Use of capillary electrophoresis to monitor wheat maturation

Summary The maturation of wheat varieties with different harvest times has been examined by high-performance capillary electrophoresis. The unique proteins of the albumin, gliadin and glutenin fractions of Hungarian winter wheat cultivars Bánkúti 1201 (early harvest time), Martonvásári 23 (medium harvest time), and Martonvásári 15 (semi-late harvest time) were analysed. An acidic phosphate buffer containing a polymeric additive and organic modifiers was used in capillary zone electrophoresis mode. Formation of albumin followed the same time scale, and the patterns were quite similar, for all three cultivars. For gliadins and glutenins the time scale and patterns were different and some correlation was observed between harvest time and gliadin formation. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001     

Varieties for cohomology with twisted coefficients

Let G be a finite group and k a field of characteristic p > 0. In this paper we consider the support variety for the cohomology module Ext _kG ^* (M, N) where M and N are kG-modules. It is the subvariety of the maximal ideal spectrum of H*(G, k) of the annihilator of the cohomology module. For modules in the principal block we show that that the variety is contained in the intersections of the varieties of M and N and the difference between the that intersection and the support variety of the cohomology module is contained in the group theoretic nucleus. For other blocks a new nucleus is defined and a similar theorem is proven. However in the case of modules in a nonprincipal block several new difficulties are highlighted by some examples. Partially supported by grants from NSF and EPSRC     

A note on the Chow groups of projective determinantal varieties; an appendix to the paper by Grzegorz Kapustka and Michal Kapustka on “A cascade of determinantal Calabi‐Yau threefolds”

We investigate the Chow groups of projective determinantal varieties and those of their strata of matrices of fixed rank, using Chern class computations (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A footnote to a theorem of Kawamata

Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note, we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka.     

Borcea–Voisin Calabi–Yau threefolds and invertible potentials

We prove that the Borcea–Voisin mirror pairs of Calabi–Yau threefolds admit projective birational models that satisfy the Berglund–Hübsch–Chiodo–Ruan transposition rule. This shows that the two mirror constructions provide the same mirror pairs, as soon as both can be defined.     

Discrimination between 2AP producing and non‐producing rice rhizobacterial isolates using volatile profiling: a chemometric approach

2‐Acetyl‐1‐pyrroline (2AP) is known as a principal basmati aroma compound. The present study aims at discriminating rhizobacteria isolated from soils cultivated with basmati and non‐basmati rice for long duration. Volatile profiling was used as marker to discriminate the rhizobacterial isolates. Quantification of 2AP and other volatile compounds (VCs) produced by rhizobacteria was undertaken using HS‐SPME coupled with GC‐MS. Chemometrics tools such as hierarchical cluster analysis (HCA), principle component analysis (PCA) and multi dimensional scaling (MDS) were applied for volatile profiling of different isolates. Results showed significant discrimination of all 2AP producing (AP‐P) and non‐producing rhizobacterial isolates (AP‐NP) on the basis of their VC profile. This was validated by bacterial identification data as well. The frequency distribution for 2AP levels indicates that basmati isolates had higher frequency for 2AP production as compared to non‐basmati control. AP‐P and AP‐NP isolates have different VC profiling pattern irrespective of their origin. These isolates were found belonging to different groups when identified using 16S rDNA sequencing data. Chemometric analysis (PCA, HCA and MDS) helped to identify volatiles, which could be used as biomarker in discriminating the AP‐P and AP‐NP isolates. VC pattern of rhizobacteria could be used as volatile markers to distinguish between AP‐P and AP‐NP rhizobacterial isolates. Copyright © 2015 John Wiley & Sons, Ltd.     

Joins of Projective Varieties: A Cancellation Theorem for Curves

Abstract

Let X, Y, Z be integral subvarieties of P ⁿ . Let [X; Y]??? P ⁿ denote the join. Under what conditions on X, Y and/or Z if [X; Y]?=?[X; Z], then Y?=?Z? Here, we study the case in which X, Y and Z are curves.     

Classification of arithmetically Gorenstein divisors on some Fano varieties

We find all the arithmetically Gorenstein divisors on Fano varieties of dimension n and index r with 3 ≤ n ≤ 2r − 1 and ρ(Y) ≥ 2, where Y is smooth, connected, subcanonical and linearly normal.      

The border rank of the multiplication of matrices is seven

We prove that the bilinear map corresponding to matrix multiplication of matrices is not the limit of a sequence of bilinear maps that can be executed by performing six multiplications. This solves a longstanding problem dating back to Strassen's discovery in 1968 that the map could be executed by performing seven multiplications.

     

Non-isogenous superelliptic Jacobians

Let ℓ be an odd prime. Let K be a field of characteristic zero with algebraic closure K_a. Let n, m ≥ 4 be integers that are not divisible by ℓ. Let f(x), h(x) ∈ K[x] be irreducible separable polynomials of degree n and m respectively. Suppose that the Galois group Gal(f) of f acts doubly transitively on the set of roots of f and that Gal(h) acts doubly transitively on as well. Let J(C_f,ℓ) and J(C_h,ℓ) be the Jacobians of the superelliptic curves C_f,ℓ:y^ℓ=f(x) and C_h,ℓ:y^ℓ=h(x) respectively. We prove that J(C_f,ℓ) and J(C_h,ℓ) are not isogenous over K_a if the splitting fields of f and h are linearly disjoint over K and K contains a primitive ℓth root of unity.