First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35
首先证明了dunkl型极大算子Mα在广义dunkl型Morrey空间Mp，ω，α上对1 < p <∞和从空间M1，ω，α到弱空间WM1，ω，α上是有界的。证明了dunkl型分数阶积分算子Iβ，α， 0 < β < 2α+ 2有界于广义dunkl型Morrey空间Mp，ω，α到Mq，ωp/q，α，其中β/(2α + 2) = 1/p−1/q, 1 < p < (2α+ 2)/β。学科分类:42B20、42B25、42B35
{"title":"ON THE BOUNDEDNESS OF DUNKL-TYPE FRACTIONAL INTEGRAL OPERATOR IN THE GENERALIZED DUNKL-TYPE MORREY SPACES","authors":"Y. Mammadov, S. Hasanli","doi":"10.12732/IJAM.V31I2.4","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.4","url":null,"abstract":"First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"11 1","pages":"211-230"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87524363","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 SUFFICIENT CONDITIONS FOR THE CLASS ~$mathcal{U}$","authors":"S. Avdiji, N. Tuneski","doi":"10.12732/ijam.v31i2.10","DOIUrl":"https://doi.org/10.12732/ijam.v31i2.10","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"220 1","pages":"289-297"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87925978","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}
This paper discusses on the construction of condensed Fibonacci trees and present the Markov chain corresponding to the condensed Fibonacci trees. An n × n finite Markov probability transition matrix for this Markov chain is presented and it is proved that the limiting steady state probabilities are proportional to the first n Fibonacci numbers. AMS Subject Classification: 05C07, 05C38, 05C75, 05C85
{"title":"LIMITING PROBABILITY TRANSITION MATRIX OF A CONDENSED FIBONACCI TREE","authors":"K. A. Germina","doi":"10.12732/IJAM.V31I2.6","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.6","url":null,"abstract":"This paper discusses on the construction of condensed Fibonacci trees and present the Markov chain corresponding to the condensed Fibonacci trees. An n × n finite Markov probability transition matrix for this Markov chain is presented and it is proved that the limiting steady state probabilities are proportional to the first n Fibonacci numbers. AMS Subject Classification: 05C07, 05C38, 05C75, 05C85","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"171 1","pages":"241-249"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88461087","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}
By a graph, we mean a finite, connected, undirected planar graph without loops or multiple edges. By a planar graph, we mean that it can be drawn in a plane such that no two edges intersect. Duplication of an edge e = uv by a vertex v in a graph G is a new graph G where V (G) = V (G)∪{v} and E(G) = E(G)∪{uv, vv}. Vertex duplication of a path Pn, denoted by P̂n is formed by duplicating all the vertices of Pn, n ≥ 2. Vertex duplication of a cycle Cn, denoted by Ĉn, is formed by duplicating all the vertices of Cn, n ≥ 3, where n ≡ 0(mod 2). The middle graph M(G) is the graph whose vertex set is V (G)∪E(G) and two vertices are adjacent in M(G) if and only if either they are adjacent vertices
图是指一个有限的、连通的、无向的平面图，没有环或多条边。所谓平面图，是指它可以画在一个平面上，使两条边不相交。图G中的顶点v对边e = uv的复制是一个新的图G，其中v (G) = v (G)∪{v}和e (G) = e (G)∪{uv, vv}。路径Pn(记为Pn)的顶点复制是通过复制Pn (n≥2)的所有顶点而形成的。一个循环Cn的顶点复制，记为Ĉn，是通过复制Cn的所有顶点，n≥3，其中n≡0(mod 2)而形成的。中间图M(G)是顶点集为V (G)∪E(G)的图，并且当且仅当其中一个顶点相邻时，M(G)中的两个顶点相邻
{"title":"ON $F$-FACE MAGIC MEAN LABELING OF SOME DUPLICATED GRAPHS","authors":"S. Arockiaraj, A. Kumari","doi":"10.12732/IJAM.V31I2.5","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.5","url":null,"abstract":"By a graph, we mean a finite, connected, undirected planar graph without loops or multiple edges. By a planar graph, we mean that it can be drawn in a plane such that no two edges intersect. Duplication of an edge e = uv by a vertex v in a graph G is a new graph G where V (G) = V (G)∪{v} and E(G) = E(G)∪{uv, vv}. Vertex duplication of a path Pn, denoted by P̂n is formed by duplicating all the vertices of Pn, n ≥ 2. Vertex duplication of a cycle Cn, denoted by Ĉn, is formed by duplicating all the vertices of Cn, n ≥ 3, where n ≡ 0(mod 2). The middle graph M(G) is the graph whose vertex set is V (G)∪E(G) and two vertices are adjacent in M(G) if and only if either they are adjacent vertices","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"40 1","pages":"231-240"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78809361","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 COMBINATORIAL PROPERTIES OF THE TERNARY THUE-MORSE WORD","authors":"B. K. 'ega","doi":"10.12732/ijam.v31i2.2","DOIUrl":"https://doi.org/10.12732/ijam.v31i2.2","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"66 1","pages":"181-197"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89017186","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 consider the effect of van der Waals intermolecular forces on instability problems occurring in thin liquid film pattern formation induced by an electric field. The physical setup is a layer of thin liquid film sandwiched between two electrodes and separated by an air gap from the top mask electrode. We formulate the nonlinear parabolic fourth order thin film equation by deriving van der Waals forces, electric induced forces and incorporate the surface tension in the model. In the long wavelength limit, we find that perturbations at the interface undergo regulated dynamics and the initial film thickness plays a critical role in the pattern formation process. AMS Subject Classification: 35B36, 65P40, 76A20, 76E17
{"title":"EFFECT OF INTERMOLECULAR FORCES ON THIN FILM INSTABILITY","authors":"E. Tian","doi":"10.12732/IJAM.V31I2.1","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.1","url":null,"abstract":"We consider the effect of van der Waals intermolecular forces on instability problems occurring in thin liquid film pattern formation induced by an electric field. The physical setup is a layer of thin liquid film sandwiched between two electrodes and separated by an air gap from the top mask electrode. We formulate the nonlinear parabolic fourth order thin film equation by deriving van der Waals forces, electric induced forces and incorporate the surface tension in the model. In the long wavelength limit, we find that perturbations at the interface undergo regulated dynamics and the initial film thickness plays a critical role in the pattern formation process. AMS Subject Classification: 35B36, 65P40, 76A20, 76E17","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"1 1","pages":"171-180"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90349483","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, during one-parameter closed planar homothetic motions, the Steiner area formula and the polar moment of inertia were expressed. The Steiner point or Steiner normal concepts were described according to whether rotation number is different zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results obtained in the first section of this study were applied for this motion. AMS Subject Classification: 53A17, 70B10
{"title":"CHARACTERISTIC DIRECTIONS OF CLOSED PLANAR HOMOTHETIC MOTIONS","authors":"A. Tutar, O. Sener, E. Inan","doi":"10.12732/IJAM.V31I2.3","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.3","url":null,"abstract":"In this paper, during one-parameter closed planar homothetic motions, the Steiner area formula and the polar moment of inertia were expressed. The Steiner point or Steiner normal concepts were described according to whether rotation number is different zero or equal to zero, respectively. The moving pole point was given with its components and its relation between Steiner point or Steiner normal was specified. The sagittal motion of a telescopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results obtained in the first section of this study were applied for this motion. AMS Subject Classification: 53A17, 70B10","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"36 1","pages":"199"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77792886","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 analysis of Urysohn-Stieltjes integral operators has been studied in [1]. Here we study the existence of weakly solution of functional integral equations of Urysohn-Stieltjes type and Hammerstien-Stieltjes type in the reflexive Banach space E. Also, we prove the existence of the weak maximal and weak minimal solutions. AMS Subject Classification: 26A42, 35D30, 47H30
{"title":"ON THE WEAK SOLUTIONS OF THE URYSOHN-STIELTJES FUNCTIONAL INTEGRAL EQUATIONS","authors":"A. El-Sayed, M. M. Al-Fadel","doi":"10.12732/IJAM.V31I2.8","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.8","url":null,"abstract":"The analysis of Urysohn-Stieltjes integral operators has been studied in [1]. Here we study the existence of weakly solution of functional integral equations of Urysohn-Stieltjes type and Hammerstien-Stieltjes type in the reflexive Banach space E. Also, we prove the existence of the weak maximal and weak minimal solutions. AMS Subject Classification: 26A42, 35D30, 47H30","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"40 1","pages":"263-277"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77783870","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 a new iterative technique, named as residual power series (RPS) method, is applied to find the approximate solution of the nonlinear time-fractional Benjamin-Bona-Mahony (BBM) equation. The results obtained by numerical experiments are compared with the analytical solutions to confirm the accuracy and efficiency of the proposed technique. AMS Subject Classification: 41A58, 34A08, 26A33
{"title":"ANALYTICAL SOLUTION OF TIME-FRACTIONAL NONLINEAR BENJAMIN-BONA-MAHONY EQUATION BY RESIDUAL POWER SERIES METHOD","authors":"M. Bayrak, M. Bayrak","doi":"10.12732/IJAM.V31I2.7","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.7","url":null,"abstract":"In this paper a new iterative technique, named as residual power series (RPS) method, is applied to find the approximate solution of the nonlinear time-fractional Benjamin-Bona-Mahony (BBM) equation. The results obtained by numerical experiments are compared with the analytical solutions to confirm the accuracy and efficiency of the proposed technique. AMS Subject Classification: 41A58, 34A08, 26A33","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"35 1","pages":"251-262"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82648864","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}
J. Interlando, José Othon Dantas Lopes, T. P. D. N. Neto
A classical problem in lattice theory is to determine whether a given lattice can be realized as OK -lattice, where OK is the ring of integers of some number field K. In this work we show that the lattice D4 can be realized as an OF -lattice for infinitely many totally real biquadratic fields F . AMS Subject Classification: 11H06, 11H31, 11R16
{"title":"A NEW NUMBER FIELD CONSTRUCTION OF THE $D_4$-LATTICE","authors":"J. Interlando, José Othon Dantas Lopes, T. P. D. N. Neto","doi":"10.12732/IJAM.V31I2.11","DOIUrl":"https://doi.org/10.12732/IJAM.V31I2.11","url":null,"abstract":"A classical problem in lattice theory is to determine whether a given lattice can be realized as OK -lattice, where OK is the ring of integers of some number field K. In this work we show that the lattice D4 can be realized as an OF -lattice for infinitely many totally real biquadratic fields F . AMS Subject Classification: 11H06, 11H31, 11R16","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"42 1","pages":"299-305"},"PeriodicalIF":0.0,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87385481","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}
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