Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Some types of vector measures

Letx be a metrizable locally convex space with a Schauder basis and letB(T) be a -ring generated by the compact subsets of a locally compact Hausdorff spaceT. We prove that any vector measure :B(T)X which has an antiregular relative is antimonogenic (Theorem 16) and that can be uniquely decomposable, = ₁ + ₂, where ₁ is monogenic and ₂ has an antiregular relative (Theorem 19). These results are due to R. A. Johnshon [6] for the case whereX is the real line.     

Non linear eigenvalues problems with a small parameter

In this work we study non linear eigenvalues problems like: [–² d²/dt²+(t²–)²+1]u=0 where. More precisely we study the spectrum of the operator: Q(;)=–²d²/dt²+(t²–)²+1 when 0, >0. Our method of proof consists in replacing our problem by a linear eigenvalue problem about a non self adjoint system.     

Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms

Summary We describe a large class of one-parameter families , {}, , of two-dimensional diffeomorphisms which arestable for <0, exhibit acycle for =0, and thereafter have a bifurcation set of positive but arbitrarily smallrelative measure for in small intervals [0, ]. A main assumption is that the basic sets involved in the cycle havelimit capacities that are not too large.The second author acknowledges hospitality and financial support from IMPA/CNPq during the period this paper was prepared     

The convolution equation of Choquet and Deny on [IN]-groups

Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant     

On Generalized (σ,τ)-Derivations

We generalize the notion of (,)-derivation of Nakajima and Bresar. We define the generalized (,)-derivations, generalized Jordan (,)-derivations, and generalized Lie (,)-derivations, We study interrelations between these classes of derivations as well as their homological properties.     

QUADRATIC ESTIMATORS OF QUADRATIC FUNCTIONS WITH PARAMETERS IN NORMAL LINEAR MODELS

ＱＵＡＤＲＡＴＩＣＥＳＴＩＭＡＴＯＲＳＯＦＱＵＡＤＲＡＴＩＣＦＵＮＣＴＩＯＮＳＷＩＴＨＰＡＲＡＭＥＴＥＲＳＩＮＮＯＲＭＡＬＬＩＮＥＡＲＭＯＤＥＬＳ￥ＷＵＱＩＧＵＡＮＧ（吴启光）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｅＳｃｉｅｎｃｅ,ｔｈｅＣｈｉｎｅｓｅ...     

Flag-Transitive 2-Designs Arising from Line-Spreads in PG(2n-1,2)

A Singer cycle in GL(n,q) is an element of order q permuting cyclically all the nonzero vectors. Let be a Singer cycle in GL(2n,2). In this note we shall count the number of lines in PG (2n-1,2) whose orbit under the subgroup of index 3 in the Singer group is a spread. The lines constituting such a spread are permuted cyclically by the group ³, hence gives rise to a flag-transitive 2-(2²ⁿ ,4,1) design.     

Messbare Mengen von Massen und Inhalten

Let X be a completely regular space. The customary -field is the coarsest -field on the space of Bairemeasures on X which makes (A) measurable for any Baire set A. We compare the customary -field with the Baire and Borel -field induced by the weak* topology which lies on the dual space C(X). In (2.3) it is shown that the customary -field is just the Baire -field. In part 3 necessary and sufficient conditions are given under which the set of -smooth measures is measurable with respect to the Borel -field which lies on the positive cone of the space of finitely additive, regular measures C(X). Finally, a decomposition theorem for generalized kernels is proved. The -smooth part of a generalized kernel is a kernel again if certain conditions are fulfilled.     

Two characterization theorems for integral operators

Let (X,) be a separable -finite measure space. A bounded operator A on L²(X) is called an integral operator if it is induced by an equation: Af(x) = k(x,y)f(y)d(y), where k is a measurable function on X × X such that |k(x,y)f(y)|d(y) < a.e. for every f in L²(X).In this paper, some results on Carleman operators, due to von Neumann, Tarjonski and Weidmann, are extended to the case of the general integral operator.     

Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

Estimation of the quantile + of an exponential distribution with parameters (, ) is considered under an arbitrary strictly convex loss function. For obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when exceeds a lower bound specified below, a new minimax estimator is identified.     

Harmonic functions on nilpotent groups

For a probability measure on a locally compact groupG which is not supported on any proper closed subgroup, an elementF ofL (G) is called -harmonic if F(st)d(t)=F(s), for almost alls inG. Constant functions are -harmonic and it is known that for abelianG all -harmonic functions are constant. For other groups it is known that non constant -harmonic functions exist and the question of whether such functions exist on nilpotent groups is open, though a number of partial results are known. We show that for nilpotent groups of class 2 there are no non constant -harmonic functions. Our methods also enable us to give new proofs of results similar to the known partial results.     

Subgroups of the full linear group over a Dedekind ring

We study the subgroups of the full linear group GL(n, R) over a Dedekind ring R that contain the group of quasidiagonal matrices of fixed type with diagonal blocks of at least third order, each of which is generated by elementary matrices. For any such subgroup H there exists a unique D-net of ideals of R such that, where E() is the subgroup generated by all transvections of the net subgroup G(). and is the normalizer of G(). The subgroup E() is normal in. To study the factor group we introduce an intermediate subgroup F(), E() F() G(). The group is finite and is connected with permutations in the symmetric group. The factor group G()/F() is Abelian — these are the values of a certain determinant. In the calculation of F()/E() appears the SK₁-functor. Results are stated without proof.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 13–20, 1979.     

Topological influence of the presence of fully-λ-bases in locally convex spaces

This article reveals the topological impact of fully--bases in locally convex spaces where carries either the traditional normal topology or the fairly generalized-topology of Ruckle. It has been established that the generalized nuclearity of plays a significant role in influencing the topology of the space. Further, the equivalence of normal topology and the topology arising out of the fully--base ( being equipped with normal topology or-topology) has been investigated.We acknowledge with thanks the suggestions of the referee.     

Interpolation of spectra

By the M.Riesz Convexity Theorem, an operator T on the space of simple integrable functions into the measurable functions (on some measure space) which has continuous extensions to L^p() and L^q() , where 1 p q , also has continuous exten — sions to all L^r () , p r q . It is shown that, whenever (T_p) and (T_q) are o-dimensional (in particular, countable) then the spectra (T_r) (p r q) are pairwise identical. For q = , only w^*-continuous extensions are considered. An example due to Dayanithy shows that the conclusion fails in general.     

Complex Zeros of Algebraic Polynomial with Non-Zero Mean Random Coefficients

In this paper we obtain a formula for the average density of the distribution of complex zeros of an algebraic polynomial with random coefficients. The coefficients are assumed independent identical normally distributed random variables with mean and variance ². The value of the average density for the case of =0 and ²=1 was obtained previously. Some limits of the distribution of the complex zeros are provided using the presented formula.     

On the rate of convergence of an unstable solution of a stochastic differential equation

We study the rate of convergence of the process(tT)/T to the processw(t)/ asT , where(t) is a solution of the stochastic differential equationd(t)=a((t))dt+((t))dw(t) Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1424–1427, October, 1994.     

The connection between the zeros of the ζ-function and sequences(g(p)), p prime,mod 1

In this paper we give the connection between the zeros of the -function and sequences(g(p)), p prime, mod 1 ifg(x)=x for 0, >0 or ifg(X) is a polynomial in .     

Sufficient Conditions for the Existence of Disintegrations

Let be a probability space and a partition of . A necessary and sufficient condition is given for the existence of a -additive and measurable disintegration of P on . It is also shown that P admits a -additive (but not measurable) disintegration on whenever is a standard space and the set (₁, ₂):₁ and ₂ are in the same element of } is coanalytic in ×. Finally, sufficient statistics (in the classical Fisherian sense) are investigated by using -additive disintegrations as conditional probabilities.