On the calculation of the Kauffman bracket polynomial

In this paper, we present a new algorithm to evaluate the Kauffman bracket polynomial. The algorithm uses cyclic permutations to count the number of states obtained by the application of ‘A’ and ‘B’ type smoothings to the each crossing of the knot. We show that our algorithm can be implemented easily by computer programming.     

Korovkin type approximation theorem for BBH type operators via <Emphasis Type="Italic">J</Emphasis>-convergence

This paper provides a Korovkin type approximation theorem for a class of positive linear operators including Bleimann-Butzer and Hahn operators via J-convergence.     

SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD

In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds in a Riemannian product manifold.     

Numerical damage assessment of Haghia Sophia bell tower by nonlinear FE modeling

In the present paper, the numerical damage assessment of the masonry bell tower called “Haghia Sophia” in Trabzon, Turkey is performed by nonlinear 3D finite element modeling. The behavior of bell tower is determined under several different conditions: nonlinear static analysis containing dead and wind loads and nonlinear seismic analysis. In addition to, an assessment of the tower’s stability with respect to the tilt of the tower is carried out by means of a nonlinear analysis. In the nonlinear dynamic analysis, the east–west component of 1992 Erzincan earthquake is used. Cracking and crushing of the masonry have been taken into account, as well as the influence of material nonlinearity. The numerical analysis has given a valuable picture of possible damage evolution, providing useful hints for the prosecution of structural monitoring. The displacement and stress fields, as well as the distribution of cracking have been calculated and compared to the actual distribution of fractures in the tower. It is seen from the numerical results that there is a good agreement with present damages of the bell tower.     

A novel amperometric glucose biosensor based on reconstitution of glucose oxidase on thiophene-3-boronic acid polymer layer

The biosensor was constructed for determination of glucose by using glucose oxidase enzyme immobilized on poly(thiophene-3-boronic acid) (PTBA). Boronic acid functionalized polythiophene layer was obtained by electrochemical polymerization of Thiophene (Th) and thiophene-3-boronic acid (TBA) with different monomer rations. The reconstitution of the apo-glucose oxidase (apo-GOx) on a complexed flavin adenine dinucleotide (FAD) linked to polythiophene boronic acid (PTBA) monolayer yields an electrically contacted enzyme monolayer. The GOx-reconstituted enzyme electrode exhibited excellent electrocatalytic activities toward the reduction and oxidation of hydrogen peroxide as well. The PTBA/FAD/GOx biosensor shows an excellent performance for glucose at +0.4 V with a high sensitivity (2.14 μA/mM) and lower response time (～5 s) in a wide concentration range of 0.5–18 mM (correlation coefficient of 0.9952). Furthermore, the effects of applied potential, pH, temperature, electroactive interference, stability and reusability of the biosensors were discussed.     

Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method

In this paper, an improved Legendre collocation method is presented for a class of integro-differential equations which involves a population model. This improvement is made by using the residual function of the operator equation. The error differential equation, gained by residual function, has been solved by the Legendre collocation method (LCM). By summing the approximate solution of the error differential equation with the approximate solution of the problem, a better approximate solution is obtained. We give the illustrative examples to demonstrate the efficiency of the method. Also we compare our results with the results of the known some methods. In addition, an application of the population model is made.     

A numeric–analytic method for time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative

In this paper, the fractional variational iteration method (FVIM) was applied to obtain the approximate solutions of time-fractional Swift–Hohenberg (S–H) equation with modified Riemann–Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. Numerical results showed the FVIM is powerful, reliable and effective method when applied strongly nonlinear equations with modified Riemann–Liouville derivative.     

An exponential matrix method for solving systems of linear differential equations

This paper presents an exponential matrix method for the solutions of systems of high‐order linear differential equations with variable coefficients. The problem is considered with the mixed conditions. On the basis of the method, the matrix forms of exponential functions and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown coefficients are determined and thus the approximate solutions are obtained. Also, an error estimation based on the residual functions is presented for the method. The approximate solutions are improved by using this error estimation. To demonstrate the efficiency of the method, some numerical examples are given and the comparisons are made with the results of other methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Separation of brombuterol enantiomers in capillary electrophoresis with cyclodextrin‐type chiral selectors and investigation of structure of selector‐selectand complexes using nuclear magnetic resonance spectroscopy

The major goal of this study was to determine the affinity pattern of brombuterol (BB) enantiomers toward various cyclodextrins (CD) and to evaluate the potential of NMR spectroscopy for understanding fine mechanisms of interactions between CDs and BB enantiomers. Separation of BB enantiomers was performed in a fused‐silica capillary using a phosphate buffer, pH 2.5, at the room temperature in the normal polarity mode. It was shown once again that CE in combination with NMR spectroscopy represents a very sensitive tool for studies of affinity patterns and structure of CD complexes with chiral guests. Although opposite affinity patterns of BB enantiomers were observed toward native β‐ and γ‐CDs, no significant differences between the structures of the complexes of these two CDs with BB were detected by NMR spectroscopy. In contrary to this, the opposite affinity pattern of BB enantiomers toward β‐CD and its two sulfated derivatives, heptakis (2,3‐O‐diacetyl‐6‐sulfo)‐β‐CD (HDAS‐β‐CD) and heptakis (2‐O‐methyl‐3,6‐di‐O‐sulfo)‐β‐CD (HMDS‐β‐CD) was associated with major differences in the structure of the complexes. In addition, it was shown again that HMDS‐β‐CD provides separation of enantiomers without formation of inclusion‐type complex with the chiral analyte.