Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

background: the glutathione s-transferase (gst) family of metabolising enzymes plays an important role in the detoxification of mutagens and carcinogens. the expression of many of these cancer susceptibility enzymes is genetically polymorphic. an increased frequency of gst-null genotypes has been associated with several malignancies. objective: to investigate the rate of gstt1 and gstm1 null ge...

background: endometriosis is one of the most common gynecologic disorders. it is a complex trait and both genetic and environmental factors have been implicated in its pathogenesis. there is growing evidence indicating that exposure to environmental contaminants is a risk factor for endometriosis. glutathione-s-transferase m1 (gstm1) is one of the genes involved in detoxification of endogenous ...

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of th...

Let X ⊆ 2 . Consider the class of all Borel F ⊆ X × 2 with null vertical sections Fx, x ∈ X. We show that if for all such F and all null Z ⊆ X, ⋃ x∈Z Fx is null, then for all such F , ⋃ x∈X Fx 6= 2 . The theorem generalizes the fact that every Sierpiński set is strongly meager and was announced in [P]. A Sierpiński set is an uncountable subset of 2 which meets every null (i.e., measure zero) se...

An analog of ML-randomness in the effective descriptive set theory setting is studied, where the r.e. objects are replaced by their Π1 counterparts. We prove the analogs of the Kraft-Chaitin Theorem and Schnorr’s Theorem. In the new setting, while K-trivial sets exist that are not hyper-arithmetical, each low for random set is. Finally we study a very strong yet effective randomness notion: Z i...

In this work we will develop the canonical structure of Podolsky’s generalized electrodynamics on the nullplane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the momenta and canonical Hamiltonian of the system. On the null-plane the field equations also demand a different analysis of the initial-boundary value problem and ...

For any h ∈ N, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh−{0} such that the induced vertex labeling l+ : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ N for which G admits a zero-sum h-magic labeling. A graph G is said to be...

Classification and association rule mining are used to take decisions based on relationships between attributes and help decision makers to take correct decisions at right time. Associative classification first generates class based association rules and use that generate rule set which is used to predict the class label for unseen data. The large data sets may have many null-transactions. A nu...

background: endometriosis is one of the most commonly encountered benign problems in gynaecology. it is frequently associated with chronic pelvic pain, dysmenorrhoea, menorrhagia and dyspareunia, which lead to infertility. we determined the possible association between cyp1a1 mspi and gstm1 null polymorphism in the pathogenesis of endometriosis. materials and methods: ninety seven cases of endo...