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007 PUAL, A.C. (Dept. of Mathematics, model, which is also applicable to other models of
University of Rajshahi, Rajshahi); UDDIN, M.S. infectious diseases. The three dimensional model
(Dept. of Mathematics, Carmichael College, which assumes a non-linear incidence rate is
Ragnpur) & RASHID, M.M. (Dept. of analyzed qualitatively to determine the stability of
Mathematics, Shahjalal University of Science & its equilibria. This model is used to investigate the
Technology, Sylhet). NON-SEMI-SIMPLE potential impact of the optimal vaccine coverage
GAMMA RINGS WITH MINIMUM CONDITION. J. threshold needed for disease control and
Bang. Acad. Sci., 2007, 31(1), 109-127. eradication.
Principal indecomposable ΓM-modules are studied 010 RASHID, M.H. & ALI, D.M. (Dept. of
in this paper. Some characterizations of these Mathematics, University of Rajshahi, Rajshahi).
modules are developed. They also split up the set CRETAIN FEATURES OF INVERSE AND
of all principal indecomposable ΓM-modules into DIRECT LIMITS FOR FUZZY TOPOLOGICAL
a finite number of equivalence classes and study SPACES. J. Bang. Acad. Sci., 2007, 31(1), 67-78.
their characterizations.
The researchers deal with fuzzy products, fuzzy
008 PAUL, G.C.; PRAMANIK, J.N. & equalizers, fuzzy pullbacks and their duals in fuzzy
BHATTACHARJEE, S.K. (Dept. of topological spaces. They also deal with fuzzy
Mathematics, University of Rajshahi, Rajshahi). inverse and fuzzy direct limits of certain fuzzy
THE DISTRIDUTION OF ORBITAL inverse and fuzzy direct systems of fuzzy
DISTANCES OF THE PLANETS. J. Bang. Acad. topological spaces, respectively and study their
Sci., 2007, 31(2), 253-260. several features.
Planetary distances have been investigated within 011 SAMAD, Q.A. (Dept. of Statistics,
the context of the Protoplanetary model of Jahangirnagar University, Savar, Dhaka) &
planetary formation. It is found that, if initially PATWARY, F.K. (Computer & Information
some stable protoplanetary objects are assumed to Technology Institute, Jahangirnagar University,
have formed in a belt near Jupiter, then mass loss Savar, Dhaka). ESTIMATION OF TECHNICAL
from a set of identical massed protoplanets can EFFICIENCY AND TECHNICAL CHANGE IN
account for the observed distances of the planets of THE STOCHASTIC FRONTIER PRODUCTION
given mass. FUNCTION MODEL - AN APPLICATION TO
THE MANUFACTURING INDUSTRIES OF
009 RAHMAN, K.A. (Dept. of Mathematics, BANGLADESH. J. Bang. Acad. Sci., 2006, 30(1),
Dhaka University, Dhaka),; NAYEEM, J. (Dept. 117-126.
of Atrs and Sciences, Ahsanullah University of Technical efficiency and technical propgess
Science and Technology, Dhaka) & SALEK, M. (change) have been estimated for the Bangladesh
A. (Institute of Natural Sciences, United manufacturing sector using the stochastic frontier
International University, Dhaka). THE production function model. Panel data have been
STABILITY ANALYSIS OF A used here for 31 industries for 13 years from 198-
MATHEMATICAL MODEL IN THE 82 through 1993-94. Total number of observations
PRESENCE OF A PREVENTIVE VACCINE. for estimation was thus 403, that is, there were no
BRAC Univ. J., 2008, V (1), 19-24. missing observations. The model strongly rejected
the hypothesis of the non-stochastic inefficiency
Various kinds of deterministic models for the (H 0: γ = 0) thus justifying the use of maximum
spread of infectious disease in populations have likelihood estimation and the specification of
been analyzed mathematically and applied to stochastic translog frontier production function in
specific diseases. In this paper a deterministic the present exercise. The average technical
model for the dynamics of an infectious disease in efficiency for the Bangladesh manufacturing
the presence of a preventive vaccine is formulated. industries in estimated to be 72% and the average
The model is a special case of a more general
2