Abstract:
The goal of this work is the development of novel peptides with high efficacy of inhibiting activity of CDK6/CyclinD complex. The peptides were derived from primary sequence of P16 protein and its homologues.The interactions between CDK6 and P16/INK4a-derived peptides are studied with molecular dynamics simulation employing umbrella sampling method. The SASA implicit solvent model was used for simulation, which was accelerated using NVIDIA GPUs.

Abstract:
Novel String Banana Template Method (SBTM) for track reconstruction in high multiplicity events in non-uniform magnetic field spectrometer with emphasis on the lowest momenta tracks with significant Multiple Scattering (MS) is described. Two steps model of track with additional parameter/s which takes into account MS for this particular track is introduced. SBTM is time efficient and demonstrates better resolutions than another method equivalent to the Least Squares method (LSM).

Abstract:
This paper deals with the limiting behavior of a harmonic oscillator under the external random disturbance that is a process of the white noise type. Influence of noises is investigated in resonance and non-resonance cases.

Abstract:
We have analyzed the dependences of the threshold value of amplitude of linear density fluctuation collapsed at the current epoch, $\delta_c$, and its overdensity after virialization, $\Delta_c$, on matter density content, 3D curvature parameter and cosmological constant. Though the range for the threshold values of perturbation amplitude is quite narrow - $1.55\le \delta_c\le 1.75$ in the region of parameters $-0.4\le\Omega_k\le0.4$, $0\le\Omega_{\Lambda}\le 1$, $0.1\le\Omega_m\le 1$, the difference in the concentrations of rich clusters of galaxies (calculated within the Press-Schechter formalism framework) with real and with canonical values of $\delta_c$ reaches, and for some models exceeds, 30%. The range of changes for the overdensity after virialization, $\Delta_c$, is considerably wider for the same region of parameters: $60\le\Delta_c\le180$. It results into difference up to $\sim40$% between the X-ray temperatures of gas, as calculated for these values and for the canonical value of $\Delta_c=178$. Also we have found analytical approximations of the dependences $\delta_c(\Omega_m,\Omega_{\Lambda})$ and $\Delta_c(\Omega_m,\Omega_{\Lambda})$ with their accuracies for above mentioned region of parameters being no worse than 0.2% and 1.7% respectively.

Abstract:
We analyse the redshift dependence of space number density of quasars assuming that they are the short-lived active stages of the massive galaxies and arise immediately after the collapse of homogeneous central part of protogalaxy clouds. Obtained dependence fits the observational data ChaMP+CDF+ROSAT (Silverman et al. 2005) very well for protogalaxy clouds of mass $M\approx 8\cdot 10^{11}$ $h^{-1}M_{\odot}$ and ellipticity $e<0.4$. The lifetime of bright X-ray AGNs or QSOs with $L_X>10^{44.5}$ erg$\cdot s^{-1}$ in the range of energies $0.3-8$ keV is $\tau_{QSO}\sim 6\cdot10^6$ years when the mass of supermassive black hole is $M_{SMBH}\sim 10^{9}$ $M_{\odot}$ and the values of other quasar parameters are reasonable. The analysis and all calculations were carried out in the framework of $\Lambda$CDM-model with parameters determined from 5-years WMAP, SNIa and large scale structure data (Komatsu et al. 2009). It is concluded, that the halo model of galaxy formation in the $\Lambda$CDM cosmological model matches well observational data on AGNs and QSOs number density coming from current optical and X-ray surveys.

Abstract:
This article discusses the causes of formation of micron-size protein structures in liquid plasma or serum of the patients with different diseases, which are accompanied by inflammatory reac-tions. Self-organizing processes in sessile dry-ing drops of natural and model biological liq-uids are used for study of possible mechanisms of development the protein phase instability in serum. There was shown that violation of opti-mal ratio between albumin and osmotic active components could lead to loss of albumin ag-gregative stability and albumin coagulation structures formation. Possible role of these structures in pathogenesis of inflammation is discussed.

Abstract:
In this paper the behavior of the instantaneous energy of a harmonic oscillator is investigated in the case when at a certain angle to the vector of the phase velocity of the oscillator, random disturbances of the white and shot noises types are acting.

Abstract:
The late stages of large-scale structure evolution are treated semi-analytically within the framework of modified halo model. We suggest simple yet accurate approximation for relating the non-linear amplitude to linear one for spherical density perturbation. For halo concentration parameter, $c$, a new computation technique is proposed, which eliminates the need of interim evaluation of the $z_{col}$. Validity of the technique is proved for $\Lambda$CDM and $\Lambda$WDM cosmologies. Also, the parameters for Sheth-Tormen mass function are estimated. The modified and extended halo model is applied for determination of non-linear power spectrum of dark matter, as well as for galaxy power spectrum estimation. The semi-analytical techniques for dark matter power spectrum are verified by comparison with data from numerical simulations. Also, the predictions for the galaxy power spectra are confronted with 'observed' data from PSCz and SDSS galaxy catalogs, good accordance is found.

Abstract:
We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. Using them it was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was illustrated also, that the "accretion" of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities - the regions with negative amplitude of density perturbations of dark energy.

Abstract:
We study the dynamical properties and space distribution of dark energy in the weak and strong gravitational fields caused by inhomogeneities of matter in the static world of galaxies and clusters. We show that the dark energy in the weak gravitational fields of matter density perturbations can condense or dilute, but amplitudes of its perturbations remain very small on all scales. We illustrate also how the "accretion" of the phantom dark energy onto the matter overdensity forms the dark energy underdensity. We analyze the behavior of dark energy in the gravitational fields of stars and black holes with the Schwarzschild metric. It is shown that, in the case of stars, the static solution of the differential equations for energy-momentum conservation exists and describes the distribution of density of dark energy inside and outside of a star. We have found that for stars and galaxies its value differs slightly from the average and is a bit higher for the quintessential scalar field as dark energy and a bit lower for the phantom one. The difference grows with the decrease of the effective sound speed of dark energy and is large in the neighborhood of neutron stars. We obtain and analyze also the solutions of equations that describe the stationary accretion of the dark energy as a test component onto the Schwarzschild black hole. It is shown that the rate of change of mass of the dark energy is positive in the case of quintessential dark energy and is negative in the case of the phantom one.