Solution of the Semi-Infinite Toda Lattice for Unbounded Sequences

The semi-infinite Toda lattice is the system of differential equations d _n (t)/dt = _n (t)(b _n+1(t) – b _n (t)), db _n (t)/dt = 2( _n ²(t) – _n–1 ²(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences _n (t), b _n (t) which satisfy the conditions _n (0) = _n ,, b _n (0) = b _n , where _n > 0 and b _n are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences _n and b _n are bounded. When at least one of the known sequences _n and b _n is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences _n and b _n such that the system has a unique solution. The results are illustrated with a typical example where the sequences _i (t), b _i (t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d²/dt ² log h _n = h _n+1 + h _n–1 – 2h _n , n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation.     

Light-induced reversible hydrophilicity of ZnO structures grown by aqueous chemical growth

ZnO wurtzite microrods and flowerlike structures were deposited on glass and ITO substrates by the aqueous chemical growth (ACG) technique at mild temperature (95 °C). Wettability studies revealed that the as-deposited structures are hydrophilic and super-hydrophilic for short and long growth times, respectively. The hydrophilic ZnO surfaces could be reversibly switched to super-hydrophilic by alternation of UV illumination and dark storage. Our results demonstrate that ACG at low temperatures can be efficiently employed to deposit transparent photosensitive ZnO structures exhibiting reversible wettability changes.     

One‐pot Synthesis of Fused Dipyranocoumarins from Dihydroxycoumarins and Propargyl Chlorides under Microwave Irradiation

Dipetalolactone and 4‐methyldipetalolactone are prepared in excellent yield by a one‐pot tandem propargylation/Claisen rearrangement/cyclization reaction of the corresponding 5,7‐dihydroxycoumarins with 3‐chloro‐3‐methylbut‐1‐yne in the presence of Cs₂CO₃ under microwave irradiation. The analogous reactions of propargyl chloride with esculetins or 5,7‐dihydroxycoumarins led to dipropargyloxy derivatives. The later by treatment with gold nanoparticles supported on TiO₂ or BF₃.Et₂O in N,N‐dimethylformamide (DMF) under microwave irradiation resulted in very good to excellent yield to the corresponding fused dipyranocoumarins. The reactions of esculetins with 3‐chloro‐3‐methylbut‐1‐yne gave mainly exomethylene fused dioxino[g]coumarins.     

Fatty Acids and Their Metal Salts: A Review of Their Infrared Spectra in Light of Their Presence in Cultural Heritage

In a cultural heritage context, fatty acids are usually found as breakdown products of lipid-containing organic remains in archaeological findings, binders in aged oil paintings, and additives in modern art-related materials. They may further interact with the ionic environment transforming into metal soaps, a process that has been recognized as a threat in aged paintings but has received less attention in archaeological objects. The investigation of the above related categories of materials with infrared spectroscopy can provide an overall picture of the organic components’ identity and demonstrate their condition and prehistory. The capability of investigating and distinguishing fatty acids and their metal soaps through their rich infrared features, such as the acidic carbonyl, the carboxylate shifts, the variable splits of alkyl chain stretching, bending, twisting, wagging, and rocking vibrations, as well as the hydroxyl peak envelopes and acid dimer bands, allows for their direct detailed characterization. This paper reviews the infrared spectra of selected saturated fatty monoacids and diacids, and their corresponding sodium, calcium, and zinc salts and, supported by newly recorded data, highlights the significance of their spectroscopic features.     

Interpolation by universal,hypercyclic functions

In the present article we study an interpolation problem for classes of analytic functions, in a systematic manner. More precisely, we provide sufficient conditions so that proper and “big”, in the Baire category sense, subclasses of analytic functions have an interpolation property at an infinite set of points. We then apply our main theorems to several classes of universal, hypercyclic functions.     

Annulated 1,2,3,4-tetrahydro-β-carbolines by intramolecular Mannich-type amino- and amidoalkylations of N(9)-(ω-nitroalkyl)-3,4-dihydro-β-carbolines

2-[1-(ω-Nitroalkyl)-1H-indol-3-yl]ethylformamides 11 were transformed to the corresponding 9-(ω-nitroalkyl)-4,9-dihydro-3H-β-carbolines 5 and through a diastereoselective intramolecular aminoalkylation to the annulated tetrahydro-β-carbolines 13, in high yields. Intramolecular N-acyliminium cyclisation of compounds 5 afforded the tetracyclic diazacycloalkano[jk]fluorenes in two diastereoisomeric forms 18 and 19 with moderate selectivity. Conjugate addition reactions performed on compounds 18 and 19 led to pentacyclic indolo[3,2,1-de]pyrido[3,2,1-jk]naphthyridinone 26a or diazabenzo[a]naphtho[2,1,8-cde]azulenone 26b.     

Overconvergent series of rational functions and universal Laurent series

In this paper, series of rational functions with fixed poles, which have restricted growth near the poles are considered. If they converge with a geometric rate on a continuum, a phenomenon of overconvergence takes place, in the sense that the convergence extends to a certain maximal domain. From this result, some properties of universal Laurent series are derived.     

Targeting SARS-CoV-2 Polymerase with New Nucleoside Analogues

Despite the fact that COVID-19 vaccines are already available on the market, there have not been any effective FDA-approved drugs to treat this disease. There are several already known drugs that through drug repositioning have shown an inhibitory activity against SARS-CoV-2 RNA-dependent RNA polymerase. These drugs are included in the family of nucleoside analogues. In our efforts, we synthesized a group of new nucleoside analogues, which are modified at the sugar moiety that is replaced by a quinazoline entity. Different nucleobase derivatives are used in order to increase the inhibition. Five new nucleoside analogues were evaluated with in vitro assays for targeting polymerase of SARS-CoV-2.     

Some results,concerning the variation of eigenvalues,when these depend on a real parameter

In this article we deal with a Hamiltonial of the form H(v) = Ho + A(v) where Ho is a self-adjoint bounded or unbounded operator on a Hilbert space and A(v) is a bounded self-adjoint perturbation depending on a real parameter v. In quantum mechanics a variety of results has been obtained by taking formally the derivative of the eigenvectors and eigenvalues of H(v).The differentiability of the eigenvectors and eigenvalues has been rigorously proved under several assumptions. Among these assumptions is the assumption that the eigenvalues are simple and the assumption that the perturbation A(v) is a uniformly bounded self-adjoint operator. A part of this article is dealing with examples, which show that these two assumptions are essential. The rest of this article is devoted to different applications concerning asymptotic relations of eigenvalues and a result for the solutions of the equation d_y/d_t= M(t)y in an abstract infinite dimensional Hilbert space, where iM(t)(1²=-1) is self-adjoint for every t in an interval. This result finds a succesful application to the theory of Toda and Langmuir lattices.     

Image analysis studies of dimensional changes in swellable hydrophilic polymer matrices

Studies of the fronts which are created by the process of swelling, their movement and the effect of drug solubility on release mechanisms, are presented. Tablets comprising solely of hydroxypropyl methylcellulose (HPMC) (Metolose 90 SH 100 000 SR), HPMC with sodium diclofenac (relatively soluble in the buffer solution used) and HPMC with furosemide (insoluble in the buffer solution used) were prepared. The tablets were made by direct compression in a manual hydraulic press and the matrix swelling was studied by an optical analysis technique. During the experimental procedure measurements were taken of the gel layer dimensions, the movement of the swelling, and the erosion and diffusion fronts at different time points. These measurements allowed the investigation of the possible mechanisms involved in the swelling/release process. The results showed that the rate and mechanism of drug release from swellable matrices depends on the following factors: the dissolution, the diffusion of the drug, the translocation of undissolved drug particles in the gel layer, and the solubility of the drugs used. This is supported by the following: (a) the diffusion layer thickness, which is observed as a result of the presence of undissolved drug in the gel layer, increases in the case of the water insoluble drug furosemide and as a result the diffusion front converges on the erosion front; (b) from the analysis of the dissolution data it appears that sodium diclofenac is released as a result of diffusion via the gel layer as well as due to polymer relaxation and/or matrix erosion. Conversely, the release of furosemide is only dependent on the polymer relaxation and/or matrix erosion. Copyright © 2004 John Wiley & Sons, Ltd.