The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

A gene spans the pseudoautosomal boundary in mice

The X and Y chromosomes of the mouse, like those of other mammals, are heteromorphic over most of their length, but at the distal ends of the chromosomes is a region of sequence identity, the pseudoautosomal region (PAR), where the chromosomes pair and recombine during male meiosis. The point at which the PAR diverges into X- and Y-specific sequences is called the pseudoautosomal boundary. We have completed a genomic walk from the X-specific Amelogenin gene to the PAR. Analysis of this region revealed that the pseudoautosomal boundary of mice is located within an intron of a transcribed gene that encodes a novel RING finger protein. The first three of the exons of the gene are located on the X chromosome whereas the 3′ exons of the gene are located on both X and Y chromosomes. This unusual arrangement may indicate that the gene is in a state of transition from pseudoautosomal to X-unique and provides evidence for a process of attrition of the pseudoautosomal region on the Y chromosome.

Loss of sequences 3' to the testis-determining gene, SRY, including the Y pseudoautosomal boundary associated with partial testicular determination.

The condition termed 46,XY complete gonadal dysgenesis is characterized by a completely female phenotype and streak gonads. In contrast, subjects with 46,XY partial gonadal dysgenesis and those with embryonic testicular regression sequence usually present ambiguous genitalia and a mix of Müllerian and Wolffian structures. In 46,XY partial gonadal dysgenesis gonadal histology shows evidence of incomplete testis determination. In 46,XY embryonic testicular regression sequence there is lack of gonadal tissue on both sides. Various lines of evidence suggest that embryonic testicular regression sequence is a variant form of 46,XY gonadal dysgenesis. The sex-determining region Y chromosome gene (SRY) encodes sequences for the testis-determining factor. To date germ-line mutations in SRY have been reported in approximately 20% of subjects with 46,XY complete gonadal dysgenesis. However, no germ-line mutations of SRY have been reported in subjects with the partial forms. We studied 20 subjects who presented either 46,XY partial gonadal dysgenesis or 46,XY embryonic testicular regression sequence. We examined the SRY gene and the minimum region of Y-specific DNA known to confer a male phenotype. The SRY-open reading frame (ORF) was normal in all subjects. However a de novo interstitial deletion 3' to the SRY-ORF was found in one subject. Although it is possible that the deletion was unrelated to the subject's phenotype, we propose that the deletion was responsible for the abnormal gonadal development by diminishing expression of SRY. We suggest that the deletion resulted either in the loss of sequences necessary for normal SRY expression or in a position effect that altered SRY expression. This case provides further evidence that deletions of the Y chromosome outside the SRY-ORF can result in either complete or incomplete sex reversal.