P. Walters, `A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function', Dynam. Systems 18 (2003) 131-138, 271-278.A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-...
In the paper “Iterated function systems consisting of continuous functions satisfying Banach’s orbital condition” (An. Univ. Timi?oara, Ser. Mat.-Inform., in print), Miculescu, Mihail and Savu introduced iterated function systems consisting of continuous functions satisfying Banach’s orbital ...
where the function b is prescribed. In case of b = 0, it is the so-called homogenous Dirichlet boundary condition. That means that everything which reaches the boundary disappears. Neumann boundary condition: ∇u(x,t)⋅n(x)=b(x,t)forx∈∂Ω,t>0.n denotes the outer normal to...
We say that a function f (x) satisfies the Dirichlet conditions on the interval [a, b] if it is bounded on that interval and if the interval [a, b] can be partitioned into a finite number of subintervals inside each of which the function f (x) is continuous and monotonic. View cha...
for all [Math Processing Error]φ∈Cc∞(Ω,Rm) we have [Math Processing Error]∫Ω∇f(Bu)⋅Bφ=0; (d) The map [Math Processing Error]u↦f(u) is sequentially weakly-[Math Processing Error]∗ continuous from [Math Processing Error]L∞(Ω,Rd)∩kerA to [Math Processing ...
Find a value of b so that the function f(x) = x - b, x < 1 bx^2 + 2, x greater than or equal to 1 is continuous on (-negative infinity, infinity). 1) For values of the constant a and b are the following functions continuous on (-infinity, ...
Iff:R→Ris a function satisfying the propertyf(x+1)+f(x+3)=2for allx∈Rthanfis View Solution Let f be the continuous and differentiable function such that f(x)=f(2-x),∀x∈Rand g(x)=f(1+x), then View Solution A polynomial function f(x) satisfies the condition ...
In this paper,we give a new equivalent definition of the convex function.We also prove that the convex functionf(x)defined on (a,b) is continuous and furthermore,when f″(x) exists,f(x) is convex if and only if f″(x)0.关键词: continuity differentiability convex function necessary and...
For Abelian gauge theory, generator of the Wilson line (12) is a continuous function on R4 given that n⋅A(x) is continuous in R4. In fact, the Wilson line (12) can be written as(13)exp(ig∫0x3dzn⋅A(x0,x1,x2,z)) for Abelian gauge theory. Generator of the Wilson ...
It is interesting that, even for uniformly spaced Δn, there exists a continuous function g on [−1, 1] such that the (Lagrange) interpolating polynomials pn(t) to yi = g(tni), i = 1, … , n, do not converge uniformly to g(t) on [−1, 1]. This leads to the study of...