On the stability of a class of splitting methods for integro-differential equations

The classical convection–diffusion–reaction equation has the unphysical property that if a sudden change in the dependent variable is made at any point, it will be felt instantly everywhere. This phenomena violate the principle of causality. Over the years, several authors have proposed modifications in an effort to overcome the propagation speed defect. The purpose of this paper is to study, from analytical and numerical point of view a modification to the classical model that take into account the memory effects. Besides the finite speed of propagation, we establish an energy estimate to the exact solution. We also present a numerical method which has the same qualitative property of the exact solution. Finally we illustrate the theoretical results with some numerical simulations.     

The generalized Szendrei expansion of an ℜ-unipotent semigroup

The generalized Szendrei expansion S ^Pr is defined for an $ \mathcal{R} $ -unipotent semigroup S and the projection of S ^Pr onto S is proved to be an initial object in the category of all F-morphisms onto S. Also, the languages recognized by these expansions are described following the semidirect product principle.     

Spontaneous CP violation in a SUSY model with a complex CKM

It is pointed out that the recent measurement of the angle γ   of the unitarity triangle, providing irrefutable evidence for a complex Cabibbo–Kobayashi–Maskawa (CKM) matrix, presents a great challenge for supersymmetric models with spontaneous CP violation. We construct a new minimal extension of the minimal supersymmetric standard model (MSSM), with spontaneous CP breaking, which leads to a complex CKM matrix, thus conforming to present experimental data. This is achieved through the introduction of two singlet chiral superfields and a vector-like quark chiral superfield which mixes with the standard quarks. A Z₃$Z_3$ symmetry is introduced in order to have a potential solution to the strong CP problem.     

Extensions and covers for semigroups whose idempotents form a left regular band

Proper extensions that are “injective on ℒ-related idempotents” of ℛ-unipotent  semigroups, and much more generally of the class of generalised left restriction semigroups possessing the ample and congruence conditions, referred to here as glrac semigroups, are described as certain subalgebras of a λ-semidirect product of a left regular band by an ℛ-unipotent or by a glrac semigroup, respectively. An example of such is the generalized Szendrei expansion.     

A singular perturbation of the heat equation with memory

In this paper we consider a hyperbolic equation, with a memory term in time, which can be seen as a singular perturbation of the heat equation with memory. The qualitative properties of the solutions of the initial boundary value problems associated with both equations are studied. We propose numerical methods for the hyperbolic and parabolic models and their stability properties are analyzed. Finally, we include numerical experiments illustrating the performance of those methods.     

Differentiation of isomeric C8-substituted alkylaniline adducts of guanine by electrospray ionization and tandem quadrupole ion trap mass spectrometry

Product ion spectra from thirteen C8-substituted alkylaniline adducts of guanine and deoxyguanosine were generated using electrospray ionization and quadrupole ion trap mass spectrometry and studied to investigate the possibility of differentiating isomeric adduct structures based upon the relative abundances of fragment ions derived from the alkylaniline-modified guanine bases (BH₂⁺ ions). The structural discrimination of the BH₂⁺ ions formed by attachment of isomeric alkylanilines to the C8 position of guanine is a challenging problem because the ions tend to yield product ion spectra that are qualitatively identical upon collisional activation. In this study, a statistical method, referred to as a similarity index, was used to compare the product ion spectra of isomeric BH₂⁺ ions and differentiate their structures. All the adducts investigated could be distinguished from SIs calculated using 5–6 product ions. These results suggest that a searchable database of product ion spectra may be created and used to characterize DNA adducts from aromatic amines whenever they are detected at levels amenable to mass spectral analysis.