Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

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     

Synthesis and characterization of PAni–SiO2 and PTh–SiO2 nanocomposites' thin films by plasma polymerization

In the present work, we explore the possibility to deposit polyaniline–silicon dioxide (PAni–SiO₂) and polythiophene–silicon dioxide (PTh–SiO₂) nanocomposites through a plasma polymerization route. The films were generated by spraying of mixtures of nano-sized silica particles dispersed in the liquid monomer into a plasma stream of the DC-plasma discharge reactor. The silica in the resulted polymer matrix changes the conduction mechanisms varying from ohmic to ballistic and traps inducing the space charged limited currents (SCLC). The silica modifies the morphology and composition of the deposited films.     

Influences of changes in multitopic tris(pyrazolyl)methane ligand topology on silver(I) supramolecular structures

The reactions between silver tetrafluoroborate and the ligands 1,2,4,5-C(6)H(2)[CH(2)OCH(2)C(pz)(3)](4) (L1, pz = pyrazolyl ring), o-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (L2), and m-C(6)H(4)[CH(2)OCH(2)C(pz)(3)](2) (L3) yield coordination polymers of the formula (C(6)H(6)(-)(n)[CH(2)OCH(2)C(pz)(3)](n)(AgBF4)(m))( infinity ) (n = 4, m = 2, 1; n = 2, ortho substitution, m = 1, 2; meta substitution, m = 2, 3). In the solid state, L2 molecules dimerize by a pair of C-H.pi interactions, forming an arrangement that resembles the tetratopic ligand L1. In the solid-state structure of 1, each silver atom is kappa(2)-bonded to two tris(pyrazolyl)methane units from different ligands with the overall structure a polymer made up from 32-atom macrocyclic rings formed by bonding tris(pyrazolyl)methane groups from nonadjacent positions on the central arene rings to the same two silver atoms. In 2, each silver is bonded to two tris(pyrazolyl)methane units in the same kappa(2)-kappa(2) fashion as with 1, forming a polymer chain. The chains are organized into dimeric units by strong face-to-face pi-pi stacking between the central arene rings making bitopic L2 act as half of tetratopic L1. The chains in both structures are organized by weak C-H.F hydrogen bonds and pi-pi stacking interactions into very similar 3D supramolecular architectures. The structure of 3 contains three types of silvers with the overall 3D supramolecular sinusoidal structure comprised of 32-atom macrocycles. Infrared studies confirm the importance of the noncovalent interactions. Calculations at the DFT (B3LYP/6-31G) level of theory have been carried out on L2 and also support C-H.pi interactions. Electrospray mass spectral data collected from acetone or acetonitrile show the presence of aggregated species such as [(L)Ag(2)(BF(4))](+) and [(L)Ag(2)](2+), despite the fact that (1)H NMR spectra of all compounds show that acetonitrile completely displaces the ligand whereas acetone does not.     

Natural Compounds and Products from an Anti-Aging Perspective

Aging is a very complex process that is accompanied by a degenerative impairment in many of the major functions of the human body over time. This inevitable process is influenced by hereditary factors, lifestyle, and environmental influences such as xenobiotic pollution, infectious agents, UV radiation, diet-borne toxins, and so on. Many external and internal signs and symptoms are related with the aging process and senescence, including skin dryness and wrinkles, atherosclerosis, diabetes, neurodegenerative disorders, cancer, etc. Oxidative stress, a consequence of the imbalance between pro- and antioxidants, is one of the main provoking factors causing aging-related damages and concerns, due to the generation of highly reactive byproducts such as reactive oxygen and nitrogen species during the metabolism, which result in cellular damage and apoptosis. Antioxidants can prevent these processes and extend healthy longevity due to the ability to inhibit the formation of free radicals or interrupt their propagation, thereby lowering the level of oxidative stress. This review focuses on supporting the antioxidant system of the organism by balancing the diet through the consumption of the necessary amount of natural ingredients, including vitamins, minerals, polyunsaturated fatty acids (PUFA), essential amino acids, probiotics, plants’ fibers, nutritional supplements, polyphenols, some phytoextracts, and drinking water.     

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.