Does Cosmological Term Influence Gravitational Lensing?

We analyze the bending of light by galaxies or clusters of galaxies in the presence of the cosmological term. Going over to the Friedmann-Robertson-Walker coordinates, used in fact for the description of actual observations, we demonstrate that the cosmological constant does not influence practically the lensing effect.Comment: 5 pages, 1 figur

On digits of Mersenne numbers

Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimaterational exponential sums with $M_p$, $p \leq X$, modulo a large power of afixed odd prime $q$. In turn this immediately implies the normality of stringsof $q$-ary digits amongst about $(\log X)^{3/2+o(1)}$ rightmost digits of$M_p$, $p \leq X$. Previous results imply this only for about (\logX)^{1+o(1)} rightmost digits.<br

Metric theory of Weyl sums

We prove that there exist positive constants $C$ and $c$ such that for any integer $d \ge 2$ the set of ${\mathbf x}\in [0,1)^d$ satisfying $$cN^{1/2}\le \left|\sum^N_{n=1}\exp\left (2 \pi i \left (x_1n+\ldots+x_d n^d\right)\right) \right|\le C N^{1/2}$$ for infinitely many natural numbers $N$ is of full Lebesque measure. This substantially improves the previous results where similar sets have been measured in terms of the Hausdorff dimension. We also obtain similar bounds for exponential sums with monomials $xn^d$ when $d\neq 4$. Finally, we obtain lower bounds for the Hausdorff dimension of large values of general exponential polynomials

Clinical and service implications of a cognitive analytic therapy model of psychosis

Cognitive analytic therapy (CAT) is an integrative, interpersonal model of therapy predicated on a radically social concept of self, developed over recent years in the UK by Anthony Ryle. A CAT-based model of psychotic disorder has been developed much more recently based on encouraging early experience in this area. The model describes and accounts for many psychotic experiences and symptoms in terms of distorted, amplified or muddled enactments of normal or ‘neurotic’ reciprocal role procedures (RRPs) and of damage at a meta-procedural level to the structures of the self. Reciprocal role procedures are understood in CAT to represent the outcome of the process of internalization of early, sign-mediated, interpersonal experience and to constitute the basis for all mental activity, normal or otherwise. Enactments of maladaptive RRPs generated by early interpersonal stress are seen in this model to constitute a form of ‘internal expressed emotion’. Joint description of these RRPs and their enactments (both internally and externally) and their subsequent revision is central to the practice of CAT during which they are mapped out through written and diagrammatic reformulations. This model may usefully complement and extend existing approaches, notably recent CBT-based interventions, particularly with ‘difficult’ patients, and generate meaningful and helpful understandings of these disorders for both patients and their treating teams. We suggest that use of a coherent and robust model such as CAT could have important clinical and service implications in terms of developing and researching models of these disorders as well as for the training of multidisciplinary teams in their effective treatment

Immunocytochemical demonstration of p21 ras family oncogene product in normal mucosa and in premalignant and malignant tumours of the colorectum.

Study of the distribution of the p21 ras oncogene product as demonstrated by monoclonal antibody Y13-259 shows this protein to be apparently present in all epithelial populations of both premalignant and malignant tumours and throughout the normal foetal and adult epithelial crypt population in the colorectum. Metastatic tumour in liver shows a similar staining pattern which is less intense however than in the surrounding normal hepatocytes. Our results suggest that the presence of this protein is a widespread feature of normal cellular metabolism in certain cell types and is not restricted to those actively involved in cellular proliferation. It appears, furthermore, that neither cells at different stages of carcinogenesis nor those representing variants of a malignant phenotype can be identified using this particular antibody

The energy budget in Rayleigh-Benard convection

It is shown using three series of Rayleigh number simulations of varying aspect ratio AR and Prandtl number Pr that the normalized dissipation at the wall, while significantly greater than 1, approaches a constant dependent upon AR and Pr. It is also found that the peak velocity, not the mean square velocity, obeys the experimental scaling of Ra^{0.5}. The scaling of the mean square velocity is closer to Ra^{0.46}, which is shown to be consistent with experimental measurements and the numerical results for the scaling of Nu and the temperature if there are strong correlations between the velocity and temperature.Comment: 5 pages, 3 figures, new version 13 Mar, 200

Time-Varying Gravitomagnetism

Time-varying gravitomagnetic fields are considered within the linear post-Newtonian approach to general relativity. A simple model is developed in which the gravitomagnetic field of a localized mass-energy current varies linearly with time. The implications of this temporal variation of the source for the precession of test gyroscopes and the motion of null rays are briefly discussed.Comment: 10 pages; v2: slightly expanded version accepted for publication in Class. Quantum Gra