Bidual of <Emphasis Type="Italic">r</Emphasis>-algebras

We prove that the order continuous bidual of an Archimedean r-algebra is a Dedekind complete r-algebra with respect to the Arens multiplications.     

Genocchi polynomials associated with the Umbral algebra

The aim of this paper is to study on the Genocchi polynomials of higher order on P, the algebra of polynomials in the single variable x over the field C of characteristic zero and P^∗, the vector spaces of all linear functional on P. By using the action of a linear functional L on a polynomial p(x) Sheffer sequences and Appell sequences, we obtain some fundamental properties of the Genocchi polynomials. Furthermore, we give relations between, the first and second kind Stirling numbers, Euler polynomials of higher order and Genocchi polynomials of higher order.     

Selective extraction of triazine herbicides based on a combination of membrane assisted solvent extraction and molecularly imprinted solid phase extraction

A selective extraction technique based on the combination of membrane assisted solvent extraction and molecularly imprinted solid phase extraction for triazine herbicides in food samples was developed. Simazine, atrazine, prometon, terbumeton, terbuthylazine and prometryn were extracted from aqueous food samples into a hydrophobic polypropylene membrane bag containing 1000μL of toluene as the acceptor phase along with 100mg of MIP particles. In the acceptor phase, the compounds were re-extracted onto MIP particles. The extraction technique was optimised for the type of organic acceptor solvent, amount of molecularly imprinted polymers particles in the organic acceptor phase, extraction time and addition of salt. Toluene as the acceptor phase was found to give higher triazine binding onto MIP particles compared to hexane and cyclohexane. Extraction time of 120min and 100mg of MIP were found to be optimum parameters. Addition of salt increased the extraction efficiency for more polar triazines. The selectivity of the technique was demonstrated by extracting spiked cow pea and corn extracts where clean chromatograms were obtained compared to only membrane assisted solvent extraction or only molecularly imprinted solid phase extraction. The study revealed that this combination may be a simple way of selectively extracting compounds in complex samples.     

On the number of eigenvalues for parameter‐dependent diffusion problem on time scales

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given.     

Assessing the Impact of Bridging Analogies in Mechanics

The effects of bridging analogies teaching strategy and gender on Turkish high school students' misconceptions in mechanics were investigated. After a pilot study with 67 students in a nearby high school, the researchers administered the revised Mechanics Misconception Test to 119 high school students as a pretest. Students in the experimental group were instructed by using bridging analogies teaching strategy. At the end of a 3‐week treatment period, the same test was administered to all students as a posttest. The data were analyzed by using analysis of covariance (ANCOVA). The statistical results showed that bridging analogies teaching strategy was an effective means of reducing the number of misconceptions students held about normal forces, frictional forces, tension, gravity, inertia, and Newton's third law.     

New approach to relativity and gravitation

A theory of gravitation, where the stress-energy tensor of the gravitational field is part of the source term of the geometric curvatures, is presented. The theory predicts correctly all the Newtonian and post-Newtonian effects of gravity currently considered as crucial. For extremely strong and nonstatic fields, such as are presumed to exist in quasars and exploding stars, new predictions differing from those of the conventional theory are implied. In the correspondence limit of special relativity the theory recovers the conservation of energy-momentum properly and seems to represent a more satisfactory extension of special theory of relativity.     

Principal Congruence Subgroups of Hecke Groups H（√q）

Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H（√q）,q 〉 5 prime number.     

Light harvesting and efficient energy transfer in a boron-dipyrrin (BODIPY) functionalized perylenediimide derivative

[reaction: see text] Click chemistry has been successfully applied in the synthesis of a bay region tetraboron-dipyrrin (BODIPY) appended perylenediimide (PDI). This light-harvesting molecule presents a large cross section for the absorption of light in the visible region. Excitation energy is efficiently channeled to the perylenediimide core. This novel antenna system is the first demonstration of the efficiency of energy transfer in a BODIPY-PDI bichromophoric system and appears to be highly promising for the design and synthesis of similar dendritic structures.     

A family of p-adic twisted interpolation functions associated with the modified Bernoulli numbers

The main purpose of this paper is to construct a family of modified p-adic twisted functions, which interpolate the modified twisted q-Bernoulli polynomials and the generalized twisted q-Bernoulli numbers at negative integers. We also give some applications and examples related to these functions and numbers.     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.