A bstract We propose a twin Pati-Salam (PS) theory of flavour broken to the G 4321 gauge group at high energies, then Standard Model low yielding TeV scale vector leptoquark $$ {U}_1^{\mu } U 1 μ (3 , 1 2 / 3) which has been suggested address lept...

In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Ga...

The study of the purely leptonic decays ground charged vector mesons is very interesting and significant in determining CKM matrix elements, obtaining decay constant mesons, examining lepton flavor universality, searching for new physics beyond standard model. These are induced by weak interactions within model, usually have small branching ratios, ${\cal B}({\rho}^{-}{\to}{\ell}^{-}{\nu}_{\ell...

We generalise Merzlyakov's theorem about the first-order theory of non-abelian free groups to all acylindrically hyperbolic groups. As a corollary, we deduce that if $G$ is an group and $E(G)$ denotes unique maximal finite normal subgroup $G$, then HNN extension $G\dot{\ast}_{E(G)}$, which simply product $G\ast\mathbb{Z}$ when trivial, have same $\forall\exists$-theory. consequence, prove follo...

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that has two such frames and obtain frame's equations. find the relations between curvature functions $k_g$, $k_n$, $\tau_g$ with respect to its $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ frames. show exist along straight line ...

We show that there exist knots K ⊂ S with g(E(K)) = 2 and g(E(K#K#K)) = 6. Together with [5, Theorem 1.5], this proves existence of counterexamples to Morimoto’s Conjecture [10]. This is a special case of [6]. Let Ki (i = 1, 2) be knots in the 3-sphere S, and let K1#K2 be their connected sum. We use the notation t(·), E(·), and g(·) to denote tunnel number, exterior, and Heegaard genus respecti...