Interval type-2 fuzzy automata and Interval type-2 fuzzy grammar

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i ) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages (ii ) for a given IT2 fuzzy regular grammars, there exists an IT2 fuzzy automata such that they accept the same IT2 fuzzy languages, and vice versa. In addition, we define some operations on IT2 fuzzy languages and it is shown that IT2 fuzzy languages recognized by IT2 fuzzy automata are closed under the operations of union, intersection, concatenation and Kleene closure, but are not closed under complement

The diversity of Indian Brachionidae (Rotifera: Eurotatoria: Monogononta) and their distribution

We evaluate diversity status of the Brachionidae of India and present an annotated checklist of 46 species excluding dubious and unconfirmed reports. These merit biodiversity value as ~27% of the global diversity of the taxon and ~81% of its Oriental species. We observed two Australasian elements, two Oriental endemics, one Indian endemic, one paleotropical and one cosmo (sub) tropical species. The cold-water Keratella serrulata and Notholca squamula are new records from eastern Himalayas. Maximum brachionid diversity (32 species) from Assam state of northeast India (NEI) is followed by the reports of 27 and 26 species from Tamil Nadu and West Bengal, respectively; 25 species each from Tripura and Maharashtra; and 24 species from Jammu & Kashmir. Brachionus, the most diverse brachionid genus, is widely distributed in India with low richness in hill states of NEI and coastal waters in particular. The Indian brachionid taxonomy is confounded with unconfirmed reports, misidentifications, invalid taxa, and inconsistent treatment of morphological variants, while analysis of cryptic diversity in Brachionus calyciflorus, B. caudatus, B. forficula, B. plicatilis, B. quadridentatus, B. urceolaris, Keratella cochlearis and K. quadrata species-groups awaits attention

Application of Relativistic Coupled-cluster Theory to Electron Impact Excitations of Mg+^+ in the Plasma Environment

A relativistic coupled-cluster (RCC) theory is implemented to study electron impact excitations of atomic species. As a test case, the electron impact excitations of the $3s ~ ^2S_{1/2} - 3p ~ ^2P_{1/2;3/2}$ resonance transitions are investigated in the singly charged magnesium (Mg$^+$) ion using this theory. Accuracies of wave functions of Mg$^+$ are justified by evaluating its attachment energies of the relevant states and compared with the experimental values. The continuum wave function of the projectile electron are obtained by solving Dirac equations assuming distortion potential as static potential of the ground state of Mg$^+$. Comparison of the calculated electron impact excitation differential and total cross-sections with the available measurements are found to be in very good agreements at various incident electron energies. Further, calculations are carried out in the plasma environment in the Debye H\"uckel model framework, which could be useful in the astrophysics. Influence of plasma strength on the cross-sections as well as linear polarization of the photon emission in the $3p ~ ^2P_{3/2} - 3s ~ ^2S_{1/2}$ transition is investigated for different incident electron energies.Comment: 9 pages, 1 table and 3 figure