Codimension Two Determinantal Varieties with Isolated Singularities

We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in $\mathsf{C}^4$, we obtain a Lê-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the $1$-form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from Frühbis-Krüger and Neumer [7] list of simple determinantal surface singularities.

STABILITY AND VIBRATION ANALYSIS OF NON-PRISMATIC THIN-WALLED COMPOSITE SPATIAL MEMBERS OF GENERIC SECTION

This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.

Mirror symmetry for concavex vector bundles on projective spaces

LetX⊂Ybe smooth, projective manifolds. Assume thatι:X→ℙsis the zero locus of a generic section ofV+=⊕i∈I𝒪(ki), where all theki's are positive. Assume furthermore that𝒩X/Y=ι∗(V−), whereV−=⊕j∈J𝒪(−lj)and all thelj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants ofXinherited fromYcan be calculated via a modified Gromov-Witten theory onℙs. This leads to local mirror symmetry on theA-side.

Generic Polymerase Chain Reaction Followed by DNA Sequencing as a Means of Diagnosing Bacteraemia

There is increasing use of polymerase chain reaction techniques to diagnose infection. We report the use of polymerase chain reaction using a generic section of the bacterial 16S rDNA gene—followed by nucleotide sequencing—to determine the species of the infecting bacteria. In the first case, the clinical and microbiological diagnosis of meningococcal septicaemia was in agreement with the results from polymerase chain reaction technique. In the second case, a Yersinia enterocolitica bacteremia was detected by the polymerase chain reaction technique, but missed with conventional blood culture techniques.