Точки, прямі, площини,....аксіоми і теореми: введення в евклідову геометрію

Посилаючись на поняття математичної структури, доповнено істинно важливими аспектами, роз’яснено схему розбудови теорії евклідової геометрії на основі аксіоматики 0.В. Погорєлова, розкрито науковий стиль подання системи аксіом, продемонстровано методичні особливості строго логічного наповнення підручника фактами

Deformation of the Fermi surface in the extended Hubbard model

The deformation of the Fermi surface induced by Coulomb interactions is investigated in the t-t'-Hubbard model. The interplay of the local U and extended V interactions is analyzed. It is found that exchange interactions V enhance small anisotropies producing deformations of the Fermi surface which break the point group symmetry of the square lattice at the Van Hove filling. This Pomeranchuck instability competes with ferromagnetism and is suppressed at a critical value of U(V). The interaction V renormalizes the t' parameter to smaller values what favours nesting. It also induces changes on the topology of the Fermi surface which can go from hole to electron-like what may explain recent ARPES experiments.Comment: 5 pages, 4 ps figure

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient

Genetic variation and exercise-induced muscle damage: implications for athletic performance, injury and ageing.

Prolonged unaccustomed exercise involving muscle lengthening (eccentric) actions can result in ultrastructural muscle disruption, impaired excitation-contraction coupling, inflammation and muscle protein degradation. This process is associated with delayed onset muscle soreness and is referred to as exercise-induced muscle damage. Although a certain amount of muscle damage may be necessary for adaptation to occur, excessive damage or inadequate recovery from exercise-induced muscle damage can increase injury risk, particularly in older individuals, who experience more damage and require longer to recover from muscle damaging exercise than younger adults. Furthermore, it is apparent that inter-individual variation exists in the response to exercise-induced muscle damage, and there is evidence that genetic variability may play a key role. Although this area of research is in its infancy, certain gene variations, or polymorphisms have been associated with exercise-induced muscle damage (i.e. individuals with certain genotypes experience greater muscle damage, and require longer recovery, following strenuous exercise). These polymorphisms include ACTN3 (R577X, rs1815739), TNF (-308 G>A, rs1800629), IL6 (-174 G>C, rs1800795), and IGF2 (ApaI, 17200 G>A, rs680). Knowing how someone is likely to respond to a particular type of exercise could help coaches/practitioners individualise the exercise training of their athletes/patients, thus maximising recovery and adaptation, while reducing overload-associated injury risk. The purpose of this review is to provide a critical analysis of the literature concerning gene polymorphisms associated with exercise-induced muscle damage, both in young and older individuals, and to highlight the potential mechanisms underpinning these associations, thus providing a better understanding of exercise-induced muscle damage

Asymptotic Expansions for the Sojourn Time Distribution in the M/G/1M/G/1-PS Queue

We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. Our results demonstrate the possible tail behaviors of the unconditional distribution, which was previously known in the cases $G=M$ and $G=D$ (where it is purely exponential). We assume that the service density decays at least exponentially fast. We use various methods for the asymptotic expansion of integrals, such as the Laplace and saddle point methods.Comment: 45 page

Resource-sharing in multiple component working memory

Working memory research often focuses on measuring the capacity of the system and how it relates to other cognitive abilities. However, research into the structure of working memory is less concerned with an overall capacity measure but rather with the intricacies of underlying components and their contribution to different tasks. A number of models of working memory structure have been proposed, each with different assumptions and predictions, but none of which adequately accounts for the full range of data in the working memory literature. We report 2 experiments that investigated the effects of load manipulations on dual-task verbal temporary memory and spatial processing. Crucially, we manipulated cognitive load around the measured memory span of each individual participant. We report a clear effect of increasing memory load on processing accuracy, but only when memory load is increased above each participant’s measured memory span. However, increasing processing load did not affect memory performance. We argue that immediate verbal memory may rely both on a temporary phonological store and on activated traces in long-term memory, with the latter deployed to support memory performance for supraspan lists and when a high memory load is coupled with a processing task. We propose that future research should tailor the load manipulations to the capacities of individual participants and suggest that contrasts between models of working memory may be more apparent than real

Mammalian BTBD12 (SLX4) Protects against Genomic Instability during Mammalian Spermatogenesis

The mammalian ortholog of yeast Slx4, BTBD12, is an ATM substrate that functions as a scaffold for various DNA repair activities. Mutations of human BTBD12 have been reported in a new sub-type of Fanconi anemia patients. Recent studies have implicated the fly and worm orthologs, MUS312 and HIM-18, in the regulation of meiotic crossovers arising from double-strand break (DSB) initiating events and also in genome stability prior to meiosis. Using a Btbd12 mutant mouse, we analyzed the role of BTBD12 in mammalian gametogenesis. BTBD12 localizes to pre-meiotic spermatogonia and to meiotic spermatocytes in wildtype males. Btbd12 mutant mice have less than 15% normal spermatozoa and are subfertile. Loss of BTBD12 during embryogenesis results in impaired primordial germ cell proliferation and increased apoptosis, which reduces the spermatogonial pool in the early postnatal testis. During prophase I, DSBs initiate normally in Btbd12 mutant animals. However, DSB repair is delayed or impeded, resulting in persistent γH2AX and RAD51, and the choice of repair pathway may be altered, resulting in elevated MLH1/MLH3 focus numbers at pachynema. The result is an increase in apoptosis through prophase I and beyond. Unlike yeast Slx4, therefore, BTBD12 appears to function in meiotic prophase I, possibly during the recombination events that lead to the production of crossovers. In line with its expected regulation by ATM kinase, BTBD12 protein is reduced in the testis of Atm−/− males, and Btbd12 mutant mice exhibit increased genomic instability in the form of elevated blood cell micronucleus formation similar to that seen in Atm−/− males. Taken together, these data indicate that BTBD12 functions throughout gametogenesis to maintain genome stability, possibly by co-ordinating repair processes and/or by linking DNA repair events to the cell cycle via ATM