This paper deals with some universal spaces. For every topological space $X$, the $T_1$ is viewed as bottom element of lattice $\mathcal{L}_X$. The class morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all spaces characterized. Also, we introduce new separation axioms and characterize them. Moreover, $X$ for which associated a spectral space. Finally, give characterizations such that their $...

We prove a quantitative version of Hilbert's irreducibility theorem for function fields: If $f(T_1,\ldots, T_n,X)$ is an irreducible polynomial over the field rational functions finite $\mathbb{F}_q$ characteristic $p$, then proportion $n$-tuples $(t_1,\ldots, t_n)$ monic polynomials degree $d$ which $f(t_1,\ldots, t_n,X)$ reducible out all $O(dq^{-d/2})$.

Abstract Wiggle matching is an important and powerful technique in radiocarbon dating that can be used to improve the precision of calendar age estimates. All determinations require calibration provide This achieved by comparing against a curve $\mu ( \cdot )$ calculate probability sample arises from any particular t . involves set taken samples with known separations between their ages. Since ...

BACKGROUND Chronic obstructive pulmonary disease (COPD) is a respiratory disorder with increasing prevalence and mortality. It is associated with airway obstruction, increased airway hyper-responsiveness (AHR), and ongoing airway and lung inflammation dominated by CD8 lymphocytes and neutrophils. Single-nucleotide polymorphisms (SNPs) in a disintegrin and metalloprotease 33 (ADAM33) gene have b...

Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for periodicity threshold of powers tropical matrix. According to that approach, ultimate take form T=max(T_1,T_2), where T_1 is bound time after which expansion starts hold T_2 first term dominate. The established this make use cyclicity associated graph (tropical) factor rank ...

Astronomy has always been propelled by the discovery of new phenomena lacking precedent, often followed theories to explain their existence and properties. In modern era large surveys tiling sky at ever high precision sampling rates, these serendipitous discoveries look set continue, with recent examples including Boyajian's Star, Fast Radio Bursts `Oumuamua. Accordingly, we here ahead aim prov...

Let $n\in \mathbb{N}, n\geq 2.$ An element $x=(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x)|=\|T\|,$ where ${\mathcal denotes the space all continuous $n$-linear forms on $E.$For we define set} $T$
 \centerline{$\qopname\relax o{Norm}(T)=\Big\{(x_1, E^n: (x_1, x_n)~\mbox{is point of}~T\Big\}.$}
 By $i=(i...

In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in topological category of quantale-valued preordered spaces investigate how these characterizations are related. Moreover, prove that local hereditary productive.

We show that, in relativistic field theories, the thermal correlation function of N bosonic operators at sufficiently spacelike-separated points shows exponentially weak dependence on time variables t_1,...,t_N, when space separations are held fixed. For classical theory, vanishes all spacelike separated

Let $T_1, T_2$ be regular trees of degrees $d_1, d_2 \geq 3$. also $\Gamma \leq \mathrm{Aut}(T_1) \times \mathrm{Aut}(T_2)$ a group acting freely and transitively on $VT_1 VT_2$. For $i=1$ $2$, assume that the local action $\Gamma$ $T_i$ is $2$-transitive; if moreover $d_i 7$, contains $\mathrm{Alt}(d_i)$. We show irreducible, unless $(d_1, d_2)$ belongs to an explicit small set exceptional val...