On maximal abelian subgroups in finite 2-groups

We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups (Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation) about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).      

Fault Detection of DC Electric Motors Using the Bispectral Analysis

The two major advantages of bispectral analysis are: resistance to noise and the ability to detect nonlinearities, like quadratic phase coupling. The first aim was to study some of the theoretical aspects of bispectral estimation. A lot of attention was paid to the influence of noise, the number of segments, the influence of one or several harmonic deterministic components and aliasing. These aspects are typical of rotating machinery. An example of successful fault identification in DC electric motors is presented. The identification proved to be capable to identify quadratically coupled mechanical system when the power-spectra analysis failed. Further it proved to be quite resistant to noise.     

On quasispectral maximal subspaces of a class of Volterra-type operators

The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladi\v{c} in 1984. As an application a class of quasinilpotent operators on -spaces, close to the Volterra kernel operator, was studied. In the present Banach function space setting we determine all quasispectral maximal subspaces of analogues of such operators and prove that these subspaces are all the invariant bands. An example is given showing that (in general) they are not all the closed, invariant ideals of the operator.

     

Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function h_t(x) with corner initialization. We prove, with one exception, that the limiting distribution function of h_t(x) (suitably centered and normalized) equals a Fredholm determinant previously encountered in random matrix theory. In particular, in the universal regime of large x and large t the limiting distribution is the Fredholm determinant with Airy kernel. In the exceptional case, called the critical regime, the limiting distribution seems not to have previously occurred. The proofs use the dual RSK algorithm, Gessel's theorem, the Borodin–Okounkov identity and a novel, rigorous saddle point analysis. In the fixed x, large t regime, we find a Brownian motion representation. This model is equilvalent to the Seppäläinen–Johansson model. Hence some of our results are not new, but the proofs are.     

Finite p-groups all of whose cyclic subgroups A, Bwith A ∩ B ≠ {1} generate an abelian group

We characterize the title p-groups for all primes p.     

Homomorphisms of matrix semigroups over division rings from dimension two to four

Let D be an arbitrary division ring and M_n(D) the multiplicative semigroup of all n×n matrices over D. We study non-degenerate, injective homomorphisms from M₂(D) to M₄(D). In particular, we present a structural result for the case when D is the ring of quaternions.     

On positive commutators

Let A and B be positive operators on a Banach lattice such that the commutator C = AB − BA is also positive. We study the size of the spectrum of C.     

Activities induced in the human body by thermal neutrons

Activities of 17 radionuclides, induced in the human body by the activation of 14 elements with thermal neutrons, were calculated. Resulting dependences of these activities on the activation time are shown in graphs.     

Preparation of samples of airborne particles for determination of metals

Summary A Soxhlet extraction procedure for the preparation of samples of airborne particulate matter for analysis by atomic-absorption spectrophotometry has been developed and tested by addition of known amounts of lead, iron, manganese, copper and cadmium and by analysing portions of atmospheric samples processed by (1) Soxhlet extraction, (2) acid digestion and (3) autoclave digestion. Soxhlet extraction proved to be superior to the other two procedures. It is simple and reliable, and offers less possibility of contamination by, or loss of, trace metals.

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Probengewinnung von Schwebstaub zur Metallbestimmung

Zusammenfassung Ein Verfahren der Soxhlet-Extraktion zur Probengewinnung für die Analyse von Luftverunreinigungsteilchen durch Atomarabsorption wurde ausgearbeitet und durch Zusatz bekannter Mengen Blei, Eisen, Mangan, Kupfer und Cadmium geprüft. Die Soxhlet-Extraktion, die saure Veraschung und die Veraschung im Autoklaven wurde zwecks Analyse von Luftproben verglichen, wobei sich das erstgenannte Verfahren als überlegen erwies. Es ist einfach, zuverlässig und bietet geringe Gefahr des Verlustes oder der Einschleppung von Spurenmetallen.

     

EPR study of a copper impurity center in a single crystal of 2-thiothymine

EPR spectroscopy was used to study the complex formed in crystals of 5-methyl-2-thiouracil (2-thiothymine) containing traces of copper. The copper impurities, originally present as Cu(I)-complex of 2-thiothymine in the lattice of 2-thiothymine, are transformed into paramagnetic Cu(II)-complex by ionizing radiation. It was found that the complex is planar, the plane being defined by two pairs of S and N atoms, from two adjacent 2-thiothymine molecules. The structure of the complex suggests that a pair of hydrogen bonds between two neighboring molecules is replaced by a stronger Cu-coordination bonding, with two sulfur and two nitrogen atoms as ligands. The spectroscopic parameters (g-tensor, A(63Cu) and A(14N) tensors) are essentially similar to those earlier observed for copper planar centers in other systems.