Pub Date : 2020-03-20DOI: 10.36753/mathenot.622522
B. Tiryakioglu
Diffraction of sound wave through a cavity with partial lining is analyzed rigorously. By using the Fourier transform technique in conjunction with the Mode Matching method, the related boundary value problem is formulated as a Wiener-Hopf equation. In the solution, three infinite sets of unknown coefficients are involved that satisfy three infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The influence of the different parameters such as the lining length, cavity depth, etc. on the diffraction are illustrated graphically. A perfect agreement is observed when the results of diffracted field are compared numerically with a similar work existing in the literature.
{"title":"Sound Wave Diffraction by a Cavity with Partial Lining","authors":"B. Tiryakioglu","doi":"10.36753/mathenot.622522","DOIUrl":"https://doi.org/10.36753/mathenot.622522","url":null,"abstract":"Diffraction of sound wave through a cavity with partial lining is analyzed rigorously. By using the Fourier transform technique in conjunction with the Mode Matching method, the related boundary value problem is formulated as a Wiener-Hopf equation. In the solution, three infinite sets of unknown coefficients are involved that satisfy three infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The influence of the different parameters such as the lining length, cavity depth, etc. on the diffraction are illustrated graphically. A perfect agreement is observed when the results of diffracted field are compared numerically with a similar work existing in the literature.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128091721","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.651519
A. Yildiz
The object of the present paper is to characterize paracontact metric (k,µ)-manifolds satisfying some semisymmetry curvature conditions.
本文的目的是刻画满足某些半对称曲率条件的副接触度量(k，µ)流形。
{"title":"Certain Semisymmetry Curvature Conditions on Paracontact Metric $(k,mu )$-Manifolds","authors":"A. Yildiz","doi":"10.36753/mathenot.651519","DOIUrl":"https://doi.org/10.36753/mathenot.651519","url":null,"abstract":"The object of the present paper is to characterize paracontact metric (k,µ)-manifolds satisfying some semisymmetry curvature conditions.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116141142","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.644261
Azam A. Imomov, Yorqin Khodjaev
The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements combinatorics.
本文研究了可涉及多个回合的回合方案。提出了简化公式，允许直接计算概率，而不使用元素组合。
{"title":"Some remarks on a direct calculation of Probabilities in Urn Schemes","authors":"Azam A. Imomov, Yorqin Khodjaev","doi":"10.36753/mathenot.644261","DOIUrl":"https://doi.org/10.36753/mathenot.644261","url":null,"abstract":"The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements combinatorics.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124604643","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.685084
M. Güner
The explanation of the ground state magnetic properties of odd-mass nuclei is very informative in understanding of the complex structure of the deformed nuclei. The ground-state magnetic moments of most of the odd-A deformed nuclei have been measured by various experimental studies and there are numerous studies in the literature. However, many of the theoretical studies on magnetic moments and spin polarization effects affecting them are far from explaining these measured values. In this paper, the magnetic moments and effective spin g factors of 143,145,147Sm isotopes in the lanthanides region of the periodic table were investigated within the framework of the Quasiparticle-Phonon Nuclear Model (QPNM) for the first time. Spin-spin interaction parameters (χ) were determined by comparing theoretical and experimental values of magnetic moments of the related isotopes and it was determined that these interactions were found to have an isovector character (q = -1). It has been observed that the ground-state structures of the studied isotopes are weakly affected by quasiparticlephonon interactions and the contribution of these interactions ( values) to the ground-state wave functions is quite small (around 0.01%). Theoretical explanation of the renormalization of spin gyromagnetic factor is one of the most important problems of nuclear structure physics. The results obtained in this study for the effective spin gyromagnetic factor also agree with the phenological value .
{"title":"Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{rm{Sm}}$ Isotopes","authors":"M. Güner","doi":"10.36753/mathenot.685084","DOIUrl":"https://doi.org/10.36753/mathenot.685084","url":null,"abstract":"The explanation of the ground state magnetic properties of odd-mass nuclei is very informative in understanding of the complex structure of the deformed nuclei. The ground-state magnetic moments of most of the odd-A deformed nuclei have been measured by various experimental studies and there are numerous studies in the literature. However, many of the theoretical studies on magnetic moments and spin polarization effects affecting them are far from explaining these measured values. In this paper, the magnetic moments and effective spin g factors of 143,145,147Sm isotopes in the lanthanides region of the periodic table were investigated within the framework of the Quasiparticle-Phonon Nuclear Model (QPNM) for the first time. Spin-spin interaction parameters (χ) were determined by comparing theoretical and experimental values of magnetic moments of the related isotopes and it was determined that these interactions were found to have an isovector character (q = -1). It has been observed that the ground-state structures of the studied isotopes are weakly affected by quasiparticlephonon interactions and the contribution of these interactions ( values) to the ground-state wave functions is quite small (around 0.01%). Theoretical explanation of the renormalization of spin gyromagnetic factor is one of the most important problems of nuclear structure physics. The results obtained in this study for the effective spin gyromagnetic factor also agree with the phenological value .","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130611157","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.627066
G. C. H. Güleç
Recently, Hazar and Sarigol have defined and studied the series space |C₋₁|_{p} for 1≤p<∞ in [1]. The aim of this study is to introduce a new paranormed space |C₋₁|(p), where p=(p_{k}) is a bounded sequence of positive real numbers, which extends the results of Hazar and Sarigol in [1] to paranormed space. Besides this, we investigate topological properties and compute the α-,β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|C₋₁|(p),μ) and (μ,|C₋₁|(p)), where μ is any given sequence spaces
{"title":"A new paranormed series space and matrix transformations","authors":"G. C. H. Güleç","doi":"10.36753/mathenot.627066","DOIUrl":"https://doi.org/10.36753/mathenot.627066","url":null,"abstract":"Recently, Hazar and Sarigol have defined and studied the series space |C₋₁|_{p} for 1≤p<∞ in [1]. The aim of this study is to introduce a new paranormed space |C₋₁|(p), where p=(p_{k}) is a bounded sequence of positive real numbers, which extends the results of Hazar and Sarigol in [1] to paranormed space. Besides this, we investigate topological properties and compute the α-,β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|C₋₁|(p),μ) and (μ,|C₋₁|(p)), where μ is any given sequence spaces","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127234824","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.656850
Fatma Karaca
We classify the curvature of interpolating sesqui-harmonic Legendre curves in generalized Sasakian space forms. We investigate the necessary and sufficient conditions for these types of curves in nine cases to be interpolating sesqui-harmonic.
{"title":"A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves","authors":"Fatma Karaca","doi":"10.36753/mathenot.656850","DOIUrl":"https://doi.org/10.36753/mathenot.656850","url":null,"abstract":"We classify the curvature of interpolating sesqui-harmonic Legendre curves in generalized Sasakian space forms. We investigate the necessary and sufficient conditions for these types of curves in nine cases to be interpolating sesqui-harmonic.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130086276","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.616086
Nil Mansuroğlu
In literature, there are many papers on the sum of element orders of a finite group. In this study, in particular, we deal with the cases in finite p -groups. Our main aim is to investigate the sums of element orders in finite p -groups and to give some properties of such sums. Let ( G ) denote the sum of element orders of a finite group G . As an immediate consequence, we proved that psi( G ) ≤ 3 /4 psi ( C ) and psi( G ) < 1/ p - 1psi ( C ), where G is a non-cyclic finite p -group of order p^ r and C is a cyclic group of order p^ r for some prime p .
{"title":"Some properties on sums of element orders in finite p-groups","authors":"Nil Mansuroğlu","doi":"10.36753/mathenot.616086","DOIUrl":"https://doi.org/10.36753/mathenot.616086","url":null,"abstract":"In literature, there are many papers on the sum of element orders of a finite group. In this study, in particular, we deal with the cases in finite p -groups. Our main aim is to investigate the sums of element orders in finite p -groups and to give some properties of such sums. Let ( G ) denote the sum of element orders of a finite group G . As an immediate consequence, we proved that psi( G ) ≤ 3 /4 psi ( C ) and psi( G ) < 1/ p - 1psi ( C ), where G is a non-cyclic finite p -group of order p^ r and C is a cyclic group of order p^ r for some prime p .","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"12 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123451804","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}
Pub Date : 2020-03-20DOI: 10.36753/mathenot.621602
A. Cihan, A. Z. Azak, M. Güngör
In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
{"title":"On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients","authors":"A. Cihan, A. Z. Azak, M. Güngör","doi":"10.36753/mathenot.621602","DOIUrl":"https://doi.org/10.36753/mathenot.621602","url":null,"abstract":"In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131594421","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}
Pub Date : 2020-02-26DOI: 10.36753/mathenot.598635
Y. Uçar, Murat Yağmurlu, Ihsan Celikkaya
The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation U_{t}+UU_{x}=vU_{xx} two simpler sub problems U_{t}+UU_{x}=0 and U_{t}-vU_{xx}=0 have been obtained. A discretization process has been performed for each of these sub-problems and the stability analyzes have been carried out by Fourier (von Neumann) series method. Then, both sub-problems have been solved using the Strang splitting technique to obtain numerical results. To see the effectiveness of the present method, which is a combination of finite element method and Strang splitting technique, we have calculated the frequently used error norms ‖e‖₁, L₂ and L_{∞} in the literature and have made a comparison between exact and a numerical solution.
{"title":"Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting","authors":"Y. Uçar, Murat Yağmurlu, Ihsan Celikkaya","doi":"10.36753/mathenot.598635","DOIUrl":"https://doi.org/10.36753/mathenot.598635","url":null,"abstract":"The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation U_{t}+UU_{x}=vU_{xx} two simpler sub problems U_{t}+UU_{x}=0 and U_{t}-vU_{xx}=0 have been obtained. A discretization process has been performed for each of these sub-problems and the stability analyzes have been carried out by Fourier (von Neumann) series method. Then, both sub-problems have been solved using the Strang splitting technique to obtain numerical results. To see the effectiveness of the present method, which is a combination of finite element method and Strang splitting technique, we have calculated the frequently used error norms ‖e‖₁, L₂ and L_{∞} in the literature and have made a comparison between exact and a numerical solution.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"55 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132575514","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}
Pub Date : 2020-02-19DOI: 10.36753/mathenot.650271
Ş. Altınkaya, S. Yalçın
In this present investigation, based on the $(p,q)$-Lucas polynomials, we want to build a bridge between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields.
{"title":"Some applications of the (p,q)-Lucas polynomials to the bi-univalent function class $Sigma $","authors":"Ş. Altınkaya, S. Yalçın","doi":"10.36753/mathenot.650271","DOIUrl":"https://doi.org/10.36753/mathenot.650271","url":null,"abstract":"In this present investigation, based on the $(p,q)$-Lucas polynomials, we want to build a bridge between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132134025","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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