COMPUTATIONAL COMPLEXITY IN WORST,STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class W_p~(?)(Id), Nikolskii class H|∞~k(Id) in the worst (deterministic), stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes W_p~(?)(Id) and H_∞~k(Id) is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.     

A NOTE ON SOME FOURTH ORDER ELLIPTIC EQUATIONS

As We know, maximum principle is very important for elliptic equations. It often provides us with a simple proof for the uniqueness and continuous dependence of solutions on. boundary values,and constitutes the first step of existence proof. Furthermore, it is also useful for the study of properties of solutions. In recent years, some works on the maximum principles of fourth order elliptic equations     

FURTHER RESULTS ON THE BOUNDEDNESS AND PERIODICITY OF SOME DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER

This research investigates the ultimate boundedness of solutions of the differential equations ofthe form(1.1),where the bounding constant is independent of the initial values of solutions.Anexistence result for periodic solutions of(1.1) is also established.     

LOCAL INFLUENCE ASSESSMENT BASED ON LOCAL DIVERGENCE IN STOCHASTIC REGRESSION MODEL

Abstract. This paper describes the local influence assessment for parameter inferenceof a statistlcual model by using curvatures assoclated with Iota| divergence under ageneric perturbatlon scheme. The results are applied to examine the local influence instochastlc regresslon model under two perturbation schemes. An economic examp|e isanalyzed to ~llustrate results here.     

A THEOREM ON METABELIAN p-GROUPS AND SOME CONSEQUENCES

This paper introduces a new characteristic subgroup ζ(G)for a finite p-group G,calledthe p-center of G(Definition 1).A property of p-centers for metabelian p-groups(Theorem1)is proved.Applying this theorem to regular and p-abelian p-groups,we obtain severalknown result for these groups once again(Theorems 2,3 and 6).     

ON SOME MODEL DIFFUSION PROBLEMS WITH A NONLOCAL LOWER ORDER TERM

The authors consider a class of nonlinear parabolic problems where the lower order term is depending on a weighted integral of the solution, and address the issues of existence, uniqueness, stationary solutions and in some cases asymptotic behaviour.     

THE ZERO AND ORDER OF SOME SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPHIC COEFFICIENTS

ＴＨＥＺＥＲＯＡＮＤＯＲＤＥＲＯＦＳＯＭＥＳＥＣＯＮＤＯＲＤＥＲＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＴＲＡＮＳＣＥＮＤＥＮＴＡＬＭＥＲＯＭＯＲＰＨＩＣＣＯＥＦＦＩＣＩＥＮＴＳＣＨＥＮＺＯＮＧＸＵＡＮＡｂｓｔｒａｃｔ：Ｉｎｔｈ...     

TYPES AND CRITERIA OF NONOSCILLATORY SOLUTIONS FOR SOME SECOND ORDER NFDE

In this paper we discuss the following NFDE[r(t)[x(t)-cx(t-τ)]′]′ integral from a to b p(t,ξ)x[g(t,ξ)]dσ(ξ)=0where τ>0,1>c≥0,0≤g(t,ξ)≤t,r(t)>0,p(t,ξ)>0,and some sufficient and necessary conditionsare given,under which there are three types of nonoscillatory solutions for the above equation.     

SOME RESULTS ON A DEGENERATE AND SINGULAR DIFFUSION EQUATION

In this article,a degenerate and singular diffusion problem is studied.The ex- istence of solutions is established by parabolic regularization.Some properties of solutions, for instance,asymptotic behavior,are also discussed.     

SOME CONSISTENT RESULTS ON LINDELFNESS AND CALIBRE

This paper gives some topological propositions which are equivalent to the continuum hypothesis. The following results are also given: In the class of 1-st countable Hausdoff spaces, the existence of space which has calibre (ω_1, ω) but no calibre ω_1 is equivalent to the existence of space which has calibre (ω_1, ω) but is not point-countablely Lindelog, the existence of space which has calibre ω_1 but is not separable is equivalent to the existence of space which has calibre ω_1 but is not Lindelof, too.     

New multivariate orderings based on conditional distributions

In this paper, we propose and study new multivariate extensions of the dispersive, right‐spread, decreasing mean residual life and new better than used in expectation univariate orders. These new orders are based on the comparison of univariate marginal distributions conditional on survival data for the rest of the components. Relationships among multivariate orders and applications to some multivariate random vectors are also provided. Copyright © 2011 John Wiley & Sons, Ltd.     

Right Spread序的若干封闭性质

§1Introductionandmotivation Itisalwaysofinteresttocomparethevariabilityoftworandomvariablesinreliability theoryandeconomics.Thecomparisonsbasedonmomentssuchasvarianceandstandard deviationarenotveryinformativealthoughsuchmeasuresaresimpletouse.Meanwhile,sincethesecomparisonsarestaticones,andhencetheirapplicationsinsomefields,e.g.,reliabilityandfinance,arerestricted.Inthesefields,however,somedynamicalcomparisons areneeded.Asaresult,severalstochasticordersthataremorerefinedhavebeen establishedi…     

Characterization based on conditional distributions

The field of application of a result given by Singh and Vasudeva (1984, J. Indian Statist. Assoc., 22, 93–96) which provides a way of characterizing the distribution of a random variable X, through conditional distributions of a second variable Z, given X, is extended.     

Some stochastic comparisons of conditional coherent systems

This paper investigates coherent systems with independent and identical components. Stochastic comparison on the residual life and the inactivity time of two systems with stochastically ordered signatures is conducted. Copyright © 2008 John Wiley & Sons, Ltd.     

Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

Some representations of the multivariate Bernoulli and binomial distributions

Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the concept of Kronecker product from matrix calculus. The multivariate Bernoulli distribution entails a parameterized model, that provides an alternative to the traditional log-linear model for binary variables.     

On the angle between past and future for multivariate stationary stochastic processes

A characterization for the positivityof the angle between past and future of multivariate stationary stochastic processes is established. In order to prove the results a lemma is proved which is of independent interest, and which is very useful in other areas of prediction theory as well.     

Some properties of multivariate extreme value distributions and multivariate tail equivalence

Summary Denote byH ak-dimensional extreme value distribution with marginal distributionH _i (x)=Λ(x)=exp(−e ^−x ),x∈R ¹. Then it is proved thatH(x)=Λ(x ₁)...Λ(x _k ) for anyx=(x ₁, ...,x _k ) ∈R ^k , if and only if the equation holds forx=(0,...,0). Next some multivariate extensions of the results by Resnick (1971,J. Appl. Probab.,8, 136–156) on tail equivalence and asymptotic distributions of extremes are established.     

Third order efficiency of conditional tests for exponential families

Let P_η, η = (θ, γ) ∈ Θ × Γ ? $\text{R}$ × $\text{R}$^k, be a (k + 1)-dimensional exponential family. Let $\text{?}{}_{\mathrm{n}}{}^1$, n ∈ $\text{N}$, be an optimal similar test for the hypothesis {P_(θ,γ)ⁿ: γ ∈ Γ} (θ ∈ Θ fixed) against alternatives P_(θ1,γ1)ⁿ, θ₁ > θ, γ₁ ∈ Γ. It is shown that (?_n¹)_{n∈$\text{N}$} is third order efficient in the class of all test-sequences that are asymptotically similar of level α + o(n^?1) (locally uniformly in the nuisance parameter γ).     

On the right spread order of convolutions of heterogeneous exponential random variables

A sufficient condition for comparing convolutions of heterogeneous exponential random variables in terms of right spread order is established. As a consequence, it is shown that a convolution of heterogeneous independent exponential random variables is more skewed than that of homogeneous exponential random variables in the sense of NBUE order. This gives a new insight into the distribution theory of convolutions of independent random variables. A sufficient condition is also derived for comparing such convolutions in terms of Lorenz order.