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this paper, we study the modified Pell polynomials. We first give the proof of the generating function of these polynomials. We then give the proof of the Binet formula for the modified Pell polynomials, which gives the th modified Pell polynomial. We also obtain some summation formula for these polynomials. In addition, we investigate some well-known identities including Catalan, Cassini, d’Ocagne and Gelin-Cesaro identities involving the modified Pell polynomials. ...

In this paper, we introduce two operators associated with ψ * and * ψ operators in ideal topological spaces and discuss the properties of these operators. We give further characterizations of Hayashi-Samuel spaces with the help of these two operators. We also give a brief discussion on homeomorphism of generalized closure spaces which were induced by these two operators.

The concept of stability is studied on many different types of mathematical structures. This concept can be thought of as the small changes that will be applied in the structure studied should not disrupt the functioning of this structure. In this context, we performed the convergence and stability analysis of the new four-step iteration algorithm that we defined in this study, under appropriate conditions. In addition, we execute a speed comparison with existing algorithms to prove that the new algorithm is effective and useful, and we gave a numerical example to support our result.

Risk theory has always played a significant role in mathematical finance and actuarial sciences. A novel approach to the risk theory of non-life insurance is quantum mechanics. To compute finite-time non-ruin probability, I introduce the quantum mechanics formalism in discrete space and continuous space with the appropriately chosen Hamiltonian. By using the quantum mechanics approach and the stochastic method, the non-ruin operator is defined, and tensor products of operator concepts are presented for several examples. In this paper, Dirac notations are operated to find the Hamiltonian matrix with the eigenvector basis for two and three-state cases, and its tensor product version with a change of basis.

In this study, the failures in Transformer Centers in Mersin Province Erdemli District have been investigated. The causes of the failures have been discussed. It is aimed to create a method for the reasons of possible failures of power transformer. The data have been collected by investigating the faults occurring at the Erdemli Substations. The failure statistics of the 200 power transformer failures that occurred between 2003 and 2019 in the Erdemli district of Mersin province have been examined. Examples of different power transformer failures have been given in fault analysis. The reasons of power transformer failures and the precautions to be taken have been explained.

The purpose of this work is to investigate and quantify x-ray fluorescence, its production and its spectroscopy. Characteristic x-ray with different energies were obtained from six various elements using Am-241 source with 59.5 keV. It was found that x-ray energy and intensity increase with increasing atomic number of material. X-ray spectroscopy was studied for such elements in respect to their atomic number and intensity of Kα characteristic x-ray using proportional counter. Furthermore, x-ray fluorescence was produced from different thickness of copper foil using different energies. It was found that there is no substantial different in x-ray fluorescence yield with higher thickness of the target.

Metal oxide and metallic composites are commonly used in material science. Oxides can perform different physical features by small shift during synthesis. That commonly tends innovative results. In this study copper phthalocyanine based four different composite semiconductor materials fabricated by hydrothermal method. The samples were analyzed by optical and electrical characterization measurements. Reflectance, band gap values and conductivity results obtained and presented as graphics with discussion. ...

In this paper, we first define the Gaussian modified Pell sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1 ─ i and = 1 + i. Then we give the definition of the Gaussian modified Pell polynomial sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1─ xi and = x + i. We give Binet’s formulas, generating functions and summation formulas of these sequences. We also obtain some well-known identities such as Catalan’s identities, Cassini’s identities and d’Ocagne’s identities involving the Gaussian modified Pell sequence and Gaussian modified Pell polynomial sequence. ...

Spatial legibility is related to the obtainment of spatial information (2D and 3D) that is in the urban area according to the characteristics of the observer who perceives this space. The aim of this research is to examine the spatial legibility of the campus of Selçuk University which is located in Konya province according to the characteristics of the area and the observer. The spatial characteristics of the application area were determined with the analyzes that were conducted with the help of Geographical Information Systems (GIS) and the characteristics of the observer were determined with analyzes that reveal the understanding of the observer to the area (Lynch analysis, questionnaire application and statistical evaluations). When the conducted spatial analyzes and statistical evaluations are examined, it was determined that the spatial legibility of the campus has a statistically significant relationship with the characteristics of the area and the observer.

The aim of this work is to investigate some properties of the truncated octahedron metric introduced in the space in further studies on metric geometry. With this metric, the 3-dimensional analytical space is a Minkowski geometry which is a non-Euclidean geometry in a finite number of dimensions. In a Minkowski geometry, the unit ball is a certain symmetric closed convex set instead of the usual sphere in Euclidean space. The unit ball of the truncated octahedron geometry is a truncated octahedron which is an Archimedean solid. In this study, first, metric properties of truncated octahedron distance, d_TO, in R^2 has been examined by metric approach. Then, by using synthetic approach some distance formulae in R_TO^3, 3-dimensional analytical space furnished with the truncated octahedron metric has been found.