BACKGROUND An adverse hematological interaction between vitamins E and K has been reported, primarily in patients on anticoagulants. However, little is known regarding circulating levels or tissue concentrations of vitamin K in response to vitamin E supplementation. The purpose of this study was to examine the effect of different levels of dietary alpha-tocopherol on phylloquinone and menaquino...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

In this paper, an arti…cial neural network based-model (ANNBM) is introduced for partial shading detection losses in photovoltaic (PV) panel. A Multilayer Perceptron (MLP) is used to estimate the electrical outputs (current and voltage) of the photovoltaic module using the external meteorological data : solar irradiation G (W/m2) and the module temperature T (μrC). Firstly, a database of the BP...

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

We present updated radial-velocity (RV) analyses of the AU Mic system. is a young (22 Myr) early M dwarf known to host two transiting planets - $P_{b}\sim8.46$ days, $R_{b}=4.38_{-0.18}^{+0.18}\ R_{\oplus}$, $P_{c}\sim18.86$ $R_{c}=3.51_{-0.16}^{+0.16}\ R_{\oplus}$. With visible RVs from CARMENES-VIS, CHIRON, HARPS, HIRES, {\sc {\textsc{Minerva}}}-Australis, and TRES, as well near-infrared (NIR...

Let  be a commutative ring and  be a unitary  module. We define a semi prime sub module of a module and consider various properties of it. Also we define semi-radical of a sub module of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.

Given two coprime numbers $$q_1$$ and $$q_2$$ , let $$\Gamma =q_1\mathbb {Z}\oplus q_2 \mathbb {Z} $$ . Let $$\Delta +X$$ be the discrete periodic Schrödinger operator on $$\mathbb {Z}^2$$ where is Laplacian $$X:\mathbb {Z}^2\rightarrow {C}$$ -periodic. In this paper, we develop tools from complex analysis to study isospectrality of operators. We prove that if -periodic potentials X Y are Fermi...