Chemical algebra. V:G-weighted distance extensions and metrics

The first formulation of the definition equation of completely-G-invariant distance extensions from the action of a compact group G onto a metric space (E, d) is reminded. A more general equation ( ) is then consistently associated to a group G mapped by a numerical functionm and acting on a metric space (E, d) mapped by another continuous numerical function. A solution of ( ) is called a G-weighted distance extension ofd. A differential form of the equation is derived in order to provide a definition of a G-weighted metricds ² = (d/)² from a non-uniform map of an Euclidean space: = #G whenG is a finite group, butds ² is also defined by continuity whenG is an infinite compact group ( = oo).     

Principal vectors of crystallographic groups and applications

For a crystallographic group acting on ann-dimensional Euclidean space we consider the -invariant linear elliptic differential operatorP with constant coefficients and to it the -automorphic eigenvalue problemP [] + = 0. N() is the number of all eigenvalues smaller than or equal to the frequency bound ^q (q: order ofP). Earlier we found the asymptotic estimationN() c₀ · ⁿ + c₁ · ^n–1 (c ₀,c ₁: certain volumina). Furthermore,N() was interpreted as the number of so-called principal classes of principal lattice vectors within a convex domain. In this paper we demonstrate these results for the casen = 2 for two representative crystallographic groups and the assigned lattices. Above all we demonstrate a counting method for an exact estimation ofN() if a is not too big. In an analogous way we can treat all the 230 space groups of crystallography. It will be seen that these applications are brought about by the so-called principal vectors of these lattices.     

Two Algorithms for Computing the Randles–Sevcik Function from Electrochemistry

We derive two expansions of the Randles–Sevcik function : an asymptotic expansion of for x and its Taylor expansion at any x ₀ . These expansions are accompanied by error bounds for the remainder at any order of the approximation.     

Some analytical results forABC,ABCD, andXBCD coupled spin 1/2 systems. II

In the preceding paper, it was shown that the calculation of the density matrix(t) for multiply connectedABC, etc., spin 1/2 spin systems can be greatly simplified by subdividing the Hamiltonian into , where is a suitable linear combination of the constants of the motion. In this paper, a framework for the determination of the time evolution of high-order multipolar quantum states is presented and discussed. It is shown that the necessary mathematical labour is reduced to a minimum by (i) exploiting the fact that is a good quantum number, and (ii) using the theory of partitioned matrices. For example, it is shown that for a generaln-coupled spin 1/2 system, the spin dynamics of the multipolar states, whereK _max is the maximum tensorial rank, can be determined without the need to diagonalize the full 2 ⁿ × 2 ⁿ Hamiltonian matrix, wheren is the number of spins. In fact, to describe the time evolution of the multipolar states it is only necessary to diagonalize twon ×n matrices at most. Finally, some cautionary remarks are made concerning the use of the weak-coupling approximation.     

On theC v toC p conversion for solid linear macromolecules

TheC _v toC _p conversion for solid linear macromolecules via the Nernst-Lindemann equationC _p -C _v =A ₀,C _p ² T/T_m is discussed on hand of data for 10 crystals and seven glasses. An average value ofA ₀=(5.11±2.41) · 10^–3 mol K J^–1 was calculated if the mole is assumed to refer to heavy atoms only. ThisA ₀ is numerically equal to the original Nernst—Lindemann constant.

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Zusammenfassung An Hand von sich auf 10 Kristalle und 7 Gläser beziehenden Daten wird die Umrechnung vonC _v -inC _p -Werte für feste lineare Makromoleküle mittels der Nernst-Lindemann-GleichungC _p -C _v =A ₀ C _p ² T/T _m diskutiert. Ein Durchschnittswert vonA ₀=(5.11±2.41) · 10^–3 mol K J^–1 wurde unter der Annahme berechnet, daß sich das Mol nur auf schwere Atome bezieht. DieserA ₀-Wert ist numerisch gleich der ursprünglichen Nerns-Lindemann-Konstanten.

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10 , - C _v C _p , —C _p –C _v = _{0 p} ² / . , , ₀ (5.11±2.41) · 10^–3 · ^–1. ₀ — .

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Support by the National Science Foundation, Polymers Program (Grant No. DMR 83-17097) is gratefully acknowledged.     

Possibilities of applying the piloyan method of determination of decomposition activation energies in the differential thermal analysis of polynitroaromatic compounds and their derivatives

Piloyan activation energiesE as well as initals of exothermT _D of sevenN-monoalkyl and fiveN,N-dialkyl-2,4-dinitroanilines were determined. Relationships were found between the T_D values and R_f factors as well asE values and those R_M functions and also theET _D ^–1 term and R_M functions.

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Zusammenfassung Die AktivierungsenergienE nach Piloyan sowie die Anfangswerte der ExothermenT _D wurden für siebenN-Monoalkyl- und fünfN,N-Dialkyl-2,4-dinitroaniline bestimmt. Die Zusammenhänge zwischen denT _D-Werten und den papierchromatographischenR _f-Faktoren der gemessenen Dinitroaniline wurden abgeleitet und erörtert. Desgleichen wurden auch die Zusammenhänge zwischen denE-Werten und denR _M-Funktionen der Papierchromatographie abgeleitet und erörtert. Auch zwischen dem AusdruckE ·T _D ^–1 und denR _M-Funktionen wurde ein Zusammenhang gefunden.

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Résumé On a déterminé les températures initialesT _D de l'effet exothermique ainsi que les énergies d'activationE d'après la méthode de Piloyan, de sept N-mono alcoyl et cinqN,N-dialcoyl-2, 4-dinitroanilines. Une corrélation entre les valeursT _D et les facteursR _f de la Chromatographie sur papier des dinitroanilines étudiées a été trouvée et discutée, ainsi qu'entre les valeursE et les fonctionsR _M de la Chromatographie sur papier. Une relation entre le termeE ·T _D ^–1 et les fonctionsR _M a également été trouvée.

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E T _D N- N,N- -2,4- . _D R _f , E R _M. E. _D ^–1 R _M.

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The authors would like to thank Mrs. Anna Collàkovà for careful DTA measurements, and Dr. Ladislav Smolka for help in treatment of the measured results with the Wang 600 computer.     

Prediction of the non-Newtonian viscosity and shear stability of polymer solutions

The structure-property relationships derived here permit the prediction of both the zero-shear viscosity ₀, as well as the shear rate dependent viscosity . Using this molecular modeling it is now possible to predict over the whole concentration range, independently of the molecular weight, polymer concentration and imposed shear rate. However, the widely accepted concept: dilute — concentrated, is insufficient. Moreover it is necessary to take five distinct states of solution into account if the viscous behavior of polymeric liquids is to be described satisfactorily. For non-homogeneous, semi-dilute (moderately concentrated) solutions the slope in the linear region of the flow curve (= must be standardized against the overlap parameterc · []. As with the ₀-M-c-relationship, a-M -c- relationship can now be formulated for the complete range of concentration and molecular weight. Furthermore, it is possible to predict the onset of shear induced degradation of polymeric liquids subjected to a laminar velocity field on the basis of molecular modeling. These theoretically obtained results lead to the previously made ad hoc conclusion (Kulicke, Porter [32]) that, experimentally, it is not possible to detect the second Newtonian region.Roman and Italian symbols a exponent of the Mark-Houwink relationship - b exponent of the third term of the ₀-M -c relationship - c concentration /g · cm^–3 - E number of entanglements per molecule - F(r) connector tension - f function - G _i ^A shear modulus; A indicates that it /Pa has been evaluated by a transient shear flow experiment; i is the shear rate to whichG ^A refers to - G storage modulus /Pa - G _p plateau modulus /Pa - H() relaxation spectrum /Pa - h shift factor (₀/_r) - K _H Huggins constant - K _b third constant of the ₀-M -c relationship - K constant of the Mark-Houwink relationship - M molecular weight /g · mol^–1 - M _e molecular weight between two /g · mol^–1 entanglement couplings - N number of segments per molecule - n slope in the power-law region of the flow curve - p p-th mode of the relaxation time spectrum - R gas constant /8.314 J·K^–1·mol^–1 - r direction vector - T temperature /K Greek symbols ß reduced shear rate - shear rate /s^–1 - shear viscosity /Pa·s - _s solvent viscosity /Pa·s - _sp specific viscosity - ₀ zero-shear viscosity /Pa·s - apparent viscosity at shear rate - reduced viscosity - viscosity of polymeric liquid in /Pa·s the second Newtonian region - [] intrinsic viscosity/cm³·g^–1 - screening length/m - /g·cm ^–3 density - relaxation time/s - ₀ experimentally derived relaxation time/s - angular frequency of oscillation Indices conc concentrated - corr slope corrected - cr critical - deg degradation - e entanglement - exp experimental - mod moderately concentrated/semi-dilute - n number average - p polymer - R Rouse - rep reptation - s solvent - sp specific - theo theoretical - weight average - relaxation time - o experimental or steady state - * critical - ** transition moderately conc. — conc. - + transition dilute — moderately cone. Paper presented at the 2nd bilateral U.S.-West German Polymer Symposium, Yountville, the 7th–11th September 1987.     

Kinetics of tritium isotope exchange between H2S and CH3OH vapor in glass vessels

Two different mechanisms of tritium exchange between and CH₃OH vapor in glass vessels have been found: (i) bimolecular exchange in the gas phase, (ii) pseudomonomolecular exchange between gaseous and CH₃OH adsorbed on the surface. The total and partial orders, rate constants and activation energies are given.

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, CH₃OH , : 1) 2) CH₃OH, . , .

     

The application of thermoanalytical methods in the investigation of biological substances

The equilibria and thermodynamics of a number of naturally occuring isolated compounds (e.g. proteins, amino acids, carbohydrates) have recently been studied in several laboraties in different temperature ranges, and thermoanalytical methods have been used to study structural changes of biological materials, among them human tissues.In our investigations we succeeded in appling the derivatograph for the assay of glycosaminoglycans and for the characterization of the stability of crosslinked proteins in intact human and animal tissues. By means of this method age-related and pathological changes and repair reactions were studied in various connective and vascular tissues.Other temperature-dependent techniques (DSC, polarizing microscopy) were used successfully in another series of experiments. Alterations in the characteristic order-disorder transition temperatures of human serum lipoproteins could be demonstrated in pathological conditions; the altered physical structure of lipoproteins might give an additional explanation to the assumed mechanism of different metabolic disorders.

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Zusammenfassung Die Gleichgewichte und die Thermodynamik einer Reihe von natürlich vorkommenden isolierten Verbindungen (z. B. Proteine, Aminosäuren, Kohlenhydrate) wurden in verschiedenen Laboratorien in verschiedenen Temperaturbereichen untersucht. Hierbei wurden thermoanalytische Methoden zum Studium der Strukturänderungen von biologischem Material, u. a. von menschlichem Gewebe, eingesetzt.In unseren Untersuchungen gelang es den Derivatographen zur Prüfung von Glycosaminoglycanen und zur Charakterisierung der Stabilität quervernetzter Proteine in intakten menschlichen und tierischen Geweben einzusetzen. Durch diese Methode wurden altersbedingte und pathologische Änderungen sowie Reaktionen zur Wiederherstellung in verschiedenen Binde und Vasculärgeweben studiert.Andere temperaturabhängige Techniken (DSC, Polarisationsmikroskopie) wurden in anderen Versuchsserien mit Erfolg eingesetzt.

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, . , , , , . . , . .

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Plenary lecture     

A new concept explaining catalytic synergy between two solid phases

We propose a new mechanism for explaining the synergy between MoS₂ and Co₉S₈ in hydrodesulfurization. We suppose that spill-over hydrogen produced by Co₉S₈ exerts an effect ofremote control on the active center of MoS₂, a slight reduction leading to hydrogenation centers and stronger reduction to hydrodesulfurization centers.

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MoS₂ CoS₈ . , , CO₉S₈, MoS₂, , , , .

     

Application of DTA for investigation of hydration and dehydration of crystal hydrates

The results of the investigation of the hydration processes of the dehydration products of magnesium carbonate trihydrate are shown. The DTA curve was used to calculate the functionQ(t). It was found that the results were in good agreement with the equation , whereQ is the heat evolved during the hydration timet;Q ₀,Q _f are the same for the initial and final products, respectively,k ₁ andk ₂ are the hydration constants.

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Zusammenfassung Die benutzte Methode wurde am Beispiel der Untersuchung des Hydrationsvorganges der Dehydratisierungsprodukte des Magnesiumkarbonat-Trihydrats demonstriert. Zur Errechnung der FunktionQ(t) dienten die DTA-Kurven. Die Ergebnisse folgten gut der Gleichung , woQ die freigesetzte Wärme während der Hydratationszeitt, Q ₀,Q _f dieselbe für die Anfangs- und Endprodukte,k ₁,k ₂ die Hydratationskonstanten bedeuten.

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Résumé Pour illustrer la méthode employée, on communique les résultats se rapportant à l'étude du phénomène d'hydration des produits de déshydratation du carbonate de magnésium trihydraté. On calcule la fonctionQ(t) à l'aide des courbes d'A.T.D. Les résultats obtenus sont en bon accord avec les valeurs de l'équation oùQ est la chaleur dégagée pendant le temps d'hydratationt, Q ₀ etQ _f sont les valeurs correspondantes pour les produits initiaux et finals,k ₁ etk ₂ les constantes d'hydratation.

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. Q(t) (). , , ,t,Q ₀ Q _f — , ,k ₁ k ₂ — .

     

Darstellung,Thermisches Verhalten und Gitterparameter von Erbiumfluorooxalattetrahydrat ErFC2O4 · 4H2O

Zusammenfassung Erbiumfluorhydrat ErF₃ · 1.1 H₂O bildet in Oxalsäurelösungen Erbiumfluorooxalattetrahydrat ErFC₂O₄ · 4 H₂O. Das ErFC₂O₄ · 4 H₂O ist grobkristallin, unlöslich in verdünnten Säuren und Laugen und löslich in konzentrierter Schwefelsäure. Beim thermogravimetrischen Abbau bildet es die Verbindungen ErFC₂O₄ · 2 H₂O, ErFC₂O₄ · · H₂O, ErFC₂O₄, ErOF und ErO_1.5. Die Kristallstruktur des ErFC₂O₄ · 4 H₂O ist orthorhombisch mit den Gitterkonstantena=11.217±0.007 Å,b-13.046±0.008 Å,c=9.191±0.005 Å undZ=6.

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Erbium fluoride hydrate ErF₃ · 1.1 H₂O forms in solutions of oxalic acid erbium fluorooxalate tetrahydrate ErFC₂O₄ · 4 H₂O. The ErFC₂O₄ · 4 H₂O is coarse-crystalline, insoluble in diluted acids and bases and soluble in concentrated sulphuric acid. During thermal decomposition ErFC₂O₄ · 2 H₂O, ErFC₂O₄ · H₂O, ErFC₂O₄, ErOF and ErO_1.5 are formed. The crystal structure of ErFC₂O₄ · 4H₂O is orthorhombic, with lattice constantsa=11.217±0.007 Å,b=13.046±0.008, Å c=9.191±±0.005Å andZ=6.

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Résumé Le fluorure d'erbium hydraté (ErF₃ · 1.1 H₂O) forme dans l'acide oxalique fluorooxalate d'erbium tétrahydraté (ErFC₂O₄ · 4 H₂O), un précipité consistant à gros cristaux insoluble dans les acides et bases dilués, mais soluble dans l'acide sulfurique concentré. Au cours de sa décomposition thermique on obtient ErFC₂O₄ · 2 H₂O; ErFC₂O₄ · H₂O; ErFC₂O₄, ErOF et ErO_1.5. ErFC₂O₄ · 4 H₂O a une structure cristalline ortorhombique avec les paramètres suivants:a=11.217±0.007 Å,b=13.046±0.008 Å,c-9.191 ±0.005 Å,Z=6.

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ErF₃ · 1.1 H₂O, ErFC₂O₄ · 4H₂O. ErFC₂O₄ · 4H₂O, - , , . : ErFC₂O₄ · 2H₂O. ErFC₂O₄ · H₂O, ErFC₂O₄, ErOF ErO_1·5. ErFC₂O₄ · 4 H₂O a=11,217±0,007 Å,b=13,046±0,008 Å,c=9,191± 0,005 Å Z=6.

     

Study of the thermal dissociation of processes of nickel(II) and cobalt(II) β-diketonate adducts

Thermal dissociation processes of-diketonate adducts with the composition ML₂ · 2B (L = acetylacetone and its substituted derivatives;M = Ni, Co;B = H₂O, BuNH₂CH₃OH, Py, NH₃) were investigated. Kinetics of dissociation were studied in a flow reactor. For dehydration processes a compensation relationship is observed (lgA=E+b), demonstrating analogous mechanisms.A semi-quantitative series of the thermodynamic stabilities of the dihydrates is obtained from experimental data at quasi-equilibrium conditions (Q-derivatograph).

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Zusammenfassung Es wurden die thermischen Dissoziationsprozesse von-Diketonataddukten der Zusammensetzung ML₂ · 2B (L=Azetylazeton und dessen substituierte Abkömmlinge;M=Ni, Co;B=H₂O, BuNH₂, CH₃OH, Py, NH₃) untersucht. Die Kinetik der Dissoziation wurde in einem Flowreaktor untersucht. Als Beweis für die Ähnlichkeit der Mechanismen der Dehydrierungsprozesse konnte eine lgA=aE+b Beziehung festgestellt werden. Von unter Quasi-Gleichgewichtsbedingungen gewonnenen Daten konnte eine semiquantitative Serie der thermodynamischen Stabilitäten der Dihydrate abgeleitet werden (Q-Derivatograph).

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- ML₂·2B (L = ;M= Ni, Co;B=H₂O, BuNH₂, CH₃OH, Py, NH₃). ; (lgA=aEs+b) . (Q- ).

     

Thermal decomposition of iron(II) sulphate heptahydrate in air in the presence of (basic) beryllium carbonate

Iron(II) sulphate heptahydrate undergoes decomposition in the presence of basic beryllium carbonate without any interaction with the carbonate. The components of the mixture decompose individually. Iron(II) sulphate decomposes with the formation of tetrahydrate, monohydrate, anhydrous salt, oxysulphate and ferric sulphate as intermediate phases. The basic beryllium carbonate decomposes to the oxide with BeO·BeCO₃ as the intermediate compound.

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Zusammenfassung In Gegenwart von basischem Berylliumcarbonat zersetzt sich Eisen(II)-sulfat-Heptahydrat, ohne mit dem Carbonat in Wechselwirkung zu treten. Die Komponenten des Gemisches zersetzen sich individuell. Die Zersetzung des Eisen(II)-sulfats verläuft über die Zwischenphasen Tetrahydrat, Monohydrat, wasserfreies Salz, Oxysulfat und Eisen(III)-sulfat. Das basische Berylliumcarbonat wird über die intermediäre Verbindung BeO·BeCO₃ in das Oxid überführt.

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, . . , , , . .₃.

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The authors are grateful to Dr. B. R. Sant for his keen interest and useful suggestions throughout this work. They also express their sincere thanks to Prof. P. K. Jena, Director, for his kind permission to publish the results. One of us (MSRS) thanks the Director for a Senior Fellowship.     

Studies of the energy spectrum of α, ω- substituted polymethine chains. II. Polymethine chains with odd number of methine groups

The analysis of the experimental data for the energy of the longest wavelength optical transitions _n,opt of substituted polymethines X (CH)_2n+1 X shows that in the asymptotic case (n) _,opt does not tend to zero, as it follows from the empirically established correlations, but has a finite, non-zero value. It is shown that the energy gap of odd polymethines is the same as that of the even polymethines - the polyenes (E 2 eV). The substituents (X N, O, B) are responsible for the appearance of levels in the gap. These, depending on the substituent character, are vacant (X B) or occupied (X N, O). The transition from or to such a level determines the longest wavelength optical transition energy of polymethines.     

Thermal Investigation of 1,2-propanediamine complexes of nickel(II) in the solid phase

Thermal studies have been carried out on [NiL₃]X₂·n H₂O, whereL=1,2-propanediamine;X=Cl^–, Br^–, SCN^–, 1/2SO ₄ ^2– and 1/2 SeO ₄ ^2– ; andn= 2, 1.5 and 0. [Ni₂L₅(NCS)₂](SCN)₂ and [NiL₂SO₄] have been synthesized pyrolytically in the solid-state from their mother diamine complexes. The deaquation behaviour of [NiL₃]SO₄·2 H₂O appears interesting, and its monohydrate undergoes a solid-state reaction (88–102°) without mass loss, showing an exothermic peak at 95 °C (H=– 5.1 kJ mole^–1).

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Zusammenfassung Thermische Untersuchungen wurden an [NiL₃]X₂,n H₂O ausgeführt, wobeiL-1,2-Propandiamin;X=Cl^–, Br^–, SCN^–, 1/2 SO ₄ ^2– und 1/2 SeO ₄ ^2– ;n=2, 1.5 und 0. [Ni₂Ls(NCS)₂](SCN)₂ und [NiL₂SO₄] wurden ausgehend von den entsprechenden Diaminkomplexen pyrolytisch im festen Zustand synthetisiert. Das Dehydratisierungsverhalten von [NiL₃]SO₄·2 H₂O scheint interessant zu sein, und beim entsprechenden Monohydrat wird eine ohne Massenverlust verlaufende Festkörperreaktion (88–102°) beobachtet, die sich durch einen exothermen Peak bei 95 °C (H=– 5.1 kJ mol^–1) zu erkennen gibt.

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[N³L₃]₂· n₂O, L=1,2-,=l^–, Br^–, SCN^–, 1/2 SO ₄ ^2- , 1/2SeO ₄ ^2- , an=2, 1.5 0. [Ni₂L₅(NCS)₂](SCN)₂ [NiL₂SO₄] . [N³L₃]S₄·2 ₂ , 88–102° , 95 ° =– 5.1 ·^–1.

     

X-ray studies of interaction between magnesium chloride and ethyl benzoate, components of the catalyst for propylene polymerization

X-ray studies of the interaction between highly dispersed magnesium dichloride and ethyl benzoate (EB) at different molar ratios EB/MgCl₂, and the effect of their grinding indicate that a new compound of MgCl₂ and EB is formed. Grinding destroys the crystal phase of the new compound, thus increasing the activity and stereospecificity of the catalyst obtained.

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() /MgCl₂, . , MgCl₂. , .

     

A quantum chemical study of the influence of an electrostatic field on the reactivity of methanol over zeolites

The INDO method with an electrostatic potential term in its Hamiltonian has been used to estimate the changes in the electronic structure of methanol and methanol dimer due to the electrostatic field of zeolites. It has been shown that fields of the strength F=2–8×10¹⁰V/m change significantly the electronic structure as well as the geometry of both molecules and can cause their decomposition leading to the species H₂O, CH₃, CH₃O, CH₂O, and CH₂.

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INDO . , F=2÷8·10¹⁰ / , , H₂O, CH₃, CH₃O, CH₂O CH₂.

     

Investigation of catalytic purification of gases from aromatic hydrocarbons

1,1- (AH) ([AH]=6,9 /, 50°C). AH W_i/W_{O 3}=0,40±0,16.

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The kinetics and oxidation products of 1,1-diethoxyethane (AH) ozonolysis have been investigated at [AH]=6.9 mol/l and 50 °C. The initiation efficiency of radical oxidation by ozone is W_i/W_{O 3}=0.40±0.16.

     

Methanol conversion to hydrocarbons and dimethyl ether on decationized zeolite T

Methanol transformations over the hydrogen forms of zeolite T (32%–76% decationization and 13%–32% dealumination) during contact with methanol vapor was studied at 200°–400°C. The catalysts used show a high activity in methanol conversion into light hydrocarbons and dimethyl ether but over a short period.

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T (32–16% 13–32% ) 200–400°C. , .