The choice property in tame expansions of o-minimal structures

We establish the choice property, a weak analogue of definable choice, for certain tame expansions of o-minimal structures. Most noteworthily, this property holds for dense pairs of real closed fields, as well as for expansions of o-minimal structures by a dense independent set.     

A convenient approach directly from triglycerides toward the producing of thia-wax esters as bio- and chemical raw materials

Research on Chemical Intermediates - Practical and efficient method has been developed for the preparation of novel sulfur-containing esters from triglycerides as potential important industrial and...     

Analysis of the elliptic-profile cylindrical reflector with a non-uniform resistivity using the complex source and dual-series approach: H-polarization case

An elliptic-profile reflector with varying resistivity is analyzed under the illumination by an H-polarized beam generated by a complex-source-point (CSP) feed. The emphasis is done on the focusing ability that is potentially important in the applications in the optical range related to the partially transparent mirrors. We formulate the corresponding electromagnetic boundary-value problem and derive a singular integral equation from the resistive-surface boundary conditions. This equation is treated with the aid of the regularization technique called Riemann Hilbert Problem approach, which inverts the stronger singular part analytically, and converted to an infinite-matrix equation of the Fredholm 2nd kind. The resulting numerical algorithm has guaranteed convergence. This type of solution provides more accurate and faster results compared to the known method of moments. In the computations, a CSP feed is placed into a more distant geometrical focus of the elliptic reflector, and the near-field values at the closer focus are plotted and discussed. Various far-field radiation patterns including those for the non-uniform resistive variation on the reflector are also presented.     

Sensitivity of optimal prices to system parameters in a steady-state service facility

We consider the problem of maximizing the long-run average reward in a service facility with dynamic pricing. We investigate sensitivity of optimal pricing policies to the parameters of the service facility which is modelled as an M/M/s/K$M/M/s/K$ queueing system. Arrival process to the facility is Poisson with arrival rate a decreasing function of the price currently being charged by the facility. We prove structural results on the optimal pricing policies when the parameters in the facility change. Namely, we show that optimal prices decrease when the capacity of the facility or the number of servers in the facility increase. Under a reasonable assumption, we also show that optimal prices increase as the overall demand for the service provided by the facility increases or when the service rate of the facility decreases. We illustrate how these structural results simplify the required computational effort while finding the optimal policy.     

On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm

In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained.     

Advances in modelling saturated soft biological tissues and chemically active gels

Swelling-active materials are numerous and can be found in many applications regarding geotechnical, biological or chemical problems. In general, these materials consist of a charged solid skeleton which is saturated by a fluid mixture containing a solvent and one or more dissolved electrolytes. Following this, the swelling mechanism can either be triggered via changes of the solute concentration in the surrounding solution or by the application of an electric field. Due to the complex micro structure and the numerous coupled effects which result from the electro-mechanical coupling, this class of materials is very effectively described using the Theory of Porous Media. In this regard, the present paper will provide a brief overview of the involved mixture kinematics, the balance equations, as well as the necessary constitutive theory. The presented model is then brought into a weak formulation which is suitable for a numerical treatment using the Finite Element Method. The chosen degrees of freedom are the solid displacement, the ion concentrations, the pressure and the electrical potential, which are discontinuous over the domain boundary. These discontinuities lead to stability problems which can be solved by a penalty method. Finally, two representative examples are presented addressing a free swelling experiment of a cylindrical nucleus pulposus specimen, as well as an electrically initiated bending of a cantilever made of an electro-active polymer like hydrogel, for instance.     

Novel conducting polymer electrolyte biosensor based on poly(1-vinyl imidazole) and poly(acrylic acid) networks

Biosensor construction and characterization studies of poly(acrylic acid) (PAA) and poly(1-vinyl imidazole) (PVI) complex systems have been carried out. The biosensors were prepared by mixing PAA with PVI at several stoichiometric ratios, x (molar ratio of the monomer repeat units). The enzyme, invertase, was entrapped in the PAA/PVA interpenetrating polymer networks during complexation. Modifications were made on the PAA/PVI conducting polymer electrolyte matrixes to improve the stability and performance of the polymer electrolyte-based enzyme biosensor. The maximum reaction rate (V(max)) and Michaelis-Menten constant (K(m)) were investigated for the immobilized invertase. The temperature and pH optimization, operational stability, and shelf life of the polymer electrolyte biosensor were also examined.     

Exploring the quality of the mathematical tasks in the new Turkish elementary school mathematics curriculum guidebook: the case of algebra

To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries and previous experiences with mathematics education in Turkey. This study attempts to provide a perspective on the nature of the instructional tasks in the new elementary school mathematics curriculum. In particular, our focus is to explore the level of cognitive demands (LCD) in the algebra tasks provided in the national elementary mathematics curriculum guidebook. This curriculum document is a major resource for administrators, stakeholders, textbook publishers and ultimately for teachers. For every learning objective, it provides sample tasks to be used in mathematics instructions. In this study, our purpose is to explore the LCD of each of these tasks by utilizing a framework developed by Smith and Stein (Math Teach Middle School 3:344–350, 1998). The framework classifies mathematical tasks according to the level of demands: lower-level and higher-level demands. While the lower-level demands are related to memorization and procedures without connections, the higher-level demands are related to procedures with connections and doing mathematics. The findings revealed that 60% of algebra tasks for each grade level required higher LCD and a great majority of the remaining tasks were at the level of procedures without connections. The findings of the study particularly inform curriculum developers about issues regarding the quality of the tasks given in the curriculum guide and provide possible suggestions to improve the implementation of the curriculum change process.     

Boundedness of Riesz Potential Generated by Generalized Shift Operator on B<Emphasis Type="Italic">a</Emphasis> Spaces

In this paper, the boundedness of the Riesz potential generated by generalized shift operator from the spaces to the spaces is examined.