Diazoaldehyde Chemistry. Part 1. Transdiazotization of Acylacetaldehydes in Neutral-to-Acidic Medium. A Direct Approach to the Synthesis of α-Diazo-β-oxoaldehydes

First ever non-deformylating transdiazotization of acylacetaldehydes was achieved: the reactions of 2-azido-l-ethylpyridinium tetrafluoroborate ( 4 ) with acylacetaldehydes 3 proceeded partially without deformylation to yield 16 new α-diazo-β-oxoaldehydes 1 along with diazomethyl ketones 2 , especially in the presence of NaOAc (Scheme 1, Tables 1 and 2). The product distribution was substituent-dependent and could be correlated quantitatively. This new diazotization reaction appears as an alternative, direct, and more general method for the synthesis of these diazooxoaldehydes. α-Oxocycloalkanecarbaldehydes 5 gave only traces (if any) of α-diazocycloalkanones 7 , and rearrangement products 6 were isolated (Scheme 2). Mechanisms of the reactions are discussed (Schemes 4 and 5).     

Three-Phase Partitioning as a Rapid and Easy Method for the Purification and Recovery of Catalase from Sweet Potato Tubers (Solanum tuberosum)

Three-phase partitioning (TPP) was used to purify and recover catalase from potato crude extract. The method consists of ammonium sulfate saturation, t-butanol addition, and adjustment of pH, respectively. The best catalase recovery (262 %) and 14.1-fold purification were seen in the interfacial phase in the presence of 40 % (w/v) ammonium sulfate saturation with 1.0:1.0 crude extract/t-butanol ratio (v/v) at pH 7 in a single step. The sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS-PAGE) analysis of the enzyme showed comparatively purification and protein molecular weight was nearly found to be 56 kDa. This study shows that TPP is a simple, economical, and quick method for the recovering of catalase and can be used for the purification process.     

Binary and Ternary Copper(II) Complexes with NIPAAm/IA Copolymers and Aminoacids: Interpretation of UV‐Visible Spectra and Cyclic Voltammograms

The complex formations of homopolymers and copolymers of poly(N‐isopropyl acrylamide) (PNIPAAm), polyacrylamide (PAAm) and poly(itaconic acid) (PIA) with Cu(II) ions in aqueous solutions were studied by using UV‐visible spectra in the region of 200–1100 nm and cyclic voltammograms between ?0.800 V and 0.600 V. According to the optical and electrochemical spectra of the polymer‐ and copolymer‐Cu(II) complexes and their ternary complexes with alanine, i.e., absorptions and the shifts in the wavelength of the maximum absorptions, currents and potentials of the peaks in the pH range of 3–12, the intensities of anodic and cathodic peak currents of polymers containing IA groups decrease with increasing pH and they show maximum absorptions at lower wavelengths than do the homopolymers used in this work. The peak point of the visible band shifts from 800 to 650 nm, with increasing pH, while the intensity of the third anodic peak observed after pH=4 increases in the case of both Ala‐Cu(II) and its ternary solution with P(NIPAAm‐co‐IA, 9.8 mol%). Both the pH‐dependent shifts of maximum absorptions and the appearence of the third anodic peaks as the pH raised were interpreted as a presence of tetracoordinated Cu(II) complexes in the solution and on the electrode surface, involving combined carboxyl, amide and amine interaction.     

Stereoselective synthesis of optically active cyclopenta[c]pyrans and cyclopenta[c]furans by the intramolecular Pauson–Khand reaction

An intramolecular Pauson–Khand reaction of enynes derived from homoallyl, homopropargyl, and allyl alcohols is described. 2-Heteroaryl-substituted homoallyl, homopropargyl, and allyl alcohols are easily and efficiently resolved through enzymatic resolution in high ee (91–99%) and with a known stereochemistry. Each enantiomerically enriched enyne derived from homoallyl and homopropargyl alcohols affords the conformationally most stable diastereomeric cyclopenta[c]pyran ring system as the sole product, whereas enantiomerically enriched enynes derived from allyl alcohols give a diastereomeric cis:trans mixture of the cyclopenta[c]furan ring system.     

Renal-related perinephric fluid collections: MRI findings

We retrospectively reviewed MR studies on 10 patients with renal-related perinephric fluid collections who underwent MRI in three institutions between January 2001 and August 2004. All patients underwent MRI of the abdomen and T1-weighted, T2-weighted and serial contrast-enhanced images, including delayed-phase contrast-enhanced images 10-12 min after contrast injection, were obtained. Perinephric fluid collections in 5 patients revealed MRI findings of simple fluid content (i.e., hypointense on T1-weighted images and hyperintense on T2-weighted images). In another 5 patients, a complex perinephric fluid content (i.e., mixed hyper/hypointense on T1-weighted images and mixed hypo/hyperintense on T2-weighted images compatible with blood breakdown products and pus) was observed. In 5 patients, contrast extravasation on late-phase images that was compatible with urine leak was demonstrated. Our results suggest that MRI may determine the content of perinephric fluid collections on noncontrast T1-weighted and T2-weighted images and that contrast extravasation on late-phase images is associated with urine extravasation from renal collecting systems.     

Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization

A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.     

A taylor collocation method for solving high‐order linear pantograph equations with linear functional argument

A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011     

Preparation and properties of a new solid state borate ion selective electrode and its application

A new borate ion selective electrode using solid salts of Ag₃BO₃, Ag₂S and Cu₂S has been developed. Detailed information is provided concerning the composition, working pH and conditioning of the electrode. An analytically useful potential change occurred from 1 × 10⁻⁶ to 1 × 10⁻¹ M borate ion. The slope of the linear portion was 31 ± 2 mV/10-fold changes in borate concentration. The measurements were made at constant ionic strength (0.1 M NaNO₃) and at room temperature. The effect of Cl⁻, Br⁻, NO₃⁻, SO⁼₄, H₂PO₄⁻ anions and K⁺, Na⁺, Cu²⁺, Ag⁺, Ca²⁺ cations on borate response is evaluated and it was found that only Ag⁺ had a small interference effect. The lifetime of the electrode was more than two years, when used at least 4-5 times a day, and the response time was about 20-30 s. Borate content in waste water of borax factory, tap water of a town situated near to the borax factory and city tap water far from these mines were also determined. The validation was made with differential pulse polarography for the same water sample, and high consistency was obtained.     

A rational approximation based on Bernstein polynomials for high order initial and boundary values problems

We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ C^d+2[a, b].     

The regularized trace of a self adjoint differential operator of higher order with unbounded operator coefficient

Let L₀ and L be operators which are formed by the differential expressions.

?₀(y)=(-1)^my^(2m)(x)+Ay(x)