The central limit problem for convex bodies

It is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately Gaussian. Several quite broad classes of bodies are shown to satisfy the condition.

     

Synthesis and characterization of 1,2-cyclohexanedione bis-benzoyl-hydrazone and its application to the determination of ti in minerals and rocks

The synthesis, spectroscopic characteristics and analytical applications of 1,2-cyclo-hexanedione bis-benzoylhydrazone are reported. The reaction of this new compound with titanium(IV) has been studied spectrophotomelrically. An orange 1:2 metal/ligand complex (lambda(max)= 477 nm, = 1.05 x 10(4) l.mole(-1).cm(-1)) is formed at pH 1.75-3.0 in 3:2 v v ethanol-water medium. The method is simple and selective and has been satisfactorily applied to the determination of titanium in bauxite, Portland cement, amphibolites and granites.     

Asymptotic expansions for the truncation error in Ramanujan-type series

The Ramanujan Journal - Many of the fastest known algorithms to compute $$\pi $$ involve generalized hypergeometric series, such as the Ramanujan–Sato series. In this paper, we investigate...     

Weak solutions for a system of nonlinear Klein-Gordon equations

Summary We prove the existence and uniqueness of weak solutions of the mixed problem for a class of systems of nonlinear Klein-Gordon equations. Uniqueness is proved when the spatial dimension is either n=1, 2or 3.Partially supported by CNPq-Brasil.     

Weak solutions for a nonlinear dispersive equation

In this paper we study the existence, uniqueness, and regularity of the solutions for the Cauchy problem for the evolution equation $\text{u}{}_{\mathrm{t}}\text{+ (f (u))}{}_{\mathrm{x}}\text{? u}{}_{\mathrm{xxt}}\text{= g(x, t), (}{}^1\text{)}\text{where}\text{u = u(x, t), x}$ is in (0, 1), 0 ? t ? T, T is an arbitrary positive real number,f(s)?C¹$\text{R}$, and g(x, t)?L^∞(0, T; L²(0, 1)). We prove the existence and uniqueness of the weak solutions for (¹) using the Galerkin method and a compactness argument such as that of J. L. Lions. We obtain regular solutions using eigenfunctions of the one-dimensional Laplace operator as a basis in the Galerkin method.