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The paper provides the complete list of local models forZ 2 l -invariant generic germs of Lagrangian submanifolds of dimension ≦3. Classification is done directly for genrating functions of Lagrangian submanifolds and contains both elementary singularities and non-elementary ones with continuous moduli. The results demonstrate, in particular, that in contrast to the non-equivariant case the classification of equivariant Lagrangian singularities is not subordinated to the classification of symmetric functions up to the right equivariant equivalences. 相似文献
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Let K be the field of real or complex numbers. Let (X K2n,) be a symplectic vector space and take 0 < k < n,N =. Let L1,...,LN X be 2k-dimensionallinear subspaces which are in a sufficiently general position.It is shown that if F : X X is a linear automorphism whichpreserves the form k on all subspaces L1,...,LN, then F is ank-symplectomorphism (that is, F* = k, where ). In particular, if K = R and k is odd then F mustbe a symplectomorphism. The unitary version of this theoremis proved as well. It is also observed that the set Al,2r ofall l-dimensional linear subspaces on which the form has rank 2r is linear in the Grassmannian G(l,2n), that is, there isa linear subspace L such that Al,2r = L G(l, 2n). In particular,the set Al,2r can be computed effectively. Finally, the notionof symplectic volume is introduced and it is proved that itis another strong invariant. 相似文献
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Jacek Achrem‐Achremowicz Elżbieta Kępczyńska Marek Żylewski Zbigniew Janeczko 《Biomedical chromatography : BMC》2010,24(3):261-267
A series of superlipophilic or highly lipophilic semisynthetic betulin derivatives was prepared and their relative lipophilicity was measured by reversed‐phase thin‐layer chromatography (RP‐TLC) at different pH values using 1,4‐dioxane–acetate buffer mixtures as mobile phases. Cholesterol, 17β‐estradiol and pure betulin were used as the reference compounds. Linear relationships were found between RM values and 1,4‐dioxane concentrations in the mobile phases. LogP values were also calculated with computer programs ACD/LogP (ChemSketch 11.0, Advanced Chemistry Development Inc.) and ClogP (Daylight Chemical Information Systems Inc.). The empirical and theoretical data were compared, and the RM0 values correlated well with logP. Two of the synthesized betulin derivatives are reported for the first time. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Let be the field of real or complex numbers. Let (X 2n, )be a symplectic affine space. We study the group of polynomialsymplectomorphisms of X. We show that for an arbitrary k thegroup of polynomial symplectomorphisms acts k-transitively onX. Moreover, if 2 l 2n – 2 then elements of this groupcan be characterized by polynomial automorphisms which preservethe symplectic type of all algebraic l-dimensional subvarietiesof X. 相似文献
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Podolak Irma Hubicka Urszula Żuromska-Witek Barbara Janeczko Zbigniew Krzek Jan 《平面色谱法杂志一现代薄层色谱法》2013,26(3):248-253
JPC – Journal of Planar Chromatography – Modern TLC - Quantitative high-performance thin-layer chromatography (HPTLC) analysis of triterpene saponins in different parts of eight... 相似文献
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Stanisław Janeczko 《Letters in Mathematical Physics》1987,13(1):45-52
Reduction in the category of general constitutive sets is defined and the generic stable models for reduced constitutive sets are derived. In the context of symmetric smooth constitutive sets, the corresponding infinitesimal stability properties are studied and the examples of classical systems encountered in physics are given. 相似文献
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Andrzej Skoczowski Anna Janeczko Gábor Gullner István Tóbias Andrzej Kornas Balázs Barna 《Journal of Thermal Analysis and Calorimetry》2011,104(1):131-139
The aim of the study has been to determine the protection effect of brassinosteroid (BR27) in oilseed rape cotyledons against infection by an incompatible wild type of, a hypersensitive response mutant of and saprophytic
Pseudomonas bacteria. In this paper, membrane permeability, PSII efficiency and metabolic activity were analysed. The following strains
of Pseudomonans were used: P. syringae pv. syringae (Ps), P. syringae pv. syringae hrcC mutant (Pm) and P.
fluorescence (Pf). The study was carried out using two cultivars of spring oilseed rape (Brassica napus L.): ‘Licosmos’ and ‘Huzar’. Pre-treatment of cotyledons with BR27 caused about 50–70% increase in ion leakage for both cultivars. However, BR27 significantly decreased ion leakage from cotyledons inoculated with Ps in both cultivars. Infection with Ps and Pf caused disturbances of energy flow in PSII by lowering its efficiency in rape cotyledons. We noted insignificant impact of
24-epibrassinolide on PSII efficiency if compared to absolute control, but generally it had a positive effect in plants infected
with bacteria. The values of heat flow in all treatments, except for cotyledons infected with Ps, decreased during 20 h after inoculation. However, the curves of heat flow for Ps-infected cotyledons showed a completely different pattern with at least two peaks. BR27 pre-treated cotyledons infected with Ps had higher heat flow in comparison to Ps infected ones. BR27 treatment did not change specific enthalpy of cotyledon growth (Δgh) for both cultivars if compared with absolute control. However, infection with Ps markedly increased Δgh values by about 200% for both cultivars. We suggested protective action of BR27 in oilseed rape cotyledons after bacterial infection with Pseudomonas. 相似文献