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Turkish Journal of Mathematics and Computer Science最新文献

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New Results on a Partial Differential Equation with General Piecewise Constant Argument 关于具有一般片断常数论证的偏微分方程的新结果
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-08-14 DOI: 10.47000/tjmcs.1166651
Marat Akhmet, Duygu Aruğaslan Çinçin, Zekeriya Özkan
{"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}
引用次数: 0
Existence for a nonlocal porous medium equations of Kirchhoff type with logarithmic nonlinearity 具有对数非线性的基尔霍夫型非局部多孔介质方程的存在性
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-08-14 DOI: 10.47000/tjmcs.1260780
Uğur Sert
{"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}
引用次数: 0
Tubular Surfaces According to a Focal Curve in E^3 根据 E^3 中焦点曲线的管状表面
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-08-11 DOI: 10.47000/tjmcs.1092714
Abdullah Yildirim
{"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}
引用次数: 0
Revisiting Probabilistic Relation Analysis: Using Probabilistic Relation Graphs for Relational Similarity Analysis of Words in Short Texts 重温概率关系分析：使用概率关系图对短文中的词语进行关系相似性分析
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-08-08 DOI: 10.47000/tjmcs.1240729
Dima Alnahas, Abdullah Ateş, A. Aydin, Baris Baykant Alagöz
{"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}
引用次数: 0
On Polynomial Space Curves with Flc-frame 用 Flc 框论多项式空间曲线
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-07-17 DOI: 10.47000/tjmcs.1127766
Mustafa Dede
{"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}
引用次数: 0
A Note on the Composition of a Positive Integer whose Parts are Odd Integers 关于部分为奇数整数的正整数的组成的说明
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-20 DOI: 10.47000/tjmcs.1166566
Busra Al, Mustafa Alkan
{"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}
引用次数: 0
On a Topological Operator via Local Closure Function 通过局部封闭函数论拓扑算子
Turkish Journal of Mathematics and Computer Science Pub Date : 2023-06-15 DOI: 10.47000/tjmcs.1195540
A. Tunç, Sena ÖZEN YILDIRIM
{"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}
引用次数: 0
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