Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

The influence of the first integrals and the rolling resistance model on tippe top inversion

Nonlinear Dynamics - In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is...     

Modular Synthetic Approach to Carboranyl‒Biomolecules Conjugates

The development of novel, tumor-selective and boron-rich compounds as potential agents for use in boron neutron capture therapy (BNCT) represents a very important field in cancer treatment by radiation therapy. Here, we report the design and synthesis of two promising compounds that combine meta-carborane, a water-soluble monosaccharide and a linking unit, namely glycine or ethylenediamine, for facile coupling with various tumor-selective biomolecules bearing a free amino or carboxylic acid group. In this work, coupling experiments with two selected biomolecules, a coumarin derivative and folic acid, were included. The task of every component in this approach was carefully chosen: the carborane moiety supplies ten boron atoms, which is a tenfold increase in boron content compared to the l-boronophenylalanine (l-BPA) presently used in BNCT; the sugar moiety compensates for the hydrophobic character of the carborane; the linking unit, depending on the chosen biomolecule, acts as the connection between the tumor-selective component and the boron-rich moiety; and the respective tumor-selective biomolecule provides the necessary selectivity. This approach makes it possible to develop a modular and feasible strategy for the synthesis of readily obtainable boron-rich agents with optimized properties for potential applications in BNCT.     

Cyanide Bridged Platinum-Iron Complexes as Cisplatin Prodrug Systems: Design and Computational Study

The potential role of cyanide-bridged platinum-iron complexes as an anti-cancer Pt(IV) prodrug is studied. We present design principles of a dual-function prodrug that can upon reduction dissociate and release concurrently six cisplatin units and a ferricyanide anion per prodrug unit. The prodrug molecule is a unique complex of hepta metal centers consisting of a ferricyanide core with six Pt(IV) centers each bonded to the Fe(III) core through a cyano ligand. The functionality of the prodrug is addressed through density functional theory (DFT) calculations.     

Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

Effect of non-covalent interactions in 2,5-di-Me-pyrazine-di-N-oxide - methanol – Carbon nanotube electrocatalytic system

Catalytic oxidation of methanol (MeOH) in the absence of noble metals and noble metal oxides as catalysts, and the use of metal-free materials are inexpensive and attractive process for practical use in electrocatalysis, sensors, and in direct methanol fuel cells. In previous works, it was found that the use of single-walled (SWCNT) or multi-walled (MWCNT) carbon nanotube paper electrodes instead of GC increases the catalytic efficiency of organic compounds oxidation in the presence of aromatic di-N-oxides by several times. In this work, the effect of non-covalent interactions on the catalytic efficiency of MeOH oxidation in the presence of 2,5-di-Me-pyrazine-di-N-oxide (Pyr₁) in 0.1 M Bu₄NClO₄ solution in acetonitrile at SWCNT and MWСNT paper electrodes was studied by the methods of quantum chemical modeling, Raman spectroscopy, and using electrochemical data. New factors determined the features of mechanism of MeOH oxidation on CNT electrodes and lead to an increase in the catalytic efficiency of the electrode process in comparison with the GC electrode were established.     

Singlet Oxygen's Potential Role as a Nonoxidative Facilitator of Disulfide S–S Bond Rotation†

The role of singlet oxygen potentially mediating increased conformational flexibility of a disulfide was investigated. Density functional theory (DFT) calculations indicate that the singlet oxygenation of 1,2-dimethyldisulfane produces a peroxy intermediate. This intermediate adopts a structure with a longer S–S bond distance and a more planar torsional angle θ (C–S–S–C) compared with the nonoxygenated 1,2-dimethyldisulfane. The lengthened S–S bond enables a facile rotation about the torsional angle in the semicircle region 0° < θ < 210°, that is ~5 kcal mol⁻¹ lower in energy than the disulfane. The peroxy intermediate bears n_O → σ_S–S and n_O → σ*_S–S interactions that stabilize the S–O bond but destabilize the S–S bond, which contrasts with stabilizing n_S → σ*_S–S hyperconjugative effects in the disulfane S–S bond. Subsequent departure of O₂ from the disulfane peroxy intermediate is reminiscent of peroxy intermediates which also expel O₂, yet facilitate cis-trans isomerizations of stilbenes, hexadienes, cyanines, and carotenes. “Non-oxidative” ¹O₂ interactions with a variety of bond types are currently underappreciated. We hope to raise awareness of how these interactions can help elucidate the origins of molecular twisting.     

Synthesis,Characterization and Photocleavage of Bis-decyl Pteroic Acid: A Folate Derivative with Affinity to Biomembranes†

Here, we provide mechanistic insight to the photocleavage of a compound in the folate family, namely pteroic acid. A bis-decyl chain derivative of pteroic acid was synthesized, structurally characterized and photochemically investigated. We showed that, like folic acid, pteroic acid and the decylated derivative undergo a photocleavage reaction in the presence of H₂O, while no reaction was observed in methanol solution. Furthermore, density functional theory calculations were carried out to predict relative stabilities of hypothetical mono-, bis- and tris-decylated pteroic acid derivatives to help rationalize the regioselectivity of the bis-decyl pteroic acid product. Additionally, the lipophilicity of the bis-decyl pteroic acid appears to confer a hydrophobic property enabling an interaction with biomembranes.