in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

n = 1: 1 = 0 + 1; n = 2 (prime): 2 = 1 + 1; n = 3 (prime) is not a sum of two squares. n = 4: 4 = 2 + 0. n = 5 (prime): 5 = 2 + 1. n = 6 is not a sum of two squares. n = 7 (prime) is not a sum of two squares. n = 8: 8 = 2 + 2. n = 9: 9 = 3 + 0. n = 10: 10 = 3 + 1. n = 11 (prime) is not a sum of two squares. n = 12 is not a sum of two squares. n = 13 (prime): 13 = 3 + 2. n = 14 is not a sum of t...

n>0 (1− q) be Dedekind’s eta-function. For a prime p, denote by U Atkin’s Up-operator. We say that a function φ with a Fourier expansion φ = ∑ u(n)q is congruent to zero modulo a power of a prime p, φ = ∑ u(n)q ≡ 0 mod p if all its Fourier expansion coefficients are divisible by this power of the prime; u(n) ≡ 0 mod p for all n. In this paper we prove the following congruences. Theorem 1. (i) I...

in this paper, it was shown that , where  and , and , where  is not prime and , are od-characterizable.

We present a search for the dark photon $A^{\prime}$ in $B^0 \to A^{\prime} A^{\prime}$ decays, where subsequently decays to $e^+ e^-$, $\mu^+ \mu^-$, and $\pi^+ \pi^-$. The is performed by analyzing $772 \times 10^6$ $B\overline{B}$ events collected Belle detector at KEKB e^-$ energy-asymmetric collider $\Upsilon (4S)$ resonance. No signal found mass range $0.01~\mathrm{GeV}/c^2 \le m_{A^{\pri...

Abstract Let N be a $$\mathbb {Z}$$ Z -nearalgebra; that is, left nearring with identity satisfying $$ k(nn^{\prime })=(kn)n^{\prime }=n(kn^{\prime })$$ k ( n ′ ) =</mml:m...

In this paper, we introduce a new subclass of harmonic functions f = s + ¯ t f=s+t¯ in the open unit disk U { z ∈ C : | < 1 } U={z∈C:|z|<1} satisfying ${\text{Re}}\left[ \gamma \mathfrak{s}^{\prime }(z)+\delta z\mathfrak{s}^{\prime \prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}\mathfrak{s}^{\prime }\left( z\right) -\lambda \right]>\left \vert \mathfrak{t}^{\prime z\mathfrak{t}^{\prim...

In this work, we use the $C^3P_{\,0}$ model to calculate decay widths of low lying charmonium $J^{PC}=1^{--}$ states, nominally $J/\psi(1S)$ and $\psi(2S)$, in following common channels: $\rho\,\pi$, $\omega\,\eta$, $\omega\,\eta^\prime$, $K^{\ast +}\,K^-$, 0}\,\bar{K}^0$, $\phi\,\eta$, $\phi\,\eta^\prime$.

Given a finite set of eigenvalues regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, potential q(x) which is unknown. We show possibility to compute more without any additional information on q(x). Moreover, considering with boundary conditions y{\prime}(0)-hy(0)=0 and y{\prime}({\pi})+Hy({\pi})=0, where h, H are some constants, we complete its spectrum neithe...