On the Space of Sequences of p-Bounded Variation and Related Matrix Mappings

The difference sequence spaces (), c(), and c ₀() were studied by Kzmaz. The main purpose of the present paper is to introduce the space bv _p consisting of all sequences whose differences are in the space _p , and to fill up the gap in the existing literature. Moreover, it is proved that the space bv _p is the BK-space including the space _p . We also show that the spaces bv _p and _p are linearly isomorphic for 1 p . Furthermore, the basis and the -, -, and -duals of the space bv _p are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv _p : ), (bv : _p ), and (bv _p : ₁), and the characterizations of some other matrix classes are obtained by means of a suitable relation.     

On the nets of equi-conjugate pairs of curves in a Weyl hypersurface

In this paper, equi-conjugate pairs of curves in a hypersurfaceW _n(g_ij,T_k) are defined and the Chebyshev nets of the first kind, the second kind and the geodesic nets which are formed by the tangent vector fields of these pairs of curves are investigated.     

Special networks in the hypersurfaces of generalised recurrent and birecurrent Weyl spaces

In this paper, we study some properties of the Chebyshev nets and geodesic nets in the hypersurfaces of the generalised recurrent and birecurrent Weyl spaces. Received 4. Dezember 1998.     

On the lower-order theories of continua with application to incremental motions,stability and vibrations of rods

The relative merit of lower-order theories, which have been deduced from the three-dimensional theories of continua, is evaluated with respect to the quantified and un-quantified errors in mathematically modeling the physical response of structural elements. Then, the one-dimensional theories are derived with high accuracy, internal consistency and flexibility from the three-dimensional theory of elasticity in order to govern the nonlinear and incremental motions and stability of a functionally graded rod. First, a kinematic-based method of separation of variables is introduced as a method of reduction, which may lead to the lower-order theories with the same order of errors of the three-dimensional theories, and the nonlinear theories of the rod are derived under Leibnitz’s postulate of structural elements by use of Hamilton’s principle. A theorem of uniqueness is proved in solutions of the linear equations of the rod by means of the logarithmic convexity argument. Next, the kinematic basis is expressed by the power series expansion in the cross-sectional coordinates using Weierstrass’s theorem. Mindlin’s method is used so as to derive the equations in an invariant and fully variational form for the small motions superposed on a static finite deformation, the stability analysis and the high-frequency vibrations of the rod. Moreover, the free vibrations of the rod are considered, the basic properties of eigenvalues are examined, and Rayleigh’s quotient is obtained. The invariant equations of the rod, which are expressible in any system of orthogonal coordinates, may provide simultaneous approximations on all the field variables in a direct method of solutions. The equations are indicated to contain some of earlier equations of rods, as special cases, and also, the numerical elasticity solution of a sample application is presented.     

Free vibration of super elliptical plates with constant and variable thickness by Ritz method

In this study free vibration of simply supported and clamped super elliptical plates is investigated. This class of plates includes a wide range of external boundaries varying from an ellipse to a rectangle. Although studies on the upper and lower bounds of these plate geometries, namely circle and rectangle, are quite extensive, contributions on the mid-shapes, especially for simply supported boundary edges are very limited. The Kirchhoff plate model with isotropic and homogeneous material is studied. The super elliptical powers are chosen from 1 to 10. The Ritz method is employed for the solution of the energy equations of the plates. The effects of Poisson's ratio, which should not be neglected for simply supported plates with curved boundaries, and the aspect ratio of the plate are both examined in detail. The effect of thickness variation is also considered in this study. In order to avoid long computational run times, physically pertinent trial functions are utilized. The frequency parameters obtained are presented and compared with published results for plate shapes that match the current cases.     

Static analysis of point-supported super-elliptical plates

This paper reports the static analysis of point-supported super-elliptical plates of uniform thickness subjected to a uniformly distributed lateral load. The plate perimeter was defined by a super-elliptic function with a power, corresponding to shapes ranging from an ellipse to a rectangle. The analysis was based on the Kirchhoff–Love plate theory and the computations were carried out by the Ritz method. Lagrange multipliers were used to satisfy the boundary conditions. Isotropic and homogeneous plates with 20 different shapes were examined for two distinct aspect ratios. Convergence studies were performed for the central deflection and the central bending moments. The results were checked against those of a corner-supported square plate and good agreement was obtained.     

Antioxidant and cytotoxic properties of some new dipeptide-indole conjugates

In this study, 10 new indole-dipeptide conjugates were synthesized, and their anticancer activity was determined against on A2780 (ovarian cancer cell line) and MCF-7 (breast cancer cell line) cells. Among compounds, 5 and 10 showed better activity against A2780 cell lines than the standard drug docatexel at 0.1 and 1 μM concentrations, while only compound 5 showed better activity than docatexel, the MCF-7 cell line at 0.1 and 1 μM concentrations. The antioxidant potencies of the compounds were low in both the DPPH and iron reducing power methods tested when compared to standard antioxidants used in this work.     

Dose estimation and dating of pottery from Turkey

The luminescence method is a widely used technique for environmental dosimetry and dating archaeological, geological materials. In this study, equivalent dose (ED) and annual dose rate (AD) of an archaeological sample were measured. The age of the material was calculated by means of equivalent dose divided by the annual dose rate. The archaeological sample was taken from Antalya, Turkey. Samples were prepared by the fine grain technique and equivalent dose was found using multiple-aliquot-additive-dose (MAAD) and single aliquot regeneration (SAR) techniques. Also the short shine normalization-MAAD and long shine normalization-MAAD were applied and the results of the methods were compared with each other. The optimal preheat temperature was found to be 200 °C for 10 min. The annual doses of concentrations of the major radioactive isotopes were determined using a high-purity germanium detector and a low-level alpha counter. The age of the sample was found to be 510±40 years.     

On the fundamental equations of electromagnetoelastic media in variational form with an application to shell/laminae equations

The fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials, and the uniqueness of solutions is examined. Alternatively, the fundamental equations are stated as the Euler–Lagrange equations of a unified variational principle, which operates on all the field variables. The variational principle is deduced from a general principle of physics by modifying it through an involutory transformation. Then, a system of two-dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell. Also, a theorem is given, which states the conditions sufficient for the uniqueness in solutions of the shell equations. On the basis of a discrete layer modeling, the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers, whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness. The resulting equations in differential and fully variational, invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well. The invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell (plate) or laminae. The results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material, geometry and/or effects.