A measurable map with analytic domain and metrizable range is quotient

Real Analytic Solutions of Parabolic Equations with Time-measurable Coefficients

We use Bernstein’s technique to show that for any fixed t, strong solutions u(t, x) of the uniformly parabolic equation Lu := aij (t)uxixj−ut = 0 in Q are real analytic in Q(t) = {x : (t, x) ∈ Q}. Here, Q ⊂ Rd+1 is a bounded domain and the coefficients aij(t) are measurable. We also use Bernstein’s technique to obtain interior estimates for pure second derivatives of solutions of the fully nonl...

Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

When is the ring of real measurable functions a hereditary ring?

‎Let $M(X‎, ‎mathcal{A}‎, ‎mu)$ be the ring of real-valued measurable functions‎ ‎on a measure space $(X‎, ‎mathcal{A}‎, ‎mu)$‎. ‎In this paper‎, ‎we characterize the maximal ideals in the rings of real measurable functions‎ ‎and as a consequence‎, ‎we determine when $M(X‎, ‎mathcal{A}‎, ‎mu)$ is a hereditary ring.

A Quadratic Form on the Quotient of a Periodic Map