Abstract:
We consider the synchronization of two self-excited double pendula. We show that such pendula hanging on the same beam can have four different synchronous configurations. Our approximate analytical analysis allows us to derive the synchronization conditions and explain the observed types of synchronization. We consider an energy balance in the system and describe how the energy is transferred between the pendula via the oscillating beam, allowing thus the pendula synchronization. Changes and stability ranges of the obtained solutions with increasing and decreasing masses of the pendula are shown using path-following.

Abstract:
It is proved, there is no aether and time-space is the only medium for electromagnetic wave. However, considering time-space as the medium we may expect, there should exist field equations, describing electromagnetic wave as disturbance in time-space structure propagating in the time-space. I derive such field equations and show that gravitational field as well as electromagnetic field may be considered through one phenomena-time dilation.

Abstract:
External electric field of 0.001, 0.01 and 0.05 a.u. changes distribution of the electron density in α- and β-D-glucose, α- and β-D-galactose, α- and β-fructopyranoses and α- and β-fructofuranoses, α- and β-D-ribofuranoses and α and β-D-xylo- furanoses. Hyper-Chem 8.0 software was used together with the AM1 method for optimization of the conformation of the molecules of monosaccharides under study. Then polarizability, charge distribution, potential and dipole moment for molecules placed in the external electric field of 0.000, 0.001, 0.01 and 0.05 a.u. were calculated involving DFT 3-21G method. Application of the external field induced polarizability of electrons, atoms and dipoles, the latter resulting in eventual reorientation of the molecules along the applied field of the molecules and the electron density redistribution at particular atoms. Increase in the field strength generated mostly irregular changes of the electron densities at particular atoms of the molecules as well as polarizabilities. Energy of these molecules and their dipole moments also varied with the strength of the field applied. Results of computations imply that saccharides present in the living organisms may participate in the response of the living organisms to the external electric field affecting metabolism of the molecules in the body fluids by fitting molecules to the enzymes. Structural changes of saccharide components of the membranes can influence the membrane permeability.

Abstract:
We calculate the self-consistent in-medium T matrix for symmetric nuclear matter using realistic interactions with many partial waves. We find for the interactions used (CDBonn and Nijmegen) very similar results for on-shell quantities. The effective mass and the renormalization factor Z_F at the Fermi momentum are given for a range of densities.

Abstract:
We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and gravitational field tensor $F^{\mu\nu}$ that is associated with gravitational interaction. Next we show that gravitational four-current $J^\mu$ derived for introduced four-potential produce energy-stress tensor and reproduce main General Relativity formula. Next we introduce valid Lagrangian and equations of motion that explains obtained results. At the end we introduce new approach to quantization of gravity that results in proper quantum values and is open to further generalization.

Abstract:
In the last article we have created foundations for gravitational field oriented framework (DaF) that reproduces GR. In this article we show, that using DaF approach, we can reproduce Schwarzschild solution with orbit equations, effective potential and constants of motion. Next we generalize results to other GR solutions and show, how gravitational field affects spacetime curvature and intrinsic spin of the bodies. It also appears, that field oriented approach requests to assign some spin value to the massless particles. Derived DaF framework has therefore significant meaning for searching for field based interpretation of gravity requested by quantum gravity.

Abstract:
We study approximation algorithms for several variants of the MaxCover problem, with the focus on algorithms that run in FPT time. In the MaxCover problem we are given a set N of elements, a family S of subsets of N, and an integer K. The goal is to find up to K sets from S that jointly cover (i.e., include) as many elements as possible. This problem is well-known to be NP-hard and, under standard complexity-theoretic assumptions, the best possible polynomial-time approximation algorithm has approximation ratio (1 - 1/e). We first consider a variant of MaxCover with bounded element frequencies, i.e., a variant where there is a constant p such that each element belongs to at most p sets in S. For this case we show that there is an FPT approximation scheme (i.e., for each B there is a B-approximation algorithm running in FPT time) for the problem of maximizing the number of covered elements, and a randomized FPT approximation scheme for the problem of minimizing the number of elements left uncovered (we take K to be the parameter). Then, for the case where there is a constant p such that each element belongs to at least p sets from S, we show that the standard greedy approximation algorithm achieves approximation ratio exactly (1-e^{-max(pK/|S|, 1)}). We conclude by considering an unrestricted variant of MaxCover, and show approximation algorithms that run in exponential time and combine an exact algorithm with a greedy approximation. Some of our results improve currently known results for MaxVertexCover.

Abstract:
Electronic emission spectra of N2, (N2)2, (N2)5 O2, (O2)2, (O2)5, H2O, (H2O)5, CO2, (CO2)2, CO2..H2O, NH3 and NH3.H2O situated in the electric field of 0.001, 0.005, 0.01 0.05 and 0.1 a.u. were simulated involving Monte Carlo optimization followed by the ZINDO/S approach. The simulated spectra showed irregular dependence on the energy of the electric field applied. Molecules without influence of the electric field emit in the vacuum ultraviolet region. Applied electric field only in case of (O2)5 generated transitions above 200 nm. The mapping of isosurface of the investigated molecules revealed that the electric field applied redistributed the charge densities in the molecules in the manner approximately parallel to the energy of the field. Applied electrical field resulted in an increase in the water acidity and ammonia basicity.

Abstract:
Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.

It is widely accepted that the Marginal Value Theorem (MVT) describes optimal foraging strategies of animals and the mechanism proposed by the MVT has been supported by a number of field observations. However, findings of many researchers indicate that in natural conditions foragers do not always behave according to the MVT. To address this inconsistency, in a series of computer simulation experiments, we examined the behaviour of four types of foragers having specific foraging efficiencies and using the MVT strategies in 15 different landscapes in an ideal environment (no intra-and inter-specific interactions). We used data on elk (Cervus elaphus) to construct our virtual forager. Contrary to the widely accepted understanding of the MVT (residence time in a patch should be longer in environments where travel time between patches is longer) we found that in environments with the same average patch quality and varying average travel times between patches, patch residence times of some foragers are not affected by travel times. Based on our analysis we propose a mechanism responsible for this observation and formulate the perfect forager theorem (PFT). We also introduce the concepts of a foraging coefficient (F) and foragers’ hub (α), and propose a model to describe the relationship between the perfect forager and all other forager types.