Lego-like spheres and tori

Given a connected surface \({\mathbb {F}}^2\) with Euler characteristic \(\chi \) and three integers \(b>a\ge 1<k\), an \((\{a,b\};k)\)-\({\mathbb {F}}^2\) is a \({\mathbb {F}}^2\)-embedded graph, having vertices of degree only k and only a- and b-gonal faces. The main case are (geometric) fullerenes (5, 6; 3)-\({\mathbb {S}}^2\). By \(p_a\), \(p_b\) we denote the number of a-gonal, b-gonal faces. Call an \((\{a,b\};k)\)-map lego-admissible if either \(\frac{p_b}{p_a}\), or \(\frac{p_a}{p_b}\) is integer. Call it lego-like if it is either \(ab^f\)-lego map, or \(a^fb\)-lego map, i.e., the face-set is partitioned into \(\min (p_a,p_b)\) isomorphic clusters, legos, consisting either one a-gon and \(f=\frac{p_b}{p_a}\,b\)-gons, or, respectively, \(f=\frac{p_a}{p_b}\,a\)-gons and one b-gon; the case \(f=1\) we denote also by ab. Call a \((\{a,b\};k)\)-map elliptic, parabolic or hyperbolic if the curvature \(\kappa _b=1+\frac{b}{k}-\frac{b}{2}\) of b-gons is positive, zero or negative, respectively. There are 14 lego-like elliptic \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,2)\). No \((\{1,3\};6)\)-\({\mathbb {S}}^2\) is lego-admissible. For other 7 families of parabolic \((\{a,b\};k)\)-\({\mathbb {S}}^2\), each lego-admissible sphere with \(p_a\le p_b\) is \(a^fb\) and an infinity (by Goldberg–Coxeter operation) of \(ab^f\)-spheres exist. The number of hyperbolic \(ab^f\,(\{a,b\};k)\)-\({\mathbb {S}}^2\) with \((a,b)\ne (1,3)\) is finite. Such \(a^f b\)-spheres with \(a\ge 3\) have \((a,k)=(3,4),(3,5),(4,3),(5,3)\) or (3, 3); their number is finite for each b, but infinite for each of 5 cases (a, k). Any lego-admissible \((\{a,b\};k)\)-\({\mathbb {S}}^2\) with \(p_b=2\le a\) is \(a^f b\). We list, explicitly or by parameters, lego-admissible \((\{a,b\};k)\)-maps among: hyperbolic spheres, spheres with \(a\in \{1,2\}\), spheres with \(p_b\in \{2,\frac{p_a}{2}\}\), Goldberg–Coxeter’s spheres and \((\{a,b\};k)\)-tori. We present extensive computer search of lego-like spheres: 7 parabolic (\(p_b\)-dependent) families, basic examples of all 5 hyperbolic \(a^fb\) (b-dependent) families with \(a\ge 3\), and lego-like \((\{a,b\};3)\)-tori.     

Oxidation stability of various Ti-alloys

Since titanium metal first became a commercial reality in 1950, corrosion resistance has been an important consideration in its selection as an engineering structural material. Titanium has gained acceptance in many media where its corrosion resistance and engineering properties have provided the corrosion and design engineer with a reliable and economic material. Titanium, like any other metal, is subject to corrosion in environments of air, oxygen, moisture, and so on. In this work, high-temperature stability of Ti and various Ti-alloys (by ASTM standard) was investigated. The best results showed that for Ti-Gr.5 alloy, the oxidation at 800 °C was 3.39% and at 900 °C 8.35%. For the comparison, commercial pure Ti-alloys Ti-Gr.2 and Ti-Gr.37 containing Al were used, whereas the oxidation resistance was much worse.     

Spectrophotometric Investigation of the Complexing Reaction between Rutin and Titanyloxalate Anion in 50% Ethanol

Summary.  In the present work, rutin (3,3′ ,4′ ,5,7-pentahydrohyflavone-3-rhamnoglucoside) was determinated via a complexing reaction with a titanyloxalate anion. K₂[TiO(C₂O₄)₂] and rutin react in 50% ethanol forming a 1:2 complex in a pH range from 4.00 to 11.50, in which the TiO(C₂O₄)₂ ²⁻ ion is linked to rutin through the 4-carbonyl and 5-hydroxyl group. The thermodynamic stability constant log β₂ ⁰ of the complex is determined to 10.80 at pH = 6.50. The change of the standard Gibbs free energy Δ G⁰ amounts to −61 kJċ mol⁻¹, indicating that the process of complex formation is spontaneous. The optimal conditions for the spectrophotometric determination of microconcentrations of rutin are at pH=6.40 and λ= 430 nm, where the complex shows an absorption maximum with a molar absorption coefficient a ₄₃₀=(60±2)ċ10³ dm³ċ mol⁻¹ċ cm⁻¹. The method is applied rutin determination from tablets. Received January 4, 2000. Accepted (revised) February 17, 2000     

Hybrid sol–gel thin films doped with a pH indicator: effect of organic modification on optical pH response and film surface hydrophilicity

Optical sensors for application in innovative wearable sensing systems such as textile-integrated systems and wireless sensor platforms rely on the development of low-cost multifunctional materials compatible with standard fabrication technologies. We are developing optically responsive pH sensitive sol–gel coatings for integration with a mobile wireless smart tag sensing system. For this application, we have fabricated a range of thin pH sensitive films using bromocresol green (BCG) indicator immobilised in inorganic–organic silica hybrid matrices prepared by a sol–gel method and deposited by spin-coating onto glass substrates. The surface hydrophilicity of the films were varied by using the inorganic sol–gel precursor tetraethoxysilane together with either methyltriethoxysilane, ethyltriethoxysilane, phenyltrimethoxysilane or glycidoxypropyltrimethoxysilane as organically modified sol–gel precursors, co-polymerised in different ratios. Spectral characterisation of the films was performed using visible absorption spectroscopy. The shift in absorption maxima and other spectral changes of the different matrices have been identified, and the apparent pK _app values of the immobilised BCG pH indicator determined. The surface wettability properties of the films have been studied by measuring the contact angle of water, formamide and diiodomethane which has allowed the estimation of the surface free energy (SFE) using three different models: Owens–Wendt, Wu and van Oss-Chaudhury-Good. It is shown that the SFE of the hybrid films is directly related to the type and the degree of organic modification, which in turn has a significant effect on the pH response-time of these sensing films.     

Thermal characterization and isothermal kinetic analysis of commercial Creosote decomposition process

Isothermal decomposition process of commercial Creosote was analyzed by thermogravimetric technique in a nitrogen atmosphere, at four different operating temperatures (T = 230, 250, 270, and 290 °C). It was found that the two-parameter autocatalytic ?esták–Berggren kinetic model best describes the investigated process. It was established that the applied logistic function can successfully perform a given kinetic predictions of investigated process, at all operating temperatures. The experimental density distribution function of the apparent activation energy values was evaluated. Based of the characteristic shape of distribution curve, it was concluded that the isothermal pyrolysis of commercial Creosote represent a complex process, which probably includes primary and secondary (autocatalytic) pyrolysis reactions, together with various decomposition reactions and radicals recombination pathways.     

Kinetics of chloride substitution in [Pt(bpma)Cl]+ and [Pt(gly-met-S,N,N)Cl] complexes by thiourea, nitrites, and iodides

Substitution of chloride in [PtCl(bpma)]⁺ and [PtCl(gly-met-S,N,N)], where bpma is bis(2-pyridylmethyl)amine and gly-met-S,N,N is glycyl-l-methionine, was studied as a function of the entering nucleophile concentration and temperature. Reactions between the platinum(II) complexes and thiourea (TU), iodides (I^?), and nitrites(III) (NO ₂ ^? ) were carried out in aqueous solutions using conventional UV-VIS spectrophotometry. Suitable ionic conditions were reached by an addition of 0.1 M NaClO₄ and 0.01 M NaCl (to suppress hydrolysis). The second-order rate constants, k ₂, for the studied reactions with NO ₂ ^? varied between 0.036–0.038 M^?1 s^?1, and for the reactions with TU between 0.095–1.06 M^?1 s^?1, respectively. The reaction between TU and the [PtCl(bpma)]⁺ ion is ten times faster than that of the [PtCl(gly-met-S,N,N)] complex. An analysis of the activation parameters, ΔH ^≠ and ΔS ^≠, for the selected reactions clearly shows their associative nature.