We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...

Given $n$ distinct points $\mathbf{x}_1, \ldots, \mathbf{x}_n$ in $\mathbb{R}^d$, let $K$ denote their convex hull, which we assume to be $d$-dimensional, and $B = \partial K $ its $(d-1)$-dimensional boundary. We construct an explicit one-parameter family of continuous maps $\mathbf{f}_{\varepsilon} \colon \mathbb{S}^{d-1} \to K$ which, for $\varepsilon > 0$, are defined on the sphere have pro...

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along crystalline $a$ axis on newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. our study, when is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\si...

The ratio $\epsilon'/\epsilon$ measures the size of direct CP violation in $K_L\to\pi\pi$ decays $(\epsilon^\prime)$ relative to indirect one described by $\epsilon$ and is very sensitive new sources violation. As such it played a prominent role particle physics already for 45 years. Due smallness its measurement required heroic efforts 1980s 1990s on both sides Atlantic with final results pres...

In this paper, we consider the problem of maximizing a monotone submodular function subject to knapsack constraint in streaming setting. such setting, elements arrive sequentially and at any point time, algorithm can store only small fraction that have arrived so far. For special case all unit sizes (i.e., cardinality-constraint case), one find $$(0.5-\varepsilon )$$ -approximate solution $$O(K...

We consider maximizing a monotone submodular function under cardinality constraint or knapsack in the streaming setting. In particular, elements arrive sequentially and at any point of time, algorithm has access to only small fraction data stored primary memory. propose following algorithms taking O(ε− 1) passes: (1) (1 − e− 1 ε)-approximation for cardinality-constrained problem, (2) (0.5 knaps...

The $q$-Coloring problem asks whether the vertices of a graph can be properly colored with $q$ colors. Lokshtanov et al. [SODA 2011] showed that on graphs feedback vertex set size $k$ cannot solved in time $\mathcal{O}^*((q-\varepsilon)^k)$, for any $\varepsilon > 0$, unless Strong Exponential-Time Hypothesis (SETH) fails. In this paper we perform fine-grained analysis complexity respect to hie...