Generalised Thurston-Bennequin invariants for real algebraic surface singularities

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch singularity of a real algebraic surface. For such singularities, the value of the linking form is the Thurston-Bennequin number of the real link of the singularity. As a special case of unibranch surface singularities, the behaviour of the linking form is investigated on the Brieskorn double points x^m+yⁿ±z²=0.     

Photoelastic determination of stresses in the tube plate of a 70-mw steam generator

This article describes the examination, by three-dimensional photoelasticity, of the tube plate of a sodium steam generator. The tube plate is flat on the side of the tube bundle (121 tubes) and spherical (concave) on the other side. The photoelastic model was made by precision casting, there being no glued joints at the points which are important from the point of view of stresses, such as the tube-tube plate junctions. Both the stress distribution along important sections and the stress concentrations in different types of tube-tube plate junctions due to the internal pressure were determined. The investigation described in this article was carried out in the framework of the Association—Euratom TNO/RCN on Fast Reactors, on behalf of the TNO—Neratoom Sodium Technology Project.     

Brieskorn manifolds as contact branched covers of spheres

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.      

Sign patterns that require almost unique rank

A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive (respectively, negative, zero) entry of B by + (respectively, −, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B:sgn(B)=A}. The minimum rank mr(A) (maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost unique rank, that is to say, the sign patterns A such that MR(A) = mr(A) + 1, are established and are extended to sign patterns A for which the spread is d=MR(A)-mr(A). A complete characterization of the sign patterns that require almost unique rank is obtained.     

Chilling sensitivity in zebrafish (Brachydanio rerio) oocytes is related to lipid phase transition

Oocytes of zebrafish were used to study chilling sensitivity and membrane lipid phase transitions in tropical fish. The oocytes were divided into two groups: small (without yolk, <0.1mm) and large (with yolk, >0.1mm). After exposure of the oocytes to different temperatures (25, 22, 19, 16, 12, 8, 0, -8+0.5 degree C) for 15 minutes, the integrity of their membranes was determined by carboxyfluorescein diacetate (CFDA) staining. At 16 and 12 degree C, damage was maximum (membrane integrity decreased by 50%) for small and large sizes, respectively. Lipid phase transition (LPT), which was evaluated using Fourier transform infrared (FTIR) microscopy, indicated phase transitions at the same temperatures at which damage was maximal (between 22 and 12 degree C).In another series of experiments, the chilling sensitivity of oocytes taken from zebrafish which had been held at 16 degree C for different periods of time (0, 15, 30, 60 minutes) was determined as described above. In small oocytes membrane integrity decreased after 15 minutes, and in large oocytes integrity decreased after 30 minutes. Chilling sensitivity was also measured in oocytes from zebrafish that had been held at 16 degree C for 30 minutes and then rewarmed to 28 degree C for 2 hours. Despite this recovery period, the integrity of the oocytes remained low. We suggest that chilling sensitivity in zebrafish oocytes is related to lipid phase transition of their membranes and starts at 10 degree C below the physiological temperature     

Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.     

Does membrane lipid profile explain chilling sensitivity and membrane lipid phase transition of spermatozoa and oocytes?

Ram, fowl and bee spermatozoa, and oocytes of cows and zebrafish were used to study lipid membrane profiles, chilling sensitivity and lipid-phase transitions. The integrity of the membranes was determined by carboxyfluorescein diacetate (CFDA) staining following exposure for 15 minutes to low temperatures. Ram and fowl spermatozoa showed different degrees of loss of membrane integrity. Surprisingly, bee spermatozoa did not show any sensitivity to chilling, and their membranes remained intact down to 0 degree C. In bovine oocytes (at the GV stage) chilling injury was very severe at 16 degree C (membrane integrity decreased by 50%). Lipid phase transition (LPT) and membrane fluidity, which were evaluated by Fourier transform infrared (FTIR) microscopy, and fluorescence polarisation, showed phase transitions at the same temperatures as caused damage (between 30 and 12 degree C). The membrane lipid profiles showed high concentrations of polyunsaturated fatty acids (PUFA) in cold-sensitive ram spermatozoa and zebrafish oocytes, but the ratio between PUFA and saturated fatty acids was highest in cold-resistant bee spermatozoa and lowest in cold-sensitive bovine oocytes. These results suggest a close relationship among cold susceptibility, lipid phase transition and lipids profile in animal gametes.