Let ` → −∞. Recent developments in convex calculus [26] have raised the question of whether E = א0. We show that every closed, meager subalgebra is Y -unconditionally Darboux, combinatorially pseudo-Chern and ultra-almost surely Euclidean. It is well known that every irreducible, onto, right-canonical isometry is integrable, reversible, K-trivially universal and Dedekind. It has long been known...

A Dedekind algebra is an ordered pair (B, h) where B is a nonempty set and h is a "similarity transformation" on B. Among the Dedekind algebras is the sequence of positive integers. Each Dedekind algebra can be decomposed into a family of disjointed, countable subalgebras which are called the configurations of the algebra. There are many isomorphic types of configurations. Each Dedekind algebra...

The main aim of this paper is to analyse minimally-coupled scalar-fields -- quintessence and phantom as the candidates explain accelerated expansion universe compare its observables current cosmological observations; a byproduct we present python module. This work includes parameter $\epsilon$ which allows incorporate both fields within same analysis. Examples potentials, so far included, are $...

Vaught’s conjecture says that for any countable (complete) first-order theory T, the number of non-isomorphic countable models of T is either countable or 2, where ω is the first infinite cardinal. Vaught’s conjecture for ω-stable theories of modules was proved by Garavaglia [6, Theorem 6]. Buechler proved that Vaught’s conjecture is correct for modules of U-rank 1 [2]. It has been shown that V...

Abstract Dedekind type DC sums and their generalizations are defined in terms of Euler functions generalization. Recently, Ma et al. (Adv. Differ. Equ. 2021:30 2021) introduced the poly-Dedekind by replacing function appearing sums, they were shown to satisfy a reciprocity relation. In this paper, we consider two kinds new sums. One is unipoly-Dedekind sum associated with 2 unipoly-Euler expres...

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with polynomial (Laurent polynomial) reciprocity laws and the space of cusp (modular) forms. In this article we introduce Hecke operators on the space of weighted Dedekind...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...

A Dedekind cut of an ordered abelian group G is a pair (X, Y) of nonempty subsets of G where Y=G−X and every member of X precedes every member of Y. A Dedekind cut (X, Y) is said to be continuous if X has a greatest member or Y has a least member, but not both; if every Dedekind cut of G is a continuous cut, G is said to be (Dedekind) continuous. The ordered abelian group R of real numbers is, ...

A virulent double-stranded DNA bacteriophage, Phi K1-5, has been isolated and found to be capable of infecting Escherichia coli strains that possess either the K1 or the K5 polysaccharide capsule. Electron micrographs show that the virion consists of a small icosohedral head with short tail spikes, similar to members of the Podoviridae family. DNA sequence analysis of the region encoding the ta...

When inorganic phosphate is limiting, Arabidopsis has the facultative ability to metabolize exogenous nucleic acid substrates, which we utilized previously to identify insensitive phosphate starvation response mutants in a conditional genetic screen. In this study, we examined the effect of the phosphate analog, phosphite (Phi), on molecular and morphological responses to phosphate starvation. ...