We measured the shape and the internal dynamics of starlike dendrimers under good solvent conditions with small-angle neutron scattering and neutron spin-echo (NSE) spectroscopy, respectively. Architectural parameters such as the spacer length and generation were varied in a systematic manner. Structural changes occurring in the dendrimers as a function of these parameters are discussed, i.e., ...

The transmission of a vertex v graph G is the sum distances from to all other vertices in . A irregular if its have pairwise different transmissions. starlike tree T ( k 1 , … t ) obtained by attaching an isolated pendant paths lengths respectively. It proved that + ? 2 odd order, then it irregular. ? 3 and only ? { r : } Additional infinite families among trees bi-starlike are determined. Tran...

In [6] it was shown that if f ∈ is starlike of order α, α= 0.294, . . . , so is the Libera integral operator F . We also know that (see, e.g., [1]) there are functions which are univalent or spiral-like in so that their Libera integral operators are not univalent or spiral-like in . Li and Owa [5] proved that if f ∈ is univalent in , then Fn(z) is starlike in |z| < 3/8. The number 3/8 is sharp....

We say that a class F consisting of analytic functions f(z)=?n=0?anzn in the unit disk D:={z?C:|z|<1} satisfies Bohr phenomenon if there exists rf?(0,1) such that?n=1?|anzn|?d(f(0),?f(D)) for every function f?F and |z|=r?rf, where d is Euclidean distance. The largest radius rf F. In this paper, we establish classes Ma-Minda type starlike convex as well with respect to boundary point.

"A normalized function $f$ on the open unit disc is starlike (or convex) univalent if associated $zf'(z)/f(z)$ $1+zf''(z)/f'(z)$) a with positive real part. The radius of starlikeness or convexity usually obtained by using estimates for functions Using subordination, we examine various starlikeness, in particular, radii Janowski and order $\beta$, when either convex $(zf'(z)+\alpha z^2f''(z))/f...

Using the Lebedev–Milin inequalities, bounds on logarithmic coefficients of an analytic function can be transferred to estimates itself and related functions. From this fact, study logarithmic-related problems a certain subclass univalent functions has attracted much attention in recent years. In our present investigation, starlike Se* connected with exponential mapping was considered. The main...