On singularities of the Galilean spherical darboux ruled surface of a space curve in G₃

We study the singularities of Galilean height functions intrinsically related to the Frenet frame along a curve embedded into the Galilean space. We establish the relationships between the singularities of the discriminant and the sets of bifurcations of the function and geometric invariants of curves in the Galilean space.Досліджено особливості галілеївських функцій висоти, що внутрішньо пов'язані із рамкою Френе вздовж кривої, вкладеної у галілеївський простір. Встановлено співвідношення між особливостями множини дискримінантів та множини біфуркацій функції і геометричними інваріантами кривих у галілеївському просторі

Dualisation of the D=7 Heterotic String

The dualisation and the first-order formulation of the D=7 abelian Yang-Mills supergravity which is the low energy effective limit of the D=7 fully Higssed heterotic string is discussed. The non-linear coset formulation of the scalars is enlarged to include the entire bosonic sector by introducing dual fields and by constructing the Lie superalgebra which generates the dualized coset element.Comment: 20 page

Exponential Metric Fields

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein's theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.Comment: Accepted for publication in Astrophysics and Space Science, 17 page

The effect of initial pH and retention time on boron removal by continuous electrocoagulation process

In this study, factors influencing boron removal via the continuous electrocoagulation process were investigated at lab-scale. Different influent pH values (4, 5, 6, 7.45 and 9) and contact times (10, 25, 50 and 100 min) were examined as variable parameters. Plate-type aluminium electrodes with 5 mm distance between them were used. All the experiments were conducted in continuous mode and the current density was kept constant at 5 A throughout the whole experimental period. The initial boron concentration was selected to be 1000 mg L-1. The first set of experiments concerning the influence of the influent pH showed that the highest boron removal (67%) was obtained at pH=6 since it was the optimal pH for boron precipitation through aluminium borate formation. Under the constant current density of the study and with the initial pH adjusted to 6, increasing the duration of the electrocoagulation process from 10 to 100 min resulted in raising the boron removal from 45 to 79% during the second set of experiments. The greater duration of the electrocagulation process enabled higher aluminium dissolution, thus allowing the existence of a higher number of coagulants within the reactor. Moreover, it enhanced boron precipitation because of the longer contact time between the boron ions and the coagulants. After optimizing significant parameters such as the influent pH and the electrocagulation duration, the continuous electrocoagulation process was found to constitute an effective alternative for boron removal

Interpolation function of the genocchi type polynomials

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary positive real parameters. We prove multiplication theorem of these polynomials. Furthermore, we give some identities and applications associated with these numbers, polynomials and their interpolation functions.Comment: 14 page

Towards large-scale what-if traffic simulation with exact-differential simulation

To analyze and predict a behavior of large-scale traffics with what-if simulation, it needs to repeat many times with various patterns of what-if scenarios. In this paper, we propose new techniques to efficiently repeat what-if simulation tasks with exact-differential simulation. The paper consists of two main efforts: what-if scenario filtering and exact-differential cloning. The what-if scenario filtering enables to pick up meaningful what-if scenarios and reduces the number of what-if scenarios, which directly decreases total execution time of repeating. The exact-differential cloning enables to execute exact-differential simulation tasks in parallel to improve its total execution time. In our preliminary evaluation in Tokyo bay area's traffic simulation, we show potential of our proposals by estimating how the what-if scenarios filtering reduces the number of meaningless scenarios and also by estimating a performance improvement from our previous works with the exact-differential cloning

Infrared renormalons and single meson production in proton-proton collisions

In this article, we investigate the contribution of the higher twist Feynman diagrams to the large-$p_T$ inclusive pion production cross section in proton-proton collisions and present the general formulae for the higher twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher twist cross sections with the ones obtained in the framework of the frozen coupling approximation and leading twist cross section. We obtain, that ratio $R$ for all values of the transverse momentum $p_{T}$ of the pion identical equivalent to ratio $r$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.Comment: 28 pages, 13 figure

An edge-based approach for robust foreground detection

Foreground segmentation is an essential task in many image processing applications and a commonly used approach to obtain foreground objects from the background. Many techniques exist, but due to shadows and changes in illumination the segmentation of foreground objects from the background remains challenging. In this paper, we present a powerful framework for detections of moving objects in real-time video processing applications under various lighting changes. The novel approach is based on a combination of edge detection and recursive smoothing techniques.We use edge dependencies as statistical features of foreground and background regions and define the foreground as regions containing moving edges. The background is described by short- and long-term estimates. Experiments prove the robustness of our method in the presence of lighting changes in sequences compared to other widely used background subtraction techniques