Logistic equation of arbitrary order

The paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems X vs. number of tasks N, operating at limited resources K, at non-extensive, heterogeneous self-organization processes characterized by parameter f. In contrast to the classical logistic equation which exclusively relates to the special case of sub-extensive homogeneous self-organization processes at f=1, the proposed model concerns both homogeneous and heterogeneous processes in sub-extensive and super-extensive areas. The parameter of arbitrary order f, where −∞<f<+∞, depends on both the coefficient of external resource utilization u=N/K, where 0<u<1, and the internal microscopic character of realized processes related to the depth of feedback β. The coefficient β directly influences self-organization of processes by the change of microscopic parameters V_i, S_i, i and Z, where V_i is the number of references (visit) to the ith component of the system during the service of each task, S_i is the time of serving the task by the ith component, and Z is the think time of a given process. In the general case of complex system, parameters V_i, S_i, i and Z can have values in the range from 0 to +∞. In this way the new equation includes all possible cases of a complex executive system’s operation. Furthermore, it allows us to define the optimal matching point between X and N with f as the parameter. It also helps to balance the load in complex systems and to equip artificial systems with self-optimization mechanisms similar to those observed in natural systems.     

α-Iminohydroxylamine-α-aminonitrone tautomerism: a 1∶1 mixture of two tautomeric forms in crystals of N-(4,5-dihydro-1H-imidazol-2-yl)-N-phenyl-hydroxylamine

Crystals consisting of two distinct chemical entities, tautomers of each other, in exact 11 ratio, have been obtained and their structure determined by X-ray analysis. The crystals of C₉H₁₁N₃·C₉H₁₁N₃ are monoclinic,P2₁/c,a=15.674(3),b=17.085(3),c=13.758(3)Å, =90.78(2)°,Z=8. There are two hydroxylamine and two aminonitrone molecules in the asymmetric unit. Hydrogen bonds connect those molecules into chiral layers. Layers of opposite chirality alternate andthe crystal is centrosymmetric as a whole. Within those layers chains of tautomers joined by very strong O–H... O and strong N–H... N bonds can be recognized. Proton transfer along those chains with simultaneous rearrangement of -bonds within the molecules would result in interconversion of tautomers and would affect chirality of the layer.     

Synthesis,molecular structure,and applications of 2-hydroxylamino-4,5-dihydroimidazolium-O-sulfonate to the synthesis of novel heterocyclic ring systems

2-hydroxylamino-4,5-dihydroimidazolium-O-sulfonate (1) has been prepared by reacting 2-chloro-4,5-dihydroimidazole with hydroxylamine-O-sulfonic acid. Deprotonated compound 1a containing both the nucleophilic endocyclic nitrogen atoms and electrophilic exocyclic nitrogen was used for the syntheses of 3-substituted 6,7-dihydro-5H-imidazo[2,1-c][1,2,4]oxadiazoles 2-9 and 6,7-dihydro-5H-imidazo[2,1-c][1,2,4]thiadiazole-3-thione (10) by tandem nucleophilic addition-electrophilic amination reaction. The method promises utility in the synthesis of a variety of other heterocycles. On the other hand, the convenient routes to 7,8-dihydroimidazo[1,2-c][1,3,5]thiadiazine-2,4(6H)-dithione (16) and 2,6,7,8-tetrahydroimidazo[1,2-a][1,3,5]triazine-4(3H)-thione derivative (17) are reported starting from compound 1. The structures of the compounds prepared were established by elemental analyses, IR, NMR, and MS spectra, and in some instances X-ray analyses.     

Electrical and mechanical properties of thin metal films: Size effects

A general expression for the function of electron scattering in thin films of a grain structure is derived which takes account of both the external and internal size effects. Limiting and particular values of this function are given for polycrystalline and single-crystal films. Theoretical results are compared to the experimental results obtained for aluminium and tin. The relationship between size effects and resistivity, temperature coefficient of resistance, longitudinal and transverse strain coefficient of resistance and thermoelectric power is studied. The dependence of the orientation of monocrystalline copper and aluminium films on thermal stress, the direction of the energy density of elastic strains and the anistropy of elastoresistance coefficients in these films are examined. An expression for the gauge factor in single-crystal metal films of given orientations is derived.     

Spectrophotometric method for the determination of manganese with phenylfluorone in the presence of Triton X-100 and cetylpyridinium chloride in pharmacological preparations and vegetable fertilizers

A simple and very sensitive method for the spectrophotometric determination of manganese in pharmacological preparations and vegetable fertilizers is proposed. The method is based on the formation of a blue coloured complex of Mn (II) with 9-phenyl-2,3,7-trihydroxy-6-fluorone (PF) in the presence of cetylpyridinium chloride (CP) and Triton X-100. Optimum concentrations of PF, CP, Triton X-100 and pH ensuring maximum absorbance were defined. The complex Mn(II)-PF-CP-Triton X-100 shows maximum absorbance at 591 nm with the molar absorptivity value 1.77x10(5 )L mol(-1 )cm(-1). The detection limit of the method is 0.004 microg mL(-1). The Beer's law is obeyed for manganese concentrations in the range 0.02-0.2 microg mL(-1). The effect of foreign ions was elucidated. The statistical evaluation of the method was carried out for six determination using 5 microg Mn and the following results were obtained: standard deviation 0.021, confidence interval 5.05+/-0.05 microg Mn. The method has been applied for the determination of manganese in pharmacological preparations (Biovital, Kinder Biovital) and vegetable fertilizers (Hydrovit 100, Florovit).     

Quecksilber(II)-titrationen mit Variaminblau als Redoxindicator

Zusammenfassung Es wird ein volumetrisches Verfahren zur Bestimmung von Rhodanid mit Quecksilber(II)-nitratmaßlösung gegen Variaminblau als Redoxindicator angegeben. Auch Quecksilber(II)-ionen können bestimmt werden, wenn man mit einem Überschuß an Rhodanid versetzt und mit der Maßlösung zurücktitriert. Die Methode liefert genaue und wenig streuende Resultate.

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Summary Thiocyanate can be determined by titration with mercuric nitrate standard solution using Variamine blue as redox indicator. The determination of mercuric ions is possible by adding an excess of thiocyanate and back titrating with the standard solution. Results are exact and deviations are small.

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I. Mitteilung: Gregorowicz, Z., u. F. Buhl: diese Z. 173, 115 (1960).     

XRF Analysis of Microsamples of Semiconductor Type Multielement Materials by the Thin Layer Method. Determination of Cr, Co, Ni, Cu, Zn, Ga, Se, Sb, Yb

 A simple and quick method of durable samples preparation by the thin layer method through direct digesting of the analysed material on the substrate has been presented. Four- and three-component mono- and polycrystals have been analysed. Standards have been used in calibration containing: Cr, Co, Ni, Cu, Zn, Ga, Se, Sb, Yb. To improve the correlation between the concentration and the fluorescent radiation models of mathematical corrections have additionally been used: multiple linear regression, Lucas-Tooth-Pyne model (L. T. P.) and de Jongh model (d. J.). Statistical parameters: detection limits for 0.5 mg samples: Cr–0.041%, Co–0.034%, Ni–0.042%, Cu–0.053%, Zn–0.054%, Ga–0.057%, Se–0.057%, Sb–0.113%, Yb–0.077%. Correlation coefficients: simple regression 0.9946–0.9997, multiple regression 0.9974–1.0000, L. T. P. 0.9993–1.0000, d. J. 0.9995–1.0000. Received August, 1, 1998. Revision March 25, 1999.