Covalent Immobilization of α-Galactosidase from <Emphasis Type="Italic">Penicillium griseoroseum</Emphasis> and its Application in Oligosaccharides Hydrolysis

Partially purified α-Galactosidase from Penicillium griseoroseum was immobilized onto modified silica using glutaraldehyde linkages. The effective activity of immobilized enzyme was 33%. Free and immobilized α-galactosidase showed optimal activity at 45 °C and pH values of 5 and 4, respectively. Immobilized α-galactosidase was more stable at higher temperatures and pH values. Immobilized α-galactosidase from P. griseoroseum maintained 100% activity after 24 h of incubation at 40 °C, while free enzyme showed only 32% activity under the same incubation conditions. Defatted soybean flour was treated with free and immobilized α-galactosidase in batch reactors. After 8 h of incubation, stachyose was completely hydrolyzed in both treatments. After 8 h of incubation, 39% and 70% of raffinose was hydrolyzed with free and immobilized α-galactosidase respectively. Immobilized α-galactosidase was reutilized eight times without any decrease in its activity.     

The Asymptotics of Wilkinson’s Shift: Loss of Cubic Convergence

One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: Here, the shift s is the eigenvalue of the bottom 2×2 principal minor closest to the corner entry. It has been a long-standing question whether the rate of convergence of the algorithm is always cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_{ {\mathcal {X}}}One of the most widely used methods for eigenvalue computation is the QR iteration with Wilkinson’s shift: Here, the shift s is the eigenvalue of the bottom 2×2 principal minor closest to the corner entry. It has been a long-standing question whether the rate of convergence of the algorithm is always cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let T _XT_{ {\mathcal {X}}} be the 3×3 matrix having only two nonzero entries (T _X)₁₂=(T _X)₂₁=1(T_{ {\mathcal {X}}})_{12}=(T_{ {\mathcal {X}}})_{21}=1 and let T_\varLambda {\mathcal {T}}_{\varLambda } be the set of real, symmetric tridiagonal matrices with the same spectrum as T _XT_{ {\mathcal {X}}} . There exists a neighborhood U ì T_\varLambda \boldsymbol {{\mathcal {U}}}\subset {\mathcal {T}}_{\varLambda } of T _XT_{ {\mathcal {X}}} which is invariant under Wilkinson’s shift strategy with the following properties. For T₀ ? UT_{0}\in \boldsymbol {{\mathcal {U}}} , the sequence of iterates (T _k ) exhibits either strictly quadratic or strictly cubic convergence to zero of the entry (T _k )₂₃. In fact, quadratic convergence occurs exactly when limT_k=T _X\lim T_{k}=T_{ {\mathcal {X}}} . Let X\boldsymbol {{\mathcal {X}}} be the union of such quadratically convergent sequences (T _k ): The set X\boldsymbol {{\mathcal {X}}} has Hausdorff dimension 1 and is a union of disjoint arcs X^s\boldsymbol {{\mathcal {X}}}^{\sigma} meeting at T _XT_{ {\mathcal {X}}} , where σ ranges over a Cantor set.     

Cut-and-paste of quadriculated disks and arithmetic properties of the adjacency matrix

We define cut-and-paste, a construction which, given a quadriculated disk obtains a disjoint union of quadriculated disks of smaller total area. We provide two examples of the use of this procedure as a recursive step. Tilings of a disk Δ receive a parity: we construct a perfect or near-perfect matching of tilings of opposite parities. Let B_Δ be the black-to-white adjacency matrix: we factor , where L and U are lower and upper triangular matrices, is obtained from a larger identity matrix by removing rows and columns and all entries of L, and U are equal to 0, 1 or -1.     

The generalized corona theorem

The results of this paper have been presented by the second author at the joint AMS-DMV Meeting 1993 in Heidelberg (Germany)     

Thin-layer chromatographic determination of catecholamines, 5-hydroxytryptamine, and their metabolites in biological samples: a review

A review of methodology for separation, detection, and quantitative determination of catecholamines, 5-hydroxytryptamine, and their acidic metabolites in biological tissue and fluids by thin-layer chromatography is presented. Selected procedures, including fluorometric scanning densitometry for catecholamine acetyl derivatives and color scanning densitometry for acids, are described.     

Free interpolation by nonvanishing analytic functions

We are concerned with interpolation problems in where the values prescribed and the function to be found are both zero-free. More precisely, given a sequence in the unit disk, we ask whether there exists a nontrivial minorant (i.e., a sequence of positive numbers bounded by 1 and tending to 0) such that every interpolation problem has a nonvanishing solution whenever for all . The sequences with this property are completely characterized. Namely, we identify them as `` thin" sequences, a class that arose earlier in Wolff's work on free interpolation in VMO.

     

Synthesis of nickel(II) triazolenaphthalocyanine and related macrocycles.

The synthesis of novel monbenzotriazolephthalocyanines (3-6), low-symmetry phthalocyanine analogues, is described for the first time using a novel and simple stepwise strategy which involves the use of substituted naphthalodinitriles 8-11 and appropriately substituted three-unit compounds such as 7. Belonging to the same family, compound 1, which we have called triazolenaphthalocyanine, has been prepared by a statistical method from compound 2 and 3,5-diamino-1,2,4-triazole. Compound 1 shows a bathochromic shift of the Q-band in UV-vis spectrum due to the fusing of benzene rings to the triazolephthalocyanine core.     

Oscillation of Functions in the Hölder Class

Potential Analysis - We study the size of the set of points where the α-divided difference of a function in the Hölder class Λα is bounded below by a fixed positive constant....