We construct a folding potential between the $\alpha$ and $\Lambda$ particles based on underlying nucleon-nucleon hyperon-nucleon interactions. Starting from phenomenological $\Lambda$-N Gaussian form of $\alpha$-particle wave function we obtain for built $\alpha$-$\Lambda$ interaction bound $^5_\Lambda$He state with binding energy (3.10 MeV), which is consistent recent experimental data $3.12 ...

A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and $L={(x,y):x^{k}equiv y~(bmod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of th...

Given an RSA modulus n, a ciphertext c and the encryption exponent e, one can construct the sequence x 0 = c mod n; x i+1 = x e i mod n; i = 0; 1; : : : until gcd(x i+1 ? x 0 ; n) 6 = 1 or i > B, B a given boundary. If i B, there are two cases. Case 1: gcd(x i+1 ? x 0 ; n) = n. In this case x i = m and the secret message m can be recovered. Case 2: 1 6 = gcd(x i+1 ? x 0 ; n) 6 = n. In this case...

We study solutions of Hamilton--Jacobi equations the form $$\lambda \alpha(x) u_\lambda(x) + H(x, D_x u_\lambda) = c,$$ where $\alpha$ is a nonnegative function, $\lambda$ positive constant, $c$ constant and $H $ convex coercive Hamiltonian. Under suitable conditions on we prove that functions $u_\lambda$ converge as $\lambda\to 0$ to function $u_0$ solution critical equation $H(x, u_0) c$.

Erdős conjectured that there are x1−o(1) Carmichael numbers up to x, whereas Shanks was skeptical as to whether one might even find an x up to which there are more than √ x Carmichael numbers. Alford, Granville and Pomerance showed that there are more than x2/7 Carmichael numbers up to x, and gave arguments which even convinced Shanks (in person-to-person discussions) that Erdős must be correct...