Generalizations of a theorem of Rolewicz

The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz.     

A fluorescent broad-spectrum proteasome inhibitor for labeling proteasomes in vitro and in vivo

The proteasome is an essential evolutionary conserved protease involved in many regulatory systems. Here, we describe the synthesis and characterization of the activity-based, fluorescent, and cell-permeable inhibitor Bodipy TMR-Ahx(3)L(3)VS (MV151), which specifically targets all active subunits of the proteasome and immunoproteasome in living cells, allowing for rapid and sensitive in-gel detection. The inhibition profile of a panel of commonly used proteasome inhibitors could be readily determined by MV151 labeling. Administration of MV151 to mice allowed for in vivo labeling of proteasomes, which correlated with inhibition of proteasomal degradation in the affected tissues. This probe can be used for many applications ranging from clinical profiling of proteasome activity, to biochemical analysis of subunit specificity of inhibitors, and to cell biological analysis of the proteasome function and dynamics in living cells.     

Topologically novel multiple rotaxanes and catenanes based on tetraurea calix[4]arenes

Calix[4]arenes bearing at their wide rim four urea residues easily form hydrogen bonded dimeric capsules. This has been used to preorganise alkenyl functions attached to these urea groups for their controlled connection via metathesis reaction. Multimacrocyclic tetraurea derivatives are thus obtained in excellent yields via heterodimers which are formed exclusively with tetratosylurea derivatives. Heterodimerisation of such bis- and tetraloop tetraureas leads analogously to multicatenanes, or to rotaxanes by stoppering. Huge macrocycles are detached from tetraloop derivatives by cleavage of the urea function.     

A new selective approach to 1,1-bis(silyl)-2-arylethenes and 1,1-bis(silyl)-1,3-butadienes via sequential silylative coupling-Heck coupling reactions

A novel selective route to 1,1-bis(silyl)-1-alkenes has been developed. Sequential one-pot silylative coupling exo-cyclization of 1,2-bis(dimethylvinylsiloxy)ethane followed by the reaction with Grignard reagents leads to the desired 1,1-bis(silyl)ethenes, which are then efficiently coupled in the presence of silver nitrate and palladium acetate with aryl or alkenyl idodides to give the corresponding 1,1-bis(silyl)-2-arylethenes or 1,1,4-trisubstituted 1,3-butadienes with high yield.     

Implementation of a symplectic multiple-time-step molecular dynamics algorithm, based on the united-residue mesoscopic potential energy function

A symplectic multiple-time-step (MTS) algorithm has been developed for the united-residue (UNRES) force field. In this algorithm, the slow-varying forces (which contain most of the long-range interactions and are, therefore, expensive to compute) are integrated with a larger time step, termed the basic time step, and the fast-varying forces are integrated with a shorter time step, which is an integral fraction of the basic time step. Based on the split operator formalism, the equations of motion were derived. Separation of the fast- and slow-varying forces leads to stable molecular dynamics with longer time steps. The algorithms were tested with the Ala(10) polypeptide chain and two versions of the UNRES force field: the current one in which the energy components accounting for the energetics of side-chain rotamers (U(rot)) can lead to numerically unstable forces and a modified one in which the the present U(rot) was replaced by a numerically stable expression which, at present, is parametrized only for polyalanine chains. With the modified UNRES potential, stable trajectories were obtained even when extending the basic time step to 15 fs and, with the original UNRES potentials, the basic time step is 1 fs. An adaptive multiple-time-step (A-MTS) algorithm is proposed to handle instabilities in the forces; in this method, the number of substeps in the basic time step varies depending on the change of the magnitude of the acceleration. With this algorithm, the basic time step is 1 fs but the number of substeps and, consequently, the computational cost are reduced with respect to the MTS algorithm. The use of the UNRES mesoscopic energy function and the algorithms derived in this work enables one to increase the simulation time period by several orders of magnitude compared to conventional atomic-resolution molecular dynamics approaches and, consequently, such an approach appears applicable to simulating protein-folding pathways, protein functional dynamics in a real molecular environment, and dynamical molecular recognition processes.     

Equilibrium thermodynamics from basin-sampling

We present a "basin-sampling" approach for calculation of the potential energy density of states for classical statistical models. It combines a Wang-Landau-type uniform sampling of local minima and a novel approach for approximating the relative contributions from local minima in terms of the volumes of basins of attraction. We have employed basin-sampling to study phase changes in atomic clusters modeled by the Lennard-Jones potential and for ionic clusters. The approach proves to be efficient for systems involving broken ergodicity and has allowed us to calculate converged heat capacity curves for systems that could previously only be treated using the harmonic superposition approximation. Benchmarks are also provided by comparison with parallel tempering and Wang-Landau simulations, where these proved feasible.     

The analysis of seasonal air pollution pattern with application of neural networks

Air pollution monitoring includes measuring the concentrations of air contaminants such as nitrogen dioxide, sulfur dioxide, some polycyclic aromatic hydrocarbons(PAHs), suspended particulate matter (PM) and tar substances. The purpose of this study was to determine the possibility of using artificial neural networks for identification of any patterns occurring during heating and nonheating seasons. The samples included in the study were collected over a period of 5 years (1997–2001) in the area of the city of Gdansk and the levels of pollutants measured in the samples collected were used as inputs to two different types of neural networks: multilayer perceptron (MLP) and self-organizing map (SOM). The MLP was used as a tool to predict in what heating season a certain sample was collected, and the SOM was applied for mapping all samples to recognize any similarities between them. This study also presents the comparison between two projection methods—linear (principal component analysis, PCA) and nonlinear (SOM)—in extracting valuable information from multidimensional environmental data. In the research the MLP model with 13-12-1 topology was developed and successfully trained for classification of air samples from different seasons. The sensitivity analysis on the inputs to the MLP indicated benz[α]anthracene, benzo[α]pyrene, PM₁, SO₂, tar substances and PM₁₀ as the most distinctive variables, while PCA pointed to PAHs and PM₁.     

Exponential trichotomy and p-admissibility for evolution families on the real line

The aim of this paper is to obtain necessary and sufficient conditions for uniform exponential trichotomy of evolution families on the real line. We prove that if p ∈ (1,∞) and the pair (C_b(R,X),C_c(R,X)) is uniformly p-admissible for an evolution family ={U(t,s)}_t≥_s then is uniformly exponentially trichotomic. After that we analyze when the uniform p-admissibility of the pair (C_b(R, X), C_c(R, X)) becomes a necessary condition for uniform exponential trichotomy. As applications of these results we study the uniform exponential dichotomy of evolution families. We obtain that in certain conditions, the admissibility of the pair (C_b(R,X),L^p(R,X)) for an evolution family ={U(t,s)}_t≥_s is equivalent with its uniform exponential dichotomy.     

View factors in a finite length axysymmetric cylindrical annulus enclosure

View factor – defined as fraction of total outgoing radiation from surface 1 intercepted by surface 2 – is a key concept in solving the radiative heat transfer in systems of surfaces. Analytical forms of the view factor have been developed by means of integration for many conventional systems of 2D and 3D surfaces in various spatial positions. However, little investigation has been carried out for situations in which there is no complete visibility between the surfaces involved in radiative exchange due to configuration of 3D surfaces or due to presence of interposing object that obstruct partially the mutual visibility.Radiative heat exchange was modeled in a finite length cylindrical annulus consisting of non-isothermal diffusely-emitting surfaces. The canonical definition of the view factor was extended by means of an analytical approach to both 3D and 2D surfaces with shading effects (incomplete mutual visibility) and numerical algorithms were developed in order to calculate view factors values and test view factor algebra rules. The system considered in this paper was an axysymmetric cylindrical annulus – frequently used in many heat transfer applications. View factor values for various surface elements were calculated by means of numerical integration. View factor algebra rules – summation and reciprocity – were verified.