Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.     

Quantum Spin Half Algebra and Generalized Megrelishvili Protocol for Confidentiality of Digital Images

International Journal of Theoretical Physics - Most of the enciphering structures are based on the transformation of mediums by describing the strict criteria. The presented article is based on...     

Study on Steady Shear,Morphology and Mechanical Behavior of Nanocomposites based on Polyamide 6

Nanocomposites of two different grades of polyamide 6 (PA6) with organically modified nanoclay were prepared via melt compounding in a twin‐screw extruder. The rheological behavior, morphology and mechanical properties of the nanocomposites were studied using a capillary rheometer, x‐ray diffraction (XRD), tapping‐mode atomic force microscopy (AFM), and tensile and flexural tests. XRD patterns indicate that the organically modified layered silicate was well dispersed in the PA6 matrix. From the AFM images the surface roughness of PA6 slightly increases with addition of organoclay. The rheological studies showed that the prepared nanocomposites have shear thinning behavior, obeying the power law equation. Addition of organoclay increases the shear stress and shear viscosity. At high rate of shear deformation the viscosity of nanocomposites are comparable to those of the pure polyamides. The activation energy of flow decreases with increasing nanoclay content. For most of the prepared nanocomposites the activation energy values increase with increasing shear rate. The tensile strength and flexural modulus and strength of the nanocomposites increase with increase of nanoclay content, but the extension at yield decreases with increasing clay loading.     

Survey of Phenolic Acids,Flavonoids and In Vitro Antioxidant Potency Between Fig Peels and Pulps: Chemical and Chemometric Approach

In the present study, chromatic coordinates, phenolic acids, flavonoids and antioxidant capacity assessed by 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonate (ABTS) and lipid peroxidation inhibition capacity (LPIC) essays and their relative IC50 were investigated in 25 fig cultivars growing in Morocco. The aims of this study were to determine (i) the variation in these compounds among light and dark-colored cultivars, (ii) their partitioning between fruit peel and pulp and (iii) to display network connections among these variables. Twelve phenolic compounds (PCs) were isolated in peel extract versus eight in pulp samples. Anthocyanins, mainly cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the predominant compounds in peels, where the mean concentrations were 75.90 ± 18.76 and 77.97 ± 18.95 µg/g dw, respectively. On the other hand, (−)-epicatechin and cyanidin-3-O-rutinoside were the major compounds in the pulp extracts, where the mean values were 5.23 ± 4.03 and 9.01 ± 5.67 µg/g dw, respectively. A two-dimensional hierarchically clustered heatmap was applied to the dataset to explore correlations in the dataset and similarities between cultivars, without dimensionality reduction. Results showed that anthocyanins, particularly pelargonidin-3-O-rutinoside, cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the main contributors to the peels’ free radical scavenging capacity. This capacity was particularly higher in the peel of dark-colored figs compared to the fruit pulp. The local cultivar “INRA 1301” showed the most promising phenolic profile due to its very high levels of almost all detected PCs, especially (−)-epicatechin, quercetin-3-O-rutinoside, quercetin-3-O-glucoside, cyanidine-3,5-diglucoside, cyanidine-3-O-rutinoside and pelargonidin-3-O-rutinoside (54.66, 141.08, 35.48, 494.08, 478.66, 12.56 µg/g dw, respectively). Having the darkest figs in the collection (L* = 25.72, c* = 22.09 and h° = 20.99), this cultivar has also combined promising IC50 values, which were of 19.85, 40.58 and 124.78 µg/mL for DPPH, ABTS and LPIC essays, respectively.     

Inside-Needle Extraction Method Based on Molecularly Imprinted Polymer for Solid-Phase Dynamic Extraction and Preconcentration of Triazine Herbicides Followed by GC–FID Determination

An inside-needle extraction method was developed through thermal polymerization of atrazine-molecularly imprinted polymer (MIP) on the internal surface of a stainless steel hollow needle, which was oxidized and silylated. The fabricated coating (MIP layer) for the needle was durable and showed very good chemical and thermal stability. It could be mounted on a glass syringe and be directly coupled with gas chromatographic (GC) systems. The parameters being effective on the coating and extraction processes, namely nature of oxidizing agent, silylation time, nature and amount of porogen, template-to-MIP components ratio, polymerization time and temperature, sample volume, flow rate, pH and ionic strength of the sample were investigated and optimized. The extraction needle showed high selectivity as well as a great extraction capacity for triazines. The extraction of atrazine, simazine, cyanazine, ametryn, prometryn and terbutryn using the fabricated extraction needle and followed by GC analysis resulted in detection limits of 2.6, 21, 24, 32, 38 and 42 ng mL⁻¹, respectively. The fabricated needle proved to be applicable to the analysis of real samples by comparing the results obtained for non-spiked and spiked samples of grape juice, tap water and groundwater.

     

Molecular monolayer-mediated control over semiconductor surfaces: evidence for molecular depolarization of silane monolayers on Si/SiO(x)

We show that, for molecules with particularly strong dipoles, their organization into a monomolecular layer can lead to depolarization, something that limits the range over which the substrate's work function can be changed. It appears that, with molecules, depolarization is achieved by changes in orientation and conformation, rather than by charge transfer to the substrate as is common for atomic layers.     

Some spectroscopic aspects of electron transfer in ruthenium(II) polypyridyl complexes

The metal-to-ligand charge transfer (MLCT) absorption and emission properties of several ruthenium(II)-bipyridine am(m)ine complexes are compared. The Gaussian deconvolution of the spectra indicates that: (a) the emission MLCT bandwidths are smaller than the absorption bandwidths for the first components of the apparent vibronic progressions; (b) the emission bands decrease in energy and width when a polypyridyl is replaced by an am(m)ine. The observations can be interpreted in terms of a two state model and the perturbation theory-based treatment of the attenuation of the effective reorganizational energy, λ_r =^~ λ_r ^o(1- 4α² _DA), where λ_r ^o is the reorganizational energy corresponding to no mixing between the two electron transfer states and α_DA = (H_DA/E_DA) is the mixing coefficient. Both the solvent and molecular contributions to λ_r are attenuated. The MLCT excited state lifetimes also decrease with am(m)ine substitution, and the non-radiative decay rate constant at 77 K is roughly proportional to the number of am(m)ine moieties coordinated to the ruthenium center.     

Chemical characterisation of bioactive compounds in Medicago sativa growing in the desert of Oman

Medicago sativa Linn growing in Omani desert were chemically characterised using flame photometry, inductively coupled plasma, gas chromatography–mass spectrometry and high performance liquid chromatographic (HPLC) analysis. HPLC analyses were performed to determine the phenolics and flavonoids present in M. sativa. The major compounds detected in M. sativa leaves were protchaechenic acid (3.22%), hydroxyl benzoic acid (1.05%), β-Phenyl caffate (0.97%) and kaempherol (0.89%). Pterostilbene, a cholesterol-lowering compound, was detected in M. sativa.