On certain generalizations of the Levi-Civita and Wilson functional equations

We study the functional equation

$$\begin{aligned} \sum _{i=1}^mf_i(b_ix+c_iy)= \sum _{k=1}^nu_k(y)v_k(x) \end{aligned}$$

with \(x,y\in \mathbb {R}^d\) and \(b_i,c_i\in {GL}(d,\mathbb {R})\), both in the classical context of continuous complex-valued functions and in the framework of complex-valued Schwartz distributions, where these equations are properly introduced in two different ways. The solution sets are, typically, exponential polynomials and, in some particular cases, related to the so called characterization problem of the normal distribution in Probability Theory, they reduce to ordinary polynomials.

     

Synthesis and Characterization of Canola-Based Cholesteryl Ester and Nematic E7 Mixture

Abstract

The fatty acid of Canola Oil, 61% of which is Oleic acid, was extracted. Fourier Transform Infrared Spectrophotometry (FTIR) confirmed the fatty acid extraction. Canola-based Cholesteryl Ester (CANCE) was obtained through esterification. FTIR scans of the CANCE and the fatty acid were compared to verify the complete esterification. The resulting crude product is a yellow wax with some crystals embedded on it. Thin layer chromatography was then performed to determine the appropriate solvent for the column chromatography to purify the crude sample. The purified product was characterized using Optical Polarizing Microscopy and Differential Scanning Calorimetry. Mixtures of the Nematic E7 and CANCE in different ratios were prepared. Transition temperatures of each mixture were determined using differential scanning calorimetry and verified using optical polarizing microscopy.     

Elastic properties of chemically modified baker's yeast cells studied by AFM

Chemical pretreatment is widely used to facilitate transformation of living cells when foreign components are introduced into a cell through the cell wall. The influence of appropriate chemicals on the wall properties and mechanism of transformation is still a matter of intensive studies. Saccharomyces cerevisiae cells (also known as baker's yeast) were investigated by atomic force microscopy (AFM). The cell walls were modified by lithium acetate and dithiothreitol. The AFM imaging was performed in liquid water‐based environment. The living cells were fixed by trapping into the holes of a polycarbonate membrane. Mechanical and morphological properties of initial intact cells and treated cells were investigated. The increased stiffness of the chemically treated cells was observed. As deduced from the applied theoretical Hertz‐Sneddon model, the treated cells show completely different response mechanism to applied mechanical pressure in comparison with the intact cells. Also, the increased roughness of the cell wall of the treated yeasts was observed. Copyright © 2011 John Wiley & Sons, Ltd.     

Resonant gravimetric immunosensing based on capacitive micromachined ultrasound transducers

High-frequency (40 MHz) and low-frequency (7 MHz) capacitive micromachined ultrasound transducers (CMUT) were fabricated and tested for use in gravimetric detection of biomolecules. The low-frequency CMUT sensors have a gold-coated surface, while the high-frequency sensors have a silicon nitride surface. Both surfaces were functionalized with bovine leukemia virus antigen gp51 acting as the antigen. On addition of an a specific antibody labeled with horseradish peroxidase (HRP), the antigen/antibody complex is formed on the surface and quantified by HRP-catalyzed oxidation of tetramethylbenzidine. It has been found that a considerably smaller quantity of immuno complex is formed on the high frequency sensor surface. In parallel, the loading of the surface of the CMUT was determined via resonance frequency and electromechanical resistance readings. Following the formation of the immuno complexes, the resonance frequencies of the low-frequency and high-frequency sensors decrease by up to 420 and 440 kHz, respectively. Finite element analysis reveals that the loading of the (gold-coated) low frequency sensors is several times larger than that on high frequency sensors. The formation of the protein film with pronounced elasticity and stress on the gold surface case is discussed. We also discuss the adoption of this method for the detection of DNA using a hybridization assay following polymerase chain reaction. Figure

Resonant gravimetric immunosensing with six-channel, 7 MHz capacitive micromachined ultrasound transducer (CMUT). Initial modification by antigen gp51 builds the protein layer with 13.2 GPa elasticity modulus. This increases the resonance frequency of CMUT, which is decreasing after immune complex with antibody is established.     

Evaluation of Redox Activity of Human Myocardium‐derived Mesenchymal Stem Cells by Scanning Electrochemical Microscopy

In this study the redox activity of human myocardium‐derived mesenchymal stem cells (hmMSC) were investigated by redox‐competition (RC‐SECM) and generation‐collection (GC‐SECM) modes of scanning electrochemical microscopy (SECM), using 2‐methylnaphthalene‐1,4‐dione (menadione, MD) as a redox mediator. The redox activity of human healthy and dilated hmMSCs was evaluated by measuring reduction of MD. Measurements were performed by approaching and retracting the UME from the surface of growing hmMSC cells. The current study shows that the RC‐SECM mode can be applied to investigate integrity of cell membranes, whereas the most promising results were observed by using the GC‐SECM mode and applying the Hill's equation for the calculation/fitting of dependencies of electrical current vs menadione concentration. The calculated apparent Michaelis constant (K_M) for the production of menadiol (MDH₂) in the pathological hmMSC cells was 14.4 folds higher compared to that of the healthy hmMSC revealing the lover redox activity of pathological cells. Moreover, the calculated Hill's coefficient n shows a negative cooperative binding between MD and healthy hmMSC and positive cooperative binding between MD and pathological hmMSC. It means that healthy hmMSC is of lower affinity to MD, which is also related to the better membrane integrity of healthy cells. Data of this study demonstrate that SECM can be applied to investigate intracellular redox and membrane changes ongoing in human dilated myocardium‐derived hmMSC in order to improve their functioning and further regenerative potential.     

Oxidative Addition to Palladium(0) Diphosphine Complexes: Observations of Mechanistic Complexity with Iodobenzene as Reactant

Using a combination of electrochemical and NMR techniques, the oxidative addition of PhX to three closely related bis‐diphosphine P₂Pd⁰ complexes, where the steric bulk of just one substituent was varied, has been analysed quantitatively. For the complex derived from MetBu₂P, a rapid reaction ensued with PhI following an associative mechanism, and data was also obtained by cyclic voltammetry for PhOTs, PhBr and PhCl, revealing distinct relative reactivities from the related (PCx₃)₂Pd complex (Cx=cyclohexyl) previously studied. The corresponding EttBu₂P complex reacted more slowly with PhI and was studied by NMR spectroscopy. The reaction course indicated a mixture of pathways, with contribution from a component that was [PhI] independent. For the CxtBu₂P complex, reaction was again monitored by NMR spectroscopy, and was even slower. At high PhI concentrations reaction was predominantly linear in [PhI], but at lower concentrations the [PhI] independent pathway was again observed, and an accelerating influence of the reaction product was observed over the concentration range. The NMR spectra of the EttBu₂P and CxtBu₂P complexes conducted in C₆D₆ shows some line broadening that was augmented on addition of PhI. NMR experiments carried out in parallel show that there is rapid ligand exchange between free phosphine and the Pd₂Pd complex and also a slow ligand crossover between different P₂Pd complexes. DFT calculations were carried out to further test the feasibility of C₆D₆ involvement in the oxidative addition process, and located Van der Waals complexes for association of the P₂Pd⁰ complexes with either PhI or benzene. PhI or solvent‐assisted pathways for ligand loss are both lower in energy than direct ligand dissociation. Taken all together, these results provide a consistent explanation for the surprising complexity of an apparently simple reaction step. The clear dividing line between reactions that give a di‐ or monophosphine palladium complex after oxidative addition clarifies the participation of the ligand in coupling catalysis.     

Molecularly Imprinted Polypyrrole for DNA Determination

In this study graphite electrodes modified by a thin DNA‐imprinted polypyrrole layer, which was able to bind specific target‐DNA, are reported. For this aim, electrochemical synthesis of polypyrrole was performed on a pencil graphite electrode by cyclic voltammetry (CV) or by potential pulse sequences (PPS). The modified electrode surface was used for electrochemical determination of target‐DNA by differential pulse voltammetry. According to our best knowledge this is a first report on the application of DNA‐imprinted polymer for the determination of target‐DNA. The results showed that the molecularly imprinted polypyrrole (MIPPy) layer that formed on the carbon electrode surface was sensitive for target‐DNA, while the nonimprinted polypyrrole layer was not sensitive to the same target‐DNA. Comparison of electrodes modified using PPS and CV techniques is presented.     

Specificity of Glucose Oxidase from Penicillium funiculosum 46.1 Towards Some Redox Mediators

Glucose oxidase (GOx) from Penicillium funiculosum 46.1 was purified using step-by-step ultrafiltration and it was characterized by spectrophotometric and spectrofluorometric methods. It was shown that spectra of GOx produced by P. funiculosum are typical for flavoproteins. Absorption spectrum has distinct peaks at 380 and 457 nm, excitation spectrum at 373 and 447 nm, and emission spectrum at 530 and 562 nm. The pH correlation of enzyme activity and catalytic characteristics in various buffer systems (phosphate (pH 5.0–9.0), citrate (pH 3.0–5.0), citrate-phosphate (pH 3.0–9.0), and universal (pH 3.0–9.0)) were registered. It was determined that the GOx is the most efficiently interacting with substrate (glucose) in phosphate buffer at pH 7.0 with k _cat/K _m?=?21,825 M^?1 s^?1. Interaction of several different redox mediators (9,10-phenantroline-5,6-dione, 9,10-phenanthrenequinone, N-methylphenazonium methyl sulfate, ferrocene, ferrocenecarboxylic acid, α-methylferrocenemethanol, ferrocenecarboxaldehyde) with GOx from P. funiculosum was investigated by evaluation of the difference in fluorescence emission intensity of FAD_(oxidized) and FADH_2(reduced) forms. It was found that 9,10-phenantroline-5,6-dione and 9,10-phenanthrenequinone are the best redox mediators for this type of GOx.