Ricci flatness of certain compact pseudo-Kähler solvmanifolds

It is well known that a pseudo-Kähler structure is one of the natural generalizations of a Kähler structure. In this paper, we consider Ricci curvature tensor of certain compact pseudo-Kähler solvmanifolds.     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

Lipase-catalyzed kinetic resolution approach toward enantiomerically enriched 1-(β-hydroxypropyl)indoles

In a route towards enantiomerically enriched 1-(β-hydroxypropyl)indoles, which are potentially useful building blocks for high value-added chemicals synthesis, a kinetic resolution approach by means of lipase-catalyzed enantioselective acylation as well as hydrolysis/methanolysis has been elaborated for the first time. The enzymatic resolution of chiral N-substituted indole-based sec-alcohols was successfully accomplished, yielding both enantiomeric forms of the employed derivatives with up to >99% enantiomeric purity via an enantioselective transesterification under mild reaction conditions. The most selective resolutions were obtained using fungal (CAL-B and TLL) and bacterial (PFL and BCL) lipases and vinyl acetate as the acyl?group donor. The synthetic protocol described herein is very simple, user-friendly and efficient, thus paving the way for future access towards more complex compounds of this type. The absolute configurations of novel enantiomeric derivatives, and thus stereoselectivity of the described enzymatic reactions were confirmed by application of CDA-based NMR methodology and single-crystal X-ray diffraction analysis.     

ON θ-PROXIMITIES AND RELATED f-PROXIMITIES

Abstract

We show that every θ-proximity as defined by V.V. Fedor?uk is an f-proximity which we call a k-proximity. Two related f-proximities are introduced, viz. t- and d-proximities. The smallest and largest members of M_f(X, c) for f=k, d and t are characterised where M_f(X, c) is the family of f-proximities compatible with a given closure space (X, c).     

ESSENTIALLY ALGEBRAIC CATEGORIES

Abstract

Various familiar concepts of algebraic categories (such as primitive and quasiprimitive categories of algebras as well as varietal, monadic, regular monadic, and regular categories) are contrasted with each other and with the new notion of essentially algebraic categories.

The new notion has pleasant features and covers several cases of an apparently algebraic nature, which are not covered by any of the older concepts.     

Development and validation of a UPLC–MS/MS method for determination of Sarsasapogenin‐AA22 in rat plasma and its application to a pharmacokinetic study

A sarsasapogenin derivative, sarsasapogenin‐AA22 (AA22), with cyclobutylamine at the 3‐hydroxyl position of sarsasapogenin, has great neuroprotective activity in PC12 cells and NO production inhibitory activity in RAW264.7 cell lines. A method was developed to determine AA22 in rat plasma which was further applied to evaluate the pharmacokinetics of AA22 after taking a single dose of AA22. Liquid chromatography tandem mass spectrometry was used in the method, while diosgenin was used as internal standard. A simple protein precipitation based on acetonitrile was utilized. A simple sample cleanup promoted the throughput of the method considerably. The method was validated over the range of 1–1000 ng/mL with a correlation coefficient > 0.99. The lower limit of quantification was 1 ng/mL for AA22 in plasma. Intra‐ and inter‐day accuracies for AA22 were 92–111 and 100–103%, respectively, and the inter‐day precision was <15%. After a single oral dose of 25 mg/kg of AA22, the mean peak plasma concentration of AA22 was 2114 ± 362 ng/mL at 6 h. The area under the plasma concentration–time curve was 196,098 ± 69,375 h ng/mL, and the elimination half‐life was 8.7 ± 2.2 h.     

An improved edge detection algorithm for depth map inpainting

Three-dimensional (3D) measurement technology has been widely used in many scientific and engineering areas. The emergence of Kinect sensor makes 3D measurement much easier. However the depth map captured by Kinect sensor has some invalid regions, especially at object boundaries. These missing regions should be filled firstly. This paper proposes a depth-assisted edge detection algorithm and improves existing depth map inpainting algorithm using extracted edges. In the proposed algorithm, both color image and raw depth data are used to extract initial edges. Then the edges are optimized and are utilized to assist depth map inpainting. Comparative experiments demonstrate that the proposed edge detection algorithm can extract object boundaries and inhibit non-boundary edges caused by textures on object surfaces. The proposed depth inpainting algorithm can predict missing depth values successfully and has better performance than existing algorithm around object boundaries.     

Melham's Conjecture on Odd Power Sums of Fibonacci Numbers

Ozeki and Prodinger showed that the odd power sum of the first several consecutive Fibonacci numbers of even order is equal to a polynomial evaluated at a certain Fibonacci number of odd order. We prove that this polynomial and its derivative both vanish at 1, and will be an integer polynomial after multiplying it by a product of the first consecutive Lucas numbers of odd order. This presents an a?rmative answer to a conjecture of Melham.     

Organic field effect transistor composed by fullerene C60 and heterojunctions

We present a study of the complex electronic behavior of a fullerene (C₆₀) molecule attached to six leads (heterojunctions), which works as a three-dimension rectifier. In addition, we confirmed that the fullerene works not only as an electron donor, but also as barrier and transport channel to electrons through the molecule. Moreover, when the phenylpropanodinilla (PPP) lead is orthogonally subjected to bias voltage, the charge distribution and the current displays regions of saturation and resonance similar to semiconductor devices. In order to understand the electronic transport in the molecule, we applied non-equilibrium green function (NEGF) method and performed Fowler-Nordheim (FN) and Millikan-Lauritsen (ML) analyses. The ML curves proved to be sufficient to describe the FN characteristics. In this work, we report the theoretical design for electronic transport of a 3D device (6-terminal).