The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

Sampling Geostatistical Structures in Extremal Framework

Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.

Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

一类具有Star Extremal性质的循环图(英文)

圆色数和分式色数是图的点色数的 2个推广 .当图的圆色数等于分式色数时 ,称此图是starextremal.本文研究了生成集为 {± 1。

顶点可迁图为star extremal的一个充要条件(英文)

一个图当它的圆色数和分色数相等称之为starextremal.本文首先给出一个图的圆色数等于顶点数除以独立数的充要条件 .然后利用这个结果给出了顶点可迁图是starextremal的一个充要条件 .并由此得到了几类新的starextremal图 .

一类关联图的Star Extremal性质(英文)

证明了Cn的关联图I(Cn)是循环图,还证明了所有Cn的关联图I(Cn)及一些与I(Cn)有关的图是starextremal的.并用一种同构的方法得到了它们的圆色数和分色数.

EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

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The Extremal Problem on Cartan-egg Domain of the First Type

在这份报纸，我们由使用一些不平等在第一种类型的 Cartan 鸡蛋领域上学习 extremal 问题。印射的 extremal 和在 Cartan 鸡蛋领域和单位的第一种类型之间的 extremal 价值成球形什么时候 k1 和 k = 2；m = 2 被构造。

Unicyclic graphs with extremal Lanzhou index

Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.

Uniform Convergence of Extremal Polynomials When Domains Have Corners and Special Cusps on the Boundary

We study the approximation properties of the extremal polynomials in Ap?norm and C?norm. We prove estimates for the rate of such convergence of the sequence of the extremal polynomials on domains with corners and special cusps.

REVISITING A NON-DEGENERACY PROPERTY FOR EXTREMAL MAPPINGS

We extend an earlier result obtained by the author in [7].

Destroying Extremal Kerr-Newman-AdS Black Holes with Test Particles

Neglecting the self-force,self-energy and radiative effects,we follow the spirit of Wald's gedanken experiment and further discuss whether an extremal Kerr-Newman-AdS(KNA)black hole can turn into a naked singularity when it captures charged and spinning massive particles.It is found that feeding a test particle into an extremal KNA black hole could lead to a violation of cosmic censorship for the black hole.

Geometric Aspects of Extremal Kerr Black Hole Entropy

Extreme Black Holes is an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.

Asymptotic Extremal Distribution for Non-Stationary, Strongly-Dependent Data

Fisher-Tippet-Gnedenko classical theory shows that the normalized maximum of n iid random variables with distribution F belonging to a very wide class of functions, converges in law to an extremal distribution H, that is determined by the tail of F. Extensions of this theory from the iid case to stationary and weak dependent sequences are well known from the work of Leadbetter, Lindgreen and Rootzén. In this paper, we present a very simple class of random processes that runs from iid sequences to non-stationary and strongly dependent processes, and we study the asymptotic behavior of its normalized maximum. More interesting, we show that when the process is strongly dependent, the asymptotic distribution is no longer an extremal one, but a mixture of extremal distributions. We present very simple theoretical and simulated examples of this result. This provides a simple framework to asymptotic approximations of extremes values not covered by classical extremal theory and its well-known extensions.

Extremal Kähler Metrics of Toric Manifolds

This paper is a survey of some recent developments concerning extremal Kähler metrics on Toric Manifolds.

Extremal P_(8)-Free/P_(9)-Free Planar Graphs

An H-free graph is a graph not containing the given graph H as a subgraph.It is well known that the Turán number ex(n,H)is the maximum number of edges in an H-free graph on n vertices.Based on this definition,we define ex_(P)(n,H)to restrict the graph classes to planar graphs,that is,ex_(P)(n,H)=max{|E(G)|:G∈G,where G is a family of all H-free planar graphs on n vertices.Obviously,we have ex_(P)(n,H)=3n−6 if the graph H is not a planar graph.The study is initiated by Dowden(J Graph Theory 83:213–230,2016),who obtained some results when H is considered as C_(4)or C_(5).In this paper,we determine the values of ex_(P)(n,Pk)with k∈{8,9},where Pk is a path with k vertices.

Extremal Functions for an Improved Trudinger-Moser Inequality Involving L^(P)-Norm in R^(n)

Let W^(1,n)(R^(n))be the standard Sobolev space.For any T>0 and p>n>2,we denote■Define a norm in W^(1,n)(R^(n))by■where 0≤α<λ_(n,p).Using a rearrangement argument and blow-up analysis,we will prove■can be attained by some function u_(0)∈W^(1,n)(R^(n))∩C^(1)(R^(n))with ||u_(0)||_(n,p)=1,here a_(n)=n■_(n-1)^(1/n-1) and ■_(n-1) is the measure of the unit sphere in R^(n).

一类四阶差分方程边值问题Extremal解的存在性

本文运用上,下解单调迭代技巧讨论四阶差分方程两点边值问题■解的存在性,其中N>2是一个固定的自然数,f:{2,3,…,N}×R^2→R连续,g:R→R连续,严格单调递增且g(0)=0.

The value does not exist!A motivation for extremal analysis

Standard mathematical economics studies the production,exchange,and consumption of goods“provided with units of measurement,”as in physics,in order to be enumerated,quantified,added,etc.Therefore,“baskets of goods,”which should describe subsets of goods,are mathematically represented as commodity vectors of a vector space,linear combination of units of goods,evaluated by prices,which are linear numerical functions.Therefore,in this sense,mathematical economics is a branch of physics.However,economics,and many other domains of life sciences,investigate also what will be called entities,defining elements deprived of units of measure,which thus cannot be enumerated.(1)Denoting by X the set of entities x∈X deprived of units of measurement,a“basket of goods”is actually a subset K■X of the set entities,i.e.,an element of the“hyperset”P(X),the family of subsets of X,and no longer a commodity vector of the vector space of commodities;(2)Entities can be“gathered”instead of being“added”;(3)Entities can still be evaluated by a family of functions A:x 2 X 7!A(x)2 Rregarded as a“valuators,”in lieu and place of linear“prices”evaluating the units of economic goods.(4)Subsets of entities can be evaluated by an“interval of values”between two extremal ones,the minimum and the maximum,instead of the sum of values of units of goods weighted by their quantities.Life sciences dealing with intertwined relations among many combinations of entities,hypersets offer metaphors of“Lamarckian complexity”that keeps us away from binary relations,graphs of functions,and set-valued maps,to focus our attention on“multinary relations”between families of hypersets.Even deprived of units of measurement,these“proletarian”entities still enjoy enough properties for this pauperization to be mathematically consistent.This is the object of this extremal manifesto:in economics and other domains of life sciences,vector spaces should yield their imperial status of“state space”to hypersets and linear prices to hypervaluators.We no longer have to add goods which can only be gathered,prices do not have to be linear,although it costs some effort to deprive oneself of the powerful and luxurious charms of convex and linear functional analysis motivated by physics.These sacrifices concern only economics and other fields of life science,since physicists deal with experimental observations of objects endowed with unit of measurement by adequate processes of measurement.They can happily live in vector spaces without any guilt.This is not the case of life scientists,who have mainly history to support and validate their observations,with,sometimes,the privilege to statistically measure the frequency of some of them.

Competitive oxidation behavior of Ni-based superalloy GH4738 at extreme temperature

A high thrust-to-weight ratio poses challenges to the high-temperature performance of Ni-based superalloys. The oxidation behavior of GH4738 at extreme temperatures has been investigated by isothermal and non-isothermal experiments. As a result of the competitive diffusion of alloying elements, the oxide scale included an outermost porous oxide layer (OOL), an inner relatively dense oxide layer (IOL), and an internal oxide zone (IOZ), depending on the temperature and time. A high temperature led to the formation of large voids at the IOL/IOZ interface. At 1200℃, the continuity of the Cr-rich oxide layer in the IOL was destroyed, and thus, spallation occurred. Extension of oxidation time contributed to the size of Al-rich oxide particles with the increase in the IOZ. Based on this finding,the oxidation kinetics of GH4738 was discussed, and the corresponding oxidation behavior at 900-1100℃ was predicted.