Proper holomorphic mappings between some nonsmooth domains

Sunto In questo lavoro si studia il problema dell'existenza o meno di mappe olomorfe proprie, F: (p,q) (pq) dove (,) Cⁿ sono domini limitati, pseudoconvessi, non lisci, di Reinhardt con centro di simmetria sulla frontiera (per la definizione v. (2), introduzione). In caso affermativo si fornisee esplicitamente l'espressione di tali mappe (v, teoremi I e II nell'introduzione).

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The author, during the redaction of this paper, was supported by MPI (40% and 60%) funds.     

Critical star multigraphs

A star-multigraphG is a multigraph in which there is a vertexv ⁺ which is incident with each non-simple edge. It is critical if it is connected, Class 2 and(G\e) < (G) for eache E(G). We show that, ifG is any star multigraph, then(G) (G) + 1. We investigate the edge-chromatic class of star multigraphs with at most two vertices of maximum degree. We also obtain a number of results on critical star multigraphs. We shall make use of these results in later papers.     

Eine Bemerkung zum Primzahlsatz

It is shown that the function (s) (k large) can be used to derive the prime number theorem from the known zero-free regions for the Riemann Zeta-function. For the proof no upper bound for |/(s)| is required.     

Sur la répartition des valeurs de la fonction d'Euler

Let (x) denote the number of those integers n with (n) x, where denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that (x)-Ax R(x), where A=(2)(3)/(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem.     

Inequalities in Products of Minors of Totally Nonnegative Matrices

Let _I,I be the minor of a matrix which corresponds to row set I and column set I. We give a characterization of the inequalities of the form _{I,I K,K J,J L,L} which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson.     

Über die Quadratwurzel-Schranke für Quadratische-Rest-Codes

The minimal distanced of any QR-Code of lengthn 3mod4 over a prime fieldGF (p) with p3 mod4 satisfies the improved square root bound d(3d-2)4(n–1).

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Helmut Karzel zum 60. Geburtstag gewidmet     

Rationale Homotopietypen

We call a CW-complex unstable, if all attaching maps vanish under suspension. For a one-connected CW-space X we construct a unstable CW-complex ¯X and a mapping ¯XX, which is a rational homotopy equivalence. As an application we imbed the rational Hurewicz-homomorphism into an exact sequence.

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Der Autor wurde von der CNRS Frankreich unterstützt.     

On ortbogonal polynomial bases in the spacesC andL

, >0 C L - ( ) {Q _n(x)} , Q _n (x)–v _n n ¹⁺ nn ₀ (). , =0.     

Parties d'ensembles B-normaux

For a given subset A of the set R of real numbers, we defined M(A) as the infimum of all the lengths of the finite intervals I such that there exists a sequence of real numbers in I such that A is the associated normal set B(). We prove that if A is a subset of A, such that all the multiples k.a' belongs to A (for each non zero integer k and each element a of A), then M(A) is less or equal to 2.M(A). Thus the family of the subsets A such that M(A) is finite is closed under intersection and finite union.     

Triangular extension identities

It is shown that if the - -bimodule M generates a category of - -bimodules, then the ideal of identities of the triangular extension of the direct sum of algebras and by means of the bimodule M is equal to the product of ideals of identities of the algebras and .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 5–11, 1983.     

On the solution of a generalized Schrödinger-type equation

Lu(t)+(u,F)g(t)=f(t), tS. , ( F, g). .

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The authors wish to thank Professor Yu. A. Rozanov for his help and discussions.     

Absorption spectroscopy and excitation of YAlO3∶Er (50%) crystals

Absorption spectra have been measured in highly doped YAlO₃Er (50 %) in the wavelength range from 300 nm up to 2m. The spectra were taken with irradiation to the crystallographic b-axis with polarization a- or c-axis. From the measured spectra the Er energy levels have been determied. Based on the results of absorption spectroscopy the pumplight absorption in a Xenon-flashlamp-pumped YAlO₃Er laser slab has been calculated as a function of wavelength and depth.

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Zusammenfassung In hochdotiertem YAlO₃Er (50%) wurden Absorptionsspektren im Wellenlängenbereich von 300 nm bis 2m gemessen. Die Spektren wurden mit Bestrahlung zu der kristallographischen b-Achse mit Polarisation zur a- oder c-Achse aufgenommen. Aus den gemessenen Spektren wurden die Energieniveaus bestimmt. Mit den Ergebnissen aus der Absorptionsspektroskopie wurde die Pumplichtabsorption in einer mit Xenonblitzlampen gepumpten YAlO₃Er Platte in Abhängigkeit von der Wellenlänge berechnet.

     

A generalized integral with applications to trigonometric series

, . . .

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The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee.     

Adjungierte Funktoren in der Kategorie der p-Bornologischen Räume

In the category p b of p-convex vector spaces and linear maps preserving bounded sets a p-bornological topology will be introduced on the tensor product of two spaces, likewise on the spaces of morphisms Hom(E,F). Thus one gets a pair of adjoint functors from p to p , p being the category of p-bornological spaces and continuous linear maps, and the topologies being introduced will be characterized by extreme properties with respect to the adjoint transformations.

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Dieser Arbeit liegt ein Teil der Dissertation des Autors, Kiel 1967, zugrunde.     

On strong summability of polynomial expansions

—.

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Dedicated to Professor L. Leindler on his 50^th birthday     

Density profiles of charged test particles diffusing in a slab of finite thickness

Summary In the paper a detailed study of the diffusion of charged test particles in the interior of a slab of finite thickness is carried out upon a suitable functional formulation of the stationary Boltzmann equation. Either the boundary effects and the action of an external conservative force are accounted for. Numerical results for the shape function and the total density of the test particles considered are at last reported for an appropriate specialization of the relevant physical parameters.

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Sommario Nel presente lavoro viene sviluppato-tramite una opportuna formulazione funzionale dell'equazione di Boltzmann nel caso stazionario — uno studio dettagliato della diffusione di particelle cavia cariche all'interno di una lastra piana di spessore finito. Sia gli effetti del contorno che l'azione esercitata da una forza conservativa esterna sono portati in conto. In corrispondenza di una appropriata specifica dei parametri fisici di interesse vengono infine illustrati i risultati numerici ottenuti per la funzione di forma e per la densità totale delle particelle cavia considerate.

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Work performed during the preparation of the thesis for the degree of Dottore in Nuclear Engineering.     

On an application of infinitely divisible distributions to quadrature problems

— - , .     

Die Dupinschen Zykliden im pseudoeuklidischen Raum

In the pseudoeuclidean space¹ E ³ a surface of degree 3 or 4 is calledDupin-cyclide if there exists a (pseudoeuclidean) torus such that a (pseudoeuclidean) spherical inversion maps upon . If the axis of is respectively space-like, isotropic or time-like is calledDupin-r-,-l- or-z-cyclide. ADupin-cyclide is the envelope of two families of spheres, the caustic surfaces of degenerate in caustic curves and the lines of curvature of constitute two (orthogonal) families of circles.     

On the exactness of a theorem of G.A. Fomin

, . . [1] - . .     

Famiglie di dischi analitici con bordo su sottovarietàCR non generiche

Summary In this work the authors prove that all sufficiently small analytic discs in the tangent space of a non generic embedded CR manifold MC^N (M at least of class C⁴) can be lifted uniquely to analytic discs in C^N with boundaries on M Moreover if M is real analytic or C then real analytic or C discs lift without loss of derivatives. If M is of class C^K then there is a 1+ loss of derivatives in the lifting. A stability result is also proven.