ISSN:0028-1441    

DOI:10.1002/nav.3800110202

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractAsymptotically efficient estimators are developed for the problem of estimating a location and a scale parameter, using only the observations between the pthand qthsample quantiles.

ISSN:0028-1441    

DOI:10.1002/nav.3800110203

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800110204

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractThis paper analyzes a two person zero‐sum game in which the strategies on the two sides are probability distributions. The solutions always turn out to contain jumps. In most cases the distributions are combinations of delta functions and density functions.The problem is as follows: a submarine chooses a range r, within a declared war zone, at which to fire his missile. If he is detected at a larger range he attempts to fire at that larger range with the effectiveness at that range decreased by defense measures such as attempts to kill the submarine, shoot down the missile, or protect the target. If this defense effectiveness is denoted by ω, with ω = 0 referring to perfect defensive reaction measures, and ω = 1 referring to poor defensive reaction measures, the following is true. If ω = 0, the problem is analogous to a problem (“The Two Machine‐gun Duel”) solved by L. Gillman and the author in 1949 (Ref. 2) and is not difficult. The defenses in this case are in close to the coast. If ω = 1 the problem is different but not difficult and the defenses are well out towards (and in some cases at) maximum missile range. There are for ω = 1 no defenses near the coast; this is referred to as an “initial gap.”.The first problem that arises is to find for what values of ω is there an “initial gap.” A necessary and sufficient condition for such gaps was found. For general ω there may be instead an “interior gap,” i.e., defense contiguous to the coast and out near or at maximum missile range, but none at intermediate ranges. Necessary and sufficient conditions for such interior gaps were found. In a typical case the solution for the defense follows one function out to a certain target, then is zero, then follows another function to maximum missile range, then has a delta function at maximum missile range.It was necessary to study in detail the behavior of expressions involving discontinuous functions by breaking into continuous parts and discontinuous parts. A great deal of the complexity of the paper arises from this fact. A second cause is that it is essential to admit completely arbitrary distribution functions on the two sides as strategies. There is no a priori reason for instance, why the attacking player could not choose his plays from the Cantor distribution, a function increasing on (0, 1) from 0 to 1, but having almost everywhere a zero derivative. These possibilities emphasize the need for great care in the analysis and for the somewhat tedious existence proof of a

ISSN:0028-1441    

DOI:10.1002/nav.3800110205

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractThe decomposition principle of Dantzig and Wolfe is a method for breaking large linear programs with a block diagonal structure into a set of smaller subprograms. An alternative decomposition scheme derived from a dynamic programming approach is proposed here. This results in a series of parametric linear subprograms whose recursive solution yields the solution to the original linear program.

ISSN:0028-1441    

DOI:10.1002/nav.3800110206

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractProgramming problems with linear constraints and certain objective functions containing fractions of linear functions are reduced to parametric linear programming problems by treating the value of one of the linear forms in the objective function as a parameter. Conditions for extrema are derived and the possibilities for local and global extrema are discussed.

ISSN:0028-1441    

DOI:10.1002/nav.3800110207

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractA direct sum and tensor product of matrix games and of their equivalent linear programs are defined. The relationship of a “composed” game to the corresponding “composed” linear program is derived. Conditions are obtained for the solution of the direct sum or tensor product game to be determined from the solutions of the component games. Examples are given to show how many actual conflicts can be represented by direct sum or tensor produc

ISSN:0028-1441    

DOI:10.1002/nav.3800110208

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

摘要:

AbstractIn many military problems, it is impossible to establish a function describing the relative military worth of resources. Demand for these resources is usually created from some higher level goal. The algorithm described in this paper provides a procedure for allocating scarce resources among competing demands in such a situation.

ISSN:0028-1441    

DOI:10.1002/nav.3800110209

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800110210

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800110211

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1964

数据来源: WILEY