we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.

For Y a closed normal subvariety of codimension c of a smooth C–variety X, Brylinski and Kashiwara showed in [BK81] that the local cohomology module HcY (X,OX) contains a unique simple DX– submodule, denoted by L(Y, X). In this paper the analogous result is shown for X and Y defined over a perfect field of finite characteristic. Moreover, a local construction of L(Y,X) is given, relating it to ...

Let Fn be a free group of rank n. An automorphism of Fn is called an IA-automorphism if it trivially acts on the abelianization H of Fn. We denote by IAn the group of IA-automorphisms and call it the IA-automorphism group of Fn. For any integer d ≥ 2, let IAn,d be the group of automorphisms of Fn which trivially acts on H⊗ZZ/dZ. We call IAn,d the congruence IA-automorphism group of Fn of level ...

Vitamin D deficiency is highly prevalent in newly settled refugees in Western Australia (WA). If adherence to daily vitamin D therapy is problematic, depot therapy is a therapeutic alternative. The aim of this study was to compare daily versus depot treatment and factors influencing the therapeutic outcome. Newly settled refugees (n = 151) with 25(OH)D levels less than 78 nmol/L were randomised...

where D is some small category, F is a functor from D to the category of spaces, and, for each object d ∈ D, F (d) has the homotopy type of BH for some subgroup H of G. The operator “hocolim” is the homotopy colimit in the sense of Bousfield and Kan [4], which amounts to a homotopy invariant method of gluing together the values of the functor F according to the pattern of the maps in D. There i...

Given $n$ distinct points $\mathbf{x}_1, \ldots, \mathbf{x}_n$ in $\mathbb{R}^d$, let $K$ denote their convex hull, which we assume to be $d$-dimensional, and $B = \partial K $ its $(d-1)$-dimensional boundary. We construct an explicit one-parameter family of continuous maps $\mathbf{f}_{\varepsilon} \colon \mathbb{S}^{d-1} \to K$ which, for $\varepsilon > 0$, are defined on the sphere have pro...

We use generating function techniques developed by Givental, Th\'eret and ourselves to deduce a proof in $\mathbb{C}\text{P}^d$ of the homological generalization Franks theorem due Shelukhin. This result proves particular Hofer-Zehnder conjecture non-degenerated case: every Hamiltonian diffeomorphism that has at least $d+2$ periodic points infinitely many points. Our does not appeal Floer homol...

We consider the problem when lens spaces are given from homology spheres, and demonstrate that many lens spaces are obtained from L-space homology sphere which the correction term d(Y ) is equal to 2. We show an inequality of slope and genus when Y is L-space and Yp(K) is lens space. 1 2

In [2] Chas and Sullivan defined an intersection-type product on the homology of the free loop space LM of an oriented manifoldM. In this paper we show how to extend this construction to a homological conformal field theory of degree d. In particular, we get operations on H∗LM which are parameterized by the twisted homology of the moduli space of Riemann surfaces.

We examined production of ADP-ribosyltransferase C3 in 11 strains of Clostridium botldinum type C and D and their nontoxigenic derivatives. Antisera to C3 proteins of type C organisms divided C3 proteins roughly into at least two groups, bearing no relation to their bacterial types. The C3 gene of type D strain South African was isolated from a toxigenic phage library, and the complete sequence...