Projection representable relations on Menger (2, n)-semigroups

Abstract characterizations of relations of nonempty intersection, inclusion end equality of domains for partial n-place functions are presented. Representations of Menger (2, n)-semigroups by partial n-place functions closed with respect to these relations are investigated.     

Linearly ordered compacta and Banach spaces with a projectional resolution of the identity

We construct a compact linearly ordered space Kω₁ of weight ℵ₁, such that the space C(Kω₁) is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, Kω₁ is a continuous image of a Valdivia compact and every separable subspace of C(Kω₁) is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos.     

The limit of detection in differential scanning calorimetry

A procedure is described to determine the limit of detection of DSC instruments by using tiny signals from spontaneous polymorphic transitions of CsCl, K₂Cr₂O₇ and Na₂SO₄. It is shown how such signals can be found well-resolved in DSC diagrams of powder samples. To distinguish them from the baseline noise they should exhibit a height at least twice that of the baseline width. For the instrument employed the corresponding smallest amount of heat, i.e., the limit of detection, was found to be 0.1 mJ.The authors thank Mr. H. Maltry for technical help and the Deutsche Forschungsgemeinschaft for support.     

Observables in a noncommutative approach to the unification of quanta and gravity: a finite model

We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a groupoid given by the action of a finite group on a space E. The geometry of the model is constructed in terms of suitable (noncommutative) algebras on . We investigate observables of the model, especially its position and momentum observables. This is not a trivial thing since the model is based on a noncommutative geometry and has strong nonlocal properties. We show that, in the position representation of the model, the position observable is a coderivation of a corresponding coalgebra, coparallelly to the well-known fact that the momentum observable is a derivation of the algebra. We also study the momentum representation of the model. It turns out that, in the case of the algebra of smooth, quickly decreasing functions on , the model in its quantum sector is nonlocal, i.e., there are no nontrivial coderivations of the corresponding coalgebra, whereas in its gravity sector such coderivations do exist. They are investigated.This revised version was published online in April 2005. The publishing date was inserted.     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Preparation and properties of yttrium,lanthanum and lanthanideo-nitrobenzoates

The conditions of the formation of yttrium, lanthanum and lanthanideo-nitrobenzoates were studied and their quantitative composition and solubilities in water at 298 K were determined (their solubilities are of the order of 10^–2 mol dm^–3). The IR and X-ray spectra for the obtained complexes and the dehydrated rare earth elemento-nitrobenzoates were recorded; all prepared complexes are crystalline compounds. The conditions of thermal decomposition of the complexes were also studied. It was found that on heating above 523 K the complexes decompose explosively and undergo a melting process at the same time. Therefore the thermal decomposition for complexes being studied was carried out in the temperature range 273–523 K. From the results it appears that during the dehydration process or with the increase of temperature no transformation of the nitro group to nitrito occurs.

---

Darstellung und Eigenschaften von Y, La und Lanthanidenorthonitrobenzoaten

Zusammenfassung Die Bedingungen zur Darstellung von Y-, La- und Lanthanidenorthonitrobenzoaten wurden untersucht. Ihre quantitative Zusammensetzung und ihre Wasserlöslichkeit bei 298 K wurde bestimmt; die Löslichkeit ist in der Größenordnung 10^–2 mol dm^–3. Die Infrarot- und Röntgenspektren der erhaltenen Komplexe sowie der Orthonitrobenzoate der seltenen Erden nach der Dehydratisierung wurden gemessen und dabei festgestellt, daß es sich um kristalline Verbindungen handelt. Das thermische Verhalten der erhaltenen Komplexe wurde festgestellt: sie zerfallen über 523 K explosiv und schmelzen zugleich. Der thermische Zerfall der erhaltenen Orthonitrobenzoate der seltenen Erden wurde im Temperaturbereich von 273–523 K untersucht. Es wurde festgestellt, daß die Y-, La- und Lanthanidenorthonitrobenzoate bei Temperaturzunahme oder im Dehydratisierungsprozeß keiner Umgruppierung in entsprechende Nitritoverbindungen unterliegen.

     

Preparation and properties of yttrium,lanthanum and lanthanide 2,4-dinitrobenzoates

Summary The conditions of the formation of rare earth 2,4-dinitrobenzoates were studied and their quantitative composition and solubilities in water at 298 K determined (their solubilities are of the order of 10^–2 mol dm^–2). The IR and X-ray spectra for the hydrated and dehydrated complexes were recorded. All complexes are crystalline compounds. The condition of thermal decomposition of the complexes were also investigated. On heating above 573 K the complexes were found to decompose explosively and undergo a melting process at the same time. Accordingly, the thermal decomposition for the complexes was carried out in the temperature range 273–573 K. The thermal stability data reveal them to dehydrate in one step and the crystallization water molecules to be bound in various ways. From the obtained results it appears that during the dehydration process no isomerisation of the nitro group to nitrito occurs.

---

Herstellung und Eigenschaften von Y-, La- und Lanthaniden-2,4-Dinitrobenzoaten

Zusammenfassung Die Bedingungen zur Darstellung von Y-, La-, und Lanthaniden-2,4-dinitrobenzoaten wurden untersucht. Ihre quantitative Zusammensetzung und ihre Wasserlöslichkeit bei 298 K wurden bestimmt (die Löslichkeit ist in der Größenordnung 10^–2 mol dm^–3). Die Infrarot- und Röntgenspektren der erhaltenen Komplexe sowie der dehydratisierten wurden gemessen und dabei festgestellt, daß es sich um kristalline Verbindungen handelt. Das thermische Verhalten der Komplexe wurde ebenfalls untersucht: sie zerfallen über 573 K explosiv und schmelzen zugleich. Der thermische Zerfall der 2,4-Dinitrobenzoate wurde im Temperaturbereich von 273–573 K untersucht. Aus der thermischen Analyse ergibt sich, daß die Komplexe und die Kristallwassermoleküle in einer Stufe dehydratisiert werden und verschiedenartig gebunden sind. Es wurde festgestellt, daß die Y-, La-, und Lanthaniden-2,4-Dinitrobenzoate bei Temperaturzunahme oder im Dehydratisierungsprozeß keiner Umgruppierung in entsprechenden Nitritoverbindungen unterliegen.