Equivalence relation groupoids associated with certain linearly ordered dimension groups

We consider linearly ordered, Archimedean dimension groups (G,G⁺,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G⁺,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C^*-algebra is the Fibonacci C^*-algebra.     

A geometric analysis of Renegar’s condition number,and its interplay with conic curvature

For a conic linear system of the form Ax ∈K, K a convex cone, several condition measures have been extensively studied in the last dozen years. Among these, Renegar’s condition number is arguably the most prominent for its relation to data perturbation, error bounds, problem geometry, and computational complexity of algorithms. Nonetheless, is a representation-dependent measure which is usually difficult to interpret and may lead to overly conservative bounds of computational complexity and/or geometric quantities associated with the set of feasible solutions. Herein we show that Renegar’s condition number is bounded from above and below by certain purely geometric quantities associated with A and K; furthermore our bounds highlight the role of the singular values of A and their relationship with the condition number. Moreover, by using the notion of conic curvature, we show how Renegar’s condition number can be used to provide both lower and upper bounds on the width of the set of feasible solutions. This complements the literature where only lower bounds have heretofore been developed.     

Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations

We use variational methods to obtain a pointwise estimate near a boundary point for quasisubminimizers of the p-energy integral and other integral functionals in doubling metric measure spaces admitting a p-Poincaré inequality. It implies a Wiener type condition necessary for boundary regularity for p-harmonic functions on metric spaces, as well as for (quasi)minimizers of various integral functionals and solutions of nonlinear elliptic equations on R ⁿ .     

Instance-optimality in probability with an -minimization decoder

Let Φ(ω), ωΩ, be a family of n×N random matrices whose entries _i,j are independent realizations of a symmetric, real random variable η with expectation and variance . Such matrices are used in compressed sensing to encode a vector by y=Φx. The information y holds about x is extracted by using a decoder . The most prominent decoder is the ℓ₁-minimization decoder Δ which gives for a given the element which has minimal ℓ₁-norm among all with Φz=y. This paper is interested in properties of the random family Φ(ω) which guarantee that the vector will with high probability approximate x in to an accuracy comparable with the best k-term error of approximation in for the range kan/log₂(N/n). This means that for the above range of k, for each signal , the vector satisfies

with high probability on the draw of Φ. Here, Σ_k consists of all vectors with at most k nonzero coordinates. The first result of this type was proved by Wojtaszczyk [P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press] who showed this property when η is a normalized Gaussian random variable. We extend this property to more general random variables, including the particular case where η is the Bernoulli random variable which takes the values with equal probability. The proofs of our results use geometric mapping properties of such random matrices some of which were recently obtained in [A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005) 491–523].     

Toward a better description of gallo-phosphate materials in solid-state NMR: 1D and 2D correlation studies

We show that weak 2J(71Ga-O-31P), typically approximately 12 Hz in GaPO4, can be used to efficiently establish heteronuclear 31P-71Ga correlation using a MAS HMQC experiment in gallo-phosphate materials. The experiment demonstrated for cristobalite GaPO4 is then applied to Ga(PO3)3, where it allows the differentiation of the signature of three different Ga sites overlapping in the 1D spectrum.     

Monitoring of the insecticide trichlorfon by phosphorus-31 nuclear magnetic resonance (31P NMR) spectroscopy

Trichlorfon is an organophosphorus insecticide, which is extensively being used for protection of fruit crops. Trichlorfon is a thermal labile compound, which cannot be easily determined by gas chromatography (GC) and has no suitable group for sensitive detection by high performance liquid chromatography (HPLC). In this study, a ³¹P nuclear magnetic resonance (³¹P NMR) has been described for monitoring of trichlorfon without any separation step. The quantitative works of ³¹P NMR spectroscopy has been performed in the presence of an internal standard (hexamethylphosphoramide). Limit of detection (LOD) for this method has been found to be 55 mg L⁻¹, without any sample preparation, and the linear working range was 150-5500 mg L⁻¹. Relative standard deviation (R.S.D.%) of the method for three replicates within and between days was obtained ≤9%. The average recovery efficiency was approximately 99-112%. This method was applied for monitoring trichlorfon in a commercial insecticide sample and tomato sample.     

Tris(5-O-nitro-1,4:3,6-dianhydro-D-sorbit-2-yl) phosphate: synthesis and structure

The reaction of 1,4:3,6-dianhydro-D-sorbitol 5-nitrate with phosphorus oxychloride afforded tris(5-O-nitro-1,4:3,6-dianhydro-D-sorbit-2-yl) phosphate, whose structure was confirmed by X-ray diffraction and ¹H, ³¹P, and ¹³C NMR spectroscopy. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 380–382, February, 2006.     

Investigation in thorium phosphate by NMR II-phosphorus dipolar networks

With through space and through bond experiments in two-dimensional NMR we analyze the transformation from the thorium phosphate-hydrogen phosphate hydrate (TPHPH) to the β form of the thorium phosphate diphosphate (β-TPD) in relation with the phosphorus networks. These techniques are complementary: the through space coupling gives an insight on the dipolar phosphorus networks while the through bond coupling is particularly efficient in the detection of the P₂O₇ groups. With these experiments we show that in a first step, by heating the precursor TPHPH above 250 °C, it transforms into an form of TPD. This transformation is due to the complete condensation of hydrogen phosphate groups HPO₄ into P₂O₇ entities. By heating -TPD above 950 °C it transforms into its well-known β form. The form is characterized by a hygroscopic behavior: some water molecules are present near the P₂O₇ groups that makes non-equivalent their phosphorus nuclei. PO₄ dipolar networks are always present in the form. The main effect of these PO₄ and P₂O₇ units is to give the system a channel structure and the water enters in them.     

浇注温度对AZ31镁合金连续流变挤压成形组织的影响

研究了不同浇注温度、辊靴型腔中不同位置的AZ31镁合金组织.结果表明,浇注温度高于750℃时,半固态区减小,工作辊对半固态区枝晶的剪切时间变短,枝晶破碎不充分,得不到优质的半固态金属浆料;浇注温度低于730℃时,固相区变大,半固态区部分枝晶未得到充分剪切就进入了固相区,固相区的枝晶更是难以断裂,因此得不到理想的半固态组织;随着固相区的增加,合金变形更加困难,设备工作压力增加,使用寿命降低;AZ31镁合金连续流变挤压最佳浇注温度为730～750℃.     

HZSM-5催化剂上超临界乙醇中生物油催化提质及检测方法研究

采用不同硅铝比的HZSM-5催化剂,在不同条件下(超临界、亚超临界、非超临界乙醇)催化提质生物油中的高沸点组分(HBF),应用磷核磁共振(31P-NMR)定量检测了提质前后生物油中醇、酚和羧酸类羟基的质量比(羟基质量/生物油质量)变化,研究和评价了催化剂和超临界条件对生物油催化提质的效果.研究表明,超临界条件有利于生物油中脂肪族羟基的转化,但是不利于非缩合羟基的转化;使用不同酸强度的HZSM-5都能使生物油中的羧基完全转化,增加催化剂的酸强度可以促进脂肪族羟基的转化,而只有酸性较弱的催化剂才能顺利转化非缩合酚羟基.