{"title":"On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group","authors":"Zuhal KUCUKARSLAN YUZBASİ, Sevinç Taze","doi":"10.53570/jnt.1165809","DOIUrl":"https://doi.org/10.53570/jnt.1165809","url":null,"abstract":"This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the TN, NB, and TB Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given TN, NB, and TB Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126420684","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}
{"title":"Random Ensemble MARS: Model Selection in Multivariate Adaptive Regression Splines Using Random Forest Approach","authors":"Dilek Sabancı, M. Cengiz","doi":"10.53570/jnt.1147323","DOIUrl":"https://doi.org/10.53570/jnt.1147323","url":null,"abstract":"Multivariate Adaptive Regression Splines (MARS) is a supervised learning model in machine learning, not obtained by an ensemble learning method. Ensemble learning methods are gathered from samples comprising hundreds or thousands of learners that serve the common purpose of improving the stability and accuracy of machine learning algorithms. This study presented REMARS (Random Ensemble MARS), a new MARS model selection approach obtained using the Random Forest (RF) algorithm. 200 training and test data set generated via the Bagging method were analysed in the MARS analysis engine. At the end of the analysis, two different MARS model sets were created, one yielding the smallest Mean Square Error for the test data (Test MSE) and the other yielding the smallest Generalised Cross-Validation (GCV) value. The best model was estimated for both Test MSE and GCV criteria by examining the error of measurement criteria, variable importance averages, and frequencies of the knot values for each model. Eventually, a new model was obtained via the ensemble learning method, i.e., REMARS, that yields result as good as the MARS model obtained from the original data set. The MARS model, which works better in the larger data set, provides more reliable results with smaller data sets utilising the proposed method.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114429732","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}
{"title":"4-Dimensional 2-Crossed Modules","authors":"Elis SOYLU YILMAZ","doi":"10.53570/jnt.1148482","DOIUrl":"https://doi.org/10.53570/jnt.1148482","url":null,"abstract":"In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in this category. The notion of the subobject is a generalization of ideas like subsets from set theory, subspaces from topology, and subgroups from group theory. We then exemplified subobjects and ideals in the category of 4-Dimensional 2-crossed modules. A quotient object is the dual concept of a subobject. Concepts like quotient sets, spaces, groups, graphs, etc. are generalized with the notion of a quotient object. Using the ideal, we obtain the quotient of two subobjects and prove that the intersection of finite ideals is also an ideal in this category.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134045870","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}
{"title":"Salkowski Curves and Their Modified Orthogonal Frames in $mathbb{E}^{3}$","authors":"Sümeyye GÜR MAZLUM, S. Şenyurt, M. Bektaş","doi":"10.53570/jnt.1140546","DOIUrl":"https://doi.org/10.53570/jnt.1140546","url":null,"abstract":"In this study, we examine some properties of Salkowski curves in $mathbb{E}^{3}$. We then make sense of the angle $(nt)$ in the parametric equation of the Salkowski curves. We provide the relationship between this angle and the angle between the binormal vector and the Darboux vector of the Salkowski curves. Through this angle, we obtain the unit vector in the direction of the Darboux vector of the curve. Finally, we calculate the modified orthogonal frames with both the curvature and the torsion and give the relationships between the Frenet frame and the modified orthogonal frames of the curve.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126073702","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}
{"title":"On the Characterisations of Curves with Modified Orthogonal Frame in $mathbb{E}^{3}$","authors":"Şeyda Özel, M. Bektaş","doi":"10.53570/jnt.1148933","DOIUrl":"https://doi.org/10.53570/jnt.1148933","url":null,"abstract":"This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame in 3-dimensional Euclidean space ($mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves with modified orthogonal frames in $mathbb{E}^{3}$.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"33 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123338228","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}
{"title":"Some New Estimates for Maximal Commutator and Commutator of Maximal Function in $L_{p,lambda}(Gamma)$","authors":"Metin Türkay","doi":"10.53570/jnt.1162966","DOIUrl":"https://doi.org/10.53570/jnt.1162966","url":null,"abstract":"The theory of boundedness of classical operators of real analyses on Morrey spaces defined on Carleson curves has made significant progress in recent years as it allows for various applications. This study obtains new estimates about the boundedness of the maximal commutator operator $M_b$ and the commutator of the maximal function $[M, b]$ in Morrey spaces defined on Carleson curves.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"347 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122477496","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}
{"title":"A New Transformation Method for Solving High-Order Boundary Value Problems","authors":"M. Yücel, F. Muhtarov, O. Mukhtarov","doi":"10.53570/jnt.1171760","DOIUrl":"https://doi.org/10.53570/jnt.1171760","url":null,"abstract":"The main purpose of this work is to provide a new approximation method, the so-called parameterised differential transform method (PDTM), for solving high-order boundary value problems (HOBVPs). Our method is based on the classical differential transform method and differs from it by calculating the coefficients of the solution, which has the form of a series. We applied the proposed new method to fourth-order boundary value problems to substantiate it. The resulting solution is graphically compared with the exact solution and the solutions obtained by the classical DTM and ADM methods.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127428207","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}
{"title":"Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures","authors":"Sezin AYKURT SEPET, Hülya Gün Bozok, M. Aydın","doi":"10.53570/jnt.1137525","DOIUrl":"https://doi.org/10.53570/jnt.1137525","url":null,"abstract":"We study the so-called factorable surfaces in the pseudo-Galilean space, the graphs of the product of two functions of one variable. We then classify these surfaces when the mean and Gaussian curvatures are functions of one variable.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114219855","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}
{"title":"I-Connectedness","authors":"Selahattin Kilinç","doi":"10.53570/jnt.1104540","DOIUrl":"https://doi.org/10.53570/jnt.1104540","url":null,"abstract":"In this paper, we introduce a weak form of connectedness with respect to an ideal. We also investigate its relation to connectedness. We examine the I-connectedness property on the new topology introduced by the ideal. In addition, it is revealed under what conditions I-connectedness and connectedness coincide and one differs from another.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123256839","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}
{"title":"Distribution Formulae of the Solute in Transport of Advection-Dispersion of Air Pollution for Different Wind Velocities and Dispersion Coefficients","authors":"Hemantha U Kumar, M. Pathan, F. Ayant","doi":"10.53570/jnt.1129890","DOIUrl":"https://doi.org/10.53570/jnt.1129890","url":null,"abstract":"In this paper, we obtain certain distribution formulae of the solute in transport of the typical advection-dispersion of air pollution through separation in two-dimensional space variables by introducing different wind velocities and dispersion coefficients. As a consequence, by introducing different values of the solute velocity and dispersion coefficients, we evaluate the solute distribution formulae of the air pollution in terms of various known and unknown special functions.","PeriodicalId":347850,"journal":{"name":"Journal of New Theory","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129493614","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}