Curran猜想的解答

本文确定了能作为有限群自同构群的Ｐ－群的最佳下最，彻底解决了Ｃｕｒｒａｎ在１９８９年提出的关于此最佳下界的三个猜想。     

Axiomatizing subcategories of Abelian categories

We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.     

Chains of strongly non-reflexive dual groups of integer-valued continuous functions

Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.

     

Some results about zero‐cycles on abelian and semi‐abelian varieties

In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Antioxidant potential in the leaves of grape varieties (Vitis vinifera L.) grown in different soil compositions

Grape plant (Vitis vinifera L.) is a species of the family Vitaceae. It is an economically important fruit plant abundantly grown all over the world. Vitaceae comprised of 900 species distributed across tropical, sub-tropical and partially temperate sorts of climatic zones. In the current study we aimed to evaluate the antioxidant activities of grape leaves extract from different Pakistani varieties.We have analyzed the crude methanolic extract from the leaves of Pakistani grape varieties (i.e. NARC Black, Sundar Khani, Shogran-1, Shogran-2, Haita, Sheghali, Perlette, and Sultania-C) cultivated in various soil compositions. Total phenolic contents (TPC) of the extract were determind by using Folin-ciocalteu reagent method. Total flavonoid contents (TFC) were determind by the Aluminum Chloride Calorimetric method. Antioxidant activities of the extracts of different concentration were evaluated using Phosphomolybdenum method, Reducing power and DPPH (2, 2-disphenyl-1-picryl-hydrazyl) assays. Assays performed for grape varieties showed great antioxidant potential. All varieties significantly depicted with variation in polyphenolic contents and antioxidant potential with changes in the soil conditions. The highest TPC and TFC were quantified in Shogran-1 97.58 ± 0.09 (GAE, g⁻¹) and Sultania-C 97.47 ± 0.12 (µg QE/g DE) varieties respectively which were grown in (T6) and (T5), while lower were recorded in Sundar khani 5.16 ± 0.23 in (T6). Likewise, Shogran-1 128.26 ± 0.23 (µg AAE/g extract) variety grown in (T6) depicted highest total antioxidant capacity, NARC black 182.06 ± 0.24 (µg AAE/g extract) variety grown in (T6) resulted in maximum reducing power while DPPH free radical scavenging potential were determinded in Sultania-C 80.91 ± 0.10 (T4) equivalent µg/g. In the terms of bioassays, the promising results were showed by compost + sand + clay (T4), compost + clay + dung (T5) and sand + clay + dung (T6). Therefore, we conclude that variation in soil composition has a significant contribution in the quantity of phytochemicals and antioxidants expression. Our study further suggest that use of organic fertilizer (Compost) and loamy sort of soil enhance functioning of most of the varieties in terms of important phytochemicals.     

The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.     

Limit Cycles Bifurcating from a k-dimensional Isochronous Center Contained in ?n with k ? n

The goal of this paper is double. First, we illustrate a method for studying the bifurcation of limit cycles from the continuum periodic orbits of a k-dimensional isochronous center contained in ℝ ⁿ with n ⩾ k, when we perturb it in a class of differential systems. The method is based in the averaging theory. Second, we consider a particular polynomial differential system in the plane having a center and a non-rational first integral. Then we study the bifurcation of limit cycles from the periodic orbits of this center when we perturb it in the class of all polynomial differential systems of a given degree. As far as we know this is one of the first examples that this study can be made for a polynomial differential system having a center and a non-rational first integral. The first and third authors are partially supported by a MCYT/FEDER grant MTM2005-06098-C01, and by a CIRIT grant number 2005SGR-00550. The second author is partially supported by a FAPESP–BRAZIL grant 10246-2. The first two authors are also supported by the joint project CAPES–MECD grant HBP2003-0017.     

Influence of ultrasound on the functional characteristics of indigenous varieties of mango (Mangifera indica L.)

The present study was conducted to evaluate the effect of ultrasonic (US) treatment on chemical characteristics and antioxidant potential of pulps obtained from eight mango varieties indigenous to Pakistan. There was a significant (p < 0.05) effect of varieties and US treatment on chemical characteristics i.e. pH, acidity, TSS, vitamin C contents, total sugars (%), reducing sugars (%) and non-reducing sugars (%). Microstructure evaluation of pulp from all mango varieties showed deshaped middle lamella and cell wall of cells after 8 min of US treatment. At 4 min of US treatment as per shaped cell wall and middle lamella, the chemical characteristics and antioxidant potential were higher. The total phenolics (TP), flavonoids (TF) and total antioxidant activity (TAA) of pulp from most varieties increased significantly (p < 0.05) after US treatment for 4 min but decreased successively after each treatment i.e. 8 and 12 min. The maximum value (314.17 μg AAE/mL pulp) of DPPH was shown by pulp from Dosehri and the minimum (158.67 μg AAE/mL pulp) was found in pulp from Langra before US treatment. The DPPH values of pulp from most of the varieties increased significantly (p < 0.05) after US treatment for 4 min but decreased successively after each treatment but pulp from Langra showed increasing trend after 8 min of US treatment which decreased after 12 min of treatment. The total anthocyanin (TA) values of pulp from Chaunsa, Dosehri, Sindhri, Gulab Khas and Langra increased abruptly after US treatment for 4 min but decreased successively after subsequent treatment. The pulp from Desi, Anwar Ratol, Gulab Khas and Langra showed an abrupt decrease in TA after 8 min of US treatment. An increasing trend of values of total carotenoids (TC) was shown by pulp from all mango varieties after 4 min of US treatment but decreasing trend was observed with subsequent increase in time of US treatment.