We consider the form factors for radiative semileptonic decays $\bar{B}(v) \rightarrow D^{(*)}(v') \ell {\bar \nu}_\ell \gamma$ in kinematic region where photon momentum, $k$, is small enough that heavy quark symmetry (HQS) can be applied without radiated changing velocity (i.e., $v^{(\prime)} \cdot k < m_{(b,c)}$). find HQS remarkably powerful, leaving only four new undetermined at leading ord...

For a finite collection of graphs \(\mathcal {F} \) , the -TM-Deletion problem has as input an n -vertex graph G and integer k asks whether there exists set S ⊆ V ( ) with | ≤ such that ∖ does not contain any in topological minor. We prove for every is fixed parameter tractable on planar graphs. Our algorithm runs \(2^{\mathcal {O}(k^2)}\cdot n^{2} time or, alternatively {O}(k)}\cdot n^{4} time...

The $b$-parts, $b$-addition of real numbers and some their&#x0D; extensions (e.g., $f$-multiplications) were introduced studied&#x0D; by the author. In this paper, we introduce $f$-representatives&#x0D; groups a given group $(G,\cdot)$ which can be considered as a&#x0D; generalization least non-negative residues&#x0D; (modulo $n$). Thereafter, study their important&#x0D; properties relations am...

The cross section of a given process fundamentally quantifies the probability for that to occur. In quantum regime low energies, can vary strongly with collision energy due effects. Here, we report on method directly measure atom-ion collisional in range 0.2-12 mK$\cdot$ k$_B$, by shuttling ultracold atoms trapped an optical-lattice across radio-frequency ion. this method, average number collis...

This paper deals with existence, uniqueness and energy decay of solutions to a degenerate hyperbolic equations given by \begin{align*} K(x,t)u'' - M\left(\int_\Omega |\nabla u|^2\,dx \right) \Delta u u' = 0, \end{align*} operator coefficient $K(x,t)$ satisfying suitable properties $M(\,\cdot \,) \in C^1([0, \infty))$ is function which greatest lower bound for $ M (\,\cdot\,) zero. For global we...

For any $\epsilon>0$, Laue and Matijevic [CCCG'07, IPL'08] give a PTAS for finding $(1+\epsilon)$-approximate solution to the $k$-hop MST problem in Euclidean plane that runs time $(n/\epsilon)^{O(k/\epsilon)}$. In this paper, we present an algorithm $(n/\epsilon)^{O(\log k \cdot(1/\epsilon)^2\cdot\log^2(1/\epsilon))}$. This gives improvement on dependency $k$ exponent, while having worse $\eps...

The interplay between set-theoretic solutions of the Yang--Baxter equation Mathematical Physics, skew braces, regular subgroups, and Hopf--Galois structures has spawned a considerable body literature in recent years. In paper, Alan Koch generalised construction Lindsay N.~Childs, showing how one can obtain bi-skew braces $(G, \cdot, \circ)$ from an endomorphism group \cdot)$ whose image is abel...

A stability result in terms of the perimeter is obtained for first Dirichlet eigenvalue Laplacian operator. In particular, we prove that, once fix dimension $n\geq2$, there exists a constant $c>0$, depending only on $n$, such every $\Omega\subset\mathbb{R}^n$ open, bounded, and convex set with volume equal to ball $B$ radius $1$, it holds that $\lambda\_1(\Omega)-\lambda\_1(B)\geq c(P(\Omega)-P...

Abstract We obtain a polynomial upper bound on the mixing time $T_{CHR}(\epsilon)$ of coordinate Hit-and-Run (CHR) random walk an $n-$ dimensional convex body, where is number steps needed to reach within $\epsilon$ uniform distribution with respect total variation distance, starting from warm start (i.e., which has density body that bounded above by constant). Our in n , R and $\frac{1}{\epsil...

Motivated by the heat flow and bubble analysis of biharmonic mappings, we study further regularity issues fourth order Lamm–Rivière system $$\begin{aligned} \Delta ^{2}u=\Delta (V\cdot \nabla u)+\mathrm{div}(w\nabla u)+(\nabla \omega +F)\cdot u+f \end{aligned}$$ in dimension four, with an inhomogeneous term f which belongs to some natural function space. We obtain optimal higher sharp Hölder co...