We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We show that the following combinatorial example is a commuting algebra determinant. Let Bq(n) denote the set of all subspaces of an n-dimensional vector space over Fq. The type of an ordered pair (U, V ) of subspaces, where U, V ∈ Bq(n), is the ordered tripl...

In this brief note we study how the fractional mean curvature of order s ∈ (0, 1) varies with respect to C diffeomorphisms. We prove that, if α > s, then the variation under a C diffeomorphism Ψ of the s-mean curvature of a set E is controlled by the C norm of the Jacobian of Ψ. When α = 1 we discuss the stability of these estimates as s → 1− and comment on the consistency of our result with th...

We generalise our previous observation on the invariance of the Jarlskog determinant to matter effects in neutrino oscillations. Within the context of standard neutrino oscillation theory with matter effects, we present the complete set of (five) matter invariant observables for neutrino propagation in matter. We give some examples of their application. E-mail:[email protected] E-mail:w.g...

This article extends relations of Mumford’s UV W -expressions to those in subvariety in a hyperelliptic Jacobian using Baker’s method.

Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal pol...

Consider the Jacobian of a genus two curve defined over a finite field and with complex multiplication. In this paper we show that if the l-Sylow subgroup of the Jacobian is not cyclic, then the embedding degree of the Jacobian with respect to l is one.

The aim here is to continue the investigation in [1] of Jacobians of a Klein surface and also to correct an error in [1].

We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties Af attached by Shimura to normalized newforms f ∈ S2(Γ0(N)). We present all the curves corresponding to principally polarized surfaces Af for N ≤ 500.

In this paper, we examine the characteristics of titles (average length, proportion of titles with subtitles, proportion of interrogatory, and indicative titles) and how they changed over a substantial period of time (half a century). We consistently analyze core literature in five diverse fields, in order to probe the usage of titles as a disciplinary identity building tool. In addition, we st...