Bridges 1992 has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers wi...

Ice-templating technique offers a viable means for constructing ordered macro-porous architectures in materials; nevertheless, it is generally limited by low efficiency fabrication, large difficulty manipulation, along with the small dimension, and poor structural uniformity of ice-templated materials. Here, new approach was exploited continuous ice-templating uniformly materials based on estab...

Abstract A critical transition for a system modelled by concave quadratic scalar ordinary differential equation occurs when small variation of the coefficients changes dramatically dynamics, from existence an attractor–repeller pair hyperbolic solutions to lack bounded solutions. In this paper, tool analyze phenomenon asymptotically nonautonomous ODEs with uniformly continuous or piecewise is d...

Let R be an o-minimal expansion of a real closed field. Given definable continuous functions f : U → R and : U → (0,+∞), where U is an open subset of Rn, we construct a definable Cm-function g : U → R with |g(x)− f(x)| < (x) for all x ∈ U . Moreover, we show that if f is uniformly continuous, then g can also chosen to be uniformly continuous.

Let H be an ultraspherical hypergroup associated to a locally compact group G and let A(H) the Fourier algebra of H. For left Banach A(H)-submodule X VN(H), define QX norm closure linear span set {u f : u ?A(H), ? X} in BA(H)(A(H),X