A note on relations between sets

From the definition of a strong and weakn-ary relation betweenn sets, given in a previous paper (Bulletin of Mathematical Biophysics,27, 477–492), it follows that for a given set ofn sets and givenn-ary relationR between them there can exist only one strong relation, but a large number of weak ones. An expression for the total number of possible weak relations is derived and the notion of the degree of weakness of a relation is introduced and discussed.     

On relations between sets: II

The notion of relations between sets, defined in a previous publication (Bull. Math. Biophysics,23, 233–235, 1961) is generalized and some biological examples are given. A generalization ton-ary relation is suggested.     

Mathematical theory of biological periodicities: Formulation of then-body case

In a series of papers, L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956;19, 9–18, 1957) showed that a non-linear biochemical interaction between the anterior pituary gland and the thyroid gland may result under certain conditions in sustained periodical oscillations of the rates of production and of the blood level of the thyrotropic and of the thyroid hormone. They treated the systems, however, as a homogeneous one. N. Rashevsky (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1965;Bull. Math. Biophysics,29, 395–401, 1967) generalized the above results by taking into account the histological structures of the two glands as well as the diffusion coefficients and permeabilities of cells involved. The present paper is the first step toward the theory of interaction of any numbern of glands or, more generally,n components. The differential equations which govern the behavior of such a system represent a system of2n ²+n non-linear first order ordinary equations and involve a total of 7 n ²+3n parameters of partly histological, partly biochemical nature. The requirements of the existence of sustained oscillations demand 4n ²+2n+2 inequalities between those 7n ²+3n parameters.     

A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units

A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π _i=1 ⁿ (2i−3) possible rooted binary phylogenies and the π _i=1 ⁿ⁻¹ (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.     

On relations between sets: III

The theory of relations between sets, proposed and outlined in previous publications (Bull. Math. Biophysics,23, 233–235, 1961;28, 117–124, 1966;28, 309–313, 1966), is tentatively expanded and generalized with a view to biological applications.     

Three New Species of Gelechiid Moths (Lepidoptera,Gelechiidae) from the Southeastern Regions of the European Part of Russia

Three new species of gelechiid moths (Gelechiidae) are described from the arid regions of the southeastern European part of Russia (Astrakhan and Orenburg provinces): Bryotropha satschkovisp. n., Monochroa aenigmasp. n., and Scrobipalpa achtubicasp. n.

     

Cytological observations on some West Himalayan mosses V.

Abstract

The chromosome numbers in the genus Gymnostomiella, G. vernicosa n=13, and in the three members of Bartramiaceae, Anacolia sinensis n=6, Philonotis angustata n=12 and P. revoluta n=6 are reported for the first time. The counts for Physcomitrium cyathicarpum n=52, P. repandum n=52, Bartramia hallerana n=9, B. subpellucida n=6 and Philonotis falcata n=12 are at variance with earlier reports. Intraspecific polyploidy is recorded in Philonotis turnerana with n=6 12. Quadrivalents are observed in Philonotis angustata. A dimorphic bivalent, rare in monoecious bryophytes, is observed in Bartramia hallerana. Unlike that of many moss species, the smallest member of the set is heteromorphic in Bartramidula bartramioides, Philonotis calcarea, P. revoluta and P. turnerana.     

Two new species of Serjania (Sapindaceae) from southeastern Brazil

One new species ofSerjania (S. erythrocaulis) belonging to theS. paradoxa group ofSerjania sect.Eurycoccus is described and illustrated bringing the total number of species in this group to eight. A second new species,Serjania divaricocca, belonging to sect.Serjania is also described and illustrated.

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Resumen  Una especie neuva deSerjania (S. erythrocaulis) perteneciente al grupoS. paradoxa de la secciónEurycoccus es descrita e ilustrada. Con esta especie, el numero total de especies conocidas para este grupo aumenta a ocho. Una segunda nueva especie,Serjania divaricocca, perteneciente a la secciónSerjania es también descrita e ilustrada.

     

A note on the development of organismic sets

It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value, as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops.     

Genomic dispersion of 28S rDNA during karyotypic evolution in the ant genusMyrmecia (formicidae)

Figure 2a–r of the above article is reprinted here at the request of the author because the print quality was not up to standard in the issue. Fig. 2a–r. Localization of 28S rDNA (white arrowheads) by fluorescence in situ hybridization of preparations from various Myrmecia species with different chromosome numbers. a–d, i–m Hybridized in situ and propidium iodide-stained chromosomes. e–h, n–r 4’,6-diamidino-2-phenylindole-stained chromosomes. a, e M. croslandi (2n=4). b, f M. pilosula (2n=22); the inset in b shows repeated layers of rDNA-positive signals in C-band. c, g M. pilosula (2n=23). d, h M. gulosa (2n=38). i, n M. forficata (2n=52). j, o M. mandibularis (2n=56). k, p Myrmecia sp. cf. M. arnoldi (2n=60) i, q M. occidentalis (2n=64) m, r M. simillima (2n=70). Bars represent 10 μm. The long bar in h applies also to d; the short bar in r to all other panels Chromosoma (1996) 105:190–196 Received: 22 March 1996; in revised form: 3 June 1996 / Accepted: 4 June 1996     

Role des stimuli chimiques dans l'attraction sociale chezCalotermes flavicollis (Fabr.)

Sans résuméCf.Insectes Sociaux, 1963,X, n^o 2, pp. 167–184 et n^o 3, pp. 185–296.Insectes sociaux, tome X, n ^o4, 1963.     

Distribution and Variability of n‐Alkanes in Epicuticular Waxes of Sedum Species from the Central Balkan Peninsula: Chemotaxonomic Importance

For the first time, the n‐alkane distribution and variability of the epicuticular waxes within 22 Sedum taxa was reported with focus on the chemotaxonomy of native Sedum representatives from the central Balkan Peninsula, compared to their relations with four other species of the Crassulaceae family. By GC/MS and GC‐FID identification and quantification, it was established that n‐alkanes C₂₇, C₂₉, C₃₁, C₃₃, and C₃₅ were the dominant constituents of the examined epicuticular wax samples. Applying multivariate statistical analyses including agglomerative hierarchical clustering (AHC) and principal component analysis (PCA), the relation according to the n‐alkane composition between the examined samples was established. It was shown that the n‐alkane variability of the central Balkan Sedum species was considerable and that n‐alkanes might not be very reliable taxonomic markers for these species.     

Cytological observations on some West Himalayan mosses VII

Abstract

Cytological observations are made on seven species belonging to seven families. The genera Solmslella (S. ceylonica, n= 11+m) and Pterobryopsis (P. orientalis, n=7) and the species Macromitrium himalayanum (n = 11), Chrysocladium phaeum (n=10) and Homaliodendron obtusatum (n=10+m) are reported on for the first time. One bivalent in the complements of Macromitrium himalayanum, Leucodon secundus and Trachypodopsis serrulata was found to be heteromorphic.     

The chemical constituents of Piper kadsura and their cytotoxic and anti-neuroinflammtaory activities

The n-hexane and CHCl₃ soluble fractions of the MeOH extract of the aerial parts of Piper kadsura were found to potently inhibit nitric oxide (NO) production in LPS-activated BV-2 cells, a microglial cell line. From the active fractions, a new stereoisomer of guaiane sesquiterpene, 1α,5β-guai-4(15)-ene-6β,10β-diol, kadsuguain A (1) and a new cyclohexadienone, kadsuketanone A (2), together with twelve known compounds (3–14) were isolated. The structures of these compounds were elucidated by extensive NMR spectral studies. The absolute configuration of 2 was determined by circular dichroism (CD) spectra. Compounds 2, 6, and 11–14 significantly inhibited both nitric oxide (NO) and prostaglandin E₂ (PGE₂) production in the LPS-activated microglia cells. In addition, compounds 4, 6, and 11–14 exhibited cytotoxicity against the A549, SK-OV-3, SK-MEL-2, and HCT15 human tumour cells.     

Genome constitutions of Pseudoroegneriageniculata, P. geniculata ssp. scythica and P. geniculata ssp. pruinifera (Poaceae: Triticeae) revealed by genomic in situ hybridization

Genomic constitutions of three taxa of Pseudoroegneria á. L?ve, P. geniculata, P. geniculata ssp. scythica, and P. geniculata ssp. pruinifera, were characterized using genomic in situ hybridization (GISH). The results indicated that ploidy level and genomic constitution in the three Pseudoroegneria taxa studied were as follows: P. geniculata (2n = 4x = 28; genomic formula StSt ^g ), P. geniculata ssp. scythica (2n = 4x = 28; genomic formula ESt), and P. geniculata ssp. pruinifera (2n = 6x = 42; genomic formula EESt). P. geniculata ssp. scythica and P. geniculata ssp. pruinifera should be transferred to Trichopyrum á. L?ve following L?ve’s principles and treated as T. scythicum and T. pruiniferum, respectively.     

Synthesis,antimicrobial activity and cytotoxicity of some new carbazole derivatives

In this work, some N-(9-Ethyl-9H-carbazole-3-yl)-2-(phenoxy)acetamide derivatives were synthesised and evaluated for their antimicrobial activity and cytotoxicity. The structural elucidation of the compounds was performed by IR, ¹H-NMR, ¹³C-NMR and FAB⁺-MS spectral data and elemental analyses. The title compounds were obtained by reacting 2-chloro-N-(9-ethyl-9H-carbazole-3-yl)acetamide with some substituted phenols. The synthesised compounds were investigated for their antibacterial and antifungal activities against Micrococcus luteus, Bacillus subtilis, Pseudomonas aeruginosa, Staphylococcus aureus, Escherichia coli, Listeria monocytogenes and Candida albicans. The compounds N-(9-Ethyl-9H-carbazole-3-yl)-2-(4-ethylphenoxy)acetamide (2c) and N-(9-Ethyl-9H-carbazole-3-yl)-2-(quinolin-8-yloxy)acetamide (2n) showed notable antimicrobial activity. The compounds were also studied for their cytotoxic effects using MTT assay, and it was seen that 2n had the lowest cytotoxic activity against NIH/3T3 cells.     

Some considerations on relational equilibria

A previous study (Bull. Math. Biophysics,31, 417–427, 1969) on the definitions of stability of equilibria in organismic sets determined byQ relations is continued. An attempt is made to bring this definition into a form as similar as possible to that used in physical systems determined byF-relations. With examples taken from physics, biology and sociology, it is shown that a definition of equilibria forQ-relational systems similar to the definitions used in physics can be obtained, provided the concept of stable or unstable structures of a system determined byQ-relations is considered in a probabilistic manner. This offers an illustration of “fuzzy categories,” a notion introduced by I. Bąianu and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968), in their paper on organismic supercategories, which is designed to provide a mathematical formalism for Rashevsky's theory of Organismic Sets (Bull. Math. Biophysics,29, 389–393, 1967;30, 163–174, 1968;31, 159–198, 1969). A suggestion is made for a method of mapping the abstract discrete space ofQ-relations on a continuum of variables ofF-relations. Problems of polymorphism and metamorphosis, both in biological and social organisms, are discussed in the light of the theory.     

Some aspects of cooperativity in human hemoglobin

The cooperativity in hemoglobin can be described by the Hill parameter n, the free energy of interaction ΔF₁ and the allosteric free energy ΔF_A. By this latter is meant here the free energy change associated with the transition from the deoxy to the oxy conformation in hemoglobin. In this paper some general relations between n, ΔF₁ and ΔF_A are given. A method is presented by which ΔF_A can be calculated from oxygenation data.     

Karyology of a few species of south Indian acridids. II Male germ line karyotypic instability inGastrimargus

Gastrimargus africanus orientalis,an acridid grasshopper has revealed the existence of karyotypic mosaicism in the male germ line cells of a few individuals with 2 n = 23, 19, 21, 25 and 27 chromosomes. Details of this chromosomal instability are presented in this paper. We dedicate this paper to our teacher Prof. L Siddaveere Gowda on the eve of his 60th birthday.