Dickson Kande - Academia.edu (original) (raw)

Papers by Dickson Kande

International Journal of Systems Science and Applied Mathematics

From a mathematical perspective, a surface is a generalization of a plane which does not necessar... more From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametr...

International Journal of Theoretical and Applied Mathematics

Differential geometry is a discipline of mathematics that uses the techniques of calculus and lin... more Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.

Differential geometry is a discipline of mathematics that uses the techniques of calculus and lin... more Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.

From a mathematical perspective, a surface is a generalization of a plane which does not necessar... more From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametric surface is the image of an open subset of the Euclidean plane by a continuous function, in a topological space, generally a Euclidean space of dimension at least three. The paper aims at giving an introduction to the theory of surfaces from differential geometry perspective.

Mathematical Modelling and Applications, 2017

Greenhouses are mainly used with a purpose of improving the environmental conditions in which pla... more Greenhouses are mainly used with a purpose of improving the environmental conditions in which plants are grown. The parameters that affect the growth of plants inside greenhouse, such as air temperature and relative humidity are controlled appropriately. They are done so efficiently to retain relatively low levels of solar energy; but without specialized ventilating and cooling systems, they will quickly fry a crop during high temperature periods. Over the past few decades CFD has been a useful tool in development of numerical models that improve the understanding of the interaction of the gases and vapors constituting micro-climate inside greenhouses. It is however, necessary to perform a CFD analysis to show us the trends, strengths and weaknesses in the use of this tool. This paper discusses an introduction of CFD analysis of airflow and climate inside greenhouses, analyzing the issues that help us understand how it has evolved, as well as trends and limitations on their use.

Mathematical Modelling and Applications, 2017

Greenhouses are mainly used with a purpose of improving the environmental conditions in which pla... more Greenhouses are mainly used with a purpose of improving the environmental conditions in which plants are grown. The parameters that affect the growth of plants inside greenhouse, such as air temperature and relative humidity are controlled appropriately. They are done so efficiently to retain relatively low levels of solar energy; but without specialized ventilating and cooling systems, they will quickly fry a crop during high temperature periods. Over the past few decades CFD has been a useful tool in development of numerical models that improve the understanding of the interaction of the gases and vapors constituting micro-climate inside greenhouses. It is however, necessary to perform a CFD analysis to show us the trends, strengths and weaknesses in the use of this tool. This paper discusses an introduction of CFD analysis of airflow and climate inside greenhouses, analyzing the issues that help us understand how it has evolved, as well as trends and limitations on their use.

International Journal of Systems Science and Applied Mathematics

From a mathematical perspective, a surface is a generalization of a plane which does not necessar... more From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametr...

International Journal of Theoretical and Applied Mathematics

Differential geometry is a discipline of mathematics that uses the techniques of calculus and lin... more Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.

Differential geometry is a discipline of mathematics that uses the techniques of calculus and lin... more Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.

From a mathematical perspective, a surface is a generalization of a plane which does not necessar... more From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametric surface is the image of an open subset of the Euclidean plane by a continuous function, in a topological space, generally a Euclidean space of dimension at least three. The paper aims at giving an introduction to the theory of surfaces from differential geometry perspective.

Mathematical Modelling and Applications, 2017

Greenhouses are mainly used with a purpose of improving the environmental conditions in which pla... more Greenhouses are mainly used with a purpose of improving the environmental conditions in which plants are grown. The parameters that affect the growth of plants inside greenhouse, such as air temperature and relative humidity are controlled appropriately. They are done so efficiently to retain relatively low levels of solar energy; but without specialized ventilating and cooling systems, they will quickly fry a crop during high temperature periods. Over the past few decades CFD has been a useful tool in development of numerical models that improve the understanding of the interaction of the gases and vapors constituting micro-climate inside greenhouses. It is however, necessary to perform a CFD analysis to show us the trends, strengths and weaknesses in the use of this tool. This paper discusses an introduction of CFD analysis of airflow and climate inside greenhouses, analyzing the issues that help us understand how it has evolved, as well as trends and limitations on their use.

Mathematical Modelling and Applications, 2017

Greenhouses are mainly used with a purpose of improving the environmental conditions in which pla... more Greenhouses are mainly used with a purpose of improving the environmental conditions in which plants are grown. The parameters that affect the growth of plants inside greenhouse, such as air temperature and relative humidity are controlled appropriately. They are done so efficiently to retain relatively low levels of solar energy; but without specialized ventilating and cooling systems, they will quickly fry a crop during high temperature periods. Over the past few decades CFD has been a useful tool in development of numerical models that improve the understanding of the interaction of the gases and vapors constituting micro-climate inside greenhouses. It is however, necessary to perform a CFD analysis to show us the trends, strengths and weaknesses in the use of this tool. This paper discusses an introduction of CFD analysis of airflow and climate inside greenhouses, analyzing the issues that help us understand how it has evolved, as well as trends and limitations on their use.