Let E be an elliptic curve having Complex Multiplication by the ring OK of integers of K = Q( √−D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module. Its Steinitz class St(E) is studied here. In particular, when D is a prime number, St(E) is determined: If D ≡ 3 (mod 4) then St(E) = 1; if D ≡ 1 (mod 4) then St(E) = [P]t, where P is any prime-idea...

‎in this paper, we study some kinds of majorizations on $textbf{m}_{n}$ and their linear or strong linear preservers. also, we find the structure of linear or strong linear preservers which are multiplicative, i.e.  linear or strong linear preservers like $phi $ with the property $phi (ab)=phi (a)phi (b)$ for every $a,bin textbf{m}_{n}$.

1. In the stretch receptor neurones of the crayfish Astacus astacus, the intracellular pH (pHi), the intracellular Na+ concentration ([Na+]i) and the membrane potential (Em) were measured simultaneously using ion-selective and conventional microelectrodes. Normal Astacus saline (NAS), and salines containing varying amounts of Ca2+ (Ca2+-NAS) but of constant ionic strength, with Na+, Mg2+ or Ba2...

Let E be an elliptic curve having Complex Multiplication by the full ring OK of integers of K = Q( √ −D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module, and its Steinitz class St(E) is studied. When D is a prime number, it is proved that St(E) = 1 if D ≡ 3 (mod 4); and St(E) = [P]t if p ≡ 1 (mod 4), where [P] is the ideal class of K represente...

We investigate the cosmological observational test of extended quintessence model, i.e. a scalar-tensor gravity model with scalar field potential serving as dark energy, by using Planck 2018 cosmic microwave background (CMB) data, together baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider Brans-Dicke kinetic term $\frac{\omega(\phi)}{\phi} \...

Some results are obtained on the group of rational points on elliptic curves over infinite algebraic number fields. A certain naturally defined class of Dedekind domains, elliptic Dedekind domains, are described and it is shown that every countable abelian group can be realized as the class group of an elliptic Dedekind domain. Introduction. Let E be an elliptic curve defined over a field K. Le...

A bipartite monoid is a commutative monoid Q together with an identified subset P ⊂ Q. In this paper we study a class of bipartite monoids, known as misère quotients, that are naturally associated to impartial combinatorial games. We introduce a structure theory for misère quotients with |P| = 2, and give a complete classification of all such quotients up to isomorphism. One consequence is that...

In this paper, we study Dedekind sums and we connect them to the mean values of Dirichlet L-functions. For this, we introduce and investigate higher order dimensional Dedekind-Rademacher sums given by the expression Sd( −→ a0 , −→ m0) = 1 a0 0 a0−1 ∑

We define a combinatorial game in R from which we derive numerous new inequalities between higher-dimensional Dedekind sums. Our approach is motivated by a recent article by Dilcher and Girstmair, who gave a nice probabilistic interpretation for the classical Dedekind sum. Here we introduce a game analogous to Dilcher and Girstmair’s model in higher dimensions.