Visualizing Vectors in 2-D and 3-D Prof. Mike May Test for primes Prof. Mike May Conversion of data formats Prof. Mike May Color Plate: Function of Two Variables in Cartesian Coordinates Prof. Mike May Caesar codes I Prof. Mike May Accuracy of error correcting codes Prof. Mike Ma...
This paper introduces a concept of differentiability for functions in several variables which has a very natural definition and shares all the properties one expects of a notion of differentiability, but is shown to be weaker than the usual concept of differentiability defined as local linearizability...
The aforementioned power grid problems are naturally, in their exact formulation, non-convex, non-differentiable and sometimes non-continuous. Some of these shortcomings can be compensated by applying assumptions on the differentiability of OFs [56] and the continuity of discrete design variables [57,...
Derivatives of implicit functions is the process of differentiating an implicit equation with respect to the desired variable x while treating the other variables as unspecified functions of x. Derivatives of inverse trigonometric functions are the process of finding angles for the given trigonometric val...
We revisit the assumption of differentiability of solutions with respect to exogenous variables in the differential games literature (e.g., Ling and Caputo (J Optim Theory Appl 149:151–174, 2011). We show that differentiability can be replaced with a weaker condition that preserves the sign of...
var foo(const var& x, const var& y) { if(x < 1) return y; else if(y < 1) return x; else return x / foo(x / 2, y) + y * foo(x, y / 3); } To test it, we declare two instances of var. var x=10; var y=13; Variables with respect to which differentiation is ...
The extension of the Diamond-Stiglitz result is accomplished via Hadamard differentiability which provides a natural tool for the derivation of comparative statics results when the changes in the underlying distribution is “smooth” relative to changes in the exogenous variables. Our comparative statics ...
It is shown that the stress velocities of the body have fractional derivatives of order - up to the boundary in the direction of the loading parameter, and of order - in the interior of the body in direction of the space variables.doi:10.1002/zamm.201100023...
This paper is devoted to the study of approximate and global smoothness and smoothness along curves of functions f(x_1,... ,x_m) of variables x_1,... ,x_m in infinite fields with nontrivial non-Archimedean valuations and relations between them. Theorems on classes of smoothness C~n or...
The analogue of Lagrange’s theorem is also valid in the case of a real function of several variables, even when the domain of the function is not necessarily open, nor is the differential necessarily unique at all points of the observed segment in the domain. Theorem 7. Let 𝑋⊂ℝ...