On normal solvability of the Riemann problem with singular coefficient

Suppose is a singular matrix function on a simple, closed, rectifiable contour . We present a necessary and sufficient condition for normal solvability of the Riemann problem with coefficient in the case where admits a spectral (or generalized Wiener-Hopf) factorization with essentially bounded. The boundedness of is not required when takes injective values a.e. on .

     

Adjoints and formal adjoints of matrices of unbounded operators

In this paper we discuss diverse aspects of the mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter as it is the troublemaker.

     

Detection of surface changes of materials caused by intense irradiation with laser-plasma EUV source utilizing scattered or luminescent radiation excited with the EUV pulses

Extreme ultraviolet (EUV) radiation is absorbed in a thin surface layer of any material. Irradiation of material samples with intense EUV pulses may cause different surface changes. Some of them, especially connected with material desorption, can be clearly visible using an optical or electron microscope. Other changes concerning crystal structure or chemical composition may not be visible under the microscope. They can however be detected using the EUV radiation itself. In this paper a new method of measurement of surface changes by irradiation with a laser-plasma EUV source is presented. The radiation was collected and focused on a material surface using a specially designed multifoil collector. Radiation scattered or excited in the material was detected with the use of a Wolter-type mirror coupled to a back-illuminated CCD camera. Depending on material samples, images with different intensity distributions were registered. For some samples, the intensity distributions of the images obtained before and after irradiation were slightly different. The intensity differences in such cases allowed us to obtain differential images. The appearance of such images was assumed to be evidence of surface changes. PACS 42.62.-b; 61.80.-x; 52.25.Os     

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).     

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.     

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.     

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.     

Connections on vector bundles over super Riemann surfaces

We show that the globally inequivalent off-shell N=1 super Yang-Mills theories in two dimensions classify the superholomorphic structures on vector bundles over super Riemann surfaces. More precisely, there is a one-to-one correspondence between superholomorphic structures on vector bundles over super Riemann surfaces and unitary connections satisfying certain curvature constraints. These curvature constraints are the canonical constraints used in superspace formulations of super Yang-Mills theories, but arise in our considerations as integrability requirements for the local existence of solutions to certain differential equations. Finally, we discuss the relationship of this work with some aspects of Witten's twistor-like transform.