Assume that \(f\) lies in the class of starlike functions order \(\alpha\in[0,1)\), is, which are regular and univalent for \(|z|<1\) such that
 Re\(\left(\frac{zf'(z)}{f(z)}\right)>\alpha\) \(|z|<1.\)
 In this paper we show each following sharp inequality holds:
 \(|f(re^{i\theta})|^{-1}\int_{0}^{r}|f'(ue^{i\theta})|\,du\leq\frac{\Gamma(\frac{1}{2})\Gamma(2-\alph...

IN THE TITLE COMPOUND (SYSTEMATIC NAME (R)-dimeth-yl{2-[1-phenyl-1-(pyridin-2-yl)eth-oxy]eth-yl}aza-nium (R,R)-3-carb-oxy-2,3-dihy-droxy-propano-ate), C(17)H(23)N(2)O(+)·C(4)H(5)O(6) (-), the doxylaminium cation is protonated at the N atom. The tartrate monoanions are linked by short, almost linear O-H⋯O hydrogen bonds into chains extended along [100]. These chains are inter-linked by anion-pyr...

We discuss the anomalous behavior of Faraday (transmission) and polar Kerr (reflection) rotation angles propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries ordinary dielectric slab. It shown that, for a given set parameters describing system, ...

In many scienti c and commercial applications such as Earth Observation System (EOSDIS) and mobile phone services tracking a large number of clients, it is a daunting task to archive and index ever increasing volume of complex data that are continuously added to databases. To eÆciently manage multidimensional data in scienti c and data warehousing environments, R-tree based index structures hav...

This paper classifies the even unimodular lattices that have a structure as a Hermitian OK-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For arbitrary imaginary quadratic fields we derive ...

We report new measurements of mixing of passive temperature field in a turbulent flow. The use of low temperature helium gas allows us to span a range of microscale Reynolds number, R(lambda), from 100 to 650. The exponents xi(n) of the temperature structure functions approximately r(xi(n)) are shown to saturate to xi(infinity) approximately 1.45+/-0...

In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...

We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set $$s_1, \ldots , s_n \in {\mathbb {R}}^p$$ with corresponding responses $$t_1,\ldots ,t_n {R}}^q$$ fitting k-layer network $$\nu _\theta : {R}}^p \rightarrow involves estimation of weights $$\theta {R}}^m$$ via an ERM: $$\begin{aligned} \inf _{\theta {R}}^m} \ \sum _{i=...