In the general two Higgs doublet model (g2HDM) that has extra Yukawa couplings, we analyze their New Physics (NP) contributions to kaon mixing parameter $\varepsilon_K$, direct CP violation $\varepsilon^\prime/\varepsilon$, and rare $K^+ \to \pi^+\nu\bar\nu$, $K_L \pi^0\nu\bar\nu$, $K_{L, S} \mu^+ \mu^-$ decays. We study correlations between these observables, call special attention a unique co...

In this note, we prove that the following function space with absolutely convergent Fourier series \[ F_d:=\left\{ f\in L^2([0,1)^d)\:\middle| \: \|f\|:=\sum_{\boldsymbol{k}\in \mathbb{Z}^d}|\hat{f}(\boldsymbol{k})| \max\left(1,\min_{j\in \mathrm{supp}(\boldsymbol{k})}\log |k_j|\right) <\infty \right\}\] $\hat{f}(\boldsymbol{k})$ being $\boldsymbol{k}$-th coefficient of $f$ and $\mathrm{supp}(\...

In a spatially heterogeneous environment the propagation speed of biological invasion varies in space. The traveling wave theory homogeneous case is not extended to case. Taking singular limit hyperbolic scale good way study such with constant speed. goal this project understand effect diffusion on spatial environment. For purpose, we consider \begin{document}$ U_t = {\varepsilon}(\gamma(s)U)_{...

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from centers given input points. Examples are $k$-Means, Geometric $k$-Median/Center, Continuous Facility Location, $m$-Variance, etc. We prove that, for any fixed $\varepsilon>0$, every set of $n$ fixed-dimensional with metric ind...

We study the problem of constructing coresets for clustering problems with time series data. This has gained importance across many fields including biology, medicine, and economics due to proliferation sensors facilitating real-time measurement rapid drop in storage costs. In particular, we consider setting where data on $N$ entities is generated from a Gaussian mixture model autocorrelations ...

The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study problem following a priori unstable Hamiltonian system with time-periodic perturbation \[\mathcal{H}_\varepsilon(p,q,I,\varphi,t)=h(I)+\sum_{i=1}^n\pm \left(\frac{1}{2}p_i^2+V_i(q_i)\right)+\varepsilon H_1(p,q,I,\varphi, t), \] where $(p,q)\in \mathbb{R}^n\times\mathbb{T}^n$, $(I,\varphi)\in\...

Abstract Given a dataset V of points from some metric space, popular robust formulation the k -center clustering problem requires to select (centers) which minimize maximum distance any point its closest center, excluding z most distant (outliers) computation maximum. In this paper, we focus on an important constrained variant problem, namely, Robust Matroid Center (RMC) where set returned cent...

Given a stable SISO LTI system $G$, we investigate the problem of estimating the $\mathcal{H}_\infty$-norm of $G$, denoted $||G||_\infty$, when $G$ is only accessible via noisy observations. Wahlberg et al. recently proposed a nonparametric algorithm based on the power method for estimating the top eigenvalue of a matrix. In particular, by applying a clever time-reversal trick, Wahlberg et al. ...

Two oligomers, each containing 3 l-lysine residues, were used as model molecules for the simulation of the beta-sheet conformation of varepsilon-polylysine (varepsilon-PLL) chains. Their C terminals were capped with ethylamine and N terminals were capped with alpha-l-aminobutanoic acid, respectively. The calculations were carried out with the hybrid two-level ONOIM (B3LYP/6-31G:PM3) computation...