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.

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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.

     

Extraction of copper ions using silica gel with chemically modified surface

The applicability of silica gels for the application in solid-phase extraction was tested. Silica was modified with ketoimine groups. Surface characteristics of the modified silica were determined by elemental analysis, NMR spectra of solid phases (²⁹Si CP MAS NMR), analysis of pore size distribution of the silica support, and nitrogen adsorption-desorption. Newly proposed sorbents with ketoimine groups were applied in the preconcentration of trace amounts of the Cu (II) ions from lake water, post-industrial water, and demineralized water unburdened back to the lake. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

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.     

On Topological Classification of Non-Archimedean Fréchet Spaces

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .     

Rotational invariance as an additional constraint on local realism

Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2 correlations. This new constraint rules out such models even in some situations in which standard Bell inequalities allow for explicit construction of such models. The whole analysis is performed without any additional assumptions on the form of local realistic models.     

Mechanistic and synthetic aspects of the reaction of gamma-halogeno-alpha,beta-unsaturated ketones and esters with simple trialkyl phosphites

Phosphorylation of different gamma-halogeno-alpha,beta-unsaturated ketones, ketoesters and diesters 11a-h with simple trialkyl phosphites gives 1,3-dienylphosphates 14, cyclopropylphosphonates 15, ketovinylphosphonates 17 and other products depending on the nature and number of activating groups and halogen atoms in the substrate. Most likely the reaction proceeds via oxaphospholene 23 which is in equilibrium with pseudorotamer 24 and an open, dipolar form 22. Dipolar form 33 is a likely intermediate when two activating groups are present.     

Differentiable functions defined in closed sets. A problem of Whitney

In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of ℝ ⁿ is the restriction of a function of class 𝒞 ^p . A necessary and sufficient criterion was given in the case n=1 by Whitney, using limits of finite differences, and in the case p=1 by Glaeser (1958), using limits of secants. We introduce a necessary geometric criterion, for general n and p, involving limits of finite differences, that we conjecture is sufficient at least if X has a “tame topology”. We prove that, if X is a compact subanalytic set, then there exists q=q _X (p) such that the criterion of order q implies that f is 𝒞 ^p . The result gives a new approach to higher-order tangent bundles (or bundles of differential operators) on singular spaces. Oblatum 21-XI-2001 & 3-VII-2002?Published online: 8 November 2002 RID="*" ID="*"Research partially supported by the following grants: E.B. – NSERC OGP0009070, P.M. – NSERC OGP0008949 and the Killam Foundation, W.P. – KBN 5 PO3A 005 21.