family of curves वाक्य

उदाहरण वाक्य

1. One begins by noting that an arbitrary smooth vector field X on a manifold M defines a family of curves, its integral curves u : I \ to M ( for intervals I ).
2. There was a controversy, one of the final issues in the conflict between'old'and'new'points of view in algebraic geometry, over Henri Poincar?s characteristic linear system of an algebraic family of curves on an algebraic surface.
3. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material's critical stress value.
4. The Cayley & ndash; Bacharach theorem thus asserts that the last point of intersection of any two members in the family of curves does not move if eight intersection points ( without seven co-conic ones ) are already prescribed.
5. Under the guidance of Ernest Julius Wilczynski, her doctoral thesis, " Properties of a certain projectively defined two-parameter family of curves on a general surface ", drew on his work as the founder of the American school of projective differential geometry.
6. In a similar way, we can define the Koch & ndash; Peano family of curves as the set of De Rham curves generated by affine transformations reversing orientation, with fixed points p _ 0 = 0 and p _ 1 = 1.
7. In other words, if you plot the reaction rate against [ M ] for various M, you get a family of curves with more or less parallel upward slopes merging into a common horizontal line after a certain concentration [ M ].
8. Her paper " On certain factors of c-and p-discriminants and their relations to fixed points in the family of curves " which she published in the " Journal of Pure and Applied Mathematics " was based on her doctoral dissertation and she was awarded the Gambel Prize.
9. "' A-weighting "'is the most commonly used of a family of curves defined in the International standard dB . The resulting octave band measurements are usually added ( logarithmic method ) to provide a single A-weighted value describing the sound; the units are written as dB ( A ).
10. The Tate curve is really a curve over a formal power series ring rather than a curve over C . Intuitively, it's a family of curves depending on a formal parameter ( when that formal parameter is zero it degenerates to a pinched torus, and when it's nonzero it's a torus ).