A Generalization of a Theorem of Dimensional Analysis
نویسنده
چکیده
Any function relating several variables for which admissible scale transformations are specified is assumed to satisfy a functional equation that requires admissible transformations of the independent variables to effect only admissible transformations of the dependent variable. When there are not any dimensional constants that, in effect, cancel out the admissible transformations of the independent variables, this equation severely limits the possible functions relating the variables. The equation is solved for any finite number of variables that are either ratio or interval scales.
منابع مشابه
A generalization of Martindale's theorem to $(alpha, beta)-$homomorphism
Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.
متن کاملGeneralization of Darbo's fixed point theorem and application
In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.
متن کاملTriangularization over finite-dimensional division rings using the reduced trace
In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one...
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl transform
Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.
متن کاملSimultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications
In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.
متن کاملA GENERALIZATION OF A JACOBSON’S COMMUTATIVITY THEOREM
In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.
متن کامل