ardy and littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. they believed that the number $mathcal{r}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{r}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...

Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is introduced as a new variant of such communication scenarios‎. First, it is shown that the additive Gaussian ch...

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

In this paper, undoped TiO2 and Ag-Nd-codoped TiO2 nanocomposites with different molar ratios of dopants were synthesized by the sol-gel method using starch as a natural additive. Structures were investigated by FT-IR and UV–Vis spectroscopy, SEM, and XRD methods. Moreover, the direct band gap was calculated by Tauc's approach. Furthermore, photocatalytic activity of all s...

due to cereal are affected by drought stress in their lifetime. in order to study gene action of bread wheat under drought stress condition, a generation mean analysis was performed using f1, f2 and f3 generations derived from roushan and kavir. generation mean analysis was performed based on joint scaling test. genetic parameters including additive effect (d), dominance effect (h), additive×ad...

§1. The basic definitions and the main theorem. 1. Definition. (1) We define addition on 2 as addition modulo 2 on each component, i.e., if x, y, z ∈ 2 and x+ y = z then for every n we have z(n) = x(n) + y(n) (mod 2). (2) For A,B ⊆ 2 and x ∈ 2 we set x + A = {x + y : y ∈ A}, and we define A + B similarly. (3) We denote the Lebesgue measure on 2 with μ. We say that X ⊆ 2 is null-additive if for ...

this study evaluated the effects of various dietary levels of maros nigra's powder on some immune factors and blood parameters of rainbow trout (oncorhynchus my kiss). 320 fish with average initial weight 75 + 0.01 g randomly distributed in 12 tanks and fed by 0, 20, 40, and 60 ppm additive powder for 8 weeks. the results showed that the treatments, which fed more additive powder, had the ...