An improvement of Ozaki’s P-valent conditions

The old result due to[Ozaki,S.:On the theory of multivalent functions Ⅱ.Sci.Rep.Tokyo Bunrika Daigaku Sect.A,45-87(1941)],says that if f(z) = z~p + ∑_(n=p+1~(a_nz~n))~∞ is analytic in a convex domain D and for some real α we have Re{exp(iα)f~((p))(z)} 0 in D,then f(z) is at most p-valent in ED.In this paper,we consider similar problems in the unit disc B = {z ∈ C:|z| 1}.     

Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?

We have synthesized, characterized, and computationally simulated/validated the behavior of two new metal-organic framework (MOF) materials displaying the highest experimental Brunauer-Emmett-Teller (BET) surface areas of any porous materials reported to date (～7000 m(2)/g). Key to evacuating the initially solvent-filled materials without pore collapse, and thereby accessing the ultrahigh areas, is the use of a supercritical CO(2) activation technique. Additionally, we demonstrate computationally that by shifting from phenyl groups to "space efficient" acetylene moieties as linker expansion units, the hypothetical maximum surface area for a MOF material is substantially greater than previously envisioned (～14600 m(2)/g (or greater) versus ～10500 m(2)/g).     

SANDWICH-TYPE THEOREMS FOR MEROMORPHIC MULTIVALENT FUNCTIONS ASSOCIATED WITH THE LIU-SRIVASTAVA OPERATOR＊

The purpose of this article is to obtain some subordination and superordination preserving properties of meromorphic multivalent functions in the punctured open unit disk associated with the Liu-Srivas...