On the Ideals of Secant Varieties of Segre Varieties

We establish basic techniques for determining the ideals of secant varieties of Segre varieties.We solve a conjecture of Garcia, Stillman, and Sturmfels on the generators of the ideal of the first secant variety in the case of three factors and solve the conjecture set-theoretically for an arbitrary number of factors. We determine the low degree components of the ideals of secant varieties of small dimension in a few cases.     

Method development for the determination of iron in milligram amounts of rice plants (Oryza sativa L.) from cultivation experiments using graphite furnace atomic absorption spectrometry

The amount of sample that is available for analysis in laboratory plant cultivation experiments is usually very limited. Highly sensitive analytical techniques are therefore required, even for elements that are present in the plants at mg g^–1 concentrations, and graphite furnace atomic absorption spectrometry (GFAAS) was chosen in this work because of its micro-sampling capability, and its relatively simple operation. Four micro-methods were investigated for the determination of iron in roots and leaves of rice plants: i) a micro-digestion with nitric and hydrochloric acids, ii) a slurry procedure using tetramethylammonium hydroxide (TMAH) tissue solubilizer, iii) a slurry prepared in 1.4 mol L^–1 nitric acid, and treated in an ultrasonic bath, and iv) the direct analysis of solid samples. The micro-digestion was suffering from high blank values and contamination problems, so that it could not be recommended for routine purposes. The TMAH method exhibited poor precision and occasional low recoveries, particularly for real samples. Direct solid sampling analysis gave results similar to those obtained with the slurry technique with ultrasonic agitation for the determination of iron in certified reference materials with iron content up to about 100 g g^–1, but was too sensitive for the investigated rice plants, which had an iron content up to several mg g^–1. The slurry technique with ultrasonic treatment of the samples, suspended in dilute nitric acid, was finally adopted as the method of choice.The method was then applied for the determination of iron in the leaves and in different compartments of the roots of two rice cultivars, one sensitive to iron toxicity, an important nutritional disorder, and the other one resistant to iron toxicity. The results suggest that the higher resistance to iron toxicity of the second cultivar is due to a smaller uptake of iron from the soil, resulting in lower iron levels in all compartments of the plant.     

Geometric structure in stochastic approximation

1. IntroductionLet f: Re -- R be a differelltiable fUnction. f reaChes its extremes on the setJ = {x E R"lfx(x) = 0}, (1.1)where,x(X) = (V,..., V)". (1.2)If jx can be observed exactly at any x e R", then there are various numerical methods toconstruct {xh}, xk E Re such that the distance d(xk, J) between uk and J tends to zero ask -- co. However, in many application problems jx can only be observed with noise, i.e.,the observation at time k 1 isYk 1 = fi(~k) (k 1, (1'3)where xk is …     

A Calculation of the Culler-shalen Seminorms Associated to Small Seifert Dehn Fillings

We determine the relationship between the multiplicities ofthe zeros of certain rational functions defined on the SL₂(C)and PSL₂C character varieties of knot exteriors. This leadsto a formula for the Culler–Shalen seminorms associatedto small Seifert Dehn fillings of such manifolds. 2000 MathematicsSubject Classification: 57M05, 57M27, 57R65.     

On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

The Variety of Commutative BCI-Algebras is 2-Based

In this note, we first solve the following open problem in [5]: Can the variety of commutative BCI-algebras be defined by two identities? An algebra of type (2, 0) is a commutative BCI-algebra if and only if it satisfies $u\ast\left(((x \ast y) \ast (x \ast y))(z \ast y)\right) = uIn this note, we first solve the following open problem in [5]: Can the variety of commutative BCI-algebras be defined by two identities? An algebra of type (2, 0) is a commutative BCI-algebra if and only if it satisfies and (see Theorem 2 below).Next, we prove that I-variety [2] is also 2-based. Finally, we show that I-variety is a proper subvariety of the variety of commutative BCI-algebras.AMS Subject Classification (2000): 03G25, 06A10, 06D99     

Undecidability of the word problem in relatively free rings

An example of a series of varieties of rings with the finite basis property is constructed for which the word problem in the relatively free ring of rankn in the variety is decidable if and only ifn <p. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000.     

Effect of acidity on the formation of silica–chitosan hybrid materials and thermal conductive property

In this study, the formation of silica–chitosan hybrid materials via sol–gel process under pH values of 2–6 were investigated using N₂ sorption analysis, scanning electron microscopy, transmission electron microscopy, thermal analysis and zeta potential analyzer. The hierarchical structure consisting of meso- and macropore was formed when pH value was higher than 2. Mesopores were formed as the interparticle channels of silica nanoparticles aggregates, whereas macropores were the void between the aggregates (clusters). The clusters size was decreased with increasing the pH value, resulting in the increase of the macroporosity. The thermal conductivity of the products was controlled in the range of 0.06 and 0.13 W m⁻¹ K⁻¹ by varying the product porosity between 88 and 69% (pH 6 and pH 2, respectively).     

Elementary equivalence for the lattices of subalgebras and automorphism groups of free algebras

We find an elementary equivalence criterion for the lattices of subalgebras of free algebras in regular varieties. The question is addressed of elementary equivalence for the automorphism groups of algebras of this type.