Differential Inequalities and Univalent Functions

Let ${\mathcal M}$ be the class of analytic functions in the unit disk \ID with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition \left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right |\leq 1, \quad z\in \ID. Functions in $\mathcal{M}$ are known to be univalent in \ID. In this paper, it is shown that the harmonic mean of two functions in ${\mathcal M}$ are closed, that is, it belongs again to ${\mathcal M}$. This result also holds for other related classes of normalized univalent functions. A number of new examples of functions in $\mathcal{M}$ are shown to be starlike in \ID. However we conjecture that functions in $\mathcal{M}$ are not necessarily starlike, as apparently supported by other examples.Comment: 10 pages; To appear in Lobachevskii Journal of Mathematic

Optimization of a charge-state analyzer for ECRIS beams

A detailed experimental and simulation study of the extraction of a 24 keV He-ion beam from an ECR ion source and the subsequent beam transport through an analyzing magnet is presented. We find that such a slow ion beam is very sensitive to space-charge forces, but also that the neutralization of the beam's space charge by secondary electrons is virtually complete for beam currents up to at least 0.5 mA. The beam emittance directly behind the extraction system is 65 pi mm mrad and is determined by the fact that the ion beam is extracted in the strong magnetic fringe field of the ion source. The relatively large emittance of the beam and its non-paraxiality lead, in combination with a relatively small magnet gap, to significant beam losses and a five-fold increase of the effective beam emittance during its transport through the analyzing magnet. The calculated beam profile and phase-space distributions in the image plane of the analyzing magnet agree well with measurements. The kinematic and magnet aberrations have been studied using the calculated second-order transfer map of the analyzing magnet, with which we can reproduce the phase-space distributions of the ion beam behind the analyzing magnet. Using the transfer map and trajectory calculations we have worked out an aberration compensation scheme based on the addition of compensating hexapole components to the main dipole field by modifying the shape of the poles. The simulations predict that by compensating the kinematic and geometric aberrations in this way and enlarging the pole gap the overall beam transport efficiency can be increased from 16 to 45%

On the Bohr inequality for the Cesáro operator

We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is also estimated

Therapeutic effect of hydroethanolic extract of Trianthema portulacastrum L. against N-Nitroso-N-Methylurea-induced mammary tumors in Wistar rats

406-415This study evaluated the therapeutic action of hydroethanolic extract of Trianthema portulacastrum L. (TPE) on N-nitroso-N-methylurea (NMU)-induced mammary tumors in Wistar rats. A hydroethanolic was prepared and subjected to qualitative and quantitative phytochemical screening. After acclimatization, Wistar rats were divided into 4 groups of 6 rats each: Group A (vehicle control), Group B (TPE control), Group C (TPE treatment) and group D (NMU control). NMU (50 mg/kg body weight) was injected intraperitoneally at 50, 80 and 110 days of age. After the induction of palpable tumors, the rats were administered 200 mg/kg bw of TPE by oral gavage for 2 months. The treatment with TPE significantly (pin vivo therapeutic action of TPE extract on NMU-induced mammary tumors. TPE exhibited antitumor activity through its antiproliferative, antiangiogenic, pro-apoptotic, and estrogen receptor-modulatory properties

On the Bohr inequality for the Cesáro operator

We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is also estimated

Therapeutic effect of hydroethanolic extract of Trianthema portulacastrum L. against N-Nitroso-N-Methylurea-induced mammary tumors in Wistar rats

This study evaluated the therapeutic action of hydroethanolic extract of Trianthema portulacastrum L. (TPE) on N-nitroso-N-methylurea (NMU)-induced mammary tumors in Wistar rats. A hydroethanolic was prepared and subjected to qualitative and quantitative phytochemical screening. After acclimatization, Wistar rats were divided into 4 groups of 6 rats each: Group A (vehicle control), Group B (TPE control), Group C (TPE treatment) and group D (NMU control). NMU (50 mg/kg body weight) was injected intraperitoneally at 50, 80 and 110 days of age. After the induction of palpable tumors,the rats were administered 200 mg/kg bw of TPE by oral gavage for 2 months. The treatment with TPE significantly (p<0.05) decreased tumor incidence, frequency, size and malignancy in comparison to the tumor-bearing rats that were not administered TPE. Immunohistochemical analysis revealed that TPE treatment significantly reduced the expression of PCNA, VEGF, ER-α and ER-β, and caused non-significant reductions in matrix metallopeptidase-9 (MMP-9). Caspase-3 expression significantly increased in TPE-treated rats in comparison with NMU-treated controls. The qRT-PCR resultsshowed PCNA and ER-β expression was down regulated and caspase-3 expression was up regulated in the TPE-treated group. The present study showed the in vivo therapeutic action of TPE extract on NMU-induced mammary tumors. TPE exhibited antitumor activity through its antiproliferative, antiangiogenic, pro-apoptotic, and estrogen receptor-modulatory properties

Phase diagram of aggregation of oppositely charged colloids in salty water

Aggregation of two oppositely charged colloids in salty water is studied. We focus on the role of Coulomb interaction in strongly asymmetric systems in which the charge and size of one colloid is much larger than the other one. In the solution, each large colloid (macroion) attracts certain number of oppositely charged small colloids ($Z$-ion) to form a complex. If the concentration ratio of the two colloids is such that complexes are not strongly charged, they condense in a macroscopic aggregate. As a result, the phase diagram in a plane of concentrations of two colloids consists of an aggregation domain sandwiched between two domains of stable solutions of complexes. The aggregation domain has a central part of total aggregation and two wings corresponding to partial aggregation. A quantitative theory of the phase diagram in the presence of monovalent salt is developed. It is shown that as the Debye-H\"{u}ckel screening radius $r_s$ decreases, the aggregation domain grows, but the relative size of the partial aggregation domains becomes much smaller. As an important application of the theory, we consider solutions of long double-helix DNA with strongly charged positive spheres (artificial chromatin). We also consider implications of our theory for in vitro experiments with the natural chromatin. Finally, the effect of different shapes of macroions on the phase diagram is discussed.Comment: 10 pages, 9 figures. The text is rewritten, but results are not change