The adjacency-Jacobsthal-Hurwitz sequences in groups

In [3 Deveci, O., Aküzüm, Y. (in press). The adjacency-Jacobsthal-Hurwitz type numbers. Filomat. [Google Scholar]], Deveci and Aküzüm defined the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind. In this work, firstly we produce the cyclic groups from the multiplicative orders of the generating matrices of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind when read modulo λ and we study the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Then, we give the relationship between the orders of the cyclic groups obtained and the periods of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Further, we extend the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind to groups and then we examine these sequences in the quaternion group Q₈ in detail.     

On the Strong Solutions and the Structural Stability of the g-Bénard Problem

In this paper, we study a type of modified Boussinesq equations which is called g-Bénard problem. We show the existence and uniqueness of strong solutions of the problem in two dimensions, and then, we investigate the continuous dependence of the solutions on the viscosity parameter.     

Real matrix representations of complex split quaternions with applications

In this paper, we introduce 8×8 real matrix representations of complex split quaternions. Then, the relations between real matrix representations of split and complex split quaternions are stated. Moreover, we investigate some linear split and complex split quaternionic equations with split Fibonacci and complex split Fibonacci quaternion coefficients. Finally, we also give some numerical examples as applications of real matrix representation of complex split quaternions.     

A local hybrid kernel meshless method for numerical solutions of two-dimensional fractional cable equation in neuronal dynamics

This study deals with obtaining numerical solutions of two-dimensional (2D) fractional cable equation in neuronal dynamics by using a recently introduced meshless method. In solution process at first stage, time derivatives that are appeared in the considered problem are discretized by using finite difference method. Then a meshless method based on hybridization of Gaussian and cubic kernels is developed in local fashion. The problem is solved both on regular and irregular domians. L_∞ and RMS error norms are calculated and compared with other numerical methods in literature as well as exact solutions. Also, obtained condition numbers are monitored. Numerical simulations show that local hybrid kernel meshless method is a thriving method for solving 2D fractional cable equation on regular and irregular domians.     

Performance of CdTe detector in the 13–1333 keV energy range

The photopeak efficiency, peak to valley ratio and energy resolution of a 3×3×1 mm³ CdTe detector were determined experimentally for 13–1333 keV photon energy by using polyester coated radioisotopes ²⁴¹Am, ²²Na, ⁵⁴Mn, ⁵⁷Co, ⁶⁰Co, ¹⁰⁹Cd, ¹³⁷Cs and ¹³³Ba. The data were analyzed by using PX4 from Amptek. The experimental values were fitted to an analytical function of photon energy, and an agreement was observed for the entire range of the studied energies. The results have shown that the CdTe detector has a high performance due to both the improved charge collection efficiency comparable with that of SI GaAs detectors (Vittone et al., 1999), and the low leakage current. Also, CdTe detector is very attractive for field application as it works at room temperature.     

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.     

Comparison of active and passive radon survey in cave atmosphere,and estimation of the radon exposed dose equivalents and gamma absorbed dose rates

Radon (²²²Rn) measurements were conducted in the Pileki Cave with Radim 3A Active Radon Monitor equipment. Measurements were also done with the passive sampling method with CR-39 nuclear track detectors by exposing them for three months in the cave. Radon concentrations obtained from the active and passive sampling methods showed that, firstly, the concentrations inside the cave measured by the latter method differed greatly due to high humidity levels up to 88%. The total inside radon exposure dose equivalent people were subjected to was estimated to be 19?µSv a^?1 for visitors and 24,065?µSv a^?1 for guides. The gamma absorbed dose rates were determined for inside and outside the cave. The dose rates were calculated by means of using the ²²⁶Ra, ²³²Th and ⁴⁰K activity concentrations and by means of real-time measurements. The gamma absorbed dose rates were found to be much higher than the value of 55?nGy?h^?1 given by UNSCEAR. In addition, the mineralogical compositions and elemental analyses of samples taken from the cave were determined by XRD and WD-XRF methods.     

Impact of symmetry breaking on the Flame Transfer Function of a laminar premixed flame

This work presents a numerical study of the acoustic response of a laminar flame with tunable asymmetry. A V-shaped premixed flame is stabilised in the wake of a cylindrical flame holder that can be rotated. The configuration is symmetric when the flame holder is fixed but increasing its rotation rate breaks the symmetry of the flow. This configuration is submitted to acoustic forcing to measure the effect of rotation of the flame holder on the Flame Transfer Functions. It appears that the asymmetry of the two flame branches changes their respective time delays, resulting in interference in the global unsteady heat release rate fluctuations. Consequently, the Flame Transfer Function exhibits dips and bumps, which are studied via laminar Direct Numerical Simulation. Potential applications for the control of combustion instabilities are discussed.     

Assessment of 210Po and 210Pb by moss biomonitoring technique in Thrace region of Turkey

Journal of Radioanalytical and Nuclear Chemistry - This study presents the first data of 210Po and 210Pb activity concentrations using moss species Hypnum cupressiforme from Thrace region, the...     

3D Raman Spectroscopy of Large Zeolite ZSM-5 Crystals

Hydrothermal treatment is a common method used to modify the physicochemical properties of zeolite-based catalyst materials. It alters the number and type of acid sites through dealumination and increases molecular diffusion by mesopore formation. Steaming also reduces the structural integrity of zeolite frameworks. In this study, Raman microscopy has been used to map large zeolite ZSM-5 crystals before and after steaming. 3D elemental maps of T−O (T: Al or Si) sites of the zeolite were obtained. The Raman active vibrational bands were determined, which are indicative of (non-) framework Al, as well as of structural integrity. Zeolite steaming caused the introduction of additional heterogeneities within the zeolite framework. Al migration and the formation of extra-framework Al species were observed. The described experiments demonstrate the capability of 3D Raman spectroscopy as a valuable tool to obtain information on the spatial distributions of framework elements as well as defects within a zeolite-based material.