Format

Share Document