In a scenario where data-storage qubits are kept in isolation as far possible, with minimal measurements and controls, noise mitigation can still be done using additional probes, corrections applied only when needed. Motivated by the case of solid-state qubits, we consider dephasing arising from two-state fluctuator, described random telegraph process, probe which is also qubit, so-called spect...

Based on the Lenard recursion relation and zero-curvature equation, we derive a hierarchy of long wave-short wave type equations associated with 3 × matrix spectral problem three potentials. Resorting to characteristic polynomial Lax matrix, trigonal curve is defined, which Baker-Akhiezer function two meromorphic functions are introduced. Analyzing some properties functions, including asymptoti...

Abstract We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application obtain case theta divisors this answers Schottky problem. Our proof computes by specialization Lagrangian cycles cotangent bundle. also get similar results for intersection cohomology with a finite morphism to variety; it follows many components Andreo...

A generalized bc-system associated to a Hermitian vector bundle over a Riemann surface is introduced in close analogy to the usual rank one case. Some of the geometric analogies to the well-known case are studied. In particular, if there are no zero-modes, the \nonabelian" theta divisor appears. In the general case where zero-modes exist, it seems to be more diicult to nd a natural description....

The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups of Drinfeld modular curves. These groups are nite for congruence subgroups and may be described through the corresponding quotients of the Bruhat-Tits tree by . The description given is fairly expl...

The purpose of this paper is to prove, assuming that the conjecture of Lang and Vojta holds true, that there is a uniform bound on the number of stably integral points in the complement of the theta divisor on a principally polarized abelian surface defined over a number field. Most of our argument works in arbitrary dimension and the restriction on the dimension ≤ 2 is used only at the last st...

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...

‎Let $R$ be commutative ring with identity and $M$ be an $R$-module‎. ‎The zero divisor graph of $M$ is denoted $Gamma{(M)}$‎. ‎In this study‎, ‎we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M‎, ‎N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$‎. ‎The main objective of this pa...

To any pair of coverings fi : X → Xi, i = 1, 2 of smooth projective curves one can associate an abelian subvariety of the Jacobian JX , the Prym variety P (f1, f2) of the pair (f1, f2). In some cases we can compute the type of the restriction of the canonical principal polarization of JX . We obtain 2 families of Prym-Tyurin varieties of exponent 6.