The alicyclic ring contraction of perfluoro-1-phenyltetralin in reaction with antimony pentafluoride

Perfluoro-1-phenyltetralin (1) heated with antimony pentafluoride at 130 °C, then treated with water, gave a mixture of perfluorinated 3-methyl-2-phenylindenone (3), 3-methyl-2-phenylindene (4), 3-hydroxy-1-methyl-3-phenylindan (5), 1-methyl-3-phenylindan (6), 9-methyl-1,2,3,4,5,6,7,8-octahydroanthracene (7), and 1,9-dimethyl-5,6,7,8-tetrahydro-β-naphthindan (8). When heated with SbF₅ in the presence of HF, then treated with water, compound 1 is transformed to a mixture of products 3-6. The reaction at 170 and 200 °C forms compounds 3-6 together with perfluoro-2-(cyclohexen-1-yl)-3-methylindene (10).     

Network manipulation algorithm based on inexact alternating minimization

In this paper, we present a network manipulation algorithm based on an alternating minimization scheme from Nesterov (Soft Comput 1–12, 2020). In our context, the alternative process mimics the natural behavior of agents and organizations operating on a network. By selecting starting distributions, the organizations determine the short-term dynamics of the network. While choosing an organization in accordance with their manipulation goals, agents are prone to errors. This rational inattentive behavior leads to discrete choice probabilities. We extend the analysis of our algorithm to the inexact case, where the corresponding subproblems can only be solved with numerical inaccuracies. The parameters reflecting the imperfect behavior of agents and the credibility of organizations, as well as the condition number of the network transition matrix have a significant impact on the convergence of our algorithm. Namely, they turn out not only to improve the rate of convergence, but also to reduce the accumulated errors. From the mathematical perspective, this is due to the induced strong convexity of an appropriate potential function.

     

On equivalence of Floer's and quantum cohomology

We show that the Floer cohomology and quantum cohomology rings of the almost Kähler manifoldM, both defined over the Novikov ring of the loop space M, are isomorphic. We do it using a BRST trivial deformation of the topological A-model. The relevant aspect of noncompactness of the moduli of pseudoholomorphic instantons is discussed. It is shown nonperturbatively that any BRST trivial deformation of A model which does not change the dimensions of BRST cohomology does not change the topological correlation functions either.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Integrable structure of conformal field theory,quantum KdV theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as “T-operators,” act in highest weight Virasoro modules. TheT-operators depend on the spectral parameter λ and their expansion around λ=∞ generates an infinite set of commuting Hamiltonians of the quantum KdV system. TheT-operators can be viewed as the continuous field theory versions of the commuting transfermatrices of integrable lattice theory. In particular, we show that for the values $c = 1 - 3\frac{{3(2n + 1)^2 }}{{2n + 3}}$ ,n=1,2,3 .... of the Virasoro central charge the eigenvalues of theT-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of the massless Thermodynamic Bethe Ansatz for the minimal conformal field theoryM _2,2n+3; in general they provide a way to generalize the technique of the Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator Φ_1,3. The relation of theseT-operators to the boundary states is also briefly described.     

Changing DNA grooves--a 1,4,5,8-naphthalene tetracarboxylic diimide bis-intercalator with the linker (beta-Ala)(3)-Lys in the minor groove

We have been investigating a modular, threading DNA polyintercalator design based upon the 1,4,5,8-naphthalene tetracarboxylic diimide (NDI) intercalating unit. Previously, we have reported the NMR analysis of a bis-intercalator-DNA complex in which the peptide linker between NDI units was found to occupy the DNA major groove (Guelev, Lee, Sorey, Hoffman, Iverson, Chem. Biol. 2001, 8, 415-425). Here we describe the NMR analysis of a complex between a related bis-intercalator known to display altered DNA sequence specificity. In this case, the linker resides in the DNA minor groove. We have thus shown that within this set of sequence specific bis-intercalators, both DNA grooves can be accessed, setting the stage for longer threading polyintercalators designed to have linkers occupying both grooves in an alternating fashion.     

Amphiphilic treelike rods at interfaces: layered stems and circular aggregation

Amphiphilic dendron-rod molecules with three hydrophilic poly(ethylene oxide) (PEO) branches attached to a hydrophobic octa-p-phenylene rod stem were investigated for their ability to form two-dimensional micellar structures on a solid surface. A treelike shape of the molecules was reported to be a major factor in the formation of nonplanar micellar structures in solution and in the bulk state (cylindrical and spherical). We observed that in these treelike amphiphilic molecules the hydrophilic terminated dendron branches assemble themselves in surface monolayers with the formation of two-dimensional layered or circular micellar structures. We suggested the formation of the planar ribbon-like structures with interdigitated layering within the loosely packed monolayers and circular, ringlike structures (2D circular aggregates) in the precollapsed state.     

Effect of cholesterol on the properties of phospholipid membranes. 4. Interatomic voids

The properties of the interatomic voids present in fully hydrated dimyristoylphosphatidylcholine (DMPC)-cholesterol mixed membranes of different compositions are analyzed in detail using a generalized variant of the Voronoi-Delaunay method on the basis of computer simulation results. The systems investigated are chosen from both sides of the DMPC-cholesterol miscibility gap; the pure DMPC bilayer has also been included in the analysis as a reference system. The results obtained show that the empty space is organized in a more compact way, forming larger voids in the presence than in the absence of cholesterol. The voids located in the region of the rigid cholesterol rings become, on average, less spherical, oriented more parallel with the membrane normal axis with increasing cholesterol concentration, whereas an opposite effect of cholesterol is observed in the middle of the membrane among the chain terminal methyl groups. In general, the preferential orientation of the voids is found to strongly correlate with that of the molecules in the hydrocarbon phase of the membranes. The membranes are found to contain rather large voids, the volume of which can be an order of magnitude larger than the largest spherical cavities present in the systems. These voids are elongated or branching channels rather than big empty holes. The voids located among the DMPC and cholesterol molecules are lying preferably parallel with the membrane normal axis. The existence of such empty channels can be of great importance in the cross-membrane permeation of small, uncharged penetrants, in particular, of polar molecules.     

Field operators and their spectral properties in finite-dimensional quantum field theory

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C ^r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L ²(R^r,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We shall show that the isomorphism between the exponential ofV andL ²(R^r,dx) can be understood as the decomposition by generalized eigenvectors of field operators (Fourier transform).