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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



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