On the support of midconvex operators

Summary LetX be a real vector space,D a convex subset ofX and (Y, K) an order complete ordered vector space. The following sandwich theorem holds: Iff: D Y is midconvex,g: D Y {– } is midconcave andg f onD, then there exists a Jensen mappingh: D Y {– } such thatg h f onD. Using this theorem we show that a mappingf: D Y is midconvex if and only if it has Jensen support at every point ofD. Moreover, ifX is a Baire topological vector space and (Y, K) is an ordered topological vector space satisfying some additional conditions, then a mappingf: D Y is continuous whenever it has continuous Jensen support at every point ofD. As an application of these results we obtain the equality of some set-classes connected with additive and midconvex operators.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

X射线荧光光谱(XRF)法测定绿泥石中镁、铝、硅、磷、钾、钙、钛、铁元素含量

建立了X射线荧光光谱法测定绿泥石中镁、铝、硅、磷、钾、钙、钛、铁元素含量的快速分析方法。以标准物质及标准物质与基准试剂氧化镁、氧化钙人工混合配制标样的方法建立标准工作曲线,重点讨论了熔剂和脱模剂的选取。最佳熔样条件：采用8.0g四硼酸锂和偏硼酸锂混合熔剂(质量比67: 33)+0.8g样品并添加溴化锂作为脱模剂,熔样温度1100℃,熔样时间10min。该方法相对标准偏差(n=12)均小于5.57%,绿泥石样品测定结果与化学法一致,硅酸盐标准物质测定结果均满足不确定度要求。     

Impact of the Cooking Process on Metabolite Profiling of Acanthocereus tetragonus,a Plant Traditionally Consumed in Mexico

Acanthocereus tetragonus (L.) Hummelinck is used as an alternative food source in some Mexican communities. It has been shown that the young stems of A. tetragonus provide crude protein, fiber, and essential minerals for humans. In this work, we analyzed the phytochemical profile, the total phenolic content (TPC), and the antioxidant activity of cooked and crude samples of A. tetragonus to assess its functional metabolite contribution to humans. The phytochemical profile was analyzed using Ultra-High-Performance Liquid Chromatography coupled to High-Resolution Mass Spectrometry (UHPLC-PDA-HESI-Orbitrap-MS/MS). Under the proposed conditions, 35 metabolites were separated and tentatively identified. Of the separated metabolites, 16 occurred exclusively in cooked samples, 6 in crude samples, and 9 in both crude and cooked samples. Among the detected compounds, carboxylic acids, such as threonic, citric, and malic acids, phenolic acids, and glycosylated flavonoids (luteolin-O-rutinoside) were detected. The TPC and antioxidant activity were analyzed using the Folin–Ciocalteu method and the 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radical inhibition method, respectively. The TPC and antioxidant activity were significantly reduced in the cooked samples. We found that some metabolites remained intact after the cooking process, suggesting that A. tetragonus represents a source of functional metabolites for people who consume this plant species.     

First Organic–Inorganic Hybrid Compounds Formed by Ge-V-O Clusters and Transition Metal Complexes of Aromatic Organic Ligands

Three compounds based on Ge-V-O clusters were hydrothermally synthesized and characterized by IR, UV-Vis, XRD, ESR, elemental analysis and X-ray crystal structural analysis. Both [Cd(phen)(en)]₂[Cd₂(phen)₂V₁₂O₄₀Ge₈(OH)₈(H₂O)]∙12.5H₂O (1) and [Cd(DETA)]₂[Cd(DETA)₂]_0.5[Cd₂(phen)₂V₁₂O₄₁Ge₈(OH)₇(0.5H₂O)]∙7.5H₂O (2) (1,10-phen = 1,10-phenanthroline, en = ethylenediamine, DETA = diethylenetriamine) are the first Ge-V-O cluster compounds containing aromatic organic ligands. Compound 1 is the first dimer of Ge-V-O clusters, which is linked by a double bridge of two [Cd(phen)(en)]²⁺. Compound 2 exhibits an unprecedented 1-D chain structure formed by Ge-V-O clusters and [Cd₂(DETA)₂]⁴⁺ transition metal complexes (TMCs). [Cd(en)₃]{[Cd(η₂-en)₂]₃[Cd(η₂-en)(η₂-μ₂-en)(η₂-en)Cd][Ge₆V₁₅O₄₈(H₂O)]}∙5.5H₂O (3) is a novel 3-D structure which is constructed from [Ge₆V₁₅O₄₈(H₂O)]¹²⁻ and four different types of TMCs. We also synthesized [Zn₂(enMe)₃][Zn(enMe)]₂[Zn(enMe)₂(H₂O)]₂[Ge₆V₁₅O₄₈(H₂O)]∙3H₂O (4) and [Cd(en)₂]₂{H₈[Cd(en)]₂Ge₈V₁₂O₄₈(H₂O)}∙6H₂O (5) (enMe = 1,2-propanediamine), which have been reported previously. In addition, the catalytic properties of these five compounds for styrene epoxidation have been assessed.     

A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.     

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

The Yamabe problem for almost Hermitian manifolds

The conformal class of a Hermitian metric g on a compact almost complex manifold (M^2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature s^J. We ask if the conformal class of g carries a metric with constant s^J, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the affirmative. In fact, we show that (2m−1)s^J−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well. We discuss some applications.     

On an Archimedean analogue of Tate's conjecture

We consider an Archimedean analogue of Tate's conjecture, and verify the conjecture in the examples of isospectral Riemann surfaces constructed by Vignéras and Sunada. We prove a simple lemma in group theory which lies at the heart of T. Sunada's theorem about isospectral manifolds.     

An elementary construction of tilting complexes

Let A be an artin algebra and e∈A an idempotent with add(eA_A)=add(D(_AAe)). Then a projective resolution of Ae_eAe gives rise to tilting complexes for A, where P(l)^• is of term length l+1. In particular, if A is self-injective, then is self-injective and has the same Nakayama permutation as A. In case A is a finite dimensional algebra over a field and eAe is a Nakayama algebra, a projective resolution of eAe over the enveloping algebra of eAe gives rise to two-sided tilting complexes {T(2l)^•}_l?1 for A, where T(2l)^• is of term length 2l+1. In particular, if eAe is of Loewy length two, then we get tilting complexes {T(l)^•}_l?1 for A, where T(l)^• is of term length l+1.