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Copyright of Duzce University Journal of Science & Technology is the property of Duzce University Journal of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Mediterranean Journal of Sport Science (MJSS) is the property of Mediterranean Journal of Sport Science (MJSS) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, solution of inverse nodal problem for p−Laplacian Bessel equation is extended to the case that boundary condition depends on polynomial eigenparameter. To find spectral datas as eigenvalues and nodal parameters of this problem, we used a modified Prüfer substitution. Then, reconstruction formula of the potential functions is also obtained by using nodal lenghts. However, this method is similar to used in [Koyunbakan H., Inverse nodal problem for p−Laplacian energy-dependent Sturm-Liouville equation, Bound. Value Probl., 2013, 2013:272, 1-8], our results are more general.

In this study, considering the proportional fractional derivative, which is a generalization of the conformable fractional derivative, we provided some important spectral properties such as the reality of eigenvalues, the orthogonality of eigenfunctions, the self-adjointness of the operator, the asymptotic estimations of eigenfunctions, and Picone's identity for a proportional Dirac system on an arbitrary time scale. We also presented graphics representing the eigenfunctions of the Dirac system on a time scale, produced by taking advantage of the proportional fractional derivative with some special cases. The main purpose of presenting these graphics was to examine the effect of the proportional fractional derivative on the Dirac system on a time scale, as well as the effect of the eigenvalues, which are meaningful for the subject we were studying for the solution functions. [ABSTRACT FROM AUTHOR]

In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the proposal of improved approximation expressions for computational application. One such expression is the diamond alpha ( ⋄ α ) derivative, which is defined as a linear combination of delta and nabla derivatives. Several dynamic equations and inequalities, as well as hybrid dynamic behavior—which does not occur in the real line or on discrete time scales—are analyzed using this combined concept. In this study, we consider a ⋄ α Dirac system under boundary conditions on a uniform time scale. We examined some basic spectral properties of the problem we are considering, such as the simplicity, the reality of eigenvalues, orthogonality of eigenfunctions, and self adjointness of the operator. Finally, we construct an expression for the eigenfunction of the ⋄ α Dirac boundary value problem (BVP) on a uniform time scale. [ABSTRACT FROM AUTHOR]

Knowledge is acquired as a result of some activities but is forgotten over time. Much work has been done on this subject in fields such as mathematics, engineering and psychology. There are many learning and forgetting models in literature. In this study, a learning and forgetting model considered in classical analysis is redefined with the help of proportional derivative on time scales. The cases where the learning and forgetting rates are constant and the Araştırma Makalesi Araştırma Makalesi learning function shows exponential and hyperbolic functions properties are analyzed. These models are solved with the help of the proportional Laplace transform. Finally, the models considered with the general solution method of first-order proportional dynamic equations were examined on the time scale. [ABSTRACT FROM AUTHOR]

The security of information has been a significant part of human civilization since the ancient era. In the information society, the protection of information becomes increasingly crucial for humankind, and new technologies are progressing in an unending stream. Cryptography is one of the greatest methods intended for protecting the transmission of messages and the security of data. For instance, digital commerce, electronic telecommunications such as mobile phone networks, sending personal emails, commercial transactions, paying television, the security of bank cards, cryptocurrency, etc affect many areas of our everyday lives. Cryptography enables secrecy and protection for secret information by concealing it. It is made through a mathematical method. In this study, we built a new mathematical technique for cryptography in which we applied the Laplace transform (L-Transform) for the Mittag-Leffler function (or E-function) to plain text for encryption and the correspondent inverse L-Transform related to the E-function for decryption. Eventually, we use the Monobit test and correlation test for measuring the security level of encryption and the Python programming language for easily attaining cipher text, the original message, and computations of statistical tests. [ABSTRACT FROM AUTHOR]

We construct λ − Wijsman density and λ − Wijsman statistical convergence (SC) on a time scale. Furthermore, strongly Wijsman λ p − summability is defined. Also, inclusion relations for sets of Wijsman statistical convergent sequences are given by considering the sequences μ Δ λ (t) and μ Δ β (t) in the classΛ on time scales. These theoretical parts are supported by some results and examples. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Eurasian Education & Culture is the property of Ayse Burcu Ulusoy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study considers Sturm–Liouville (S–L) equation with a special function which includes spectral parameter at boundary conditions and expresses asymptotic forms of inverse problem solution, nodal points, and lengths. Furthermore, it proves some uniqueness theorems. Doing this, approximate solution of inverse S–L problem is obtained by second‐kind Chebyshev polynomials whereby the second‐kind Chebyshev wavelets (SCW) method is used to solve these types of problems. Finally, effectiveness of the method is demonstrated in a few examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider p-Laplacian type Diffusion boundary value problem on an arbitrary time scale. We generalize some spectral properties of p-Laplacian Diffusion problem to an arbitrary time scale. Moreover, we prove Picone's identity for this problem.

Turkmens; with its rich oral cultural products, strong national ties and dynamic lifestyle, it forms an important part of the Turkish cultural circle. In various sources, there is information that the epic is composed of poetry or parable genres, with the mention that it is based on the literary reworking of prose genres such as tales, legends, and narrations, and that it is written as a mixture of verse and prose in literatures based on the Turkish language. In this respect, the concept of epic is considered as an important part of the literary heritage, social memory, written and oral tradition, although it is considered within the category of "parable" in folk literature in Turkmen culture. In this tradition, under the title of "dessan", the concept of the term is quite broad compared to other traditions and Turkish literature, since many topics related to social life are covered besides the themes of heroism, love, religion, history and music. In this study, the nature of the concept of epic, which has an important place in the literary tradition of Turkmenistan, the performers, the musical instruments used, the schools of bahshilik and the ways of epic are emphasized [ABSTRACT FROM AUTHOR]

In this study, integro-differential equation under separated boundary conditions is considered. In fact, we study the inverse nodal problem, which includes differential part of Sturm–Liouville equation and Volterra type integral to obtain approximative solutions by Legendre polynomials. And, we use Legendre wavelets method to solve these types of problems. In addition, we present the error bound of q (x) for continuous derivatives with its approximative solution. Once and for all, the strength of the method can be seen in a few examples. [ABSTRACT FROM AUTHOR]

We define a Dirac system in multiplicative calculus by some algebraic structures. Asymptotic estimates for eigenfunctions of the multiplicative Dirac system are obtained. Eventually, some fundamental properties of the multiplicative Dirac system are examined in detail. [ABSTRACT FROM AUTHOR]

In multiplicative fractional calculus, the well-known Dirac system in fractional calculus is redefined. The aim of this study is to analyze some spectral properties such as self-adjointness of the operator, structure of all eigenvalues, orthogonality of distinct eigenfunctions, etc. for this system. Moreover, Green's function in multiplicative case is reconstructed for this system. [ABSTRACT FROM AUTHOR]

We define the multiplicative derivative and its properties on time scales. Then, we restate many concepts for multiplicative analysis such as derivative, Rolle's theorem, mean value theorem, and increasing‐decreasing property on time scales. We aim to create important fields of study by carrying this most important issue of multiplicative analysis, which has applications in economics, finance and many other fields, to time scale calculus. [ABSTRACT FROM AUTHOR]

In this study, we introduce deferred statistical convergence and strongly deferred Cesàro summability on an arbitrary time scale. Moreover, we examine some relationship between deferred statistical convergence and strongly deferred Cesàro summability on time scales. [ABSTRACT FROM AUTHOR]

In this study, we examine the notion of Δλ-statistical boundedness on an arbitrary time scale. Moreover, some inclusion relations are obtained. [ABSTRACT FROM AUTHOR]

In this study, we consider parameter‐dependent diffusion eigenvalue problem on time scales. An upper bound on the number of eigenvalues for this problem on a finite time scale is given. [ABSTRACT FROM AUTHOR]

Inverse nodal problem on Dirac operator is determination problem of the parameters in the boundary conditions, number m and potential function V by using a set of nodal points of a component of two component vector eigenfunctions as the given spectral data. In this study, we solve a stability problem using nodal set of vector eigenfunctions and show that the space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Moreover, we give a reconstruction formula for the potential function as a limit of a sequence of functions and associated nodal data of one component of vector eigenfunction. Our technique depends on the explicit asymptotic expressions of the nodal parameters and, it is basically similar to [1, 2] which is given for Sturm-Liouville and Hill's operators, respectively. [ABSTRACT FROM AUTHOR]

In this study, we extend the concepts and fundamental results on statistical convergence from a single time scale to any product time scale. Various characterizations about these new notions are also obtained. [ABSTRACT FROM AUTHOR]

In parallel with the major developments witnessed in information technologies, social media, supported by its broad area of usage, is gaining significance in every field, with the tourism sector being no exception in this regard. The transfer of changing marketing strategies via digital channels into social media has transformed the way customers interact with the tourism sector, having now the ability to access the comments of other consumers via social media, and adjusting their preferences accordingly. In this study, the impact of the content analysis on the star rating given to hotels is examined with a "Panel Data Analysis" of all the hotels in Istanbul that have received a maximum of 25 reviews on the TripAdvisor website, with a total of 12,000 comments assessed. It was found that the location of the hotel, the access to transport facilities, the food and beverage concept, the quality of staff/service, and the cleanliness of the facilities all affected the star ratings given to hotels; while the architectural structure and the recommendations of other guests had a lesser effect. It was further noted that entertainmentanimation programs had little effect on guest preferences. [ABSTRACT FROM AUTHOR]

We give definition of (λ, ν) statistical convergence on a product time scale. Furthermore, we generalize de la Vallée Poussin mean and define strongly (V, λ, ν) and [V, λ, ν]Ψp2_summable functions, statistical limit superior and inferior on a product time scale. Then, a few inclusion relations are expressed between the sets of (V, λ, ν) summable, p_strongly [V, λ, ν]Ψp2_summable and (λ, ν) statistical convergent functions. Furthermore, some theorems are proved related to statistical limit superior and inferior on a product time scale. [ABSTRACT FROM AUTHOR]

In this study, we present the basic concepts of statistical convergence for double sequences on an arbitrary product time scale. Moreover, we investigate the connection between statistical convergence for double sequences and double Cesàro summability on a product time scale. [ABSTRACT FROM AUTHOR]