New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.     

A silver optical sensor based on 5(p-dimethylaminobenzylidene)rhodanine immobilized on a triacetylcellulose membrane

An optical sensor has been proposed for the determination of silver by spectrophotometry. The sensor was prepared by immobilizing 5(p-dimethylaminobenzylidene)rhodanine on a transparent triacetylcellulose membrane. The effect of different variables on the response of the sensor was studied and the optimum conditions were established. The sensor responded linearly in the range 1.8–55.6 μM of silver with a limit of detection of 0.8 μM and a response time range of 8–10 min depending on the concentration of the silver ions. The presented optode is reversible and stable if stored in water for more than one month without reagent leaching. The relative standard deviation for seven replicated measurement of 4.6 and 37 μM silver was 3.15 and 2.76%, respectively. The sensor was successfully applied to the determination of silver in a silver sulphadiazine cream, an ore sample, and a radiology film. The text was submitted by the authors in English.     

An infinite family of bounds on zeros of analytic functions and relationship to Smale's bound

Smale's analysis of Newton's iteration function induce a lower bound on the gap between two distinct zeros of a given complex-valued analytic function . In this paper we make use of a fundamental family of iteration functions , , to derive an infinite family of lower bounds on the above gap. However, even for , where coincides with Newton's, our lower bound is more than twice as good as Smale's bound or its improved version given by Blum, Cucker, Shub, and Smale. When is a complex polynomial of degree , for small the corresponding bound is computable in arithmetic operations. For quadratic polynomials, as increases the lower bounds converge to the actual gap. We show how to use these bounds to compute lower bounds on the distance between an arbitrary point and the nearest root of . In particular, using the latter result, we show that, given a complex polynomial , , for each we can compute upper and lower bounds and such that the roots of lie in the annulus . In particular, , ; and , , where . An application of the latter bounds is within Weyl's classical quad-tree algorithm for computing all roots of a given complex polynomial.

     

Flow-injection determination of ascorbic acid and cysteine simultaneously with spectrofluorometric detection.

A simple and sensitive spectrofluorometric method was developed for the simultaneous determination of ascorbic acid and cysteine by a flow-injection system. This method is based on the reduction of Tl(III) with ascorbic acid or cysteine in acidic media, producing fluorescence reagent, TlCl3(2-) (lambdaex = 227 nm, lambdaem = 419 nm). The injected sample solution was divided into two separate streams. The first stream was treated with Tl(III) at pH 3.0 and then passed through a 270 cm reaction coil to the flow cell of the spectrofluorometer, where the fluorescence intensity was measured. This signal is related to ascorbic acid and cysteine concentration. The second part of the injected sample solution was treated with Tl(III) in HCl solution and then passed through a 50 cm reaction coil to the flow cell and the fluorescence intensity was measured. This signal is related only to cysteine. Thus, the ascorbic acid content was determined directly by the difference according to the calibration curve. Ascorbic acid and cysteine can be determined in the range of 1 x 10(-6) to 5.0 x 10(-5) M, at a rate of 16 samples per hour. The limits of detection (S/N = 3) were 8 x 10(-7) M for ascorbic acid and 7 x 10(-7) M for cysteine. The influence of potential interfering substances was studied. The proposed method was successfully applied to the simultaneous determination of both analytes in real samples.     

Antimicrobial activity of nanocellulose conjugated with allicin and lysozyme

In this study, cellulose nanoparticles were prepared by acid hydrolysis, separately conjugated with allicin and lysozyme by a carbodiimide cross-linker, and characterized by scanning electron microscopy, dynamic light scattering, and Fourier transform infrared spectroscopy. Then, their antimicrobial properties were evaluated by the microdilution method and compared with allicin, lysozyme, and nanocellulose alone. The results showed that nanocellulose had few antimicrobial activities, but allicin-conjugated nanocellulose (ACNC) and lysozyme-conjugated nanocellulose (LCNC) had good antifungal and antibacterial effects against standard strains of Candida albicans, Aspergillus niger, Staphylococcus aureus, and Escherichia coli. Noticeably, although allicin and lysozyme had different minimum inhibitory concentrations (MICs) against all strains, the same quantity of MIC₅₀ and MIC₉₀ was observed for both ACNC and LCNC. The authors suggest that both ACNC and LCNC can be used in industries as an antimicrobial agent in food packaging, inside foodstuffs, and in textile materials.     

Biaryl formation via Suzuki and Stille coupling reactions using palladium nanoparticle/polymeric N‐heterocyclic carbene grafted silica as recyclable and efficient catalyst

Palladium nanoparticles supported on polymeric N‐heterocyclic carbene grafted silica as an efficient organic–inorganic hybrid catalyst is introduced. Pd⁰ nanoparticle formation, which is stabilized by the polymeric N‐heterocyclic carbene ligands and ionic liquid units, was confirmed using X‐ray photoelectron spectroscopy. Scanning electron microscopy images showed microparticles of modified silica while transmission electron microscopy images displayed a fine distribution of Pd nanoparticles. The modified structure was applied successfully in biaryl formation via Suzuki and Stille coupling reactions. Various biaryls were generated through the reaction of phenylboronic acid or tetraphenyltin with a variety of haloarenes via cross‐coupling reactions. This catalyst showed promising activity after being recycled several times. Copyright © 2016 John Wiley & Sons, Ltd.