Summand intersection property of modules via z-closed submodules

In this paper, we define a module [Formula: see text] to be [Formula: see text] if and only if intersection of each pair of [Formula: see text]-closed direct summands is also a direct summand of [Formula: see text]. We investigate structural properties of [Formula: see text]-modules and locate the implications between the other module properties which are essentially based on direct summands. We deal with decomposition theory as well as direct summands of [Formula: see text]-modules. We apply our results to matrix rings. To this end, it is obtained that the [Formula: see text] property is not Morita invariant.

TREASURE: Text Mining Algorithm Based On Affinity Analysis and Set Intersection to Find the Action of Tuberculosis Drugs against Other Pathogens

Tuberculosis (TB) is one of the top causes of death in the world. Though TB is known as the world’s most infectious killer, it can be treated with a combination of TB drugs. Some of these drugs can be active against other infective agents, in addition to TB. We propose a framework called TREASURE (Text mining algoRithm basEd on Affinity analysis and Set intersection to find the action of tUberculosis dRugs against other pathogEns), which particularly focuses on the extraction of various drug–pathogen relationships in eight different TB drugs, namely pyrazinamide, moxifloxacin, ethambutol, isoniazid, rifampicin, linezolid, streptomycin and amikacin. More than 1500 research papers from PubMed are collected for each drug. The data collected for this purpose are first preprocessed, and various relation records are generated for each drug using affinity analysis. These records are then filtered based on the maximum co-occurrence value and set intersection property to obtain the required inferences. The inferences produced by this framework can help the medical researchers in finding cures for other bacterial diseases. Additionally, the analysis presented in this model can be utilized by the medical experts in their disease and drug experiments.

Existence Of Best Proximity Points On Geometrical Properties Of Proximal Sets

The notion of proximal intersection property and UC property is used to establish the existence of the best proximity point for mappings satisfying contractive conditions.

BOUNDNESS OF INTERSECTION NUMBERS FOR ACTIONS BY TWO-DIMENSIONAL BIHOLOMORPHISMS

We say that a group G of local (maybe formal) biholomorphisms satisfies the uniform intersection property if the intersection multiplicity $(\phi (V), W)$ takes only finitely many values as a function of G for any choice of analytic sets V and W of complementary dimension. In dimension $2$ we show that G satisfies the uniform intersection property if and only if it is finitely determined – that is, if there exists a natural number k such that different elements of G have different Taylor expansions of degree k at the origin. We also prove that G is finitely determined if and only if the action of G on the space of germs of analytic curves has discrete orbits.

On exceptional Lie geometries

Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular, many of the exceptional Lie incidence geometries occur. In an appendix, we extend our result to the locally disconnected case and discuss the locally disconnected case of some other well-known characterizations.