On the Kolmogorov Inequality for M Φ -Norm

In this paper, we prove the Kolmogorov inequality for M | -norms generated by concave functions (with the same constants as in the Kolmogorov inequality).     

Non-parametric Estimation for the M/G/∞ Queue

Given an M/G/ queue with input rate and service-time distribution G, we consider the problem of estimating and G from data on the queue-length process Q = (Q_t). Our motivation is to study departures of G from exponentiality, following recent work of Bingham and Dunham (1997, Ann. Inst. Statist. Math., 49, 667–679).     

Some Asymptotic Results for the M/M/∞ Queue with Ranked Servers

We consider an M/M/ model with m primary servers and infinitely many secondary ones. An arriving customer takes a primary server, if one is available. We derive integral representations for the joint steady state distribution of the number of occupied primary and secondary servers. Letting =/ be the ratio of arrival and service rates (all servers work at rate ), we study the joint distribution asymptotically for . We consider both m=O(1) and m scaled to be of the same order as . We also give results for the marginal distribution of the number of secondary servers that are occupied.     

An Explicit Derivation of the Möbius Function for Bruhat Order

We give an explicit nonrecursive complete matching for the Hasse diagram of the strong Bruhat order of any interval in any Coxeter group. This yields a new derivation of the Möbius function, recovering a classical result due to Verma.     

An Approximate M—estimation for the Parameters of Mixed Regression Model

In this paper, to keep scale inveriance, we propose an approximate M-estrmation for the mixed regression model and show consistency of the estimation under weaker conditions than that in [1].     

A necessary and sufficient condition for the finite μM,D-orthogonality

The self-affine measure μM,D associated with an expanding matrix M ∈ Mn(Z) and a finite digit set D ? Znis uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E(Λ) := {e2πiλ,x : λ∈Λ} in the Hilbert space L2(μM,D) is simply called μM,D-orthogonal exponentials. We consider in this paper the finiteness of μM,D-orthogonality. A necessary and sufficient condition is obtained for the set E(Λ) to be a finite μM,D-orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures.     

Explicit Formulas for Green’s Functions on the Annulus and on the Möbius Strip

Given a fixed point free antianalytic involution k of a domain G in thecomplex plane, bounded by a finite number of analytic curves, k-invariant Greensfunctions are defined on G. The Lindelöfs principle is extended to k-invariantGreens functions. When G is the annulus, k-invariant Greens functions areobtained in the explicit form. Since the factorization of the annulus by the group kgenerated by k produces a Möbius strip, the respective result helped us to obtain explicitforms for Greens functions on the Möbius strip.     

Asysmptotic Normality of the M－estimators for Parametric Components in Partly Linear Models

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A Simple Method for Computing the Homeomorphism Class of G． M．  and G． M． 

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ch for the three-dimention

regulation of the muscle length and the arm of muscular force when the hip was at standard anatomic attitude and in the whole distance range with exercise.Result enunciation: In regard to the machine axes of lower extr     

Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties

The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile’s monotonicity conditions are not satisfied.     

A four-point criterion for the Möbius property of a homeomorphism of plane domains

An ordered quadruple of pairwise distinct points T = {z ₁, z ₂, z ₃, z ₄} ? C is called regular whenever z ₂ and z ₄ lie at the opposite sides of the line through z ₁ and z ₃. Consider Φ(T) = ∠z ₁ z ₂ z ₃ + ∠z ₁ z ₄ z ₃ (the angles are undirected) as some geometric characteristic of a regular tetrad. We prove the following theorem: For every fixed α ∈ (0, 2π) the Möbius property of a homeomorphism f: D → D* of domains in C is equivalent to the requirement that each regular tetrad T ? D with Φ(T) = α whose image fT is also a regular tetrad satisfies Φ(fT) = α. In 1994 Haruki and Rassias established this criterion for the Möbius property only in the class of univalent analytic functions f(z).     

Strichartz estimates for the Schrödinger propagator for the Laguerre operator

We obtain homogeneous Strichartz estimate for the Schrödinger propagator e $^{-itL_{\alpha}}$ for the Laguerre operator L _α on ${\mathbb R}_+^n$ . We follow regularization technique as introduced in J. Funct. Anal. 224(2) (2005) 371–385. We also establish inhomogeneous Strichartz estimates for different admissible pairs.     

Anti-integrability for the Logistic Maps

The embedding of the Bernoulli shift into the logistic map x→μx(1- x) forμ> 4 is reinterpreted by the theory of anti-integrability: it is inherited from the anti-integrable limitμ→∞.     

The Möbius invariants for circle packings

Möbius invariants of general circle packings are defined in terms of cross ratios. The necessary and sufficient conditions of existence of circle packings are established by the techniques of Möbius invariants. It is shown that circle packings are uniquely determined, up to Möbius transformations, by their Möbius invariants. The rigidity of infinite circle packings with bounded degree is proved using the approach of Möbius invariants.     

Harnack estimate for the H~k-flow

We obtain the Harnack estimate of the solution to H~k-flow in Euclidean space R~(n 1),for k>0.By using this estimate,we get some corollaries about the translation soliton.