‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

Isolates from closely related fungi in the Rhizoctonia species complex were examined for the occurrence of the M2 double-stranded RNA (dsRNA) by amplifying a conserved 1000 nucleotide region of the dsRNA with reverse transcription PCR. The M2 dsRNA was detected in representative isolates belonging to three anastomosis groups (AG) of R. solani (AG-1-IA, AG-4 and AG-6; teleomorph = Thanatephorus)...

The rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. The rational bi-cubic function involves six parameters in each rectangular patch. Data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

The asymptotic spectrum of graphs, introduced by Zuiddam (Combinatorica, 2019), is the space graph parameters that are additive under disjoint union, multiplicative strong product, normalized and monotone homomorphisms between complements. He used it to obtain a dual characterization Shannon capacity graphs as minimum evaluation function over noted several known upper bounds, including Lovász n...

making use of an extended fractional differintegral operator ( introduced recently by patel and mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.

For Denjoy–Carleman differentiable function classes C where the weight sequence M = (Mk) is logarithmically convex, stable under derivations, and non-quasianalytic of moderate growth, we prove the following: A mapping is C if it maps C -curves to C -curves. The category of C -mappings is cartesian closed in the sense that C (E, C (F, G)) = C (E × F, G) for convenient vector spaces. Applications...

We have investigated the characteristics of a silicon oxynitride/silver/silicon oxynitride [SiON/Ag/SiON] multilayer passivation grown using a specially designed roll-to-roll [R2R] sputtering system on a flexible polyethersulfone substrate. Optical, structural, and surface properties of the R2R grown SiON/Ag/SiON multilayer were investigated as a function of the SiON thickness at a constant Ag ...