Abstract We establish a one-to-one correspondence between, on the one hand, Finsler structures $2$ -sphere with constant curvature $1$ and all geodesics closed, other Weyl connections certain spindle orbifolds whose symmetric Ricci is positive definite are closed. As an application of our duality result, we show that suitable holomorphic deformations Veronese embedding $\mathbb {CP}(a_1,a_2)\ri...

For positive integers $s,t,u,v$, we define a bipartite graph $\Gamma_{\mathbb{R}}(X^s Y^t,X^u Y^v)$ where each partite set is copy of $\mathbb{R}^3$, and vertex $(a_1,a_2,a_3)$ in the first adjacent to $[x_1,x_2,x_3]$ second if only \[ a_2 + x_2 = a_1^s x_1^t \quad \text{and} a_3+x_3=a_1^ux_1^v. \] In this paper, classify all such graphs according girth.

We investigate infinite-time admissibility of a control operator B in Hilbert space state-delayed dynamical system setting the form $${\dot{z}}(t)=Az(t)+A_1 z(t-\tau )+Bu(t)$$ , where A generates diagonal $$C_0$$ -semigroup, $$A_1\in {\mathcal {L}}(X)$$ is also and $$u\in L^2(0,\infty ;{\mathbb {C}})$$ . Our approach based on Laplace embedding between $$L^2$$ Hardy $$H^2({\mathbb {C}}_+)$$ The ...

The Minkowski question-mark function $?(x)$ is a continuous strictly increasing defined on $[0,1]$ interval. It well known fact that the derivative of this function, if exists, can take only two values: $0$ and $+\infty$. also value $?'(x)$ at point $x=[0;a_1,a_2,\ldots,a_t,\ldots]$ connected with limit behavior arithmetic mean $(a_1+a_2+\ldots+a_t)/t$. Particularly, N. Moshchevitin A. Dushisto...

Let H and F be two Hénon maps with biholomorphically equivalent escaping sets, then there exist affine automorphisms $$A_1$$ $$A_2$$ in $${\mathbb {C}}^2$$ such that $$\begin{aligned} F=A_1\circ \circ A_2 \end{aligned}$$ .

Abstract We evaluate the $$a_1(1260) \rightarrow \pi \sigma (f_0(500))$$ a 1 ( 1260 ) → π σ f 0 500 </mml:...

We study the behavior of solutions for parametric equation $$-\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z)=\lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0,$$ under Dirichlet condition, where $\Omega \subseteq \mathbb{R}^N$ is a bounded domain with $C^2$-boundary $\partial \Omega$, $a_1,a_2 \in L^\infty(\Omega)$ $a_1(z),a_2(z)>0$ a.a. $z $p,q (1,\infty)$ and $\Delta_{p}^...

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

Let $\mathbb {N}=\{0,1,2,\ldots \}$ and $A\subset \mathbb {N}$. $h\geq 2$ let $r_h(A,n)=\sharp \{ (a_1,\ldots ,a_h) \in A^{h}: a_1+\cdots +a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently la