On the number of generators needed for free profinite products of finite groups

We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C ₁, ..., C _n are finite cyclic groups then there exists a finite group G which is generated by isomorphic copies of C ₁, ..., C _n and the minimal number of generators of G is n. The first author’s research is partially supported by NSF grant DMS-0701105. The second author’s research is partially supported by OTKA grant T38059 and the Magyary Zoltán Postdoctoral Fellowship.     

A study on the possible usefulness of detrended fluctuation analysis of the electroencephalogram background activity in Alzheimer's disease

We studied the EEG background activity of Alzheimer's disease (AD) patients with detrended fluctuation analysis (DFA). DFA provides an estimation of the scaling information and long-range correlations in time series. We recorded the EEG in 11 AD patients and 11 age-matched controls. Our results showed two scaling regions in all subjects' channels (for limited time scales from 0.01 to 0.04 s and from 0.08 to 0.43 s, respectively), with a clear bend when their corresponding slopes ($alpha_{1}$ and $alpha_{2}$) were different. No significant differences between groups were found with $alpha_{1}$. However, $alpha_{2}$ values were significantly lower in control subjects at electrodes T5, T6, and O1 ($p$ $≪$ 0.01, Student's $t$-test). These findings suggest that the scaling behavior of the EEG is sensitive to AD. Although $alpha_{2}$ values allowed us to separate AD patients and controls, accuracies were lower than with spectral analysis. However, a forward stepwise linear discriminant analysis with a leave-one-out cross-validation procedure showed that the combined use of DFA and spectral analysis could improve the diagnostic accuracy of each individual technique. Thus, although spectral analysis outperforms DFA, the combined use of both techniques may increase the insight into brain dysfunction in AD.      

A finite difference method with non-uniform meshes for a non-linear heat conduction problem

Summary Iterative solutions of finite difference approximations with nonuniform meshes of the nonlinear heat conduction equation are presented. Results are obtained for the temperature distribution in the wall of a long hollow cylinder, separating two fluids with different temperatures. By introducing nonuniform meshes, the amount of numerical computations can be reduced considerably without loss of accuracy. The mesh points are distributed according to the variation of the third derivative of temperature curve obtained by a linear theory.

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Übersicht Es werden iterative Lösungen der nichtlinearen Wärmeleitungsgleichung mit Hilfe eines Differenzen-Verfahrens mit ungleicher Maschenweite abgeleitet. Die Temperaturverteilung im Inneren eines Zylindermantels, der zwei Flüssigkeiten verschiedener Temperatur voneinander trennt, wird berechnet. Durch Verwendung ungleicher Maschenweite kann der Rechenaufwand erheblich verringert werden, ohne da die Genauigkeit verloren geht. Die Maschenweite wird der 3. Ableitung der Temperaturkurve entsprechend gewählt, so wie sie sich aus der linearen Theorie ergibt.

     

C–H···π and C=O···π Intermolecular Interactions in Dibenzyl-3,6-dimethylpyrazine-2,5-dicarboxylate

Abstract A new pyrazine compound, has been synthesised and characterised by single-crystal X-ray diffraction: monoclinic, P2₁/c with a = 11.0707(3) ?, b = 5.23700(10) ?, c = 16.6997(5) ?, β = 103.5385(16)°, Mr = 376.40, V = 941.30(4) ?³, Z = 2. Each molecule possesses C _i symmetry with the two halves of the molecule related by an inversion centre. C–H···π and C=O···π interactions held the molecules together. Index Abstract C–H···π and C=O···π intermolecular interactions in dibenzyl-3,6-dimethylpyrazine-2,5-dicarboxylate Joana A. Silva, Ana C. Santos, Ana T. Marques, Manuela Ramos Silva, Ana Matos Beja, Abílio J. F. N. Sobrala In dibenzyl-3,6-dimethylpyrazine-2,5-dicarboxylate, each molecule possesses C _i symmetry. The molecules are assembled in chains via carbonyl···π interactions. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Geometric Roots of –1 in Clifford Algebras Cℓ p,q with p + q ≤ 4

It is known that Clifford (geometric) algebra offers a geometric interpretation for square roots of –1 in the form of blades that square to –1. This extends to a geometric interpretation of quaternions as the side face bivectors of a unit cube. Research has been done [1] on the biquaternion roots of –1, abandoning the restriction to blades. Biquaternions are isomorphic to the Clifford (geometric) algebra Cℓ ₃ of \mathbb R³{{\mathbb R^3}} . All these roots of –1 find immediate applications in the construction of new types of geometric Clifford Fourier transformations.     

Analysis of recombinant monoclonal antibodies by capillary zone electrophoresis

Analytical platforms that characterize charge heterogeneity in therapeutic proteins, such as mAbs, are important tools that can be used to define quality attributes. CZE separates protein moieties close to their native state and is a valuable physicochemical analytical method that can be used in parallel with other orthogonal methods for characterization and comparability. In this study, custom conditions for the analysis of charge heterogeneity of two mAbs were developed with regard to critical parameters in the BGE, running conditions, and sample treatment. The method application was tested for up to four mAbs and one mAb fragment. The electropherograms showed specific profiles and contrasting levels of basic and acidic isoforms with respect to the main isoform. Issues that surround this method, such as peak tailing and capillary lifetime, are summarized. Using this method, the identities of rituximab and trastuzumab were confirmed, based on the correspondence between the biosimilars and reference products, noninterference of the sample matrix, and the ability to separate spiked samples of related mAbs. The RSD of the isoform content and migration time for the method repeatability were less than 2 and 1%, respectively.     

Evaluation of Row-wise Manipulations for the Forensic Differentiation of Malaysian Soils based on Ultra-performance Liquid Chromatographic Profiles

Journal of Analytical Chemistry - Soil is useful physical evidence for linking a suspect/victim to a particular crime scene. However, the discrimination of soils from neighboring locations can be a...     

Impact of polyvinylpyrrolidone and quantity of silver nitrate on silver nanoparticles sizing via solvothermal method for dye-sensitized solar cells

The multiple sizing of silver nanoparticles (AgNPs) were synthesized from the miscible compound of ethylene glycol (EG), polyvinylpyrrolidone (PVP) and silver nitrate (AgNO3) via the solvothermal method. During the synthesis, the PVP-AgNO3 was contemplated as a paramount parameter. Using the simple method of solvothermal, the sizing of AgNPs was easily controlled in accord with the augmentation of PVP-AgNO3 at secured and moderate temperature. In regards to the sizing of AgNPs, the presence of minimum agglomeration, the absorption capability and chemical structures were highlighted through a series of verification includes ultraviolet–visible (UV–Vis) spectroscopy, Fourier-transform infrared (FTIR) spectroscopy and transmission electron microscopy (TEM) analysis. The effectiveness of the synthesized AgNPs was further investigated and compared with the commercial AgNPs by incorporating the AgNPs into titanium dioxide (TiO2) semiconductor film-based dye-sensitized solar cells (DSSCs). Results signified that the spherical AgNPs with produced sizing within the range of 19.6 to 45.2 nm were greatly impacting by tunable quantities of PVP-AgNO3, which was validated in the forms of linear equations. A larger size promotes a slower nucleation rate that conduces agglomeration. In opposition to this, the smallest size of AgNPs develops a faster formation rate of Ag ions into AgNPs, inducing the deterrent of agglomeration in light of notable particle dispersion. The power conversion efficiency (PCE) contributed by the incorporation of synthesized AgNPs into TiO2 is also 41.2% higher than that of the commercial AgNPs-TiO2. This is because the synthesized AgNPs provides less agglomeration which led to a better surface plasmonic effect towards the nanoparticles.