Left conjugacy closed loops of nilpotency class two

Every LCC loop Q with Inn Q abelian is nilpotent class two. A loop Q of nilpotency class two is LCC ? L(x, y) = L(y, x) for all x, y ∈ Q ? ?/Z(Mlt Q) is abelian ? [x, y, z] = [x,z,y] for all x, y, z ∈ Q ? [x, y, z] = [xy, z][x, z]^?1 for all x, y, z ∈ Q. All nilpotent LCC loops of order p² are described, and some of their multiplication groups are computed.     

On multiplication groups of relatively free quasigroups isotopic to Abelian groups

If Q is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group Mlt Q is a Frobenius group. Conversely, if Mlt Q is a Frobenius group, Q a quasigroup, then Q has to be isotopic to an Abelian group. If Q is, in addition, finite, then it must be a central quasigroup (a T-quasigroup).This work was supported by institutional grant MSM 113200007, and by Grant Agency of Czech Republic, grant number 201/99/0263.     

Revisiting the normalized Born approximation: effects of scattering

The normalized Born approximation has been suggested as a ratiometric method in fluorescence molecular tomography (FMT) applications, to account for heterogeneity variations. The method enabled practical inversions, as it offered fluorescence reconstruction accuracy over a wide range of absorption heterogeneity, while also accounting for unknown experimental factors, such as the various system gains and losses. Yet it was noted that scattering variations affect the robustness and accuracy. Herein we decompose the effects of absorption and scattering and capitalize on the recent development of hybrid FMT/x-ray computed tomography imaging methods to proposed amendments to the method, which improve the overall accuracy of the approach.     

Categorical Geometry and Integration Without Points

The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article (Segal, Bull Am Math Soc 71:419–489, 1965). In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology. First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical σ-algebra). Second (and here we have a major difference from the classical theory), we prove that every finite-additive function μ with values in [0,1] can be extended to a measure on an abstract σ-algebra; this correspondence is functorial and yields uniqueness. As an example we show that the Segal space can be characterized by completely canonical data. Furthermore, from our results it follows that a satisfactory point-free integration arises everywhere where we have a finite-additive probability function on a Boolean algebra.     

Preserving the activity of cellulase in a batch foam fractionation process

Foam fractionation isone of the low operating-cost techniques for removing proteins from a dilute solution. The initial bulk solution pH and air superficial velocity play an importantrole in the foam-fractionation process. Denaturation of proteins (enzymes) can occur, however, during the foamfractionation process from the shear forces resulting from bursting air bubbles. At the extreme bulk solution pHs (lower than 3.0 and higher than 10.0), the en zymatic activity of cellulase in the foamate phase drops significantly. Within these two pH boundsan increase in the air superficial velocity, V_o, and a decrease in the bulk solution pH leads to a decrease in the separation ratio (SR), defined as theratio of the protein concentration in the foamate to the protein concentration in the residue. On the other hand, an increase in V_o provides a higher foamate-protein recovery. The process efficiency is defined as the product of foamate-protein recovery times the SR times the cellulase activity. The optimal operating condition of the cellulase foamfractionation process is taken into account at the maximum value of the processefficiency. In this study, that optimal condition is atan air superficial velocity of 32 cm/min and a bulk-solution pH of 10.0. At this condition, the recovered foamate is about 80% of the original protein mass, the SR is about 12, and the en zymatic activity is about 60% of the original cellulase activity.     

1,2,4‐Triazole‐based N‐heterocyclic carbene complexes of gold(I): synthesis,characterization and biological activity

Two gold(I) complexes of the (NHC)AuX type bearing a triazole‐based N‐heterocyclic carbene (NHC) ligand (1‐tert‐butyl‐4‐(4‐methylphenyl)‐3‐phenyl‐1H‐1,2,4‐triazol‐4‐ium‐5‐ylidene) and various halide ligands (X = Br, I) were synthesized and characterized in solution using NMR spectroscopy as well as in the solid state using X‐ray diffraction techniques. The cytotoxic properties of both compounds and the precursor, (NHC)AuCl, were screened against a panel of human tumour cell lines including liver cancer (HepG2), cervical cancer (HeLa S3) and leukaemia (CCRF‐CEM, HL‐60) and compared to cisplatin and auranofin. It was found that the activities of the chloro and bromo derivatives were generally superior to that of cisplatin and slightly less effective compared to auranofin, except for HepG2 cells where auranofin was not as effective. In addition, the ability to induce membrane phosphatidyl serine externalization as a hallmark of apoptosis in CCRF‐CEM leukaemic cells was investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Palladium(II) complexes of Y,C,Y‐chelated phosphines: synthesis,structure, and catalytic activity in Suzuki–Miyaura reaction

The phosphines L¹PPh₂ (1) and L²PPh₂ (2) containing different Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₃^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₃^?, were treated with PdCl₂ and di‐µ‐chloro‐bis[2‐[(N,N‐dimethylamino)methyl]phenyl‐C,N]‐dipalladium(II) and yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PdCl₂ (3), {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂} PdCl₂ (4), {[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (5) and {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (6) as the result of different ability of starting phosphines 1 and 2 to complex PdCl₂. Compounds 3–6 were characterized by ¹H, ¹³C, ³¹P NMR spectroscopy and ESI‐MS. The molecular structures of 3,4 and 6 were also determined by X‐ray diffraction analysis. The catalytic activity of complexes 3–6 was evaluated in the Suzuki‐Miyaura cross‐coupling reaction. Copyright © 2010 John Wiley & Sons, Ltd.