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 ...

[1] Bacastow [1996], Broecker et al. [1999], and Archer et al. [2000] have called attention recently to the fact that box models and general circulation models (GCMs) represent the thermal partitioning of CO2 between the warm surface ocean and cold deep ocean in different ways. They attribute these differences to mixing and circulation effects in GCMs that are not resolved in box models. The me...

In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...

The separations of alcohols with hydrophilic and hydrophobic parts, and the separation of aromatic mixtures, are extremely important processes in gas and petroleum industries. Choosing an adsorbent for performing this separation is the most important part of the process. Silica gel is used as an adsorbent is various techniques such as pressure swing adsorption (PSA) and gas and liquid chromatog...

Polar Bears (Ursus maritimus) are facing a range of threats that might impact their future population status (see section Threats below). The IUCN Polar Bear Specialist Group (PBSG) regards loss of sea-ice habitat due to climate warming as the most serious threat to future Polar Bear survival. We therefore based our Red List assessment on this threat factor only, recognizing that sea-ice condit...

The differential solubility of polar and apolar groups in water is important for the self-assembly of globular proteins, lipid membranes, nucleic acids, and other specific biological structures through hydrophobic and hydrophilic effects. The increase in water's heat capacity upon hydration of apolar compounds is one signature of the hydrophobic effect and differentiates it from the hydration o...

Sporulation in the bacterium Bacillus subtilis is a developmental program in which a progenitor cell differentiates into two different cell types, the smaller of which eventually becomes a dormant cell called a spore. The process begins with an asymmetric cell division event, followed by the activation of a transcription factor, σF, specifically in the smaller cell. Here, we show that the struc...

the aim of the present study was to investigate the relationship between the polar surface area and other molecular properties of the model drugs and their transdermal permeability across the rat skin. few model drugs which are weakly acidic (ibuprofen, aceclofenac and glipizide) and weakly basic (olanzapine, telmisartan and sildenafil citrate) were selected for the study based on polar surface...