Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/classification-of-graph-surfaces-induced-by-weighted-homogeneous-6k8TS0eJG0
References (61)
-
L. Hyatt, S. Magleby, L. Howell (2020)
Developable mechanisms on right conical surfacesMechanism and Machine Theory, 149
-
Haila Alodan, Bang‐Yen Chen, Sharief Deshmukh, G. Vîlcu (2015)
On some geometric properties of quasi-product production modelsJournal of Mathematical Analysis and Applications
-
T. Hasanis, Rafael L'opez (2019)
Classification of separable surfaces with constant Gaussian curvaturemanuscripta mathematica, 166
-
Xiaoshu Wang (2016)
A geometric characterization of homogeneous production models in economicsFilomat, 30
-
Aroop Mahanty (1980)
THEORY OF PRODUCTION -
(1983)
Losungmethoden und Losungen -
D. Struik (1951)
Lectures on classical differential geometry -
Bang‐Yen Chen (2013)
Solutions to homogeneous Monge-Amp\`ere equations of homothetic functions and their applications to production models in economicsarXiv: Analysis of PDEs
-
Alina-Daniela Vîlcu, G. Vîlcu (2019)
On Quasi-Homogeneous Production FunctionsSymmetry, 11
-
D. Bayanjargal, B. Yerkyebulan, Ts. Battsukh (2020)
A New Class of Production FunctionTheoretical Economics Letters
-
M Moruz, MI Munteanu (2016)
Minimal translation hypersurfaces in E4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}^4$$\end{document}J. Math. Anal. Appl., 439
-
Bang‐Yen Chen, G. Vîlcu (2013)
Geometric classifications of homogeneous production functionsAppl. Math. Comput., 225
-
G. Vîlcu (2018)
On a generalization of a class of production functionsApplied Economics Letters, 25
-
Alina-Daniela Vîlcu, G. Vîlcu (2011)
On some geometric properties of the generalized CES production functionsAppl. Math. Comput., 218
-
Rafael L'opez, Marilena Moruz (2014)
Translation and homothetical surfaces in Euclidean space with constant curvaturearXiv: Differential Geometry
-
A. Haraux, T. Pham (2015)
On the Lojasiewicz exponents of quasi-homogeneous functions -
A. Hankey, H. Stanley (1972)
Systematic Application of Generalized Homogeneous Functions to Static Scaling, Dynamic Scaling, and UniversalityPhysical Review B, 6
-
MJOM Classification of Graph Surfaces Induced -
W Eichhorn, W Oettli (1969)
Mehrproduktunternehmungen mit linearen expansionswegenOper. Res. Verfahren., 6
-
Marilena Moruz, M. Munteanu (2016)
Minimal translation hypersurfaces in E4Journal of Mathematical Analysis and Applications, 439
-
C. Ioan, G. Ioan (2011)
A generalization of a class of production functionsApplied Economics Letters, 18
-
Gheorghe Mihoc-Caius Iacob -
G. Vîlcu (2011)
A geometric perspective on the generalized Cobb-Douglas production functionsAppl. Math. Lett., 24
-
M. Aydın, M. Ergut (2014)
Composite functions with Allen determinants and their applications to production models in economicsTamkang Journal of Mathematics, 45
-
J. Donato (1994)
MINIMAL SURFACES IN ECONOMIC THEORY -
SK Mishra (2010)
A brief history of production functionsIUP J. Manage. Econ., 8
-
D. Anosov, S. Aranson, V. Arnold, I. Bronshtein, Y. Ilyashenko, V. Grines (1997)
Ordinary differential equations and smooth dynamical systems -
Xiaoshu Wang, Yu Fu (2013)
Some Characterizations of the Cobb-Douglas and CES Production Functions in MicroeconomicsAbstract and Applied Analysis, 2013
-
King-Tim Mak (1988)
General Homothetic Production Correspondences -
M. Aydın, A. Mihai (2015)
Classification of Quasi-Sum Production Functions with Allen DeterminantsFilomat, 29
-
T. Nelson, Trent Zimmerman, S. Magleby, R. Lang, L. Howell (2019)
Developable mechanisms on developable surfacesScience Robotics, 4
-
CW Cobb, PH Douglas (1928)
A theory of productionAm. Econ. Rev., 18
-
R. Solow (1956)
A Contribution to the Theory of Economic GrowthQuarterly Journal of Economics, 70
-
V. Toponogov, V. Rovenski (2005)
Differential Geometry of Curves and Surfaces: A Concise Guide -
Yu Fu, Wei Wang (2017)
Geometric characterizations of quasi-product production models in economicsFilomat, 31
-
A. Goriely (2001)
Integrability and Nonintegrability of Dynamical Systems -
Tadashi Inoue (1984)
On the Shape of the Production Possibility Frontier with More Commodities than Primary FactorsInternational Economic Review, 25
-
W. Eichhorn, W. Oettli (1969)
Mehrproduktunternehmungen mit linearen Expansionswegenaequationes mathematicae, 2
-
Tadashi Inoue, L. Wegge (1986)
On the Geometry of the Production Possibility FrontierInternational Economic Review, 27
-
GA Khatskevich, AF Pranevich (2017)
On quasi-homogeneous production functions with constant elasticity of factors substitutionJ. Belarus. State Univ. Econ., 1
-
M. Cheng, Mingyin Xiang (2020)
Application of a modified CES production function model based on improved firefly algorithmJournal of Industrial & Management Optimization
-
Jacob Greenwood, S. Magleby, L. Howell (2019)
Developable mechanisms on regular cylindrical surfacesMechanism and Machine Theory, 142
-
L. Losonczi (2010)
Production functions having the CES property -
Sudhanshu Mishra (2007)
A Brief History of Production FunctionsHistory of Economics eJournal
-
Alina-Daniela Vîlcu, G. Vîlcu (2014)
Some characterizations of the quasi-sum production models with proportional marginal rate of substitutionComptes Rendus Mathematique, 353
-
Huili Liu (1999)
Translation surfaces with constant mean curvature in 3-dimensional spacesJournal of Geometry, 64
-
Bjarne Jensen (1994)
The Dynamic Systems of Basic Economic Growth Models -
(1947)
Methods of Mathematical PhysicsNature, 160
-
W. Eichhorn (1970)
Theorie der homogenen Produktionsfunktion -
R. Shephard (1971)
Some remarks on the theory of homogeneous production functionsZeitschrift für Nationalökonomie, 31
-
Haila Alodan, Bang‐Yen Chen, Sharief Deshmukh, G. Vîlcu (2012)
On some geometric properties of quasi-sum production modelsJournal of Mathematical Analysis and Applications, 392
-
R. Färe, R. Shephard (1977)
Ray-Homothetic Production Functions.Econometrica, 45
-
F. Reynès (2017)
The Cobb-Douglas function as a flexible function: A new perspective on homogeneous functions through the lens of output elasticitiesMath. Soc. Sci., 97
-
S. Lawrence (2011)
Developable Surfaces: Their History and ApplicationNexus Network Journal, 13
-
(2013)
A note on the isotropical geometry of production surfaces -
Romania e-mail: daniela.vilcu@upg-ploiesti.ro -
H. Quevedo, M. Quevedo, A. Sánchez (2018)
Quasi-homogeneous black hole thermodynamicsThe European Physical Journal C, 79
-
Kenzo Abe, Hisayuki Okamoto, M. Tawada (1986)
A Note on the Production Possibility Frontier with Pure Public Intermediate GoodsCanadian Journal of Economics, 19
-
Haila Alodan, Bang‐Yen Chen, Sharief Deshmukh, G. Vîlcu (2021)
Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditionsAdvances in Difference Equations, 2021
-
M. Cheng, Yun Han (2020)
Application of a modified CES production function model based on improved PSO algorithmAppl. Math. Comput., 387
-
M. Kemp, C. Khang, Yasuo Uekawa (1978)
On the flatness of the transformation surfaceJournal of International Economics, 8
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022
- ISSN
- 1660-5446
- eISSN
- 1660-5454
- DOI
- 10.1007/s00009-022-02106-2
- Publisher site
- See Article on Publisher Site
Abstract
Developable surfaces are surfaces in three-dimensional Euclidean space with zero Gaussian curvature. If these surfaces are explicitly defined in the functional form z=f(x,y)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$z=f(x,y)$$\end{document}, then f is nothing but a solution of the homogeneous Monge–Ampère equation. The main aim of this paper is to classify developable surfaces defined as graphs of weighted-homogeneous functions and to apply the result in economic analysis. We establish a complete classification of weighted-homogeneous production models through associated production surfaces, proving that there exist five classes of weighted-homogeneous production functions exhibiting vanishing Gaussian curvature, generalizing the result established in Chen and Vîlcu (Appl Math Comput 225, 345–351, 2013), where it was stated that only two classes of homogeneous production functions define developable surfaces, namely those having constant return to scale and those defined by binomial functions. We also propose some challenging problems for further research.
Journal
Mediterranean Journal of Mathematics – Springer Journals
Published: Aug 1, 2022
Keywords: Gauss curvature; developable surface; production surface; return to scale; Primary 53A05; Secondary 91B38