Pyridazine derivatives. XIX: Functionalization studies at the 5 position in the 6-phenyl-3(2H)-pyridazinone system

A series of 6-phenyl-3(2H)-pyridazinones bearing different substitution at the 5 position of the pyridazinone ring were prepared in the search for new platelet aggregation inhibitors. The structure of the final compounds was determined on the basis of spectroscopics methods.     

Nanoscratch-induced deformation behaviour in B4C particle reinforced ultrafine grained Al alloy composites: a novel diagnostic approach

We report on the novel application of nanoscratch characterization to provide insight into the plasticity mechanisms responsible for the behaviour of composites. Accordingly, we conduct deformation characterization with nanoscratch testing (DCNT) to study the deformation behaviour of two B₄C reinforced ultrafine grained Al alloy tri-modal composites with average B₄C particle sizes of ~1–6?μm and ~500?nm, respectively. To highlight the type of mechanistic information revealed in a DCNT study of composites, we concentrate on the influence of B₄C particle size on deformation mechanisms.     

A unifying approach to integration for bounded positive charges

This paper deals with n-monotone functionals, which constitute a generalisation of n-monotone set functions. Using the notion of exactness of a functional, we introduce a new notion of lower and upper integral which subsumes as particular cases most of the approaches to integration in the literature. As a consequence, we can characterise which types of integrals can be used to calculate the natural extension (the lower envelope of all linear extensions) of a positive bounded charge.     

Regularity of solutions of convolution equations

This paper investigates the regularity of solutions of convolution equations in the frame of classes of ultradifferentiable functions and ultradistributions. We improve previous work by Bonet, Chou, Fernández, Galbis, Meise and others.     

Sets of monotonicity for Euler’s totient function

We study subsets of [1,x] on which the Euler φ-function is monotone (nondecreasing or nonincreasing). For example, we show that for any ?>0, every such subset has size smaller than ?x, once x>x ₀(?). This confirms a conjecture of the second author.     

The rate at which energy decays in a damped String

The energy in a string subject to positive viscous damping is known to decay exponentially in time. Under the assumption that the damping is of bounded variation, we identify the best rate of decay with the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup. We analyze the spectrum of this nonselfadjoint operator in some detail. Our bounds on its real eigenvalues and asymptotic form of its large eigenvalues translate into criteria for over/underdamping and a proof that the decay rate achieves its (negative) minimum over those dampings whose total variation does not exceed a prescribed value.     

Bivariate distributions characterized by one family of conditionals and conditional percentile or mode functions

It is well known that full knowledge of all conditional distributions will typically serve to completely characterize a bivariate distribution. Partial knowledge will often suffice. For example, knowledge of the conditional distribution of X given Y and the conditional mean of Y given X is often adequate to determine the joint distribution of X and Y. In this paper, we investigate the extent to which a conditional percentile function or a conditional mode function (of Y given X), together with knowledge of the conditional distribution of X given Y will determine the joint distribution. Finally, using this methodology a new characterization of the classical bivariate normal distribution is given.     

Pointwise ergodic theorems for the symmetric exclusion process

Summary Almost sure convergence theorems are proved for Cesaro averages of continous functions in the case of the symmetric exclsion processes in dimension d≧3. For the occupation time of a single site the same result is proved in all dimensions. Partially supported by CNPq     

The Diagnosis of Deep-Vein Thrombosis: An Application of Decision Analysis

Using information from the medical literature on the accuracy and complications of diagnostic tests and therapy, a decision-analysis model is developed and used to evaluate alternative diagnostic strategies for deep-vein thrombosis. With the help of an integrated computer-software package, the probability of death or major complication of different diagnostic strategies is computed, and the strategies exhibiting the least morbidity and mortality are identified. The sensitivity of the results to changes in the parameters of the model are explored. The work provides surprising insights into the role of diagnostic tests.     

Mixed disproportionation versus radical trapping in titanocene(III)-promoted epoxide openings

The formation of either deoxygenation products or allylic alcohols from epoxides is observed when these substrates are treated with Cp₂TiCl under anhydrous conditions. It seems that processes via trisubstituted radicals give allylic alcohols whereas processes via disubstituted radicals may give deoxygenation products or allylic alcohols depending on the structure of the original epoxide. This method allows a controlled access to these functional groups, providing a useful tool in organic synthesis. A mechanistic discussion for these transformations is reported.