There have been very few analyses on partial differential equations with piecewise constant arguments and as far as we know, there is no study conducted on heat equation with piecewise constant argument of generalized type. Motivated by this fact, this study aims to solve and analyse heat equation with piecewise constant argument of generalized type. We obtain formal solution of heat equation with piecewise constant argument of generalized type by separation of variables. We apply the Laplace transform method using unit step function and method of steps on each consecutive intervals. We investigate stability, oscillation, boundedness properties of solutions.
{"title":"New Results on a Partial Differential Equation with General Piecewise Constant Argument","authors":"Marat Akhmet, Duygu Aruğaslan Çinçin, Zekeriya Özkan","doi":"10.47000/tjmcs.1166651","DOIUrl":"https://doi.org/10.47000/tjmcs.1166651","url":null,"abstract":"There have been very few analyses on partial differential equations with piecewise constant arguments and as far as we know, there is no study conducted on heat equation with piecewise constant argument of generalized type. Motivated by this fact, this study aims to solve and analyse heat equation with piecewise constant argument of generalized type. We obtain formal solution of heat equation with piecewise constant argument of generalized type by separation of variables. We apply the Laplace transform method using unit step function and method of steps on each consecutive intervals. We investigate stability, oscillation, boundedness properties of solutions.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139350737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the Dirichlet problem for the nonlocal parabolic equation of the Kirchhoff type [ u_{t}-aleft(|u|_{L^{p}(Omega)}^{p}right)sumlimits_{i=1}^{n}D_{i}left( leftvert urightvert ^{p-2}D_{i}uright) +b(x,t) leftvert u rightvert ^{alpha left( x,tright) -2}ulog|u|=fleft( x,tright) quad text{in $Q_T=Omega times (0,T)$}, ] where $pgeq2$, $T>0$, $Omega subsetmathbb{R}^{n}$, $ngeq 2$, is a smooth bounded domain. The coefficient $a(cdot)$ is real-valued function defined on $mathbb{R}_+$. It is shown that the problem has a weak solution under appropriate and general conditions on $a(cdot)$, $alpha(cdot,cdot)$ and $b(cdot)$.
{"title":"Existence for a nonlocal porous medium equations of Kirchhoff type with logarithmic nonlinearity","authors":"Uğur Sert","doi":"10.47000/tjmcs.1260780","DOIUrl":"https://doi.org/10.47000/tjmcs.1260780","url":null,"abstract":"We study the Dirichlet problem for the nonlocal parabolic equation of the Kirchhoff type [ u_{t}-aleft(|u|_{L^{p}(Omega)}^{p}right)sumlimits_{i=1}^{n}D_{i}left( leftvert urightvert ^{p-2}D_{i}uright) +b(x,t) leftvert u rightvert ^{alpha left( x,tright) -2}ulog|u|=fleft( x,tright) quad text{in $Q_T=Omega times (0,T)$}, ] where $pgeq2$, $T>0$, $Omega subsetmathbb{R}^{n}$, $ngeq 2$, is a smooth bounded domain. The coefficient $a(cdot)$ is real-valued function defined on $mathbb{R}_+$. It is shown that the problem has a weak solution under appropriate and general conditions on $a(cdot)$, $alpha(cdot,cdot)$ and $b(cdot)$.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139350710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A spine curve moves through the middle of a canal or a tubular surface. It might be asked whether it is possible to carry a spine curve over a tubular surface. For a tubular surface, we have seen that it can be done. In this study, we have given the general equations of a canal surface and a tubular surface according to a focal curve. In this case, we found the fundamental curvatures of a tubular surface. We gave theorems and proofs about the focal curve being a special curve.
{"title":"Tubular Surfaces According to a Focal Curve in E^3","authors":"Abdullah Yildirim","doi":"10.47000/tjmcs.1092714","DOIUrl":"https://doi.org/10.47000/tjmcs.1092714","url":null,"abstract":"A spine curve moves through the middle of a canal or a tubular surface. It might be asked whether it is possible to carry a spine curve over a tubular surface. For a tubular surface, we have seen that it can be done. In this study, we have given the general equations of a canal surface and a tubular surface according to a focal curve. In this case, we found the fundamental curvatures of a tubular surface. We gave theorems and proofs about the focal curve being a special curve.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dima Alnahas, Abdullah Ateş, A. Aydin, Baris Baykant Alagöz
Relation graphs provide useful tools for structural and relational analyses of highly complex multi-component systems. Probabilistic relation graph models can represent relations between system components by their probabilistic links. These graph types have been widely used for graphical representation of Markov models and bigram probabilities. This study presents an implication of relational similarities within probabilistic graph models of textual entries. The article discusses several utilization examples of two fundamental similarity measures in probabilistic analysis of short texts. To this end, construction of probabilistic graph models by using bigram probability matrices of textual entries is illustrated and vector spaces of input word-vectors and output word-vectors are formed. In this vector space, utilization of cosine similarity and mean squared error measures are demonstrated to evaluate probabilistic relational similarity between lexeme pairs in short texts. By using probabilistic relation graphs of the short texts, relational interchangeability analyses of lexeme pairs are conducted, and confidence index parameters are defined to express reliability of these analyses. Potential applications of these graphs in language processing and linguistics are discussed on the basis of the analysis results of example texts.
{"title":"Revisiting Probabilistic Relation Analysis: Using Probabilistic Relation Graphs for Relational Similarity Analysis of Words in Short Texts","authors":"Dima Alnahas, Abdullah Ateş, A. Aydin, Baris Baykant Alagöz","doi":"10.47000/tjmcs.1240729","DOIUrl":"https://doi.org/10.47000/tjmcs.1240729","url":null,"abstract":"Relation graphs provide useful tools for structural and relational analyses of highly complex multi-component systems. Probabilistic relation graph models can represent relations between system components by their probabilistic links. These graph types have been widely used for graphical representation of Markov models and bigram probabilities. This study presents an implication of relational similarities within probabilistic graph models of textual entries. The article discusses several utilization examples of two fundamental similarity measures in probabilistic analysis of short texts. To this end, construction of probabilistic graph models by using bigram probability matrices of textual entries is illustrated and vector spaces of input word-vectors and output word-vectors are formed. In this vector space, utilization of cosine similarity and mean squared error measures are demonstrated to evaluate probabilistic relational similarity between lexeme pairs in short texts. By using probabilistic relation graphs of the short texts, relational interchangeability analyses of lexeme pairs are conducted, and confidence index parameters are defined to express reliability of these analyses. Potential applications of these graphs in language processing and linguistics are discussed on the basis of the analysis results of example texts.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139351316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The first and second derivatives of a curve provide us fundamental information in the study of the behavior of curve near a point. However, if a curve is a polynomial space curve of degree n, we don’t know what is the geometric meaning of the n-th derivative of the curve? There is no doubt that the Frenet frame is not suitable for this purpose because it is constructed by using first and second derivatives of a curve. On the other hand, in this paper by using a new frame called as Flc-frame we are able to give the geometric meaning of the n-th derivative of a curve. Moreover, we explore some basic concepts regarding polynomial space curves from point of view of Flc-frame in three dimensional Euclidean space.
曲线的一阶导数和二阶导数为我们研究曲线在点附近的行为提供了基本信息。然而，如果曲线是一条 n 阶的多项式空间曲线，我们不知道曲线的 n 次导数的几何意义是什么？毫无疑问，Frenet 框架并不适合这一目的，因为它是通过使用曲线的一阶导数和二阶导数来构建的。另一方面，在本文中，通过使用一种称为 Flc 框架的新框架，我们能够给出曲线 n 次导数的几何意义。此外，我们还从 Flc 框架的角度探讨了三维欧几里得空间中有关多项式空间曲线的一些基本概念。
{"title":"On Polynomial Space Curves with Flc-frame","authors":"Mustafa Dede","doi":"10.47000/tjmcs.1127766","DOIUrl":"https://doi.org/10.47000/tjmcs.1127766","url":null,"abstract":"The first and second derivatives of a curve provide us fundamental information in the study of the behavior of curve near a point. However, if a curve is a polynomial space curve of degree n, we don’t know what is the geometric meaning of the n-th derivative of the curve? There is no doubt that the Frenet frame is not suitable for this purpose because it is constructed by using first and second derivatives of a curve. On the other hand, in this paper by using a new frame called as Flc-frame we are able to give the geometric meaning of the n-th derivative of a curve. Moreover, we explore some basic concepts regarding polynomial space curves from point of view of Flc-frame in three dimensional Euclidean space.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"1451 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139358754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we interested in the compostions of integers. Then the combinations of an integer whose each part is odd were examined. O_n = {(2a_1 + 1, ..., 2a_t + 1) : 2a_1 + 1 + ... + 2a_t + 1 = n and a_i positive integer} and we call the set as an odd combination set On set of an integer n . Then an action on the set are defined. Then the decomposition of the composition sets of a positive integer has been examined by using set theory. Then we also focused on the combination of an integer n whose sum is less than a fixed integer m. We have obtained the composition set of an integer whose largest part is less than m. Using these sets, we obtained recurrence relations.
在这项研究中，我们对整数的合成很感兴趣。因此，我们研究了各部分均为奇数的整数组合。 O_n = {(2a_1 + 1, ..., 2a_t + 1) : 2a_1 + 1 + ...+ 2a_t + 1 = n 且 a_i 为正整数}，我们称该集合为奇数组合集合 On set of an integer n。然后定义集合上的作用。然后用集合论研究了正整数的组合集的分解。利用这些集合，我们得到了递推关系。
{"title":"A Note on the Composition of a Positive Integer whose Parts are Odd Integers","authors":"Busra Al, Mustafa Alkan","doi":"10.47000/tjmcs.1166566","DOIUrl":"https://doi.org/10.47000/tjmcs.1166566","url":null,"abstract":"In this study, we interested in the compostions of integers. Then the combinations of an integer whose each part is odd were examined. O_n = {(2a_1 + 1, ..., 2a_t + 1) : 2a_1 + 1 + ... + 2a_t + 1 = n and a_i positive integer} and we call the set as an odd combination set On set of an integer n . Then an action on the set are defined. Then the decomposition of the composition sets of a positive integer has been examined by using set theory. Then we also focused on the combination of an integer n whose sum is less than a fixed integer m. We have obtained the composition set of an integer whose largest part is less than m. Using these sets, we obtained recurrence relations.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139369355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define and study the new topological operator called Gamma-boundary operator Bd^{Gamma} by using local closure function in ideal topological spaces. We investigate important properties of this operator and we specialize Gamma-boundary of some special sets, such as theta-open, I_{Gamma}-perfect and I_{Gamma}-dense. Moreover, we examine the properties of this operator in the topology which is formed by using local closure function. Furthermore, we compare Gamma-boundary operator with the boundary operator and the *-boundary operator. We also showed that under what conditions Gamma-boundary operator, boundary operator and *-boundary operator are coincide.
{"title":"On a Topological Operator via Local Closure Function","authors":"A. Tunç, Sena ÖZEN YILDIRIM","doi":"10.47000/tjmcs.1195540","DOIUrl":"https://doi.org/10.47000/tjmcs.1195540","url":null,"abstract":"In this paper, we define and study the new topological operator called Gamma-boundary operator Bd^{Gamma} by using local closure function in ideal topological spaces. We investigate important properties of this operator and we specialize Gamma-boundary of some special sets, such as theta-open, I_{Gamma}-perfect and I_{Gamma}-dense. Moreover, we examine the properties of this operator in the topology which is formed by using local closure function. Furthermore, we compare Gamma-boundary operator with the boundary operator and the *-boundary operator. We also showed that under what conditions Gamma-boundary operator, boundary operator and *-boundary operator are coincide.","PeriodicalId":506513,"journal":{"name":"Turkish Journal of Mathematics and Computer Science","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139369968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：