Abstract We study fast/slow systems driven by a fractional Brownian motion B with Hurst parameter $$H\in (\frac{1}{3}, 1]$$ H ∈ ( 1 3 , ] . Surprisingly, the sl...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

By $\mathcal{A}^2$ denote the class of analytic functions formBy form$f(z)=\sum_{n+m=0}^{+\infty}a_{nm}z_1^nz_2^m,$with {the} domain convergence $\mathbb{T}=\{z=(z_1,z_2)\in\mathbb C^2\colon|z_1|<1,\ |z_2|<+\infty\}=\mathbb{D}\times\mathbb{C}$ and$\frac{\partial}{\partial z_2}f(z_1,z_2)\not\equiv0$ in $\mathbb{T}.$ In this paper we prove some analogue Wiman's inequalityfor $f\in\mathcal{A...

We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed (digraphs). FOPT is coordinate space analogue of time-ordered and loop-tree duality, but it has the advantage having combinatorial canonical rules, combined with simplified $i\varepsilon$ depe...

In this paper, the analysis and homogenization of a poroelastic model for hydro-mechanical response fiber-reinforced hydrogels are considered. Here, medium in question is considered to be highly heterogeneous two-component media composed connected fiber-scaffold with periodically distributed inclusions hydrogel. While fibers assumed elastic, hydromechanical hydrogel modeled via Biot's poroelast...

In mathematical phylogenetics, types of events in a gene tree T are formalized by vertex labels t(v) and set-valued edge \(\lambda (e)\). The orthology paralogy relations between genes special case map \(\delta \) on the pairs leaves defined (x,y)=q\) if last common ancestor \({\text {lca}}(x,y)\) x y is labeled an event type q, e.g., speciation or duplication. Similarly, \(\varepsilon with \(m...

Abstract Let $\mathrm{AP}_k=\{a,a+d,\ldots,a+(k-1)d\}$ be an arithmetic progression. For $\varepsilon>0$ we call a set $\mathrm{AP}_k(\varepsilon)=\{x_0,\ldots,x_{k-1}\}$ $\varepsilon$ -approximate progression if for some and d , $|x_i-(a+id)|<\varepsilon d$ holds all $i\in\{0,1\ldots,k-1\}$ . Complementing earlier results of Dumitrescu (2011, J. Comput. Geom. 2 (1) 16–29), in this paper ...

Given two sets of natural numbers $\mathcal{A}$ and $\mathcal{B}$ density $1$ we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\mathcal{B}\}$ also has $1$. On the other hand, for any $\varepsilon>0$, show there are $>1-\varepsilon$ which $\mathcal{A}\cdot\mathcal{A}$ $<\varepsilon$. This answers questions Hegyv\'{a}ri, Hennecart Pach.

We consider a blow-up phenomenon for \begin{document}$ { \partial_t^2 u_ \varepsilon} $\end{document} id="M2">\begin{document}$ {- \varepsilon^2 \partial_x^2u_ \varepsilon } id="M3">\begin{document}$ = F(\partial_t \varepsilon)}. The derivative of the solution id="M4">\begin{document}$ \partial_t blows-up...

In this paper, we recover the boundary null controllability for degenerate heat equation by analyzing asymptotic behavior of an eligible family state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving corresponding singularly perturbed internal problems. As in other situations studied literature, our approach relies on Carleman estimates and meticulous weak convergenc...