نتایج جستجو برای: determinant
تعداد نتایج: 47937 فیلتر نتایج به سال:
ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
Numerical examples demonstrated that a prescribed positive Jacobian determinant alone can not uniquely determine a diffeomorphism. It is conjectured that the uniqueness of a transformation can be assured by its Jacobian determinant and the curl-vector. In this work, we study the uniqueness problem analytically and propose an approach to the proof of the uniqueness of a transformation with presc...
We show that for all odd primes p, there exist ordinary elliptic curves over Fp(x) with arbitrarily high rank and constant j-invariant. This shows in particular that there are elliptic curves with arbitrarily high rank over these fields for which the corresponding elliptic surface is not supersingular. The result follows from a theorem which states that for all odd prime numbers p and l, there ...
In order to successfully implement several control laws, a uniform upper bound for the Jacobian of the gravity vector is necessary. However, not all joint configurations of robot manipulators insure the existence of such a bound. In this paper we fully characterize the class of robot manipulators for which the Jacobian of the gravity vector is uniformly bounded. The results in this paper can be...
then u is continuous. This result solves a conjecture of Heinz about regularity of solutions to the prescribed boundedmean curvature equation and a conjecture of Hildebrandt about regularity of all critical points of continuously differentiable elliptic conformally invariant Lagrangians in dimension two. In particular it provides a new proof of Hélein’s theorem [10,12] about regularity of two d...
In the paper, the authors find a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.
In this article, we give an algorithm for decomposing given element of Jacobian gruop into the sum of the decomposed factor, which consists of certain subset of the points of curve.
For an equation o-f the -form £<&.>••¥., it is shown that there is at least one solution •for every y_ if F_ is eventually PB passive or the e-f-fective Jacobian matrix in all the unbounded regions is a P matrix. In addition to this, i-f the Jacobian determinant has the same sign in all the regions, then F is a homeomorphism. For equations o-f the form E is onto if H ...
In this paper it is shown that, given n ∈ Z ≥3 and a, b, c ∈ Q × , there exists a polynomial d(t) ∈ Q[t] such that the curves over Q(t) given by y 2 = x n + ad(t) resp. y 2 = x n + bd(t) and y 2 = x n + cd(t) all have a Jacobian with positive Mordell-Weil rank over Q(t). Extensions of this result to sets of four curves are discussed, as well as the problem of demanding in addition that d(t) is ...
We generalize Macdonald’s formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild cond...
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