In the theory of inverse systems, in order to study the properties of a space X or a map f : X → Y between spaces, one expands X to an inverse system X or expands f to a map f : X → Y between the inverse systems, and then work on X or f . In this paper, we define approximate injectivity (resp., surjectivity) for approximate maps, and show that a map f : X → Y between compact metric spaces is in...

Brucellosis is endemic in livestock and humans in Uganda and its transmission involves a multitude of risk factors like consumption of milk from infected cattle. To shed new light on the epidemiology of brucellosis in Uganda the present study used phenotypic and molecular approaches to delineate the Brucella species, biovars, and genotypes shed in cattle milk. Brucella abortus without a biovar ...

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of RR into R (N) R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is...

where Xs+1 is the fiber of gs. We get an exact couple of homotopy groups and a spectral sequence with E 1 = πt−s(Ks) and dr : E s,t r → Es+r,t+r−1 r . This spectral sequence converges to π∗(X) (where X = X0) if the homotopy inverse limit lim←Xs is contractible and certain lim 1 groups vanish. When X is connective, it is a first quadrant spectral sequence. For more background, see [Rav86]. In th...

This lectures were given by Florian Enescu at the mini-course on classical problems in commutative algebra held at University of Utah, June 2004. The references listed were used extensively in preparing these notes and the author makes no claim of originality. Moreover, he encourages the reader to consult these references for more details and many more results that had to be omitted due to time...

Müllerian mimicry, in which toxic species gain mutual protection from shared warning signals, is poorly understood in vertebrates, reflecting a paucity of examples. Indirect evidence for mimicry is found if monophyletic species or clades show parallel geographic variation in warning patterns. Here, we evaluate a hypothesis of Müllerian mimicry for the pitvipers in Southeast Asia using a phyloge...

We notice that for a Hopf algebra H , its antipode S is both an epimorphism and a monomorphism from H to H in the category of Hopf algebras over a field. Together with the existence of Hopf algebras with non-injective or non-surjective antipode, this proves the existence of non-surjective epimorphisms and non-injective monomorphisms in the category of Hopf algebras. Using Schauenburg’s free Hop...

A regular surface is a closed genus g surface defined as the tubular neighbourhood of the edge graph of a regular map. A regular map is a family of disc type polygons glued together to form a 2-manifold which is flag transitive. The visualization of this highly symmetric surface is an intriguing and challenging problem. Unlike regular maps, regular surfaces can always be visualized as 3D embedd...

 Population genetic structure of Vimba vimba persa was investigated using microsatellite markers from 40 regions along the Iranian coastline of the Southern Caspian Sea (Anzali lagoon and Havigh River in Gilan province, BabolRoud River in Mazandaran province and GorganRoud River in Golestan province). Genomic DNA from 121 specimens was extracted from fin tissue by the Phenol-Chlorophorm method ...