Convergence of weighted sums of random elements in D[0, 1]

Convergence in probability for Toeplitz weighted sums is obtained for convex tight random elements in D[0, 1] under pointwise conditions. The almost sure convergence of the weighted sums is proved for independent, convex tight random elements and for independent, identically distributed random elements. Special techniques and concepts are developed in order to obtain these results in the Skorohod topology of D[0, 1].     

Graph factorization,general triple systems,and cyclic triple systems

In this self-contained exposition, results are developed concerning one-factorizations of complete graphs, and incidence matrices are used to turn these factorization results into embedding theorems on Steiner triple systems. The result is a constructive graphical proof that a Steiner triple system exists for any order congruent to 1 or 3 modulo 6. A pairing construction is then introduced to show that one can also obtain triple systems which are cyclically generated.     

Isobaric analogue resonances in71As through proton elastic scattering on70Ge

The analogues of the low-lying levels in⁷¹Ge have been observed as resonances in the compound nucleus⁷¹As through proton elastic scattering on⁷⁰Ge in the energy rangeE _p=3.5 to 5.3 MeV. The excitation functions cover the analogue resonances corresponding to states upto 2.3 MeV excitation in⁷¹Ge. The sub-structures in the 5.06 MeV resonance, first observed by Temmer and co-workers have been confirmed in the present experiment. The present investigation reveals similar sub-structures in the 4.13 MeV resonance lending further support to the existence of intermediate structure near an isobaric analogue resonance. The resonance parameters and the spectroscopic factors (for the corresponding parent states) have been extracted. The results are compared with the information available from the⁷⁰Ge(d, p)⁷¹Ge reaction.     

The asymptotic number of geometries

A simple proof is given that lim_n?t8(log₂ log₂g_n)/n = 1, where g_n denotes the number of distinct combinatorial geometries on n point     

Two-dimensional convexities are join-hull commutative

It is shown that two-dimensional convex structures with certain natural properties are join-hull commutative. The main intermediate step is the computation of the so-called exchange number. We also give two examples of three-dimensional convexities which are not join-hull commutative. The second one has certain additional properties showing that the main theorem is sharp in many other respects. These properties are obtained from a study of convex hyperspaces.     

Explicit constructions of graphs without short cycles and low density codes

We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given.     

Padé-type approximants with orthogonal generating polynomials

The interpolation of the function x → 1/(1 ? xt) generating the series f(t) = ∑^∞_{i = 0}c_itⁱ at the zeros of an orthogonal polynomial with respect to a distribution d α satisfying some conditions will give us a process for accelerating the convergence of f_n(t) = ∑ⁿ_{i = 0}c_itⁱ. Then, we shall see that the polynomial of best approximation of x → 1/(1 ? xt) over some interval or its development in Chebyshev polynomials T_n or U_n are only particular cases of the main theorem.At last, we shall show that all these processes accelerate linear combinations with positive coefficients of totally monotonic and oscillating sequences.