On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

A generalized notion of compliance

It is a known fact in structural optimization that for structures subject to prescribed non-zero displacements the work done by the loads is not agood measure of compliance, neither is the stored elastic energy. We briefly discuss a possible alternative measure of compliance, valid for general boundary conditions. We also present the adjoint states (necessary for the computation of the structural derivative) for the three functionals under consideration. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model

In the two-Higgs-doublet model (THDM), generalized-CP transformations (phi(i) -> X-ij phi(*)(j) where X is unitary) and unitary Higgs-family transformations (phi(i) -> U-ij phi(j)) have recently been examined in a series of papers. In terms of gauge-invariant bilinear functions of the Higgs fields phi(i), the Higgs-family transformations and the generalized-CP transformations possess a simple geometric description. Namely, these transformations correspond in the space of scalar-field bilinears to proper and improper rotations, respectively. In this formalism, recent results relating generalized CP transformations with Higgs-family transformations have a clear geometric interpretation. We will review what is known regarding THDM symmetries, as well as derive new results concerning those symmetries, namely how they can be interpreted geometrically as applications of several CP transformations.

Translation termination and protein folding pathway genes are not correlated in gastric cancer

Background: The eukaryotic release factor 3 (eRF3) has been shown to affect both tubulin and actin cytoskeleton, suggesting a role in cytoskeleton assembly, mitotic spindle formation and chromosome segregation. Also, direct interactions between eRF3 and subunits of the cytosolic chaperonin CCT have been described. Moreover, both eRF3a and CCT subunits have been described to be up-regulated in cancer tissues. Our aim was to evaluate the hypothesis that eRF3 expression levels are correlated with the expression of genes encoding proteins involved in the tubulin folding pathways. Methods: Relative expression levels of eRF1, eRF3a/GSPT1, PFDN4, CCT2, CCT4, and TBCA genes in tumour samples relative to their adjacent normal tissues were investigated using real time-polymerase chain reaction in 20 gastric cancer patients. Results: The expression levels of eRF3a/GSPT1 were not correlated with the expression levels of the other genes studied. However, significant correlations were detected between the other genes, both within intestinal and diffuse type tumours. Conclusions: eRF3a/GSPT1 expression at the mRNA level is independent from both cell translation rates and from the expression of the genes involved in tubulin-folding pathways. The differences in the patterns of expression of the genes studied support the hypothesis of genetically independent pathways in the origin of intestinal and diffuse type gastric tumours.

Modulation of translation factor's gene expression by histone deacetylase inhibitors in breast cancer cells

The histone deacetylase inhibitors sodium butyrate (NaBu) and trichostatin A (TSA) exhibit anti-proliferative activity by causing cell cycle arrest and apoptosis. The mechanisms by which NaBu and TSA cause apoptosis and cell cycle arrest are not yet completely clarified, although these agents are known to modulate the expression of several genes including cell-cycle- and apoptosis-related genes. The enzymes involved in the process of translation have important roles in controlling cell growth and apoptosis, and several of these translation factors have been described as having a causal role in the development of cancer. The expression patterns of the translation mechanism, namely of the elongation factors eEF1A1 and eEF1A2, and of the termination factors eRF1 and eRF3, were studied in the breast cancer cell line MCF-7 by real-time quantitative reverse transcription-polymerase chain reaction after a 24-h treatment with NaBu and TSA. NaBu induced inhibition of translation factors' transcription, whereas TSA caused an increase in mRNA levels. Thus, these two agents may modulate the expression of translation factors through different pathways. We propose that the inhibition caused by NaBu may, in part, be responsible for the cell cycle arrest and apoptosis induced by this agent in MCF-7 cells.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study.