By means of elementary properties of the absolute value function, important properties of a special class of 'constrained generalized median' problems (and eventually, the most general class, vide Charnes, Cooper, Thompson) such as existence of solutions, gradient and incremented formulae, linear programming and probabilistic interpretations are obtained for all classes of joint distribution functions for which the problems make sense. Results of A. C. Williams and R. Wets obtained by involved...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR PROGRAMMING, DECISION...

The intersections of the nonnegative orthant in E to the Nth power with pairs of complementary orthogonal subspaces are investigated. Appli cations to linear inequalities and linear programming are then made by using Fredholm's alternative theorem.

Topics: DTIC Archive, BenIsrael, Adi, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *PROJECTIVE...

The convex duality theory as developed by Charnes -Cooper-Kortanek which is valid for non-differentiable quasi-concave functions is applied to derive a gradient inequality for a non-differentiable function involving a symmetric quadratic form with positivity required only on a given convex polyhedral cone, generalizing a theorem of Edmund Eisenberg. No assumption is needed either that the primal problem attain its extremal value, since the CCK duality theory includes this possibility. The...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *THEOREMS, NONLINEAR PROGRAMMING,...

This project envisions a novel concept of mechanical damping: using nanoparticles or microparticles as a damping medium and the interfacial forces as the absorbing mechanism. For thrust damping or radial damping, the mechanical components of the dampers are filled with selected particles. The advantages of particle damping over the conventional damping mechanism are as follows: (1) The performance of the small particles will be temperature independent and therefore the damping device can work...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *DAMPING, *NANOPARTICLES,...

An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the non-zero entries in the generalized incidence matrix may be random variables. Duality relationships are established for appropriate pairs of such chance-constrained programming problems by showing that their deterministic...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR PROGRAMMING, CHEMICAL...

IF A LINEAR PROGRAMMING PROBLEM (written in inequality form) has a solution, then either the primal constraint set or the dual constraint set is unbounded. The parenthetical remark is our addition to he statement of the theorem, but is implicitly assumed. The inequality form of the general linear programming problem is s metimes referred to as the canonical form and used as a standard point of departure for further analyses. Yet some care may be needed, as is true here, ifA FULL DEGREE OF...

Topics: DTIC Archive, CHARNES, A, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR PROGRAMMING,...

Sufficient conditions are derived for decision rules to be optimal for two classes of n-period P-models of chance-constrained programming. It is shown that the optimal rule for period j is the optimal piecewise linear function of the decision rules of previous periods and certain fractile points. The optimal class of rules is shown to be the same for the n-period P-model as for the corresponding n-period E-model.

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *DECISION THEORY, *MODELS,...

Topics: DTIC Archive, Ben-Israel, Adi, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR...

This report covers certain research which has been directed to analyzing and systematizing historically independent market research steps into a rational marketing program for introducing a new product. In the general case, this system is applicable to many situations where dicisions under uncertainty must be made in the light of incomplete and not necessarily comparable data. The system's inter-relationship of tasks and decisions can best be illustrated and formalized by means of a network....

Topics: DTIC Archive, Cooper, W W, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *DECISION MAKING,...

An extensive study of the micromechanics aspects and size effects associated with strain softening damage due to distributed cracking in brittle heterogeneous materials such as concrete, rocks and ceramics has been carried out and presented in a sequence of publications. The results may be grouped in five categories: (1) Size Effects, (2) Micromechanics Aspects, (3) Nonlocal Continuum Models, (4) Localization Instabilities, (5) Thermodynamic Analysis of Stable Path, and (6) Numerical...

Topics: DTIC Archive, Bazant, Zdenek P, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *CRACKS,...

Topics: DTIC Archive, Budd, Elizabeth, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *BIBLIOGRAPHIES,...

Topics: DTIC Archive, STRAND, K. Aa., NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *BINARY STARS,...

Radiant exposure values are reported for sustained flaming ignition of black a-cellulose, newspaper and kraft corrugated board exposed to constant- irradiance, thermal inputs of 30 ms duration and longer. The radiant exposure values are shown to be approximately proportional to the thickness of the exposed material and not strongly dependent on exposure duration for pulses this brief. The significance of sus tained flaming ignition, relative to ablation effects, for pulses of very brief...

Topics: DTIC Archive, Martin, S, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *IGNITION, *PAPER,...

Calculated estimates are presented of unmeasured total chain yields and of independent fission yields for the fission products resulting from fission-spectrum and 14-Mev neutron bombardment of U233, U235, U238 and Pu239 and from thermal neutron bombardment of U233, U235 and Pu239.

Topics: DTIC Archive, Weaver, L E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *FISSION, MEASUREMENT,...

Basic thermal-radiation measurements, comprising total and broad-band spectral distribution of radiant energy, radiant energy function of field of view of the measuring instrument, and total radiant power versus time, are reported for the second thermal pulse of Shots 1, 2, 3, 5, 6, 9, and 10. All data were taken from ground stations at ranges as close as feasible to the detonations. The data are reported and analyzed to obtain the total thermal energy, the total thermal emission per unit of...

Topics: DTIC Archive, Hillendahl, R W, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *NUCLEAR...

The pre-Buggy experiment was designed to measure the fraction of vented radioactivity from a series of HE underground detonations containing radioactive sources. Capsules (29) containing curie amounts of La(140) were prepared. The level of gamma activity in each capsule was sufficient to provide a radiotracing of the debris which resulted from the detonation. In addition NRDL furnished 'always open' fallout collectors to sample the debris, and a low-geometry scintillation counter to measure its...

Topics: DTIC Archive, Lane, W B, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *CRATERING, *LANTHANUM,...

An apparatus for exposing mice to an aerosol of microorganisms was developed. It is a modification of the Henderson apparatus, adapted for exposure of smaller animals. The design allows for placement of the complete apparatus in a bacteriological hood. Although of relatively simple design and operation, it has proven highly dependable.

Topics: DTIC Archive, Pribnow, J F, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *AEROSOLS, *TEST...

A brief survey of the historical development of the field of thermal stresses, with some identification of areas fruitful for future research. (Author)

Topics: DTIC Archive, Boley,Bruno A, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *THERMAL STRESSES,...

Measures of lifespan were determined for a population of male Sprague-Dawley derived male rats, comprised of 747 animals from eighteen experiments. Variations in ln measures among experiments were found even under stable environmental conditions in a single strain of rats with no known epidemic infections. Measures of central tendency and dispersion appeared to be uncorrelated with each other, and normally distributed among experiments. Within most experiments there was a definite tendency for...

Topics: DTIC Archive, Jones, D C, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *RATS, *LIFE...

Our objective is to provide a more general theoretical basis for those methods for solving constrained minimization problems that are based on successive unconstrained minimizations of a parametric auxiliary function. In order to do this, we first give basic defining properties of a general auxiliary function and obtain a proof of local convergence for the mildly regulated nonconvex problem. We proceed from this general result to develop a family of auxiliary functions by giving the general...

Topics: DTIC Archive, Fiacco, Anthony V, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *MATHEMATICAL...

A question which combines statistics and linear programming considerations was first raised by G. Tintner (Econometrica 28:2, 490-5, April 60). It concerns the distribution of optimum functional values when a linear programming problem has probabilistic constraints. It is proposed to accord a chance constrained programming formulation to this kind of problem and to deal with it in a way that bears on project scheduling of the kind that is usually associated with critical path analysis, for...

Topics: DTIC Archive, CHARNES, A, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *ANALYSIS OF VARIANCE,...

Free damped vibrations of linear elastic structures composed of uniform beam elements with a continuous distribution of mass are studied. Axial, torsional and flexural vibrations are considered. The amount of damping, which can be either internal or external viscous type, varies among the various beam elements of the structure resulting in many critical damping possibilities. A general method is developed, which, with the aid of dynamic stiffness influence coefficients defined for every...

Topics: DTIC Archive, Beskos,D E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *BEAMS(STRUCTURAL),...

Several important and efficient methods of solution of specific types of linear programming problems have the feature of sometimes providing optimal solutions which are not extreme-point (or basic) solutions, so that important and useful analyses provided by knowledge of the optimal dual evaluators are not available. It is also often desirable to be able to begin with a solution suggested by knowledgeable persons with experience in the field (or other considerations) and to proceed immediately...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *MATHEMATICAL PROGRAMMING, COMPLEX...

Groups of young adult mice received a single intraperitoneal injection of urethan prior to or after a single whole body lethal dose of X rays (880 rad) followed by transfusion of normal syngeneic bond marrow to protect against radiation death. This dose of urethan produced multiple tumors in 100% of nonirradiated animals at 24 weeks postinjection. In the irradiated animals there was marked suppression of lung tumor formation, both in number of animals with tumors, and in numbers of tumors per...

Topics: DTIC Archive, Foley, W A, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *NEOPLASMS,...

1) CO(2) Absorption with AG(2)O. 2) Low Temperature Absorption, C(O2) Solubility. 3) Freezing-Out of Carbon Dioxide.

Topics: DTIC Archive, STUTZMAN, L. F., DODDS, WAYNE S., NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST,...

Fading in Ilford K.0 and K.2 emulsions was investigated at 20 degrees C and -20 degrees C. Track segments with rates of energy loss from 0.6 to 1.8 Mev/micron were used. K.0 and K.2 emulsions stored for 30 days at -20 degrees C showed no evidence of fading. After a 30-day fading period, K.2 emulsion stored at 20 degrees C and at 50 percent relative humidity showed less than 10 percent fading. K.0 emulsion stored at 20 degrees C and at 50 percent relative humidity showed severe fading. This is...

Topics: DTIC Archive, Benton, E V, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *PHOTOGRAPHIC FILM,...

The linear programs considered here are of the form: Maximize (c,x) (LP) subject to a = or A x = or b where A is of full row rank, and (LP) is feasible with bounded optimal solutions. The main result is an explicit representation of the general optimal solution of (LP), in terms of a generalized inverse of A. This explicit solution of (LP) - explicit in the sense that A superscript (-1) b is an explicit solution of A x = b - has obvious theoretical (and possibly computational) advantages over...

Topics: DTIC Archive, Ben-Israel, Adi, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR...

Topics: DTIC Archive, Janninck, R F, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *THERMOELECTRICITY,...

An interval linear program is (IP) maximize (c superscript t)x, subject to b- = or Ax = or b+ where the matrix A, vectors b-, b+, and c are given. If A has full row rank, the optimal solutions of (IP) can be written explicitly (A. Ben-Israel and A. Charnes: 'An explicit solution of a special class of linear programming,' Operations Research, forthcoming). This result is used in conjunction with the Dantzig-Wolfe decomposition principle to develop a finite iterative technique specially suited...

Topics: DTIC Archive, Robers, Phillip D, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR...

The following paper was stimulated by a paper of the Hungarian mathematician, A. Haar (possibly one of the all-time great mathematicians). Because it was published in a relatively obscure journal, it has only recently been made generally available through the posthumous publication of his collected works. Since the theorems to be established rest heavily on this work, and Haar's paper is published in German, we present it for ease of access in free translation in the appendix. Conjectured by...

Topics: DTIC Archive, Charnes, A, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *ALGEBRA,...

The generalized network problem and the closely related restricted dyadic problem are two special model types which occur frequently in applications of linear programming. Although they are next in order after pure network or distribution problems with respect to ease of computation, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms for them comparable in speed or efficiency to those for pure network or distribution problems. There are,...

Topics: DTIC Archive, Happer, William, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *NETWORKS,...

Final results are given of measurements of the emissivity and thermal conductivity of beef and studies are given concerning the mechanism of freeze drying.

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *FREEZE DRYING, *BEEF, HEAT...

The notion of a 'weakly balanced game' under very general conditions involving no topology whatever is defined. The work of Schmeidler is extended by establishing duality results for a pair of (possibly) infinite dimensional linear programming problems arising from a generalized game. A necessary and sufficient condition is given in order that a separating hyperplane argument can be employed to prove the existence of a candidate core member for a weakly balanced game. This candidate is shown to...

Topics: DTIC Archive, Charnes, Abraham, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *GAME THEORY,...

Data are presented demonstrating the differential radio sensitivity of the first and second-set responses of sublethally irradiated (670 rad) mice previously sensitized with allogeneic (H-2 difference), xenogeneic (rat) or both allogeneic and xenogeneic skin grafts. The second-set response is more radioresistant than is the first-set response. The second-set response to a xenogeneic graft remains intact during and following recovery fro-he effects of sublethal irradiation. While intact for a...

Topics: DTIC Archive, Tyan, M L, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *SKIN(ANATOMY),...

Media planning has heretofore been restricted, by and large, only to the consideration of average frequency. A recently developed mathematical model explicitly considers both cumulative duplicating audiences over a variety of time periods and the simultaneous selection and scheduling of media. This model thus required the development of methods for handling such nonlinear concave aspects of audience characteristics within a linear programming model and for generating distribution of frequency...

Topics: DTIC Archive, Charnes, Abraham, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LINEAR...

Topics: DTIC Archive, Quon, J E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *COMBUSTION, *WASTE...

Free viscously damped vibrations of linear discrete structural systems are studied. The amount of damping varies among the various structural elements of the system resulting in several critical damping possibilities. A general method is developed for determining the critical damping surfaces of a system. These surfaces represent the loci of combinations of damping values corresponding to critically damped motions, and thus separate regions of partial or complete underdamping for those of...

Topics: DTIC Archive, Beskos,D E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *VIBRATION, *DAMPING,...

Chain yields and independent yields of the U238 fission products from a thermonuclear explosion were estimated. Since unclassified data for this kind of process are scanty, some features of the mass yield curve were inferred from published data on U238 fission by neutrons ranging from fission-spectrum energies to 14 Mev. Independent yields of the fission products were then calculated by application of the equal charge displacement theory of nuclear charge distribution in fission processes.

Topics: DTIC Archive, Crocker, G R, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *FALLOUT, *NUCLEAR...

The failure of quasibrittle materials, which include concrete, rock, high-performance ceramics and fiber composites, cannot be treated according to the classical theories of plasticity or fracture mechanics because growth of zones of strain softening damage due to cracking must be considered. The mathematical treatment involves difficulties with spurious excessive localization. To remedy them, the nonlocal continuum concept was previously introduced, however, without theoretical foundation. The...

Topics: DTIC Archive, Bazant, Zdenek P, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST,...

The effects of prolonged exposures to high concentrations of CO2 were studied. Twenty-two seamen and a medical officer were sealed for 60 days in 5 compartments of the USS Haddock, a fleet-type submarine equipped with a caustic scrubber for removing excess CO2. The scrubber adequately removed CO2 at an average rate of 9.77 lb/hr at an average caustic utilization of 90.3%. The desired 1.5% CO2 atmosphere was maintained. As expected, the averages were higher than those for maintaining the 1% CO2...

Topics: DTIC Archive, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *EXPOSURE(PHYSIOLOGY), *CARBON...

The effect of age at irradiation upon the severity and temporal distribution of the radiation-induced dental lesion was investigated. Male rats were irradiated with a high sublethal dose (215 rads) of fast neutrons at 31, 110, or 619 days of age. The typical lesion (a chalky zone extending the full width of the tooth) was observed in the exposed shafts of the incisors beginning in the second month post irradiation. While all animals exhibited the lesion in all incisors, the character of the...

Topics: DTIC Archive, Jones, D C, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *RADIATION INJURIES,...

Rats were exposed to whole-body X radiation (850 rad) at various times before or after unilateral nephrectomy, and the other kidney was removed 48 hours later. The kidneys were homogenized in isotonic sucrose-tris buffer, and the homogenate was centrifuged at 105,000xg for 1 hour. The supernatants were assayed in vitro for the DNA polymerase enzymes which catalyze the incorporation of H3-thymidine into DNA. The accumulation of these enzymes was profoundly suppressed in rats irradiated at 10...

Topics: DTIC Archive, Main, R K, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *ENZYMES, *WHOLE BODY...

Topics: DTIC Archive, Quon, J E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *THERMAL DEGRADATION,...

Natural seawater was required for use in experiments designed to determine the dissolution rate of certain nuclear fuel materials. A literature survey was conducted and a method was devised for the collection, storage and analysis of the water. In brief, the method stipulates: (1) off-shore collection of surface water in polyethylene carboys which are subsequently stored, at a reduced temperature, in a dark location and (2) monitoring biological and chemical composition via microfiltration,...

Topics: DTIC Archive, Goya, H, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *STORAGE, *SEA WATER,...

The simulation of a realistic fallout environment was required for the design of experiments to evaluate post-nuclear attack reclamation equip ment and procedures. A simplified mathematical fallout model was utilized to estimate fallout particle sizes, accumulated initial mass levels, and standard radiation intensities that might occur under specified conditions of weapon yield and downwind distance from a land surface nuclear detonation. Fallout particle size, deposited mass per unit area, and...

Topics: DTIC Archive, Clark, D E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *MATHEMATICAL MODELS,...

A set of recursive relations called NEWS (for New-Product Early Warning System) is here presented in its own right as a separable part of the DEMON system for marketing new products. NEWS is designed to distinguish the variables and relations that are usually of interest for market-planning by reference to data availability and the decisions that might be made advertising promotions and product properties. Other uses and possible further extensions are examined by reference to planning media...

Topics: DTIC Archive, Charnes, Abraham, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *MANAGEMENT...

The paper extends existing models of inter-temporal bank asset management in the following respects: (a) Bank customers are identified, with requirements that their demands for loan renewals be satisfied. Opportunities are provided for attracting new customers; (b) feedback relationships between loans and deposits are introduced; (c) costs of servicing loans with different degrees of risk are introduced explicitly; (d) future deposits and loan repayments are expressed as jointly dependent...

Topics: DTIC Archive, Charnes, Abraham, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *BANKING,...

Contents: Experimental methods for detecting twins Determination of the twinning process Uses to known twinning elements Operative twin systems during deformation Prediction of the twin reflections for a given twinning system Quantitive estimates of amount of twinning.

Topics: DTIC Archive, DeAngelis, R J, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *COPPER,...

This investigation centers on the evaluation and possible development of physical chemical methods for the conversion of urine into water suitable for drinking or other uses in fallout shelters and other isolated sites. The capacity of the multiple and mixed bed ion exchange for the demineralization of urine; and of activated carbon for the removal of urea, foaming agents, and color were evaluated. Reaction rates and products were determined for the oxidation of urea with calcium hypochlorite...

Topics: DTIC Archive, Quon, J E, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *WATER SUPPLIES,...

The Northwestern high speed rubbing apparatus has been modified to remove certain ambiguities in output data interpretation. Some experiments have been carried out with the modified apparatus, and data on friction, temperature, and contact resistance have been obtained for a graphite-steel contact region. No thermoelastic instability effects were observed over a speed range of 70M/sec. (Author)

Topics: DTIC Archive, Kistler,A L, NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST, *LABORATORY EQUIPMENT,...