Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006     

Elementary operators with H∞-symbols

Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u₁,...,u_n) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.Both authors have been partially supported by NSF grants.     

Influence of medium on the kinetics of oxidation of iron(II) ion with t-butyl hydroperoxide

The oxidation of iron(II) with tert-butyl hydroperoxide was investigated in the absence of oxygen in water, methanol, and the dichloromethane—methanol solvent mixture (φ_r = 2:1). The oxidation rate depends on solvent polarity; measured in the presence of SCN⁻ at constant 0.8 mmol dm⁻³ HCl, the rate constant increases with the polarity decrease passing from water and methanol to the dichloromethane—methanol solvent mixture. Further, in non-aqueous solutions at this acid concentration the rate constant was higher than the rate constant in the presence of Cl⁻ only. The oxidation rate measured in the [FeCl]²⁺ complex in dichloromethane—methanol was slow in acidic medium and increased by decreasing the acid concentration. Approaching the physiological pH conditions the rate constant attained the value of an order of magnitude of 10³ dm³ mol⁻¹ s⁻¹, while very little alteration of stoichiometry of the oxidation reaction was observed. The rate constant measured in the presence of Cl⁻ strongly depends on electrolyte concentration at concentrations less than 0.5 mmol dm⁻³ HCl, both in MeOH and the solvent mixture. Based on these results, a possible mechanism of the influence of solvent, acidity, and ligand type on the rate constant is discussed. We assume that the oxidation proceeds by an inner-sphere mechanism considering that the breakdown of the successor inner-sphere complex forming reactive alkoxyl radicals is probably the rate-limiting step. Presented at the 20th International Conference on the Coordination and Bioinorganic Chemistry organized by the Slovak Chemical Society, Slovak University of Technology, Comenius University, and the Slovak Academy of Sciences, Smolenice Castle, 5–10 June 2005.     

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

On non-equilibrium dynamics of multidimensional infinite particle systems in the translation invariant case

It is shown that for a set of full measure with respect to any translation invariant probability distribution on the space of initial configurarations of classical particle systems on ^d with interaction given by a smooth superstable potential of finite range there is a solution to the Newtonian equations of motion, provided that the specific energy and the particle density of the initial configuration exist a.s.     

Point mutations in SARS-CoV-2 variants induce long-range dynamical perturbations in neutralizing antibodies

Monoclonal antibodies are emerging as a viable treatment for the coronavirus disease 19 (COVID-19). However, newly evolved variants of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) can reduce the efficacy of currently available antibodies and can diminish vaccine-induced immunity. Here, we demonstrate that the microscopic dynamics of neutralizing monoclonal antibodies can be profoundly modified by the mutations present in the spike proteins of the SARS-COV-2 variants currently circulating in the world population. The dynamical perturbations within the antibody structure, which alter the thermodynamics of antigen recognition, are diverse and can depend both on the nature of the antibody and on the spatial location of the spike mutation. The correlation between the motion of the antibody and that of the spike receptor binding domain (RBD) can also be changed, modulating binding affinity. Using protein-graph-connectivity networks, we delineated the mutant-induced modifications in the information-flow along allosteric pathway throughout the antibody. Changes in the collective dynamics were spatially distributed both locally and across long-range distances within the antibody. On the receptor side, we identified an anchor-like structural element that prevents the detachment of the antibodies; individual mutations there can significantly affect the antibody binding propensity. Our study provides insight into how virus neutralization by monoclonal antibodies can be impacted by local mutations in the epitope via a change in dynamics. This realization adds a new layer of sophistication to the efforts for rational design of monoclonal antibodies against new variants of SARS-CoV2, taking the allostery in the antibody into consideration.

Mutations in the new variants of SARS-CoV-2 spike protein modulates the dynamics of the neutralizing antibodies. Capturing such modulations from MD simulations and graph network model identifies the role of mutations in facilitating immune evasion.     

Asymmetry in liquid crystalline hexaalkoxytriphenylene discotics

The synthesis and phase behaviour of a new series of unsymmetrically substituted hexaalkoxytriphenylene‐based liquid crystals are reported. One of the hexyloxy chains in hexahexyloxytriphenylene (HAT6) is replaced by either a shorter or a longer chain, HAT‐(OC₆H₁₃)₅(OC _n H_2n+1). Compounds with chain lengths n of 2–14, 16 and 18 were prepared and investigated. Compounds with n?13 were not liquid crystalline. For all compounds with n?12 Col_h textures were observed by polarizing microscopy. X‐ray investigations showed that the intercolumnar distance gradually increased with n from n = 2 to n = 12, while the interdisk distance (3.6 Å) remained constant. A small odd–even effect on the increase of the intercolumn distance with n was observed. This effect was also found in the change of ΔH of isotropization with n.     

Frequency‐dependent NMR relaxation of liquids confined inside porous media containing an increased amount of magnetic impurities

Frequency‐dependent NMR relaxation studies have been carried out on water (polar) and cyclohexane (nonpolar) molecules confined inside porous ceramics containing variable amounts of iron oxide (III). The porous ceramics were prepared by compression of powders mixed with iron oxide followed by thermal treatment. The pore size distribution was estimated using a technique based on diffusion in internal fields that exposed a narrow distribution of macropore sizes with an average pore dimension independent of iron oxide content. The relaxation dispersion curves were obtained at room temperature using a fast field cycling NMR instrument. They display an increase of the relaxation rate proportional to the iron oxide concentration. This behavior is more prominent at low Larmor frequencies and is independent of the polar character of the confined molecules. The results reported here can be fitted well with a relaxation model considering exchange between molecules in the close vicinity of the paramagnetic centers located in the surface and bulk‐like molecules inside the pores. This model allows the extraction of the transverse diffusional correlation time that can be related to the polar character of the confined molecules. Copyright © 2013 John Wiley & Sons, Ltd.     

Thermostable Trioxane-Dioxolane Copolymers Obtained with Boron Trifluoride: Acrylonitrile Complex as Initiator

Trioxane was copolymerized with small amounts of dioxolane in benzene in the presence of a boron trifluoride:a crylonitrile complex as initiator. The kinetics of reactions was expressed in terms of topoenergetic principles. The copolymerizations had no induction periods and the maximum reaction rate was found proportional to the square of both the initiator and monomers concentrations. A zwitterionic mechanism is suggested for initiation. The activation energy for the system with 5% dioxolane was determined as 18.3 kcal/mol. The melting behavior of the copolymers is briefly discussed as a function of the dioxolane initial content, and is indicative of the amorphous-crystalline coupling phenomenon. The copolymers with ～ 5% dioxolane are thermostable in air up to 250%deg; and are recommended for practical purposes.