We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic cycles on projective algebraic manifolds.

We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. Interrelations with doubly transitive permutation groups and hyperelliptic jacobians are discussed.

This survey discusses algorithms and explicit calculations for curves of genus at least 2 and their Jacobians, mainly over number fields and finite fields. Miscellaneous examples and a list of possible future projects are given at the end.

Establishing that a demand mapping is injective core first step for variety of methodologies. When version the law holds, global injectivity can be checked by seeing whether constant over any line segments. we add assumption differentiability, obtain necessary and sufficient conditions generalize classical \cite{gale1965jacobian} quasi-definite Jacobians.

We give a new proof of Shiota’s theorem on Novikov’s conjecture, which states that the K.P. equation characterizes Jacobians among all indecomposable principally polarized abelian varieties. Mathematics Subject Classifications (1991): 14K25, 14H40.

We relate the existence of Frobenius morphisms into the Jacobians ofDrinfeldmodular curves to the existence of congruences between cusp forms. Mathematics Subject Classification (2000) Primary 11F33; Secondary 11F52 · 11G10

We compute an infinite system of differential equations that characterises the quasi-periodic solutions of the KP hierarchy ; that is, the solutions of this new hierarchy are precisely those solutions of the KP hierarchy coming from theta functions of Jacobians.

In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain behaviour such as multiple equilibria, and sometimes implying stability. We first explore reaction systems and derive results which provide a deep c...

This paper presents modular dynamics for dual-arms, expressed in terms of the kinematics and dynamics of each of the stand-alone manipulators. The two arms are controlled as a single manipulator in the task space that is relative to the two end-effectors of the dual-arm robot. A modular relative Jacobian, derived from a previous work, is used which is expressed in terms of the stand-alone manip...

The Second-Order Cone Complementarity Problem (SOCCP) is a wide class of problems, which includes the Nonlinear Complementarity Problem (NCP) and the Second-Order Cone Programming Problem (SOCP). Recently, Fukushima, Luo and Tseng extended some merit functions and their smoothing functions for NCP to SOCCP. Moreover, they derived computable formulas for the Jacobians of the smoothing functions ...