810 research outputs found
Results on of general quadratic groups
No full textIn the first part of this article we discuss the relative cases of
Quillen-Suslin's local-global principle for the general quadratic (Bak's
unitary) groups, and its applications for the (relative) stable and unstable
-groups. The second part is dedicated to the graded version of
the local-global principle for the general quadratic groups and its application
to deduce a result for Bass' nil groups.Comment: 17 pages. arXiv admin note: substantial text overlap with
arXiv:2101.0702
Bahumukhī mana, bahurupī prema
No full textThe document contains a novel written by the Bengali author Nirpendra Kumar Basu (1898-1979). The monograph is from the private collection of Sharmadip Basu
Outer Length Scales in Nocturnal Stable Boundary Layers
No full textRecently, Basu and Holstlag (2021) proposed a unified framework for describing outer length scales (OLS). By utilizing this framework, we document various characteristics of OLS in nocturnal boundary layers over the US Great Plains.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Atmospheric Remote Sensin
Local-Global Principle for Transvection Groups
No full textBak A, Basu R, Rao RA. Local-Global Principle for Transvection Groups. Proceedings of the American Mathematical Society. 2010;138(4):1191-1204.In this article we extend the validity of Suslin's Local-Global Principle for the elementary transvection subgroup of the general linear group GL(n)(R), the symplectic group SP2n(R), and the orthogonal group O-2n(R), where n > 2, to a Local-Global Principle for the elementary transvection subgroup of the automorphism group Aut(P) of either a projective module P of global rank > 0 and constant local rank > 2, or of a nonsingular symplectic or orthogonal module P of global hyperbolic rank > 0 and constant local hyperbolic rank > 2. In Suslin's results, the local and global ranks are the same, because he is concerned only with free modules. Our assumption that the global (hyperbolic) rank > 0 is used to define the elementary transvection subgroups. We show further that the elementary transvection subgroup ET(P) is normal in Aut(P), that ET(P) = T(P), where the latter denotes the full transvection subgroup of Aut(P), and that the unstable K-1-group K-1(Aut(P)) = Aut(P)/ET(P) = Aut(P)/T(P) is nilpotent by abelian, provided R has finite stable dimension. The last result extends previous ones of Bak and Hazrat for CLn(R), SP2n(R), and O-2n(R). An important application to the results in the current paper can be found in a preprint of Basu and Rao in which the last two named authors studied the decrease in the injective stabilization of classical modules over a nonsingular affine algebra over perfect C-1-fields. We refer the reader to that article for more details
Cupid Joins the War
No full textThe author explores the history of love and sex in war though the ages. This monograph is from the private collection of Sharmadip Basu, Kolkata, W.B., India
Magnanimous Kunti by Samaresh Basu/ সমরেশ বসুর কলমে মনস্বিনী কুন্তী
No full textSamaresh Basu wrote a number of books based on Puran-Mahabharata under the pseudonym Bhramar and Kalkoot. Such as, ‘Shamba (1978)’, ‘Juddher Sesh Senapati (1984)’, ‘Prachetas (1984)’, \u27Pritha (1986)\u27, ‘Antim Pranay (1987)’ etc. ‘Pritha’ was published in the magazine \u27Prasad\u27 under the pseudonym \u27Bhramar\u27. In such books, the author analyzed the traditional story of the Puranas in a new perspective.
One of the memorable Panchakanyas in Puranas, Empress Kunti has been recreated in the light of the author\u27s spirit in this book. In the present article we will discuss how the character of Kunti has been recreated by Samaresh Basu in \u27Pritha\u27.
At the beginning of the story, before reaching the context of Kunti, the author undertakes a very realistic analysis of heaven-hell, Gods-demons, Samhita era-Puranic era, male-female relationship, marriage customs, child birth and the position of women in society. Then he explained the solitude, self-immolation and transition of Kunti from a feminist perspective.
The story of love-marriage-motherhood-heroism-restraint-pain-sacrifice of this remarkable female character of Mahabharata has been captured in a new way in the unique writing of Kalkoot. Inventing many thoughtful arguments the author tried to establish the father-son relationship between Yudhisthira-Vidura and Karna-Durbasha. How the author incarnated new contexts in the familiar story of Mahabharata and how he made it acceptable by arranging relevant arguments in favour of his new thoughts – this essay will try to elaborate these points
Metrocoris dinendrai Basu, Polhemus and Subramanian, NEW SPECIES
No full textMetrocoris dinendrai Basu, Polhemus and Subramanian, NEW SPECIES Figs. 33–44 Material examined. Holotype: Apterous male: INDIA, West Bengal, Darjeeling District, roadside cascades within Neora Valley National Park, 27.0828°N, 88.7437°E, 2006m. asl, 3.X.2012, coll. S. Basu, deposited at the Zoological Survey of India, H.Q., Kolkata (NZSI) Reg. No. 4774/H15. Paratypes: INDIA, West Bengal: 1 apterous male, 1 apterous female, 31 nymphs: same data as holotype Reg. No. 4775/H15; 2 apterous males, 1 apterous female, 1 macropterous female, 5 nymphs, Darjeeling District, stream on the way to Chengey Falls, near Lava, 27.0511°N, 88.6800°E, 1639 m. asl, 3.X. 2012, coll. S. Basu (NZSI) Reg. No. 4776/H15; 4 apterous males, 2 apterous females, 1 nymph, Darjeeling District, stream near Gorubathan, 26.96636°N, 88.7000°E, 370 m. asl., 1.X.2013, coll. S. Basu, (NZSI) Reg. No. 4777/H15. Description. Apterous male (Holotype): Fig.33 Size: Body length 5.42 mm, maximum width across mesoacetabula 2.53 mm. Colour: Dorsal body coloration yellowish to orange with dorsal black markings (Fig. 33). Interocular dark mark rectangular, bifid posteriorly, anterior margin not connected with dark mark of postclypeus, posterior portion in some individuals connected with dark inner margin of eye. Antennal segments black, with first segment yellow basally. Eyes black. Dark marks on pronotum broad T-shaped, connected to propleural margin (Fig.33). Meso- and metanota pale orange with dark markings as in Figs. 33, sublateral dark stripes broader than yellowish part on apical half, longitudinal dark stripe of mesopleuron extending nearly through its length. Abdominal terga black except segment VIII. Thoracic venter black, with a deep yellowish patch laterally (Fig. 36). Abdominal sterna II– VI black, sterna VII–VIII yellowish posteriorly. Fore femur black, basal one-fourth of ventral and dorsal surfaces yellowish, fore tibia and tarsus black. Rostrum black with pale yellowish lateral margins. Structural characteristics: Head width 1.36, length 0.73. Interocular region wider than eye, widths 0.61 and 0.25 respectively. Eye length 0.62, posterior half of eye covering anterior one fourth of propleuron. Length of antennal segments I–IV: 2.29, 0.97, 0.88, 0.65, first segment longer than combined lengths of remainder. Rostrum length 1.46, surpassing fore trochanter. Pronotum slightly bulbous in male, wider than long, width 1.61, length 0.57, slightly wider than head. Meso- and metanota 1.12 times wider than combined length, width 2.55, length 2.27. Fore femur (Fig. 39) slender and slightly curved at middle, ratio of length/width approximately 6.5, ventral surface with small constriction near middle, without indentation or tooth, with short dense hair fringe ventrally near apex, inner margin with rows of short hairs. Inner margin of fore tibia not modified, bearing rows of short hairs. Second tarsal segment long. Pretarsus with pair of sharp claws. Hind trochanter lacking modifications. Abdominal terga with prominent golden pubescence, combined length 1.83, maximum width 1.21. Abdominal sternum VIII bearing long dense hair fringe (Fig. 37). For measurements of leg segments see Table 1. Male genitalia: Male abdominal sternum VIII (Fig. 37) elongate, sub-oval, length 1.27, width 0.86, densely clothed with fringe of golden hairs. Posterior margin of abdominal tergum VIII straight. Pygophore (Fig. 42) elongate, heavily setiferous, apex truncate. Proctiger (Fig. 41) moderately elongate, lateral margins slightly convex, isolating angular basal lobes, apex broadly rounded, posterior margin with dense hair fringe. Parameres symmetrical (Fig.43) strongly curved near midpoint, apical section expanded to small head with outer margin concave, apex blunt, inner and outer margins with long distinct setae, several whitish dots distributed throughout. Endosomal sclerites as in Fig. 44. Apterous female: Fig. 34 Size: Body length 4.41–4.55, maximum width across mesoacetabula 2.29–2.31. Colour: Pattern of dark markings similar to that of male except much wider and more prominent; fore femur slender, lacking median invaginations; sterna VI–VII yellowish. Structural characteristics: Head length 0.74, width 1.21. Length of antennal segments 1–4: 1.87, 0.65, 0.60, 0.72. Eye length 0.61, width 0.24, interocular width 0.66. Length of rostrum 1.45. Pronotum wider than long, length 0.50, width 1.54. Combined lengths of meso- and metanota 2.12, width 2.21. Fore femur length/width ratio 6.3, lacking medial constriction; fore pretarsi bearing sharp, curved claws; hind trochanter lacking modifications. Abdominal sterna II–VI combined length 0.96, maximum width 1.57. For measurements of leg segments see Table 2. Female terminalia: Abdominal sternum VII semi-circular, length 0.30, width 1.07, slightly constricted laterally, clothed with short golden pubescence. Macropterous male: Unknown. Macropterous female: Fig. 35 Size: Body length 5.32, maximum width across mesoacetabula 2.67. Structural characteristics: Golden brown dorsally, marked with prominent black markings as shown in Fig.35. Median length of pronotum 2.41, humeral width 1.72, length of lateral margin from anterior angle to humerus 0.89, length of lateral margin from humerus to apex 1.76, apex of pronotum pointed, medially slightly bulged. Etymology. This name “dinendra” is a patronym dedicated to Professor Dinendra Roychoudhury of Department of Zoology of University of Calcutta, who had encouraged the first author to carry out entomological research. Habitat. This species was collected from high mountainous cascades within the Neora Valley National Park of the Darjeeling District in West Bengal. The insects were found in steep, rocky areas flooded with splashing water, and appear adapted to the cold waters. A preference for rushing, high gradient upland streams has also been observed by the second author (DP) for another currently undescribed species of the Metrocoris compar species group collected in northern Vietnam, suggesting this habitat association may be typical of the group as a whole. Comparative notes. Metrocoris dinendrai sp. nov. belongs to Metrocoris compar group based on the structure of male fore femur, which is slender and slightly curved; the strongly curved male parameres; the elongate male pygophore which bears dense dark pilosity; and the laterally constricted female terminal abdominal sterna. This new species can be recognized within this group by the distinctive shape of male paramere, which has a a slightly expanded apex that is somewhat concave on its outer margin (Fig. 43); the structure of male endosomal sclerites (Fig. 44); and the female trochanter clothed with thick black bristles. Within the Metrocoris compar group, M. dinendrai seems most similar to M. pardus from the Malay Peninsula (Zettel, 2011a), but has the distal arm of the male paramere more slender and elongate, and the outer margin of the paramere apex concave rather than convex (compare Fig. 43 to Fig. 8 in Zettel, 2011a). The basal lobes on the male proctiger also are more angular than in M. pardus, whereas the internal sclerotization of the male endosoma is similar in both species.Published as part of Basu, Srimoyee, Polhemus, D. A., Subramanian, K. A., Saha, G. K. & Venkatesan, T., 2016, Metrocoris Mayr (Insecta: Hemiptera: Gerridae) of India with descriptions of five new species, pp. 257-277 in Zootaxa 4178 (2) on pages 265-267, DOI: 10.11646/zootaxa.4178.2.5, http://zenodo.org/record/25873
Injective stability for K1 of classical modules
No full textAbstractIn Rao (1994) [14], the second author and W. van der Kallen showed that the injective stabilization bound for K1 of the general linear group is d+1 over a regular affine algebra over a perfect C1-field, where d is the Krull dimension of the base ring which is finite and at least 2. In this article we prove that the injective stabilization bound for K1 of the symplectic group is d+1 over a geometrically regular ring containing a field, where d is the dimension of the base ring which is finite and at least 2. Using the Local–Global Principle for the transvection subgroup of the automorphism group of projective and symplectic modules we show that the injective stabilization bound is d+1 for K1 of projective and symplectic modules of global rank at least 1 and local rank at least 3 respectively in each of the two cases above
A note on general quadratic groups
No full text We deduce an analogue of Quillen–Suslin’s local-global principle for the transvection subgroups of the general quadratic (Bak’s unitary) groups. As an application, we revisit the result of Bak–Petrov–Tang on injective stabilization for the [Formula: see text]-functor of the general quadratic groups. </jats:p
ABSENCE OF TORSION FOR <font>NK</font><sub>1</sub>(R) OVER ASSOCIATIVE RINGS
No full text When R is a commutative ring with identity, and if k ∈ ℕ, with kR = R, then it was shown in [C. Weibel, Mayer–Vietoris Sequence and Module Structure on NK0, Lecture Notes in Mathematics, Vol. 854 (Springer, 1981), pp. 466–498] that SK 1(R[X]) has no k-torsion. We prove this result for any associative ring R with identity in which kR = R. </jats:p
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