Pub Date : 2020-05-15DOI: 10.18311/jims/2020/24429
D. R. Bonde, J. N. Chaudhari
In this paper, we introduce the notion of B-ideal in a commutative semiring R. Then 1) A characterization of B-ideals in the Semiring of non-negative integers is obtained. 2) Relation between B-ideals in a semiring R containing a Q-ideal I of R and B-ideals in the quotient semiring R/I(Q) is obtained. Further study of k-Noetherian semirings is developed. Also B-ideals in polynomial semirings are studied.
{"title":"On B-Ideals in Semirings","authors":"D. R. Bonde, J. N. Chaudhari","doi":"10.18311/jims/2020/24429","DOIUrl":"https://doi.org/10.18311/jims/2020/24429","url":null,"abstract":"In this paper, we introduce the notion of <em>B</em>-ideal in a commutative semiring <em>R</em>. Then 1) A characterization of <em>B</em>-ideals in the Semiring of non-negative integers is obtained. 2) Relation between <em>B</em>-ideals in a semiring <em>R</em> containing a <em>Q</em>-ideal <em>I</em> of <em>R</em> and <em>B</em>-ideals in the quotient semiring <em>R/I<sub>(Q)</sub></em> is obtained. Further study of <em>k</em>-Noetherian semirings is developed. Also <em>B</em>-ideals in polynomial semirings are studied.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43138650","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 : 2020-05-15DOI: 10.18311/jims/2020/24874
R. Jana, B. Maheshwari, A. Shukla
An attempt is made to define the extended Pochhammer symbol (λ)n,α which leads to an extension of the classical hypergeometric functions. Differential equations and some properties have also been discussed.
{"title":"Some Results on the Extended Hypergeometric Function","authors":"R. Jana, B. Maheshwari, A. Shukla","doi":"10.18311/jims/2020/24874","DOIUrl":"https://doi.org/10.18311/jims/2020/24874","url":null,"abstract":"An attempt is made to define the extended Pochhammer symbol (λ)n,α which leads to an extension of the classical hypergeometric functions. Differential equations and some properties have also been discussed.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48164720","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 : 2020-05-15DOI: 10.18311/jims/2020/24427
H. Khotimah, Y. Susanti
Let G = (V(G),E(G)) be a simple, connected, undirected graph with non empty vertex set V(G) and edge set E(G) . The function f : V(G) ∪ E(G) ↦ {1,2, ...,k} (for some positive integer k) is called an edge irregular total k −labeling where each two edges ab and cd , having distinct weights, that are f (a)+ f (ab)+ f (b) ≠ f (c)+ f (cd)+ f (d). The minimum k for which G has an edge irregular total k −labeling is denoted by tes (G) and called total edge irregularity strength of graph G . In this paper, we determine the exact value of the total edge irregularity strength of double fan ladder graph, centralized double fan graph, and generalized parachute graph with upper path.
{"title":"On Total Edge Irregularity Strength of Some Graphs Related to Double Fan Graphs","authors":"H. Khotimah, Y. Susanti","doi":"10.18311/jims/2020/24427","DOIUrl":"https://doi.org/10.18311/jims/2020/24427","url":null,"abstract":"Let G = (V(G),E(G)) be a simple, connected, undirected graph with non empty vertex set V(G) and edge set E(G) . The function f : V(G) ∪ E(G) ↦ {1,2, ...,k} (for some positive integer k) is called an edge irregular total k −labeling where each two edges ab and cd , having distinct weights, that are f (a)+ f (ab)+ f (b) ≠ f (c)+ f (cd)+ f (d). The minimum k for which G has an edge irregular total k −labeling is denoted by tes (G) and called total edge irregularity strength of graph G . In this paper, we determine the exact value of the total edge irregularity strength of double fan ladder graph, centralized double fan graph, and generalized parachute graph with upper path.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45601934","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 : 2019-08-22DOI: 10.18311/JIMS/2019/18122
T. D. Rao, S. Chakraverty
In this paper, a novel technique has been developed for solving a general linear dierential equation with fuzzy boundary conditions. The target has been to use the developed technique to solve in particular the radon transport (subsurface soil to buildings) equation with uncertain (fuzzy) boundary conditions. The fuzzy boundary condition has been described by a triangular fuzzy number (TFN). Corresponding results are presented in term of plots and are also compared with crisp ones.
{"title":"Solving Uncertain Differential Equation with Fuzzy Boundary Conditions","authors":"T. D. Rao, S. Chakraverty","doi":"10.18311/JIMS/2019/18122","DOIUrl":"https://doi.org/10.18311/JIMS/2019/18122","url":null,"abstract":"In this paper, a novel technique has been developed for solving a general linear dierential equation with fuzzy boundary conditions. The target has been to use the developed technique to solve in particular the radon transport (subsurface soil to buildings) equation with uncertain (fuzzy) boundary conditions. The fuzzy boundary condition has been described by a triangular fuzzy number (TFN). Corresponding results are presented in term of plots and are also compared with crisp ones.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43911023","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 : 2019-08-22DOI: 10.18311/JIMS/2019/19834
Y. Shoukaku
In this paper we try to improve the conditions of [4]. Consequently, we introduce that L>e-1/e-2(k + 1/λ 1 ) - 1/e-2 is a sufficient condition for the oscillation of all solutions of first order delay differential equation x′(t) + p(t)x(σ(t)) = 0 under the conditions L < 1 and 0 < k
{"title":"Oscillation Theory of First Order Differential Equations with Delay","authors":"Y. Shoukaku","doi":"10.18311/JIMS/2019/19834","DOIUrl":"https://doi.org/10.18311/JIMS/2019/19834","url":null,"abstract":"In this paper we try to improve the conditions of [4]. Consequently, we introduce that L>e-1/e-2(k + 1/λ 1 ) - 1/e-2 is a sufficient condition for the oscillation of all solutions of first order delay differential equation x′(t) + p(t)x(σ(t)) = 0 under the conditions L < 1 and 0 < k </1/e, where k=liminf t→∞ ∫ t σ(t) p(s)ds, L=limsup t→∞ ∫ t σ(t) p(s)ds and λ 1 is the smaller root of the equation λ=e kλ","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42110051","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 : 2019-08-22DOI: 10.18311/JIMS/2019/21637
E. Nasrabadi
Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M B ] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l 1 (S) and u = l 1 (E), for unital and commutative inverse semigroup S with idempotent set E, we show that T as an u-module is (2n - 1)- ideal module amenable while is not module amenable.
设A和B是单位Banach代数，M是单位Banch A，B模。本文定义了Banach代数的（n）-理想模可修性的概念，并研究了三角Banach代数Γ=[A M B]的（2n-1）-理想模块可修性（作为α，B和M是交换Banach u—双模。最后，在A=B=M=l1（S）和u=l1（E）的情况下，对于具有幂等集E的单位交换逆半群S，我们证明了作为u模的T是（2n-1）-理想模服从的，而不是模服从的。
{"title":"Ideal Module Amenability of Triangular Banach Algebras","authors":"E. Nasrabadi","doi":"10.18311/JIMS/2019/21637","DOIUrl":"https://doi.org/10.18311/JIMS/2019/21637","url":null,"abstract":"Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M B ] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l 1 (S) and u = l 1 (E), for unital and commutative inverse semigroup S with idempotent set E, we show that T as an u-module is (2n - 1)- ideal module amenable while is not module amenable.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44711159","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 : 2019-08-22DOI: 10.18311/JIMS/2019/17898
M. Basavaraj
The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr m for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.
{"title":"Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis","authors":"M. Basavaraj","doi":"10.18311/JIMS/2019/17898","DOIUrl":"https://doi.org/10.18311/JIMS/2019/17898","url":null,"abstract":"The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr m for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46488201","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 : 2019-08-22DOI: 10.18311/JIMS/2019/21458
P. Umadevi, N. Nithyadevi, H. Oztop
Convective ow and heat transfer of uid inside a square en- closure having heat generating solid body, with various thermal boundary conditions is investigated numerically. The top wall of the enclosure is adiabatic, both the bottom and right walls are kept at constant temper- ature, while the left wall is heated using sin function. Numerical simu- lations is carried out by solving the governing equations using SIMPLE algorithm by means of the nite-volume method with power-law scheme. The important parameters focused are angle of inclination of the enclo- sure, area ratio of solid-enclosure, Hartmann number and temperature dierence ratio of solid- uid, which are ranges 0 o - 90 o , 0:0625 - 0:5625, 0 - 100 and 0 - 50, respectively. Thermal conductivity ratio of solid- uid is xed as 5 and Rayleigh number as 10 5 .
{"title":"Numerical Study on the Effect of Angle of Inclination on Magnetoconvection Inside Enclosure with Heat Generating Solid Body","authors":"P. Umadevi, N. Nithyadevi, H. Oztop","doi":"10.18311/JIMS/2019/21458","DOIUrl":"https://doi.org/10.18311/JIMS/2019/21458","url":null,"abstract":"Convective ow and heat transfer of uid inside a square en- closure having heat generating solid body, with various thermal boundary conditions is investigated numerically. The top wall of the enclosure is adiabatic, both the bottom and right walls are kept at constant temper- ature, while the left wall is heated using sin function. Numerical simu- lations is carried out by solving the governing equations using SIMPLE algorithm by means of the nite-volume method with power-law scheme. The important parameters focused are angle of inclination of the enclo- sure, area ratio of solid-enclosure, Hartmann number and temperature dierence ratio of solid- uid, which are ranges 0 o - 90 o , 0:0625 - 0:5625, 0 - 100 and 0 - 50, respectively. Thermal conductivity ratio of solid- uid is xed as 5 and Rayleigh number as 10 5 .","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48822587","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 : 2019-08-22DOI: 10.18311/JIMS/2019/22160
M. Abo-Elhamayel, Z. Salleh
In this paper, new concepts of separation axioms are intro- duced in bitopological spaces. The implications of these new separation axioms among themselves as well as with other known separation ax- ioms are obtained. Fundamental properties of the suggested concepts are also investigated. Furthermore, we introduced the concept of R ij - neighborhoods and investigate some of their characterizations.
{"title":"New Separation Axioms in Bitopological Spaces","authors":"M. Abo-Elhamayel, Z. Salleh","doi":"10.18311/JIMS/2019/22160","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22160","url":null,"abstract":"In this paper, new concepts of separation axioms are intro- duced in bitopological spaces. The implications of these new separation axioms among themselves as well as with other known separation ax- ioms are obtained. Fundamental properties of the suggested concepts are also investigated. Furthermore, we introduced the concept of R ij - neighborhoods and investigate some of their characterizations.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47831263","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 : 2019-08-22DOI: 10.18311/JIMS/2019/22515
Rajesh V. Savalia, B. I. Dave
The present work incorporates the general inverse series relations involving p -Pochhammer symbol and p -Gamma function. A general class of p-polynomials is introduced by means of this general inverse pair which is used to derive the generating function relations and summation formulas for certain p -polynomials belonging to this general class. This includes the p -deformation of Jacobi polynomials, the Brafman polynomials and Konhauser polynomials. Moreover, the orthogonal polynomials of Racah and those of Wilson are also provided p-deformation by means of the general inversion pair. The generating function relations and summation formulas for these polynomials are also derived. We then emphasize on the combinatorial identities and obtain their p-deformed versions.
{"title":"A General Inversion Pair and p-deformation of Askey Scheme","authors":"Rajesh V. Savalia, B. I. Dave","doi":"10.18311/JIMS/2019/22515","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22515","url":null,"abstract":"The present work incorporates the general inverse series relations involving p -Pochhammer symbol and p -Gamma function. A general class of p-polynomials is introduced by means of this general inverse pair which is used to derive the generating function relations and summation formulas for certain p -polynomials belonging to this general class. This includes the p -deformation of Jacobi polynomials, the Brafman polynomials and Konhauser polynomials. Moreover, the orthogonal polynomials of Racah and those of Wilson are also provided p-deformation by means of the general inversion pair. The generating function relations and summation formulas for these polynomials are also derived. We then emphasize on the combinatorial identities and obtain their p-deformed versions.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49422621","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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