integral curve वाक्य
उदाहरण वाक्य
मोबाइल
- He investigated the nature of trajectories of integral curves in a plane; classifying singular points ( saddle, focus, center, node ), introducing the concept of a limit cycle and the loop index.
- The analysis problem which intrigued Bendixson more than all others was the investigation of integral curves to first order differential equations, in particular he was intrigued by the complicated behaviour of the integral curves in the neighbourhood of singular points.
- The analysis problem which intrigued Bendixson more than all others was the investigation of integral curves to first order differential equations, in particular he was intrigued by the complicated behaviour of the integral curves in the neighbourhood of singular points.
- The Poincar?Bendixson theorem, which says an integral curve which does not end in a singular point has a limit cycle, was first proved by Henri Poincar?but a more rigorous proof with weaker hypotheses was given by Bendixson in 1901.
- Second, as Fig . 3 shows, our attempted hyperslice would lead to a " discontinuous " notion of " time " due to the " jumps " in the integral curves ( shown as a blue colored grid discontinuity ).
- For an appropriate choice of " f " equal to 1 outside a small annulus near 0, the integral curves starting at points of the smooth curve will all reach smaller circle bounding the annulus at the same time " s ".
- The above definition of an integral curve " ? " for a vector field " X ", passing through " p " at time " t " 0, is the same as saying that " ? " is a local solution to the ordinary differential equation / initial value problem
- Frame fields always correspond to a family of ideal observers immersed in the given spacetime; the integral curves of the timelike unit vector field are the worldlines of these observers, and at each event along a given worldline, the three spacelike unit vector fields specify the "'spatial triad "'carried by the observer.
- Where x \ in R ^ n, f _ 1, \ dots, f _ k are vector fields belonging to a distribution \ Delta and u _ i ( t ) are control functions, the integral curves of x are restricted to a manifold of dimension m if span ( \ Delta ) = m and \ Delta is an involutive distribution.
- Krantz has worked on the inhomogeneous Cauchy Riemann equations ( he obtained the first sharp estimates in a variety of nonisotropic norms ), on separate smoothness of functions ( most notably with hypotheses about smoothness along integral curves of vector fields ), on analysis on the Heisenberg group and other nilpotent Lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables, on partial differential equations, on complex geometry, on the automorphism groups of domains in complex space, and on the geometry of complex domains.
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