Related papers: Notes on isotropic geometry of production models
A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the…
In this article we obtain classification results on the quasi-product production functions in terms of the geometry of their associated graph hypersurfaces, generalizing in a new setting some recent results concerning basic production…
We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to…
The conventional functional form of the Constant-Elasticity-of-Substitution (CES) production function is a general production function nesting a number of other forms of production functions. Examples of such functions include Leontief,…
More than thirty years ago, Charnes, Cooper and Schinnar (1976) established an enlightening contact between economic production functions (EPFs) -- a cornerstone of neoclassical economics -- and information theory, showing how a…
In their seminal 1928 work, Charles Cobb and Paul Douglas empirically validated the Cobb-Douglas production function through statistical analysis of U.S. economic data from 1899 to 1923. While this established the function's theoretical…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production…
We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions…
We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we…
Recently isotropic basis functions of $N$ unit vector arguments were presented; these are of significant use in measuring the N-Point Correlation Functions (NPCFs) of galaxy clustering. Here we develop the generating function for these…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
While the notion of isometric deformations of surfaces is straightforward for surfaces with Euclidean metric, a corresponding notion in isotropic space has been missing. By making Gauss' Theorema Egregium a necessary condition we develop a…
Open cell foams have diverse industrial applications e.g. heat exchangers, structured reactors, filtration due to their unique properties such as high porosity and high specific surface area. In order to theoretically determine the…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
The concept of asymmetric copulas is revisited and is made more precise. We give a rigorous topological argument for opportunity to define asymmetry measures defined recently by K.F Siburg [6] through exhibiting at least three ordered…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…