LINKAGE AND DUALITY OF MODULES

Martsinkovsky and Strooker [13] recently introduced module theoretic linkage using syzygy and transpose. This generalization brings possibility of much application of linkage, especially, to homological theory of modules. In the present paper, we connect linkage of modules to certain duality of modules. We deal with Gorenstein dimension, Cohen-Macaulay modules over a Gorenstein local ring using linkage and generalize the results to non-commutative algebras.</p

Cohen-Macaulay modules and holonomic modules over filtered rings

We study Gorenstein dimension and grade of a module $M$ over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dim$M\leq{G-dim gr}M$ and an equality ${\rm grade}M={\rm grade gr}M$, whenever Gorenstein dimension of ${\rm gr}M$ is finite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying filtered rings and modules. We apply these results to a filtered ring with a Cohen-Macaulay or Gorenstein associated graded ring and study a Cohen-Macaulay, perfect or holonomic module.Comment: 21 pages, to appear in Communications in Algebr

Thermodynamics of strong coupling 2-color QCD with chiral and diquark condensates

2-color QCD (quantum chromodynamics with N_c=2) at finite temperature T and chemical potential \mu is revisited in the strong coupling limit on the lattice with staggered fermions. The phase structure in the space of T, \mu, and the quark mass m is elucidated with the use of the mean field approximation and the 1/d expansion (d being the number of spatial dimensions). We put special emphasis on the interplay among the chiral condensate , the diquark condensate , and the quark density in the T-\mu-m space. Simple analytic formulae are also derived without assuming \mu nor m being small. Qualitative comparisons are made between our results and those of recent Monte-Carlo simulations in 2-color QCD.Comment: Contribution to the Hidenaga Yamagishi Commemorative volume of Physics Reports, edited by E. Witten and I. Zahed; typos are corrected, references are update

Thanius biennis, a new gall-inducing weevil with a two-year life-cycle from Costa Rica (Coleoptera: Curculionidae: Baridinae).

Thanius biennis Prena & Nishida sp. n. wird beschrieben und illustriert. Die Larve verursachte Gallen an Stämmen von Psychotria marginata (Rubiaceae). Der vollständige Entwicklungszyklus dauerte zwei Jahr pro Generation, wobei zwei alternierende Generationen auf derselben Pflanze gemeinsam vorkamen. Jede Galle beherbergte ein einzelnes immatures oder adultes Tier. Letzteres Stadium verharrte nahezu fünf Monate in Ruhezustand, und schlüpfte zu Beginn der Regenzeit.ResumenThanius biennis Prena & Nishida sp. n. es descrito e ilustrado. Las larvas se encontraron induciendo agallas en ramas de Psychotria marginata (Rubiaceae). Se duraron dos años para completar su ciclo de vida y dos generaciones coexisten en la misma planta. Cada agalla contiene un sólo individuo de estadio inmaduro o adulto. El adulto se quedó inactivo en la agalla por cerca de cinco meses y emergió en el principio de la época lluviosa.Stichwörterweevils, Thanius, Rubiaceae, Psychotria, galls, Calliephialtes, Neotropics.Nomenklatorische Handlungenbiennis Prena &amp; Nishida, 2005 (Thanius), spec. n.Thanius biennis Prena & Nishida sp. n. is described and illustrated. The larva induced galls on stems of Psychotria marginata (Rubiaceae). The complete life-cycle took two years per generation, and two alternate generations coexisted on the same plant. Each gall harbored a single immature or adult specimen. The latter stage remained dormant in the gall for nearly five months, and emerged with the beginning of the rainy season.ResumenThanius biennis Prena & Nishida sp. n. es descrito e ilustrado. Las larvas se encontraron induciendo agallas en ramas de Psychotria marginata (Rubiaceae). Se duraron dos años para completar su ciclo de vida y dos generaciones coexisten en la misma planta. Cada agalla contiene un sólo individuo de estadio inmaduro o adulto. El adulto se quedó inactivo en la agalla por cerca de cinco meses y emergió en el principio de la época lluviosa.Keywordsweevils, Thanius, Rubiaceae, Psychotria, galls, Calliephialtes, Neotropics.Nomenclatural Actsbiennis Prena &amp; Nishida, 2005 (Thanius), spec. n

Dispensabilities of Carbonic Anhydrase in Proteobacteria

Carbonic anhydrase (CA) (E.C. 4.2.1.1) is a ubiquitous enzyme catalysing interconversion between CO2 and bicarbonate. The irregular distribution of the phylogenetically distinct classes of CA in procaryotic genome suggests its complex evolutionary history in procaryotes. Genetic evidence regarding the dispensability of CA under high-CO2 air in some model organisms indicates that CA-deficient microorganisms can persist in the natural environment by choosing high-CO2 niches. In this study, we studied the distribution of CA in the genome of Proteobacteria. While a large majority of the genome-sequenced Proteobacteria retained a CA gene(s), intracellular bacterial genera such as Buchnera and Rickettsia contained CA-defective strains. Comparison between CA-retaining and CA- deficient genomes showed the absence of whole coding sequence in some strains and the presence of frameshifted coding sequence in other strains. The evidence suggests that CA is inactivated and lost in some proteobacteria during the course of evolution based on its dispensability