We derive iterative methods for computing the Fréchet derivative of the map which 4 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 5 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 6 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 7 identity that relates the ...

Doppler images of the cool spot distribution on the RS CVn-type star HD 106225 are presented. These images, for Epoch 1995.14, were derived using four photospheric lines. The spot distribution is characterized by a large (radius = 20◦) spot at latitude 45◦ and a weak polar spot with an appendage. The polar spot is considerably smaller than similar features found on other RS CVn stars. The rotat...

Many prokaryotic protein complexes underlie polar asymmetry. In Caulobacter crescentus, a flagellum is built exclusively at the pole that arose from the previous cell division. The basis for this pole specificity is unclear but could involve a cytokinetic birth scar that marks the newborn pole as the flagellum assembly site. We identified two developmental proteins, TipN and TipF, which localiz...

We have synthesised novel ionic liquids (ILs) to show both cellulose dissolution ability and LCST-type phase transition after mixing with water. To realise both polar and hydrophobic properties, tetraalkylphosphonium cations and a series of carboxylate anions were employed to assume hydrophobic and highly polar properties, respectively. Effects of their alkyl chain length on the water compatibi...

—A system for measuring the dielectric properties of cereal grains from 1 to 350 MHz with a coaxial sample holder is presented. A signal-flow graph model was used to determine the permittivity of several polar alcohols from the full two-port S-parameter measurements. At the lowest frequencies 1-25 MHz where the phase measurements are less accurate, a lumped-parameter model was used to predict t...

Present-day surface wind stress climatology is manipulated to simulate wind conditions during the last glacial maximum. These estimated wind fields force a onelayer, wind-driven numerical model of the southern ocean to determine if a change in the strength of the surface wind stress can shift the location of the Antarctic Polar Front, which is part of the Antarctic Circumpolar Current. A change...

We derive iterative methods for computing the Fréchet derivative of the map which 6 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 7 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 8 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 9 identity that relates the ...

We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices as well as rectangular matrices having more rows than columns. Our derivation relies on a novel identity that relates the Fréchet ...

We propose a new stream cipher called “Polar Bear”. It combines constructions used successfully in other situations. The key initialization uses Rijndael, the steady state uses a dynamic table as in RC4 and we guarantee a long period through the use of a linear feedback shiftregister. The efficiency for short messages is better than that of RC4 while for long messages Polar Bear is about a fact...