The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height

We obtain new results concerning the Sato–Tate conjecture on the distribution of Frobenius angles over parametric families of elliptic curves with a rational parameter of bounded height.     

On numerical calculation of probabilities according to Dirichlet distribution

The main difficulty in numerical solution of probabilistic constrained stochastic programming problems is the calculation of the probability values according to the underlying multivariate probability distribution. In addition, when we are using a nonlinear programming algorithm for the solution of the problem, the calculation of the first and second order partial derivatives may also be necessary.     

The distribution of sublattices of ℤ m

Lattices , are similar if one can be transformed into the other by an angle-preserving linear map. Similarity classes of lattices of rankn may be parametrized by a fundamental domain of the action ofGL _n () on the generalized upper half-plane _n . Given 1<nm and, letN(D,T) be the number of sublattices of _n which have rankn, similarity class inD, and determinant T. Our most basic result will be thatN(D,T)c ₁(m, n)(D)T ^m asT for suitable setsD, where is the invariant measure on _n . The casen=2 had been dealt with by Roelcke and by Maass using the theory of modular forms.Herrn Professor Hlawka zum achtzigsten Geburtstag gewidmetSupported in part by NSF-DMS-9401426     

The Moment Convergence Rates for Largest Eigenvalues of β Ensembles

The paper focuses on the largest eigenvalues of the β-Hermite ensemble and the β-Laguerre ensemble. In particular, we obtain the precise moment convergence rates of their largest eigenvalues. The results are motivated by the complete convergence for partial sums of i.i.d. random variables, and the proofs depend on the small deviations for largest eigenvalues of the β ensembles and tail inequalities of the general β Tracy-Widom law.     

The distribution of the spine of a Fleming–Viot type process

We show uniqueness of the spine of a Fleming–Viot particle system under minimal assumptions on the driving process. If the driving process is a continuous time Markov process on a finite space, we show that asymptotically, when the number of particles goes to infinity, the distribution of the spine converges to that of the driving process conditioned to stay alive forever, the branching rate for the spine is twice that of a generic particle in the system, and every side branch has the distribution of the unconditioned generic branching tree.     

The eventual index of reducibility of parameter ideals and the sequentially Cohen–Macaulay property

Archiv der Mathematik - In this paper, our purpose is to give a characterization of a sequentially Cohen–Macaulay module, which was introduced by Stanley (Combinatorics and Commutative...     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

On the asymptotic distribution of the Koenker–Bassett estimator for a parameter of the nonlinear model of regression with strongly dependent noise

We prove that, under certain regularity conditions, the asymptotic distribution of the Koenker – Bassett estimator coincides with the asymptotic distribution of the integral of indicator process generated by a random noise weighted by the gradient of the regression function.     

The effect of torsion on the distribution of Ш among quadratic twists of an elliptic curve

Let E be an elliptic curve of rank zero defined over Q and ? an odd prime number. For E of prime conductor N, in Quattrini (2006) [Qua06], we remarked that when ?||ETor(Q)|, there is a congruence modulo ? among a modular form of weight 3/2 corresponding to E and an Eisenstein series. In this work we relate this congruence in weight 3/2, to a well-known one occurring in weight 2, which arises when E(Q) has an ? torsion point. For N prime, we prove that this last congruence can be lifted to one involving eigenvectors of Brandt matrices Bp(N) in the quaternion algebra ramified at N and infinity. From this follows the congruence in weight 3/2. For N square free we conjecture on the coefficients of a weight 3/2 Cohen-Eisenstein series of level N, which we expect to be congruent to the weight 3/2 modular form corresponding to E.     

The flux of primary cosmic ray nuclei of atomic numberZ⩾2 at geomagnetic latitude 30°

The method of determining the primary flux of nuclei with atomic number Z?3 developed by Bradt and Peters, has been extended to include all nuclei of charge Z?2. It is shown that the method permits the identification of primary helium nuclei with an efficiencyν?90%. The primary α-particle flux obtained in this way is in very good agreement with that obtained by other methods and the relative flux values for nuclei of atomic number 3?Z?5 and 6?Z?9 agree with previous determinations.     

The angular derivative of Fréchet-holomorphic maps in J*-algebras and complex Hilbert spaces

We study the problem of the existence of the angular derivative of Fréchet-holomorphic maps of the generalized right half-planes defined by non-zero partial isometries in infinite dimensional complex Banach spaces called J^*-algebras. These generalized right half-planes and open unit balls (which are bounded symmetric homogeneous domains) are holomorphically equivalent. The results obtained here also hold in C ^*-algebras, JC^*-algebras, B ^*-algebras and ternary algebras, containing non-zero partial isometries, and in complex Hilbert spaces. Some examples are given. The principal tool we use are general results of the Pick-Julia type in J^*-algebras.     

The Durrmeyer type modification of the q-Baskakov type operators with two parameter α and β

In this paper, we are dealing with q analogue of Durrmeyer type modified the Baskakov operators with two parameter α and β, which introduces a new sequence of positive linear q-integral operators. We show that this sequence is an approximation process in the polynomial weighted space of continuous function defined on the interval [0, ∞). We study moments, weighted approximation properties, the rate of convergence using a weighted modulus of smoothness, asymptotic formula and better error estimation for these operators.     

The distribution of the ‘finitely many times’ in the strong law of large numbers

Consider independent, identically distributed random variables X₁, X₂,… with common mean μ. Let S_n = Σ₁ⁿX₁. and for ε > 0 let N(ε) count the number of values of n for which n⁻¹S_n − μ > ε. This note discusses the distribution of N(ε), thereby elucidating the fluctuations associated with the Strong Law of Large Numbers.     

The existence of disjoint smallest ideals in the two natural products on β S

No abstract. September 13, 1999