Search

This paper deals with the problem of estimation of common parameters from two linear models under the assumption of normality. A set of sufficient conditions are obtained under which one can uniformly improve upon the estimates obtained from one model. Uniform improvement on both the models is also considered. We construct estimates which satisfy those conditions and apply these methods to (i) the problem of estimating the common mean of two normal populations and (ii) the problem of recovery of interblock information in incomplete block designs. Exact variances for these estimates and for some other estimates have been evaluated for some important special cases and have been computed for some designs.

This paper deals with the problem of estimation of common parameters from two linear models under the assumption of normality. A set of sufficient conditions are obtained under which one can uniformly improve upon the estimates obtained from one model. Uniform improvement on both the models is also considered. We construct estimates which satisfy those conditions and apply these methods to (i) the problem of estimating the common mean of two normal populations and (ii) the problem of recovery of interblock information in incomplete block designs.Exact variances for these estimates and for some other estimates have been evaluated for some impor tant special cases and have been computed for some designs.

A brief history of plague in Hyderabad State during the present pandemic is given. It is shown that the epidemics on the whole are on the wane, and this experience coincides with the experience of other Indian states. This general decline cannot be attributed to any specific anti-plague measures adopted earlier. Earlier measures such as fumigation of rat burrows with Cyanogas were able to control epidemics to a large extent, but were not successful in eradicating infection, particularly from the endemic zones.Recently DDT has been introduced as an anti-plague measure, relying on the assumption that control of transmitting agent alone may be able to check the epidemics and may ultimately succeed in eradicating the infection from the state.Insufflation of rat burrows with DDT I0 per cent. powder and disinfection of houses with DDT suspension spray made by mixing water with 50 per cent. DDT wettable powder for the disinfection of huts, walls, roofs and windows, etc., are the main anti-plague measures now adopted. The measures have given very encouraging results ; the record of incidence and mortality from plague in the whole state during the last year has been the lowest recorded for the last fifty years.

For distributed parameter systems, open-loop stability in the sense of bounded outputs for bounded inputs, and closed-loop asymptotic stability are considered. Frequency domain stability criteria for open and closed-loop distributed parameter systems are given. The closed-loop stability criterion is similar to V. M. Popov’s stability criterion for lumped systems. The criteria are limited to those linear, time-invariant systems whose dynamics can be described by a transfer function which is the ratio of the multiple transform of the output to the multiple transform of the input. The input may or may not be distributed. An example is given to illustrate the applications of the stability criteria.

In the design of controllers for heat transfer systems, one must often describe the plant dynamics by partial differential equations. The problem of optimizing a controller for a system described by partial differential equations is considered here using exact and approximate methods. Results equivalent to the Euler-Lagrange equations are derived for the minimization of an index of performance with integral equation constraints. These integral equation constraints represent the solution of the partial differential equations and the associated boundary conditions. The optimization of the control system using a product expansion as an approximation to the transcendental transfer function of the system is also considered. The results using the two methods are in good agreement. Two examples are given illustrating the application of both the exact and approximate methods. The approximate method requires less computation.

A frequency domain stability criterion (sufficient condition) for a class of distributed parameter, sampled-data systems containing a memoryless, nonlinear feedback element is presented. This criterion for absolute stability of the class of distributed systems considered here parallels the criterion for lumped systems obtained by Jury and Lee, and it requires that the following relationship be satisfied on the unit circle (|z| = 1). Re{W(pj,z)[1+q(z−1)]}+1K−K′|q|2|(z−1)W(pj,z)|2≥0forallj=0,1,2,…. This sufficient condition is limited to those systems whose dynamics can be described by a transfer function W(pi, z) which is the ratio of the multiple transform of the output to the multiple transform of the input. An example is given to illustrate the applications of the stability criterion.

A method is presented to identify partial differential equations and associated boundary conditions of a distributed parameter system. The method is applicable to linear, nonlinear, and time-varying systems. The technique requires that the form of the differential equation and boundary conditions be known up to a set of constant parameters. Finite differences are used to approximate derivatives. Identification is carried out by using normal operating data. The accuracy of the identification depends upon the approximation errors and measurement noise. Methods for decreasing approximation errors are presented.

A necessary condition for the optimum control of a linear system with input delay or transportation lag is derived in terms of the system weighting function. For a general quadratic integrand in an integral-type index of performance and a linear time invariant system with input delay, an expression for the optimum controller is given in the Laplace domain in terms of the system transfer function. This expression simplifies the calculation of the optimum controller. The results are applicable to systems with or without input delay. An example is given to illustrate the procedure.

If $ H \leq G$G-module is H-projective then (G, H) is a projective pairing. If Rad $ FG \subseteq ({\text{Rad}}\;FH)FG$G, H) is said to have property p. A third property considered is that for each irreducible H-module the induced G-module be completely reducible. It is shown that these three are equivalent properties in many interesting cases. Also examples are given to show that they are, in general, independent of each other.

Quick and efficient estimators are very useful in two principal ways in analysis of serum concentration or dose response relationship: (1) for providing the preliminary estimates for an iterative digital computer program, and (2) for studying the statistical properties of the estimators in Bioavailibility studies. In this paper, which is an extension of our previous paper [3], we found that the percentage efficiency of the nonlinear parameter is significantly increased even for moderate values of time-response data. A table is provided to facilitate computation.

Quick and efficient estimators are very useful in two principal ways in analysis of serum concentration or dose response relationship : (1) for providing the preliminary estimates foe an iterative digital computer pro-gram, and (2) for studying the statistical properties of the estimators in Bioavailibility studies. la this paper, which is an extension of our previous paper [3], we found chat the percentage efficiency of the nonlinear parameter is significantly increased even for moderate values of time-response data. A table is provided to facilitate computation.

The origin and the development of the Series II tools is one of those problems of Indian prehistoric archaeology which has evaded solution so far. This culture is comprised of scrapers of all sorts—side, hollow, endpoints, borers and burins (very rare) generally made on jasper, agate, chert and sometimes chalcedony also. The position of this culture in relation to other prehistoric cultures remains confused since its stratigraphical position has still to be worked out. And it awaits dating like other lithic industries because one has yet to find out the tools in association with fossils in situin the horizons which are likely to yield them.In the following pages, is presented the data, collected from the Narmada and its tributary valleys, which tends to throw light on this culture and an attempt is made to ‘fix’ this culture in the stratigraphy and to date it with the help of fossils, which were found along with it in plenty in this area. These observations were made by the writer when he was conducting the fieldwork in the Hoshangabad-Narsinghpur region of the Narmada river in Central India, in search of Fossil Man, under the auspices of the Council of Scientific and Industrial Research, Govt. of India. This Narmada data, apart from ‘fixing’ it in its proper context, illustrates also its relationship with the Handaxe-cleaver complex on one hand and the Microlithic industry on the other.

An example is presented to show that in an equi-replicate row-column design even when the row design is connected and the column design is connected, the row-column design need not be connected.

An example is presented to show that in an aqui-replicate row-column design even when the row design is connected and the column design is connected,the row-column design need not be connected.