Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H, by defining a vertex-hyperedge correspondence. This allows us to recover the classical notion of a dilation/erosion of a subset of vertices and to extend it to subhypergraphs of H. Afterward, we propose several new openings, closings, granulometries and alternate sequential filters acting (i) on the subsets of the vertex and hyperedge set of H and (ii) on the subhypergraphs of a hypergraph

पिंजऱ्यातील मत्स्यशोति विषयक व्यापार आणि आर्थिक सुसाध्यता/शक्यता

India is one of the largest fish producers in the world and contributes 5.43% to global fish production. India ranks second in fish production from aquaculture sector following China at top. Total fish production of India during 2010-11 was 8.42 million metric tones. Inland sector contributes about 5.2 million metric tones, whereas marine sector contributes 3.22 million metric tones. India has a long coastline of about 8,129 km and continental shelf area of 0.5 million km2. Declining catch rates in marine capture fisheries consequently created serious unemployment issues in rural coastal areas. Issues faced by marine fisheries sector in India have focused the attention of policy makers and rural fishers towards development of mariculture and coastal aquaculture activities as alternative livelihood option

N,N′-(1,4-Phenyl­ene)bis­(2-bromo-2-methyl­propanamide)

The mol­ecular structure of the title compound, C14H18Br2N2O2, has one half-mol­ecule in the asymmetric unit. The mol­ecule has a crystallographic inversion centre in the middle of the benzene ring. The C—C—N—C torsion angle between the benzene ring and the bromo­amide group is 149.2 (7)°. The crystal is stabilized by a strong inter­molecular N—H⋯O bond and weak C—H⋯O inter­actions. These contacts give rise to a three-dimensional network

2,4-Bis(4-eth­oxy­phen­yl)-7-methyl-3-aza­bicyclo­[3.3.1]nonan-9-one

The mol­ecule of the title compound, C25H31NO3, exists in a twin-chair conformation with an equatorial orientation of the 4-eth­oxy­phenyl groups, as observed for its ortho isomer [Parthiban, Ramkumar, Park & Jeong (2011b ▶), Acta Cryst. E67, o1475–o1476]. The methyl and 4-eth­oxy­phenyl groups are also equatorially oriented on the bicycle, as in the ortho analogue. In particular, although the cyclo­hexa­none ring deviates from an ideal chair, the piperidone ring is closer to an ideal chair, whereas in the ortho isomer both rings are significantly puckered and deviate from ideal chairs. The 4-eth­oxy­phenyl groups on both sides of the secondary amine group are oriented at an angle of 26.11 (3)° with respect to each other, but the 2-eth­oxy­phenyl groups in the ortho isomer are oriented by less than half this [12.41 (4)°]. In contrast to the absence of any significant inter­actions in the crystal packing of the ortho isomer, the title compound features N—H⋯O inter­actions, linking the mol­ecules along the b axis

2,4-Bis(2-methyl­phen­yl)-3-aza­bicyclo[3.3.1]nonan-9-one O-methyl­oxime

The mol­ecule of the title compound, C23H28N2O, exists in a twin-chair conformation, with equatorial orientation of the ortho-tolyl groups on both sides of the secondary amino group. The title oxime compound and its ketone precursor 2,4-bis­(2-methyl­phen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one exhibit similar stereochemistries, with the orientation of the o-tolyl rings almost identical in both compounds. In the title compound, the tolyl rings are at an angle of 23.77 (3)° with respect to one another; the angle in the precursor is 29.4 (1)° [Vijayalakshmi, Parthasarathi, Venkatraj & Jeyaraman (2000 ▶), Acta Cryst. C56, 1240–1241]. The cyclo­hexane ring and the oxime ether are disordered over two alternative orientations, with a refined site-occupancy ratio of 0.813 (2):0.186 (4). The crystal structure of the title compound is stabilized by inter­molecular N—H⋯π inter­actions

2,4-Bis(4-propoxyphen­yl)-3-aza­bicyclo­[3.3.1]nonan-9-one

In the title compound, C26H33NO3, a crystallographic mirror plane bis­ects the mol­ecule (two C atoms, one O atom and one N atom lie on the mirror plane). The mol­ecule exists in a twin-chair conformation with equatorial orientations of the 4-propoxyphenyl groups. The dihedral angle between the 4-propoxyphenyl groups is 31.58 (3)°

3′-Benzoyl-1′-methyl-4′-phenyl­spiro[acenaphthyl­ene-1(2H),2′-pyrrolidin]-2-one

In the title compound, C29H23NO2, the pyrrolidine ring adopts a twisted conformation about one of the C—N bonds. The acenaphthone ring (r.m.s. deviation = 0.025 Å) lies almost perpendicular to the pyrrolidine ring [dihedral angle = 88.08 (8)°]. The dihedral angle between the phenyl rings is 88.12 (11)°. In the crystal structure, weak C—H⋯π inter­actions connect the mol­ecules