On (strong) α-favorability of the Vietoris hyperspace

For a normal space X, α (i.e. the nonempty player) having a winning strategy (resp. winning tactic) in the strong Choquet game Ch(X) played on X is equivalent to α having a winning strategy (resp. winning tactic) in the strong Choquet game played on the hyperspace CL(X) of nonempty closed subsets endowed with the Vietoris topology τ _V . It is shown that for a non-normal X where α has a winning strategy (resp. winning tactic) in Ch(X), α may or may not have a winning strategy (resp. winning tactic) in the strong Choquet game played on the Vietoris hyperspace. If X is quasi-regular, then having a winning strategy (resp. winning tactic) for α in the Banach-Mazur game BM(X) played on X is sufficient for α having a winning strategy (resp. winning tactic) in BM(CL(X), τ _V ), but not necessary, not even for a separable metric X. In the absence of quasi-regularity of a space X where α has a winning strategy in BM(X), α may or may not have a winning strategy in the Banach-Mazur game played on the Vietoris hyperspace.     

Existence results for evolutionary inclusions and variational–hemivariational inequalities

We consider an abstract first-order evolutionary inclusion in a reflexive Banach space. The inclusion contains the sum of L-pseudomonotone operator and a maximal monotone operator. We provide an existence theorem which is a generalization of former results known in the literature. Next, we apply our result to the case of nonlinear variational–hemivariational inequalities considered in the setting of an evolution triple of spaces. We specify the multivalued operators in the problem and obtain existence results for several classes of variational–hemivariational inequality problems. Finally, we illustrate our existence result and treat a class of quasilinear parabolic problems under nonmonotone and multivalued flux boundary conditions.     

A Conjugated Thiophene‐Based Rotaxane: Synthesis,Spectroscopy, and Modeling

A dithiophene rotaxane 1 ?β‐CD and its shape‐persistent corresponding dumbbell 1 were synthesized and fully characterized. 2D NOESY experiments, supported by molecular dynamics calculations, revealed a very mobile macrocycle (β‐CD). Steady‐state and time‐resolved photoluminescence experiments in solution were employed to elucidate the excited‐state dynamics for both systems and to explore the effect of cyclodextrin encapsulation. The photoluminescence (PL) spectrum of 1 ?β‐CD was found to be blueshifted with respect to the dumbbell 1 (2.81 and 2.78 eV, respectively). Additionally, in contrast to previous observations, neither PL spectra nor the decay kinetics of both threaded and unthreaded systems showed changes upon increasing the concentration or changing the polarity of the solutions, thereby providing evidence for a lack of tendency toward aggregation of the unthreaded backbone.     

Three dimensional model of severe acute respiratory syndrome coronavirus helicase ATPase catalytic domain and molecular design of severe acute respiratory syndrome coronavirus helicase inhibitors

The modeling of the severe acute respiratory syndrome coronavirus helicase ATPase catalytic domain was performed using the protein structure prediction Meta Server and the 3D Jury method for model selection, which resulted in the identification of 1JPR, 1UAA and 1W36 PDB structures as suitable templates for creating a full atom 3D model. This model was further utilized to design small molecules that are expected to block an ATPase catalytic pocket thus inhibit the enzymatic activity. Binding sites for various functional groups were identified in a series of molecular dynamics calculation. Their positions in the catalytic pocket were used as constraints in the Cambridge structural database search for molecules having the pharmacophores that interacted most strongly with the enzyme in a desired position. The subsequent MD simulations followed by calculations of binding energies of the designed molecules were compared to ATP identifying the most successful candidates, for likely inhibitors—molecules possessing two phosphonic acid moieties at distal ends of the molecule.     

On (strong) α-favorability of the Wijsman hyperspace

The Banach-Mazur game as well as the strong Choquet game are investigated on the Wijsman hyperspace from the nonempty player's (i.e. α's) perspective. For the strong Choquet game we show that if X is a locally separable metrizable space, then α has a (stationary) winning strategy on X iff it has a (stationary) winning strategy on the Wijsman hyperspace for each compatible metric on X. The analogous result for the Banach-Mazur game does not hold, not even if X is separable, as we show that α may have a (stationary) winning strategy on the Wijsman hyperspace for each compatible metric on X, and not have one on X. We also show that there exists a separable 1st category metric space such that α has a (stationary) winning strategy on its Wijsman hyperspace. This answers a question of Cao and Junnila (2010) [6].     

Hydrophobic collapse in (in silico) protein folding

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.