Certain problems concerning polynomials and transcendental entire functions of exponential type

Soit $\displaystyle P(z):=\sum_{\nu=0}^na_\nu z^{\nu}$ un polynôme de degré $n$ et $\displaystyle M:=\sup_{|z|=1}|P(z)|.$ Sans aucne restriction suplémentaire, on sait que $|P'(z)|\leq Mn$ pour $|z|\leq 1$ (inégalité de Bernstein). Si nous supposons maintenant que les zéros du polynôme $P$ sont à l'extérieur du cercle $|z|=k,$ quelle amélioration peut-on apporter à l'inégalité de Bernstein? Il est déjà connu [{\bf \ref{Mal1}}] que dans le cas où $k\geq 1$ on a $$(*) \qquad |P'(z)|\leq \frac{n}{1+k}M \qquad (|z|\leq 1),$$ qu'en est-il pour le cas où $k < 1$? Quelle est l'inégalité analogue à $(*)$ pour une fonction entière de type exponentiel $\tau ?$ D'autre part, si on suppose que $P$ a tous ses zéros dans $|z|\geq k \, \, (k\geq 1),$ quelle est l'estimation de $|P'(z)|$ sur le cercle unité, en terme des quatre premiers termes de son développement en série entière autour de l'origine. Cette thèse constitue une contribution à la théorie analytique des polynômes à la lumière de ces questions.

How to pick a fight : Visualisation and sharing in catastrophic times

In a post September 11 era “the fight”, as a cultural construct, could hardly be more pertinent. We are seemingly forever poised on the edge of controversial U.S. led attacks on wayward Middle Eastern states and unexamined oppositions between the concepts of ‘good’ and ‘evil’ are evoked as valid justifications for battle. Our leaders muster us into wars of vigilance and national cohesion against unseen, unknown and uncomprehended terrorists hiding where communists once lurked under our beds. The articles in this issue examine fights in terms of media strategies and cultural divides in a range of contexts.

One year on and flood victims pick up the pieces

"For many Australians, January 10 last year is just a media memory — a vision of cars surfing down inner-city creeks in Toowoomba CBD and houses floating across farm paddocks in the Lockyer Valley. But for the people of the Lockyer Valley who were clinging to life, the terrifying visions of that day remain every time they close their eyes."

The cross-talk of LDL-cholesterol with cell migration: Insights from the Niemann Pick Type C1 mutation

Cholesterol is considered indispensible for the recruitment and functioning of integrins in focal adhesions for cell migration. However, the physiological cholesterol pools that control integrin trafficking and focal adhesion assembly remain unclear. Using Niemann Pick Type C1 (NPC) mutant cells, which accumulate Low Density lipoprotein (LDL)-derived cholesterol in late endosomes (LE), several recent studies indicate that LDL-cholesterol has multiple roles in regulating focal adhesion dynamics. Firstly, targeting of endocytosed LDL-cholesterol from LE to focal adhesions controls their formation at the leading edge of migrating cells. Other newly emerging literature suggests that this may be coupled to vesicular transport of integrins, Src kinase and metalloproteases from the LE compartment to focal adhesions. Secondly, our recent work identified LDL-cholesterol as a key factor that determines the distribution and ability of several Soluble NSF Attachment Protein (SNAP) Receptor (SNARE) proteins, key players in vesicle transport, to control integrin trafficking to the cell surface and extracellular matrix (ECM) secretion. Collectively, dietary, genetic and pathological changes in cholesterol metabolism may link with efficiency and speed of integrin and ECM cell surface delivery in metastatic cancer cells. This commentary will summarize how direct and indirect pathways enable LDL-cholesterol to modulate cell motility.

Julius Pick aged 93 at his grandson Gary Godshaw's Bar Mitzvah; Buffalo, New York Portraits Men

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Hal Godshaw (Gottschalk) with his wife Anne nee Pick Portraits Couples

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Albert Einstein with violin, Josef Schwarz at piano, and Boris Schwarz in background; Haberlandstrasse 5, Berlin Portraits Groups; Men

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Czech Gendarmes Throwing Away Half Cigarette Stumps for Jews to Pick Up Artworks

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Julius Pick aged 93 at his grandson Gary Godshaw's Bar Mitzvah; Buffalo, New York Portraits Men

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Outdoor group portrait, Haus Horst Changer?, including Ernst Peter Pick (first row center) Portraits Groups

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Two Men Pick Axing

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Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.