In this paper, we consider β-change of Finsler metric L given by L = f(L; β), where f is any positively homogeneous function of degree one in L and β. The objectives of the paper are to obtain the β-change of a Riemannian space, projective change of Finsler metric and to discuss the special cases of one-form β.
{"title":"β-Change of Riemannian Space and Special Cases of one-form β","authors":"Khageshwar Mandal","doi":"10.3126/jnms.v1i1.42172","DOIUrl":"https://doi.org/10.3126/jnms.v1i1.42172","url":null,"abstract":"In this paper, we consider β-change of Finsler metric L given by L = f(L; β), where f is any positively homogeneous function of degree one in L and β. The objectives of the paper are to obtain the β-change of a Riemannian space, projective change of Finsler metric and to discuss the special cases of one-form β.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129966557","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 article deals with the Jeep Problem (also known as Desert Crossing Problem), which reads as follows: An unlimited supply of fuel is available at one edge of a desert, but there is no source on the desert itself. A vehicle can carry enough fuel to go a certain distance, and it can built up its own refuelling stations. What is the minimum amount of fuel the vehicle will require in order to cross the desert? Under these mild conditions this question is answered since the 1940s. But what is the answer if the caches are restricted to certain areas or if the fuel consumption does not depend linearly on the distance travelled? To answer these and similar questions we develop and solve a flexible mixed-integer programming (MIP) model for the classical problem and enhance it with new further aspects of practical relevance.
{"title":"The Jeep Problem: A Flexible MIP Formulation","authors":"U. Gotzes, C. Gotzes","doi":"10.3126/jnms.v1i1.42168","DOIUrl":"https://doi.org/10.3126/jnms.v1i1.42168","url":null,"abstract":"This article deals with the Jeep Problem (also known as Desert Crossing Problem), which reads as follows: An unlimited supply of fuel is available at one edge of a desert, but there is no source on the desert itself. A vehicle can carry enough fuel to go a certain distance, and it can built up its own refuelling stations. What is the minimum amount of fuel the vehicle will require in order to cross the desert? Under these mild conditions this question is answered since the 1940s. But what is the answer if the caches are restricted to certain areas or if the fuel consumption does not depend linearly on the distance travelled? To answer these and similar questions we develop and solve a flexible mixed-integer programming (MIP) model for the classical problem and enhance it with new further aspects of practical relevance.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125806835","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 the present work, subordination results for function f(z)γ belonging to a new class of analytic function Snγ (α, β, j) defined using the concept of Hadamard product are obtained. Also coeffcient estimates, growth and distortion properties for function f(z)γ in the class RSnγ (α, β, j) of Bessel type are equally investigated.
{"title":"Subordination Results Associated With Generalized Bessel Functions","authors":"Hamzat Olusegun","doi":"10.3126/jnms.v2i1.33016","DOIUrl":"https://doi.org/10.3126/jnms.v2i1.33016","url":null,"abstract":"In the present work, subordination results for function f(z)γ belonging to a new class of analytic function Snγ (α, β, j) defined using the concept of Hadamard product are obtained. Also coeffcient estimates, growth and distortion properties for function f(z)γ in the class RSnγ (α, β, j) of Bessel type are equally investigated.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127696972","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}
Khim B. Khattri, Parameshwari Kattel, B. M. Tuladhar
Here, we consider a newly constructed generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The model is a set of coupled partial differential equations with new mechanical description of generalized bulk and shear viscosities, pressure, velocities and effective friction. The dynamical variables, physical parameters, inertial and dynamical coeffcients and drift factors involved in the equations contain certain important physics of mixture flow. So, we analyze the behaviour of some inertial and dynamical coeffcients involved in the model. These coeffcients strongly depend upon the initial material composition. We also simulate the evolution of the dynamical variables so as to reveal their strong non-linear behaviours. Through simulations, we also analyze the front position of the debris material, bottom-slip velocity and maximum velocity, which show fundamentally different dynamics for varied material compositions, from dilute to dense flows. Generalized mixture viscosity decreases as the ow moves downslope, and the rate at which it decreases depends upon the initial solid-volume fraction. We also compare the effective viscosity and the bulk mixture viscosity with respect to the norm of the strain rate tensors to reveal different non-linear behaviours.
{"title":"Some Simulation Results and Parameter Analyses of a Generalized Quasi Two-Phase Bulk Mixture Model","authors":"Khim B. Khattri, Parameshwari Kattel, B. M. Tuladhar","doi":"10.3126/jnms.v2i1.33015","DOIUrl":"https://doi.org/10.3126/jnms.v2i1.33015","url":null,"abstract":"Here, we consider a newly constructed generalized quasi two-phase bulk model for a rapid flow of a debris mixture consisting of viscous fluid and solid particles down a channel. The model is a set of coupled partial differential equations with new mechanical description of generalized bulk and shear viscosities, pressure, velocities and effective friction. The dynamical variables, physical parameters, inertial and dynamical coeffcients and drift factors involved in the equations contain certain important physics of mixture flow. So, we analyze the behaviour of some inertial and dynamical coeffcients involved in the model. These coeffcients strongly depend upon the initial material composition. We also simulate the evolution of the dynamical variables so as to reveal their strong non-linear behaviours. Through simulations, we also analyze the front position of the debris material, bottom-slip velocity and maximum velocity, which show fundamentally different dynamics for varied material compositions, from dilute to dense flows. Generalized mixture viscosity decreases as the ow moves downslope, and the rate at which it decreases depends upon the initial solid-volume fraction. We also compare the effective viscosity and the bulk mixture viscosity with respect to the norm of the strain rate tensors to reveal different non-linear behaviours.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126965062","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":"Rings close to strongly von Neumann regular","authors":"P. Danchev","doi":"10.3126/jnms.v2i1.33013","DOIUrl":"https://doi.org/10.3126/jnms.v2i1.33013","url":null,"abstract":"Abstract with the full text.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114148709","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 presents the investigation of the motion of infinitesimal body in the circular restricted five-body problem in which four bodies are taken as heterogeneous oblate spheroid with different densities in three layers and sources of radiation pressure. These four primaries are moving on the circumference of a circle and form a kite configuration. After evaluating the equations of motion and Jacobi-integral, we study the numerical part of the paper such as equilibria, zero-velocity curves and regions of motion. Finally, we examine the stability of the equilibria and observed that all the equilibria are unstable.
{"title":"Heterogeneous Oblate Primaries in Photo-gravitational CR5BP with Kite Configuration","authors":"A. A. Ansari, P. Kumar, M. Alam","doi":"10.3126/jnms.v2i1.33012","DOIUrl":"https://doi.org/10.3126/jnms.v2i1.33012","url":null,"abstract":"This paper presents the investigation of the motion of infinitesimal body in the circular restricted five-body problem in which four bodies are taken as heterogeneous oblate spheroid with different densities in three layers and sources of radiation pressure. These four primaries are moving on the circumference of a circle and form a kite configuration. After evaluating the equations of motion and Jacobi-integral, we study the numerical part of the paper such as equilibria, zero-velocity curves and regions of motion. Finally, we examine the stability of the equilibria and observed that all the equilibria are unstable.","PeriodicalId":401623,"journal":{"name":"Journal of Nepal Mathematical Society","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121983357","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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