Affine invariants of annuli

A family of regular annuli is considered. Affine invariants of annuli are introduced

On Poncelet’s porism

We consider circular annuli with Poncelet’s porism property. We prove two identities which imply Chapple’s, Steiner’s and other formulas. All porisms can be expressed in the form in which elliptic functions are not used

Rotation indices related to Poncelet’s closure theorem

Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with n- gons for any n > k

Přirozená hybridizace mezi Gladiolus palustris and G. imbricatus, zjištěná na základě morfologických, molekulárních a reprodukčních znaků

While studying the extremely rare species, Gladiolus palustris, in Poland, putative hybrid plants were discovered. Natural hybridization between G. palustris and G. imbricatus was confirmed by chloroplast (psbA-trnH and rpl32-trnL) DNA and nuclear ribosomal DNA (ITS1) sequences AFLP markers and macro-, micromorphological and reproductive characters. Based on molecular data, the hybridization events are likely to have occurred relatively recently with G. palustris as the maternal species and G. imbricatus as the pollen donor in interspecific crosses. The existence of a shared common cpDNA haplotype in all hybrids and G. palustris indicates unidirectional hybridization. A new nothospecies, G. ×sulistrovicus, is described. Analyses of AFLP data and polymorphisms of ITS1 sequences showed additive inheritance of parental genomic fragments in G. ×sulistrovicus. The hybrids exhibited either morphological similarity to G. imbricatus or intermediateness in phenotypic characters. The corm structure of flowering plants and seed capsules clearly distinguish the hybrid. The new taxon is characterized by a lower generative reproduction than the parental species, however hybrids produce ~50% viable pollen and seeds, which allows them to produce subsequent hybrid generations. The weak generative reproduction was enhanced by highly efficient vegetative propagation. The western part of the Balkan Peninsula and adjacent areas (Croatia, Bosnia and Hercegovina, Serbia, northern Italy) and central Europe (Poland, the Czech Republic, Slovakia, eastern Austria, Hungary) are the most likely areas where G. ×sulistrovicus will occur. Hybridity in the context of G. palustris conservation is discussed

On Poncelet’s porism

We consider circular annuli with Poncelet’s porism property. We prove two identities which imply Chapple’s, Steiner’s and other formulas. All porisms can be expressed in the form in which elliptic functions are not used

Affine invariants of annuli

A family of regular annuli is considered. Affine invariants of annuli are introduced

Application of Polynomials in the Old Problem of Poncelet 1

W pracy stawiamy hipotezę związaną z postacią wzorów Fussa. Hipotezę weryfikujemy dla przypadków =3,4,5,6. Wzory Fussa nie są znane w jawnej postaci dla dowolnego , więc hipotezy tej w obecnej chwili udowodnić nie można.In this paper we state a new hypothesis on the shape of the Fuss formulas. We verify the hy-pothesis for =3,4,5,6. The Fuss formulas are not known for all in explicit form, therefore the hypothesis cannot be proved at the moment

PONCELET’S PORISM IN TRANSFORMATION GROUP FRAMEWORK

In this paper we introduce a transformation group connected with Poncelet’s porism. Several open questions following from our considerations end the paper. The aim of this paper is to give a new approach to find an algebraic Fuss-type formula for all natural n>2. Developed method may be applied to investigations of Poncelet’s porism

Modyfikacja warstwy palnej prochów nitrocelulozowych za pomocą ciekłych nitroestrów

The article describes the use of liquid nitroesters (nitroglycerine, dinitrodiethyleneglycol and dinitrotriethyleneglycol) as modifiers of the burning layer of nitrocellulose powders. The properties of the modified powder were determined and compared with those of the base powder. The modification process did not change the powder’s geometry. The increase in heat of combustion is obtained by using a larger amount of nitroglycerine (from 6 to 8 phr) or by using dinitrotriethyleneglycol without an inert polymer. By using the appropriate composition and type of modifiers, a similar intensity of gas formation was obtained for different nitroesters. A faster loss of the stabilizer was observed for the powders with nitroglycerine. All modified powders will be stable for 10 years of storage at 25 °C.W artykule opisano zastosowanie ciekłych nitroestrów (nitrogliceryny, dinitrodietylenoglikolu i dinitrotrietylenoglikolu) jako modyfikatorów warstwy palnej prochów nitrocelulozowych. Określono właściwości prochów modyfikowanych i porównano je z prochem bazowym. Stwierdzono, że proces modyfikacji nie wpływa na zmianę geometrii prochów. Wzrost kaloryczności uzyskuje się przy zastosowaniu większej ilości nitrogliceryny (od 6 do 8 phr) lub zastosowaniu dinitrotrietylenoglikolu bez inertnego polimeru. Stosując odpowiedni skład i rodzaj modyfikatorów uzyskano zbliżoną intensywność powstawania gazów dla różnych nitroestrów. Dla prochów z nitrogliceryną zaobserwowano szybszy ubytek stabilizatora. Wszystkie modyfikowane prochy będą stabilne przez 10 lat składowania w temperaturze 25 °C