The fundamental groups of a triangular algebra

A finite dimensional algebra A (over an algebraically closed field) is called triangular if its ordinary quiver has no oriented cycles. To each presentation (Q I) of A is attached a fundamental group π₁(Q I), and A is called simply connected if π₁(Q I) is trivial for every presentation of A. In this paper, we provide tools for computations with the fundamental groups, as well as criteria for simple connectedness. We find relations between the fundamental groups of A and the first Hochschild cohomology H ¹ (A A).     

The heat transfer problem for inhomogeneous materials in photoacoustic applications and spectral parameter power series

A method for studying the one‐dimensional heat transfer process within an inhomogeneous spatially bounded medium in the presence of an external heat source is presented. It is based on a recently introduced technique for solving problems related to Sturm–Liouville equations that consists in the representation of solutions in the form of a spectral parameter power series. We consider a heat transfer model linked to photoacoustic and show that the introduced method, besides its relative simplicity and analytical nature, offers an efficient numerical algorithm as well as a convenient way to work separately with different physically meaningful components of the temperature distribution function. Detailed explanations and numerical examples are given. Copyright © 2013 John Wiley & Sons, Ltd.     

Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth

We study the energy-critical focusing nonlinear Schrödinger equation with an energy-subcritical perturbation. We show the existence of a ground state in the four or higher dimensions. Moreover, we give a sufficient and necessary condition for a solution to scatter, in the spirit of Kenig and Merle (Invent Math 166:645–675, 2006).     

Synthesis,spectroscopic, thermal and electrical conductivity studies of three charge transfer complexes formed between 1,3-di[(<Emphasis Type="Italic">E</Emphasis>)-1-(2-hydroxyphenyl)methylideneamino]-2-propanol Schiff base and different acceptors

Charge-transfer complexes (CTC) resulting from interactions of 1,3-di[(E)-1-(2-hydroxyphenyl) methylideneamino]-2-propanol Schiff base with some acceptors such as iodine (I₂), bromine (Br2), and picric acid (PiA) have been isolated in the solid state in a chloroform solvent at room temperature. Based on elemental analysis, UV-Vis, infrared, and ¹H NMR spectra, and thermogravimetric analysis (TG/DTG) of the solid CTC, [(Schiff)(I₂)] (1), [(Schiff)(Br₂)] complexes with a ratio of 1:1 and [(Schiff)(PiA)₃] complexes with 1:3 have been prepared. In the picric acid complex, infrared and ¹H NMR spectroscopic data indicate that the charge-transfer interaction is associated with a hydrogen bonding, whereas the iodine and bromine complexes were interpreted in terms of the formation of dative ion pairs [Schiff⁺, I₂^∙−] and [Schiff⁺, Br₂^∙−], respectively. Kinetic parameters were obtained for each stage of thermal degradation of the CT complexes using Coats–Redfern and Horowitz–Metzger methods. DC electrical properties as a function of temperature of these charge transfer complexes have been studied.     

Conductivity and optical studies of plasticized solid polymer electrolytes doped with carbon nanotube

Solid polymer electrolyte films based on Poly(ethylene oxide) (PEO) complexed with lithium hexafluorophosphate (LiPF₆), ethylene carbonate (EC) and amorphous carbon nanotube (αCNTs) were prepared by the solution cast technique. The conductivity increases from 10^?10 to 10^?5 Scm^?1 upon the addition of salt. The incorporation of EC and αCNTs to the salted polymer enhances the conductivity significantly to 10^?4 and 10^?3 Scm^?1. The complexation of doping materials with polymer were confirmed by X-ray diffraction and infrared studies. Optical properties like direct band gap and indirect band gap were investigated for pure and doped polymer films in the wavelength range 200–400 nm. It was found that the energy gaps and band edge values shifted to lower energies on doping.     

An answer to a question on the convolution of functions

Let G be a locally compact group. Recently, G?a¸b and Strobin [2] asked when f*g exists for all \({f, g \in L^p(G)}\) , and also: is the set \({\{(f,g)\in L^p(G) \times L^p(G): f\ast g \in L^p(G)\}}\) σ-c-lower porous (in particular, meager) for \({p\in(1,2]}\) ? In this paper, we answer these questions. In particular, we prove that if 1 <  p <  ∞, 1 ≤  q < ∞, and G is a non-unimodular locally compact group, then the set \({\{(f, g) \in L^p(G) \times L^q(G): f * g}\) is not λ -a.e. finite on G} is a residual set in L ^p (G) ×  L ^q (G).     

Fast fluorescence switching within hydrophilic supramolecular assemblies

We designed a supramolecular strategy to modulate fluorescence in water under optical control. It is based on the entrapment of fluorophore-photochrome dyads within the hydrophobic interior of an amphiphilic polymer. The polymeric envelope around the dyads protects them from the aqueous environment, while imposing hydrophilic character on the overall supramolecular construct. In the resulting assemblies, the photochromic component can be operated reversibly on a microsecond timescale under the influence of ultraviolet stimulations. In turn, the reversible transformations control the emission intensity of the adjacent fluorophore. As a result, the fluorescence of such nanostructured constructs can be photomodulated for hundreds of cycles in water with microsecond switching speeds. Thus, our protocol for fast fluorescence switching in aqueous solutions can eventually lead to the realization of functional probes for the investigation of biological samples.     

Boxplot for circular variables

A boxplot is a simple and flexible graphical tool which has been widely used in exploratory data analysis. One of its main applications is to identify extreme values and outliers in a univariate data set. While the boxplot is useful for a real line data set, it is not suitable for a circular data set due to the fact that there is no natural ordering of circular observations. In this paper, we propose a boxplot version for a circular data set, called the circular boxplot. The problem of finding the appropriate circular boxplot criterion of the form ν × CIQR, where CIQR is the circular interquartile range and ν is the resistant constant, is investigated through a simulation study. As might be expected, we find that the choice of ν depends on the value of the concentration parameter κ. Another simulation study is done to investigate the performance of the circular boxplot in detecting a single outlier. Our results show that the circular boxplot performs better when both the value of κ and the sample size are larger. We develop a visual display for the circular boxplot in S-Plus and illustrate its application using two real circular data sets.     

Development of a novel 96-microwell assay with high throughput for determination of olmesartan medoxomil in its tablets

A novel 96-microwell-based spectrophotometric assay has been developed and validated for determination of olmesartan medoxomil (OLM) in tablets. The formation of a colored charge-transfer (CT) complex between OLM as a n-electron donor and 2, 5-dichloro-3, 6-dihydroxy-1, 4-benzoquinone (p-chloranilic acid, pCA) as a π-electron acceptor was investigated, for the first time, and employed as a basis in the development of the proposed assay. The proposed assay was carried out in 96-microwell plates. The absorbance of the colored-CT complex was measured at 490 nm by microwell-plate absorbance reader. The optimum conditions of the reaction and the analytical procedures of the assay were established. Under the optimum conditions, linear relationship with good correlation coefficient was found between the absorbance and the concentration of OLM in the range of 1-200 μg ml^-1. The limits of detection and quantitation were 0.3 and 1 μg ml^-1, respectively. No interference was observed from the additives that are present in the pharmaceutical formulation or from hydrochlorothiazide and amlodipine that are co-formulated with OLM in some formulations. The assay was successfully applied to the analysis of OLM in tablets with good accuracy and precision. The assay described herein has great practical value in the routine analysis of OLM in quality control laboratories, as it has high throughput property, consumes minimum volume of organic solvent thus it offers the reduction in the exposures of the analysts to the toxic effects of organic solvents, and reduction in the analysis cost by 50-fold. Although the proposed assay was validated for OLM, however, the same methodology could be used for any electron-donating analyte for which a CT reaction can be performed.     

Supramolecular sheets in (4H‐chromeno[4,3‐c]isoxazol‐3‐yl)methanol and its hydrated 8‐methyl‐substituted analogue at 100 K

The title compounds, (4H‐chromeno[4,3‐c]isoxazol‐3‐yl)methanol, C₁₁H₉NO₃, (I), and (8‐methyl‐4H‐chromeno[4,3‐c]isoxazol‐3‐yl)methanol monohydrate, C₁₂H₁₁NO₃·H₂O, (II), crystallize in the monoclinic space groups P2₁/c and C2/c, respectively. The simple addition of a methyl substituent in (II) results in a change in the structure type and substantially alters the intermolecular interaction patterns, while retaining the point‐group symmetry 2/m. Compound (II) crystallizes as a hydrate and the resulting hydrogen‐bonding interactions involving the water molecule are the cause of differences in the hydrogen‐bonded supramolecular motifs present in (I) and (II). The water molecule in (II) is disordered over two positions having very similar orientations, with occupancies of 0.571 (18) and 0.429 (18), although the pattern of hydrogen‐bonding interactions for the two disordered water molecules remains essentially the same. In both compounds, the primary donor hydroxy group adopts a trans conformation with respect to the isoxazole O atom, with a torsion angle of 170.65 (8)° for (I) and 179.56 (10)° for (II), the small difference being due to differences in the hydrogen‐bonding environment of the hydroxy group. In (I), molecules are linked through two independent O—H...N and C—H...O hydrogen bonds and form sheets of centrosymmetric R₄⁴(18) and R₄⁴(14) rings extending parallel to the (100) plane. The supramolecular motifs in (II) generate two‐dimensional sheets parallel to the (100) plane through a combination of O—H...X (X = N, O) and C—H...O hydrogen bonds, leading to water‐assisted noncentrosymmetric R₂²(8) and R₆⁶(20) motifs. The present work is an example of how the simple replacement of a substituent in the main molecular scaffold may transform the structure type, paving the way for a variety of supramolecular motifs and consequently altering the complexity of the intermolecular interaction patterns.