Thus, xi'=aimxm is shorthand for three equations, each having a sum of three terms on its right-hand side. Another simple example of a free index is the following equation defining the components of a vector a in terms of a dot product with each of the base vectors ei, (2.2.4)ai=...
Then in section 4, we show how the physics that gives the leading-log behavior is semiclassical and described by a first-order equation of motion. Putting all these properties together in section 5, we derive the time- evolution of arbitrary, coincident, correlation functions, which we extend ...
40, No. I, 1999 SUMMATION OF THE WITTING SERIES IN THE SOLITARY-WAVE PROBLEM E. A. Karabut UDC 532.59 Some exact solutions of the Euler equations with a free surface in the presence of gravitation forces are found. They are obtained by summing Witting series applied in the theory of ...
The latter equation is equivalent to Eq. ( 9 ) in L08, where the tedious multiple differentiation of the cosine function is now avoided. C. Real value of the interaction energy The presence of an imaginary factor in Eq. (19), which is reproduced below, may raise concerns because the inte...
(27,28,30) finally gives the desired pressure equation p V = NkBT \Gamma 1 3 X i!j \Omega r ij \Delta F sr ij ff + 1 3\Omega U C ff ; (31) where F sr ij are the short-range pair forces. In Ref. =-=[44]-=- the virial expression r i \Delta F i for the ...
Yes, delta functions are used in a variety of scientific fields, including physics, engineering, and signal processing. They can be used to model real-world phenomena such as impulse forces, point charges, or point masses. Post reply Similar...
13 When applied to quasi-one dimensional systems, Lekner summations method is an eigen- function expansion of the Green function of Laplace equation with periodicity in only one direction (see for instance Eq.(3.10) in ref.[37]). Following the derivations done in refs.[13,15,37], an ...
(when the mirror transistor is equal in size with the reference transistor) with high accuracy, and to reduce to minimum the VDSm/VDSrvariations due to factors such as load, temperature, and power supply variations. The indices m and r in equation (1) refer to the mirror transistor and ...
1 Long Long - - range range potentials potentials LongLong--rangerangearearepotentialspotentialsthatthatdecaydecayslowerslower thanthanrr --dd ..ExamplesExamplesareareelectrostaticselectrostatics,,gravitygravity andanddipolsdipols.A.Acutcut--offoffrr cc isisnotnotpossiblepossiblesincesinceitit wouldwouldbeb...
(27,28,30) finally gives the desired pressure equation p V = NkBT \Gamma 1 3 X i!j \Omega r ij \Delta F sr ij ff + 1 3\Omega U C ff ; (31) where F sr ij are the short-range pair forces. In Ref. =-=[44]-=- the virial expression r i \Delta F i for the ...