Abstract We present novel realizations of E-model inflation within Supergravity which are largely associated with the existence a pole order one in kinetic term (gauge-singlet) inflaton superfield. This arises due to selected logarithmic Kähler potentials $$K_1$$ K 1 an...

Let $(G,G_1)$ be a symmetric pair of holomorphic type, and we consider Hermitian spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded domains in complex vector $\mathfrak{p}^+_1\subset\mathfrak{p}^+$ respectively. Then the universal covering group $\widetilde{G}$ $G$ acts unitarily on weighted Bergman space $\mathcal{H}_\lambda(D)\subset\mathcal{O}(D)$ $D$. Its restriction to subgroup $\widet...

For graphs $G$ and $H$, the Ramsey number $R(G,H)$ is minimum integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red or blue $H$. Let $G+H$ be graph obtained from vertex disjoint $H$ by adding new edges connecting completely, $F_m=K_1+mK_2$ $B_p(n)=K_p+nK_1$. It shown $R(F_m,B_p(n))=2(n+p-1)+1$ for fixed $m, p$ large $n$.

This paper deals with the zero-flux attraction-repulsion chemotaxis model \begin{document}$ \begin{align} \begin{cases} u_t = \nabla \cdot \left((u+1)^{m_1-1}\nabla u - \chi u(u+1)^{m_2-1}\nabla v \right. & \text{ in } \Omega \times (0, {T_{\text{max}}}), \\ \left. \qquad \; + \xi u(u+1)^{m_3-1} w\right)+h(u) v_t \Delta f(u)v w_t w- g(u)w& \end{cases} \end{align} ~~~~(\Diamond)$\end{doc...

Let K be a field and let $$S=K[x_1,\ldots ,x_n]$$ standard polynomial ring over K. We characterize the extremal Betti numbers, values as well positions, of t-spread strongly stable ideal S. Our approach is constructive. Indeed, given some positive integers $$a_1,\dots ,a_r$$ pairs $$(k_1,\ell _1),\ldots ,(k_r,\ell _r)$$ , we are able to determine under which conditions there exists I S with $$\...

We introduce a class of 3d theories consisting strongly-coupled ${\mathcal N}=4$ systems coupled to N}=3$ Chern-Simons gauge multiplets, which exhibit enhancements when peculiar condition on the levels is met. An example $SU(N)^3$ theory $T_N$ theory, enhances $1/k_1+1/k_2+1/k_3=0$. also show that some but not all these can be understood by considering M5-branes special Seifert manifolds. Our c...

Let $r$, $v$, $n$ be positive integers. This paper investigate the number of solutions $s_{r,v}(n)$ following infinite Diophantine equations \[ n = 1^{r} \cdot |k_{1}|^{v} + 2^{r} |k_{2}|^{v} 3^{r} |k_{3}|^{v} \cdots \] for $\boldsymbol{k} (k_1,k_2,k_3,\ldots) \in \mathbb{Z}^{\infty}$. For each $(r,v) \mathbb{N} \times \{1,2\}$, a generating function and some asymptotic formulas are established.

With the design B(v,r_1,...,r_v,b,k_1,...,k_b,λ{12},...,λ{v-1,v}),like one combinatorial configuration, can be presented organization of one experiment in which participate finite number v different elements some basic set V, which should organise in the b designs each with defined number k_j (j=1,...,v) elements from this basic set, but so that every of this elements are exactly in ri (i=1,......

A homomorphism J: 7Tk_1(SOw) -> nm+k_1(S ) from the homotopy groups of rotation groups to the homotopy groups of spheres has been defined by H. Hopf and G. W. Whitehead. This homomorphism plays an important role in the study of differentiable manifolds. We will study its relation to one particular problem: the question of possible Pontrjagin numbers of an 'almost parallelizable' manifold. Defin...

We study the Anomaly flow on $2$-step nilmanifolds with respect to any Hermitian connection in Gauduchon line. In case of flat holomorphic bundle, general solution is given for initial invariant metric. The solutions depend two constants $K_1$ and $K_2$, we qualitative behaviour terms their signs, as well convergence Gromov-Hausdorff topology. sign related conformal introduced by Fu, Wang Wu. n...