which is the standard form of elliptic equations describing diffusion phenomena. If b=0, there is only one characteristic normal v2=0, and the system is parabolic. For example, with a=1, b=0, c=−d=−1, and q1=0, q2=v, we obtain the standard parabolic equation (11.89h)∂u...
The equation of a circle is (7.7)x2+y2=r2, where r is the radius of the circle, and the circle has its center at the origin of the x, y coordinate system. If we are dealing in three dimensions, we have an “ellipsoid”. The locus of the equation (7.8)x2/a2+y2/b2+z2/c2...
ON THE HIGHER-ORDER B-FAMILY EQUATION AND EULER EQUATIONS ON THE CIRCLE Considered herein is a geometric investigation on the higher-order b-family equation describing exponential curves of the manifold of smooth orientation-pr... M Zhu - 《Discrete & Continuous Dynamical Systems》 被引量: 0发表...
A recurring theme in mathematics is that of duality: a mathematical object can either be described internally (or in physical space, or locally), by describing what physically consists of (or what kind of maps exist into ), or externally (or in frequency space, or globally), by describing ...
For a particle moving on a straight path, a list of positions and corresponding times would constitute a suitable scheme for describing the motion of the particle. A continuous description would require a mathematical formula expressing position in terms of time. When a particle moves on a curved...
Alternate translation using Google Translate: “Whenever in a final equation there are two unknown quantities, there is a locus, the end of one of them describing a straight line or curve. The line is simple and unique in its kind, species curves are indefinite in number,—circle, parabola,...
Locus is the equation of a curve which joins all the points that satisfy the given condition. For example, the locus of set of all points which are at equidistant from a fixed point is a circle.Answer and Explanation: Become a Study.com member to unlock this answ...
We start with an overview table, which is followed by sections describing the differences that appear in each column of the table. The MathType and Equation Editor sources for the comparison are in Section MathType’s Equation Format (MTEF) of the MathType 6.9 SDK. There may be features ...
As already mentioned, in QFT the Fock space for the physical states is not unique since one may have several physical phases, for example, for a metal the normal phase and the superconducting phase, and so on. Fock spaces describing different phases are unitarily inequivalent spaces and corresp...
These derivatives play a role in partial differential equations describing transfer potentials u. When phenomenological equations and conservation laws are combined, the result is a vector equation of change for the transfer potentials u. Its simplest representative is the Fourier–Kirchhoff-type vector ...