Results 1  10
of
1,224,174
An Explicit Solution for the Quaternionic Equation
"... AMS Mathematical Subject Classification: 11D09,15A06 Abstract. Though it is known that every nonconstant quaternionic polynomial with a unique highest term has a root, yet because of the noncommutativity of quaternions, it is rather difficult to find an explicit expression for the roots of a gener ..."
Abstract
 Add to MetaCart
AMS Mathematical Subject Classification: 11D09,15A06 Abstract. Though it is known that every nonconstant quaternionic polynomial with a unique highest term has a root, yet because of the noncommutativity of quaternions, it is rather difficult to find an explicit expression for the roots of a
Explicit solutions of the Rand Equation
"... In this paper the meaning of a nonlinear partial differential equation (nPDE) of the thirdorder is shown to the first time. The equation is known as the ‘Rand Equation ’ and belongs to a class of less studied nPDEs. Both the explicit physical meaning as well as the behaviour is not known until now. ..."
Abstract
 Add to MetaCart
In this paper the meaning of a nonlinear partial differential equation (nPDE) of the thirdorder is shown to the first time. The equation is known as the ‘Rand Equation ’ and belongs to a class of less studied nPDEs. Both the explicit physical meaning as well as the behaviour is not known until now
Explicit Solutions for Queueing Problems
, 1997
"... this paper attention is focussed upon the equilibrium behavior of these models, rather then upon their timedependent behavior. The equilibrium distribution of a random walk on a grid is the solution of a set of equilibrium equations. These equations can be viewed as difference equations. In the the ..."
Abstract
 Add to MetaCart
this paper attention is focussed upon the equilibrium behavior of these models, rather then upon their timedependent behavior. The equilibrium distribution of a random walk on a grid is the solution of a set of equilibrium equations. These equations can be viewed as difference equations
Floating Bodies of Equilibrium. Explicit Solution
, 2006
"... Explicit solutions of the twodimensional floating body problem (bodies that can float in all positions) for relative density ρ ̸ = 1 2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which way the bicycle went) are given, which differ from circles. Starti ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Explicit solutions of the twodimensional floating body problem (bodies that can float in all positions) for relative density ρ ̸ = 1 2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which way the bicycle went) are given, which differ from circles
Explicit solutions for relativistic acceleration and rotation
, 2005
"... The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called ..."
Abstract
 Add to MetaCart
, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a nonlinear analytic equation in one complex variable. We obtain explicit solutions
Explicit solutions for variational problems in the quadrant
, 1999
"... We study a variational problem (VP) that is related to semimartingale reflecting Brownian motions (SRBMs). Specifically, this VP appears in the large deviations analysis of the stationary distribution of SRBMs in the ddimensional orthant R d +. When d = 2, we provide an explicit analytical solution ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
solution to the VP. This solution gives an appealing characterization of the optimal path to a given point in the quadrant and also provides an explicit expression for the optimal value of the VP. For each boundary of the quadrant, we construct a “cone of boundary influence,” which determines the nature
On the explicit solutions of the elliptic Calogero system
 J. Math. Phys
, 1999
"... Let q1,q2,...,qN be the coordinates of N particles on the circle, interacting with the integrable potential ∑N j<k ℘(qj − qk), where ℘ is the Weierstrass elliptic function. We show that every symmetric elliptic function in q1,q2,...,qN is a meromorphic function in time. We give explicit formulae ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Let q1,q2,...,qN be the coordinates of N particles on the circle, interacting with the integrable potential ∑N j<k ℘(qj − qk), where ℘ is the Weierstrass elliptic function. We show that every symmetric elliptic function in q1,q2,...,qN is a meromorphic function in time. We give explicit formulae
ON EXPLICIT SOLUTIONS OF NONLINEAR DYNAMIC SYSTEMS
"... A method is proposed to obtain explicit expressions for the large signal behavior in nonlinear dynamic circuits. The method is also a n extension to the solution method for Linear Dynamic Complementary Problems. 1. ..."
Abstract
 Add to MetaCart
A method is proposed to obtain explicit expressions for the large signal behavior in nonlinear dynamic circuits. The method is also a n extension to the solution method for Linear Dynamic Complementary Problems. 1.
Results 1  10
of
1,224,174