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

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

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

Modeling visual-based pitch, lift and speed control strategies in hoverflies

<div><p>To avoid crashing onto the floor, a free falling fly needs to trigger its wingbeats quickly and control the orientation of its thrust accurately and swiftly to stabilize its pitch and hence its speed. Behavioural data have suggested that the vertical optic flow produced by the fall and crossing the visual field plays a key role in this anti-crash response. Free fall behavior analyses have also suggested that flying insect may not rely on graviception to stabilize their flight. Based on these two assumptions, we have developed a model which accounts for hoverflies´ position and pitch orientation recorded in 3D with a fast stereo camera during experimental free falls. Our dynamic model shows that optic flow-based control combined with closed-loop control of the pitch suffice to stabilize the flight properly. In addition, our model sheds a new light on the visual-based feedback control of fly´s pitch, lift and thrust. Since graviceptive cues are possibly not used by flying insects, the use of a vertical reference to control the pitch is discussed, based on the results obtained on a complete dynamic model of a virtual fly falling in a textured corridor. This model would provide a useful tool for understanding more clearly how insects may or not estimate their absolute attitude.</p></div

Multiple evolutionary origins of Trypanosoma evansi in Kenya

Trypanosoma evansi is the parasite causing surra, a form of trypanosomiasis in camels and other livestock, and a serious economic burden in Kenya and many other parts of the world. Trypanosoma evansi transmission can be sustained mechanically by tabanid and Stomoxys biting flies, whereas the closely related African trypanosomes T. brucei brucei and T. b. rhodesiense require cyclical development in tsetse flies (genus Glossina) for transmission. In this study, we investigated the evolutionary origins of T. evansi. We used 15 polymorphic microsatellites to quantify levels and patterns of genetic diversity among 41 T. evansi isolates and 66 isolates of T. b. brucei (n = 51) and T. b. rhodesiense (n = 15), including many from Kenya, a region where T. evansi may have evolved from T. brucei. We found that T. evansi strains belong to at least two distinct T. brucei genetic units and contain genetic diversity that is similar to that in T. brucei strains. Results indicated that the 41 T. evansi isolates originated from multiple T. brucei strains from different genetic backgrounds, implying independent origins of T. evansi from T. brucei strains. This surprising finding further suggested that the acquisition of the ability of T. evansi to be transmitted mechanically, and thus the ability to escape the obligate link with the African tsetse fly vector, has occurred repeatedly. These findings, if confirmed, have epidemiological implications, as T. brucei strains from different genetic backgrounds can become either causative agents of a dangerous, cosmopolitan livestock disease or of a lethal human disease, like for T. b. rhodesiense