BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH
Overview
Works:  333 works in 339 publications in 1 language and 349 library holdings 

Classifications:  QA141.4, 
Publication Timeline
.
Most widely held works by
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH
AN INTRODUCTION TO ELECTRONHOLE PLASMAS(
Book
)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The document contains two invited lectures given at the UCLA summer course on experiments and theory, June 1526, 1970. Contents include the Introduction, Nonequilibrium plasma production, Sausage mode (m=0) instability, and Feedback control of m=0 oscillations
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The document contains two invited lectures given at the UCLA summer course on experiments and theory, June 1526, 1970. Contents include the Introduction, Nonequilibrium plasma production, Sausage mode (m=0) instability, and Feedback control of m=0 oscillations
Optimum slender bodies of revolution in newtonian flow(
Book
)
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
The problem of minimizing the drag of a slender body of revolution in Newtonian flow at zero angle of attack is considered. A generalized closed form expression is obtained for the optimum shape which is valid regardless of the conditions imposed on the diameter, length, ettedAREA, AND VOLUME. This expression contains as particular cases those valid when any two of these four quantities are fixed while the remaining are free. A 3/4power law, which previous authors had recognized to be a good approximation to the exact variational solution in Newtonian flow, is found to be a rigorous solution of the EulerLagrange equations if the slender body approximation is used. For the cases considered, analytical expressions are derived for the thickness ratio and the drag coefficient. Also, to verify the minimal properties of the solutions obtained, the optimum shapes are compared. This comparison can be reduced to the bare essenti ls if an appropriate quality coefficient is introduced for the drag. Only in the case where the diameter and the length are given is the quality coefficient proportional to the drag coefficient. Otherwise, it generally involves the product of powers of three dimensionless integrals associated with the drag, the wetted area, and the volume. (Author)
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
The problem of minimizing the drag of a slender body of revolution in Newtonian flow at zero angle of attack is considered. A generalized closed form expression is obtained for the optimum shape which is valid regardless of the conditions imposed on the diameter, length, ettedAREA, AND VOLUME. This expression contains as particular cases those valid when any two of these four quantities are fixed while the remaining are free. A 3/4power law, which previous authors had recognized to be a good approximation to the exact variational solution in Newtonian flow, is found to be a rigorous solution of the EulerLagrange equations if the slender body approximation is used. For the cases considered, analytical expressions are derived for the thickness ratio and the drag coefficient. Also, to verify the minimal properties of the solutions obtained, the optimum shapes are compared. This comparison can be reduced to the bare essenti ls if an appropriate quality coefficient is introduced for the drag. Only in the case where the diameter and the length are given is the quality coefficient proportional to the drag coefficient. Otherwise, it generally involves the product of powers of three dimensionless integrals associated with the drag, the wetted area, and the volume. (Author)
Power radiated by oscillating magnetic and oscillating electric dipoles in a cold, streaming plasma(
Book
)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
The power radiated by oscillating magnetic and oscillating electric point dipoles is calculated for the case where the dipoles are immersed in a cold, streaming plasma. The power output of the dipoles in a streaming plasma is less than it is in a stationary plasma, although the correction term is of order beta squared, where beta is the ratio of the plasma's streaming velocity to the velocity of light. The power output is calculated by a generalized Poynting vector method, using electromagnetic field expressions derived from a set of linearized, covariant cold plasma equations. The results of this paper are compared with the results of Daly, Lee and Papas and of McKenzie who calculate the power output of the oscillating electric dipole from a 'dispersive medium' point of view. (Author)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
The power radiated by oscillating magnetic and oscillating electric point dipoles is calculated for the case where the dipoles are immersed in a cold, streaming plasma. The power output of the dipoles in a streaming plasma is less than it is in a stationary plasma, although the correction term is of order beta squared, where beta is the ratio of the plasma's streaming velocity to the velocity of light. The power output is calculated by a generalized Poynting vector method, using electromagnetic field expressions derived from a set of linearized, covariant cold plasma equations. The results of this paper are compared with the results of Daly, Lee and Papas and of McKenzie who calculate the power output of the oscillating electric dipole from a 'dispersive medium' point of view. (Author)
Effects of thermal expansion on the moments of inertia of the moon(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
Thermal conduction problem for a homogeneous sphere illuminated by a parallel beam of light is solved in terms of FourierBessel expansions; and the resulting nonsymmetric deformation due to thermal expansion is established on the assumption that the (selfgravitating) sphere behaves like an elastic solid. The moments of inertia about the principal axes of so deformed a body are then computed for a configuration approximating in physical properties the lunar globe as deformed by secular effects of insolation; and it is shown that the ratio of the differences of the momenta (CA)/B which can arise from this cause is much too small to account for its value deduced from the librations. (Author)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
Thermal conduction problem for a homogeneous sphere illuminated by a parallel beam of light is solved in terms of FourierBessel expansions; and the resulting nonsymmetric deformation due to thermal expansion is established on the assumption that the (selfgravitating) sphere behaves like an elastic solid. The moments of inertia about the principal axes of so deformed a body are then computed for a configuration approximating in physical properties the lunar globe as deformed by secular effects of insolation; and it is shown that the ratio of the differences of the momenta (CA)/B which can arise from this cause is much too small to account for its value deduced from the librations. (Author)
A REMARK ON CIRCULANTS(
Book
)
1 edition published in 1962 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1962 in English and held by 2 WorldCat member libraries worldwide
Improving the polar method for generating a pair of normal random variables by George Marsaglia(
Book
)
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
Mechanical properties of crust and mantle(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
Variational method for the quantum statistics of interacting particles(
Book
)
1 edition published in 1961 in English and held by 2 WorldCat member libraries worldwide
A variational method is developed for calculating the thermodynamic potential of quantummechanical manybody systems with pairwise interactions. The method is based on Peierls' theorem and yields an upper bound to the thermodynamic potential density in the limit of an infinite system. Evaluation and minimization of the bound involves solution of a set of coupled nonlinear integral equations for the distribution function of elementary excitations and for functions defining a unitary transformation from bare particles to elementary excitations. Application of the theory to the BCS model of superconductivity reproduces the BCS results, and application to a degenerate imperfect Bose gas gives equations which are shown to be equivalent to those of Tolmachev and Wentzel. (Author)
1 edition published in 1961 in English and held by 2 WorldCat member libraries worldwide
A variational method is developed for calculating the thermodynamic potential of quantummechanical manybody systems with pairwise interactions. The method is based on Peierls' theorem and yields an upper bound to the thermodynamic potential density in the limit of an infinite system. Evaluation and minimization of the bound involves solution of a set of coupled nonlinear integral equations for the distribution function of elementary excitations and for functions defining a unitary transformation from bare particles to elementary excitations. Application of the theory to the BCS model of superconductivity reproduces the BCS results, and application to a degenerate imperfect Bose gas gives equations which are shown to be equivalent to those of Tolmachev and Wentzel. (Author)
An investigation of a supersonic surface jethypersonic flow interaction with axial symmetry by Raymond Parmous Shreeve(
Book
)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The complex interaction between a supersonic air jet from a slot with a hypersonic flow of air over a surface was investigated experimentally. The conditions were such that the boundary layer was fully turbulent and both injectant and free stream, at different temperatures, could be considered to be perfect gases. The design of the experiment followed a consideration of the governing nondimensional groups. From physical arguments, the parameters considered to control major changes in the interaction structure, the angle of the jet to the surface, and the jet to free stream pressure ratio, were selected for study. The experiment was carried out at M = 6 using a 5 deg cone with a circumferential slot. Optical observations were made and surface pressures were measured. Impact pressure and stagnation temperature surveys were recorded and reduced to obtain mass flux and other flow profiles using digital computer techniques. (Author)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The complex interaction between a supersonic air jet from a slot with a hypersonic flow of air over a surface was investigated experimentally. The conditions were such that the boundary layer was fully turbulent and both injectant and free stream, at different temperatures, could be considered to be perfect gases. The design of the experiment followed a consideration of the governing nondimensional groups. From physical arguments, the parameters considered to control major changes in the interaction structure, the angle of the jet to the surface, and the jet to free stream pressure ratio, were selected for study. The experiment was carried out at M = 6 using a 5 deg cone with a circumferential slot. Optical observations were made and surface pressures were measured. Impact pressure and stagnation temperature surveys were recorded and reduced to obtain mass flux and other flow profiles using digital computer techniques. (Author)
The equilibrium flow of an ideal dissociating gas over a cone(
Book
)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
The ordinary differential equations are derived for the axiallysymmetric flow over a cone of the Lighthill ideal dissociating gas under thermodynamic equilibrium. By means of trigonometric transformations, the equations are simplified to forms containing only rational functions. The equations are integrated numerically by a fourth order RungeKutta method and a program listing in Fortran is included in the appendix. Tables of pressure, temperature, fraction of dissociation, and cotangent of the local Mach angle on the solid cone boundary are tabulated for free flight at Mach numbers of 8, 10, 12, and 14 in an atmosphere of pure oxygen corresponding to altitudes of 20,063; 32,163; and 47,350 meters and for shocks having a tangent of the cone half angle varying from 0.4 to 1.22. The results are compared with calculations for the ideal perfect gas with a ratio of specific heats = 4/3. (Author)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
The ordinary differential equations are derived for the axiallysymmetric flow over a cone of the Lighthill ideal dissociating gas under thermodynamic equilibrium. By means of trigonometric transformations, the equations are simplified to forms containing only rational functions. The equations are integrated numerically by a fourth order RungeKutta method and a program listing in Fortran is included in the appendix. Tables of pressure, temperature, fraction of dissociation, and cotangent of the local Mach angle on the solid cone boundary are tabulated for free flight at Mach numbers of 8, 10, 12, and 14 in an atmosphere of pure oxygen corresponding to altitudes of 20,063; 32,163; and 47,350 meters and for shocks having a tangent of the cone half angle varying from 0.4 to 1.22. The results are compared with calculations for the ideal perfect gas with a ratio of specific heats = 4/3. (Author)
Wear of small orifices by streaming current driven corrosion by
Theodore R Beck(
Book
)
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Wear on the upstream side of small metal orifices subject to large pressure drops (3000 psi) in phosphate ester base hydraulic fluids was found to be the result of an electrochemical corrosion driven by streaming currents. A theory for the production of the streaming current by the flowing fluid is described. Results of the theory are compared with current measurements and observed wear patterns. A large variation of wall shear stress along the metal surface is found to be necessary for the wear. (Author)
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Wear on the upstream side of small metal orifices subject to large pressure drops (3000 psi) in phosphate ester base hydraulic fluids was found to be the result of an electrochemical corrosion driven by streaming currents. A theory for the production of the streaming current by the flowing fluid is described. Results of the theory are compared with current measurements and observed wear patterns. A large variation of wall shear stress along the metal surface is found to be necessary for the wear. (Author)
IMPACT IONIZATION, BULK NEGATIVE DIFFERENTIAL CONDUCTIVITY AND OTHER NONEQUILIBRIUM CARRIER PHENOMENA IN InSb by Charles Lewis Dick(
Book
)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The hot electron effect, injection, impact ionization and bulk negative differential conductivity are nonequilibrium carrier phenomena that some semiconductors exhibit. In particular, all four phenomena affect conduction in InSb in a strongly interrelated manner. This work shows the interrelationship of these four nonequilibrium phenomena in InSb and describes two new effects: a temporal and spatial relationship between typeN and typeS bulk negative differential conductivity (BNDC) in ntype InSb and the existence of an impact ionization wavefront which is reponsible for the initiation of this carrier generation mechanism in ptype InSb. These results are presented in two parts: Part I contains a discussion of all these nonequilibrium carrier phenomena in ntype InSb, and Part II treats injection and impact ionization in ptype InSb. (Author)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
The hot electron effect, injection, impact ionization and bulk negative differential conductivity are nonequilibrium carrier phenomena that some semiconductors exhibit. In particular, all four phenomena affect conduction in InSb in a strongly interrelated manner. This work shows the interrelationship of these four nonequilibrium phenomena in InSb and describes two new effects: a temporal and spatial relationship between typeN and typeS bulk negative differential conductivity (BNDC) in ntype InSb and the existence of an impact ionization wavefront which is reponsible for the initiation of this carrier generation mechanism in ptype InSb. These results are presented in two parts: Part I contains a discussion of all these nonequilibrium carrier phenomena in ntype InSb, and Part II treats injection and impact ionization in ptype InSb. (Author)
Modules of coherent binary systems by
Z. W Birnbaum(
Book
)
1 edition published in 1964 in English and held by 2 WorldCat member libraries worldwide
The concept of a 'module', i.e. a package of components of a system which can be removed and replaced as a whole, has been long in use in systems design and analysis. In this paper a formal definition of this concept is given and its properties are studied. Most of the results are obtained for 'coherent' systems, i.e. for systems whose performance improves as the performance of their components improves. For such systems the relationship between modules and minimal paths can be fully clarified, and the results obtained lead to a criterion for deciding whether or not a given set of components constitutes a module of a given system. It is shown that a coherent system always has uniquely determined maximal modules which have the property that either all are disjoint or no two of them are disjoint. These maximal modules determine uniquely a decomposition of the system into disjoint modular factors. Furthermore, a theorem on the union of modules (the 'three modules theorem'), which has been previously known for general systems, is obtained by a rather simple argument for coherent systems. (Author)
1 edition published in 1964 in English and held by 2 WorldCat member libraries worldwide
The concept of a 'module', i.e. a package of components of a system which can be removed and replaced as a whole, has been long in use in systems design and analysis. In this paper a formal definition of this concept is given and its properties are studied. Most of the results are obtained for 'coherent' systems, i.e. for systems whose performance improves as the performance of their components improves. For such systems the relationship between modules and minimal paths can be fully clarified, and the results obtained lead to a criterion for deciding whether or not a given set of components constitutes a module of a given system. It is shown that a coherent system always has uniquely determined maximal modules which have the property that either all are disjoint or no two of them are disjoint. These maximal modules determine uniquely a decomposition of the system into disjoint modular factors. Furthermore, a theorem on the union of modules (the 'three modules theorem'), which has been previously known for general systems, is obtained by a rather simple argument for coherent systems. (Author)
On the pressure dependence of the mossbauer effect(
Book
)
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
The occurrence of recoilless radiation aroused widespread interest among solid state physicists because of the sharpness of the resonant lines and of their sensitive dependence upon both the immediate environment of the emitting nuclei and upon the lattice characteristics of the crystals in which they are located. A new relationship, namely the dependence of recoilless radiation upon the ambient pressure of a sample, is investigated and the conditions under which an observable effect is present are discussed. Also presented are brief discussions of some experiments in which this dependence may be further investigated and possibly utilized to advantage. (Author)
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
The occurrence of recoilless radiation aroused widespread interest among solid state physicists because of the sharpness of the resonant lines and of their sensitive dependence upon both the immediate environment of the emitting nuclei and upon the lattice characteristics of the crystals in which they are located. A new relationship, namely the dependence of recoilless radiation upon the ambient pressure of a sample, is investigated and the conditions under which an observable effect is present are discussed. Also presented are brief discussions of some experiments in which this dependence may be further investigated and possibly utilized to advantage. (Author)
Energy gain of a lowenergy charged particle in a standing wave near cyclotron resonance(
Book
)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
Approximate expressions are derived for the energy gain of a charged particle as a result of either being reflected from or of passing entirely through an R.F. standing wave. It is shown that energy gain is obtained only when a d.c. magnetic field is present and commences further from cyclotron resonance as the R.F. field amplitude increases. The exact equations of motion are numerically solved and curves showing energy gain, ratios of perpendicular to longitudinal energy and the time required for reflection are obtained. It is found that the approximate analysis predicts closely the actual phenomena. (Author)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
Approximate expressions are derived for the energy gain of a charged particle as a result of either being reflected from or of passing entirely through an R.F. standing wave. It is shown that energy gain is obtained only when a d.c. magnetic field is present and commences further from cyclotron resonance as the R.F. field amplitude increases. The exact equations of motion are numerically solved and curves showing energy gain, ratios of perpendicular to longitudinal energy and the time required for reflection are obtained. It is found that the approximate analysis predicts closely the actual phenomena. (Author)
Wideband hotcarrier diode gate with application to electronhole plasmas(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A sampling or toneburst gating system using hotcarrier diodes has been designed and shown to have the following characteristics: band width, dc to 1GHz; rise and fall times, typically = or <3nsec and 5nsec; power capacility, about 100mW; gating pulse frquency, 10Hz to 1MHz; gating pulse width, 50nsec to 5msec; leakage,>45db down at 100kHz and about 24 db down at 500MHz; gate isolation from common ground reference,>60db at all frequencies; input and output impedances, adjustable to match source and load. As this gating system consists of two identical gates in parallel, it presents a constant impedance to prevent undesirable loading perturbations of the rf source. The gate can be synchronized with an rf signal whose frequency is = or <1GHz and with the described design changes, may be synchronized with about 10GHz signal. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A sampling or toneburst gating system using hotcarrier diodes has been designed and shown to have the following characteristics: band width, dc to 1GHz; rise and fall times, typically = or <3nsec and 5nsec; power capacility, about 100mW; gating pulse frquency, 10Hz to 1MHz; gating pulse width, 50nsec to 5msec; leakage,>45db down at 100kHz and about 24 db down at 500MHz; gate isolation from common ground reference,>60db at all frequencies; input and output impedances, adjustable to match source and load. As this gating system consists of two identical gates in parallel, it presents a constant impedance to prevent undesirable loading perturbations of the rf source. The gate can be synchronized with an rf signal whose frequency is = or <1GHz and with the described design changes, may be synchronized with about 10GHz signal. (Author)
Pinch oscillations in electronhole plasmas(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
It is a well known fact that a strong current can produce pinching of nonequilibrium electronhole plasmas in InSb; previous reports include a few observations of oscillations in the voltage. The report is a systematic treatment of both theory and observation of pinch oscillations in electronhole plasmas. Part I contains the magnetothermal pinch theory, briefly proposed in 1964 by Drummond and AnckerJohnson and here extended so that quantitative comparison with measurements can be made. The experimental measurements are presented and the results discussed in Part II. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
It is a well known fact that a strong current can produce pinching of nonequilibrium electronhole plasmas in InSb; previous reports include a few observations of oscillations in the voltage. The report is a systematic treatment of both theory and observation of pinch oscillations in electronhole plasmas. Part I contains the magnetothermal pinch theory, briefly proposed in 1964 by Drummond and AnckerJohnson and here extended so that quantitative comparison with measurements can be made. The experimental measurements are presented and the results discussed in Part II. (Author)
The production of largediameter lowvoltage electron beams in the absence of a magnetic field(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
The production of long 10 mm diameter electron beams in the absence of a magnetic field was studied experimentally. The gun design is described at length. Pencil beams of several hundred eV energy were obtained in noble gases in the 120 microns pressure range. However, measurements disclosed that in these spacecharge focused beams there may be a severe diminution of beam electron current with axial distance from the gun. Analyses showed that a large lowenergy electron population exists in the beam volume, forming with the neutralizing positive ions a plasma in which twostream instabilities can develop and produce the spread found in the energy of the primary beam electrons. Space potential measurements showed that a positive potential well existed in the beam volume, resulting in the trapping of the lowenergy electrons. The unavoidable presence of this relatively large population of lowenergy electrons in the beam volume prevented precise measurements of the highenergy beam electron current; reasonable measurements were obtained through special experimental precautions. The beams were studied over a range of the parameters of pressure and beam current, energy, and length. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
The production of long 10 mm diameter electron beams in the absence of a magnetic field was studied experimentally. The gun design is described at length. Pencil beams of several hundred eV energy were obtained in noble gases in the 120 microns pressure range. However, measurements disclosed that in these spacecharge focused beams there may be a severe diminution of beam electron current with axial distance from the gun. Analyses showed that a large lowenergy electron population exists in the beam volume, forming with the neutralizing positive ions a plasma in which twostream instabilities can develop and produce the spread found in the energy of the primary beam electrons. Space potential measurements showed that a positive potential well existed in the beam volume, resulting in the trapping of the lowenergy electrons. The unavoidable presence of this relatively large population of lowenergy electrons in the beam volume prevented precise measurements of the highenergy beam electron current; reasonable measurements were obtained through special experimental precautions. The beams were studied over a range of the parameters of pressure and beam current, energy, and length. (Author)
The development of a thermionic converter module suitable for liquid metal heating by G. Y Eastman(
Book
)
2 editions published in 1963 in English and held by 1 WorldCat member library worldwide
This report describes the continuation of work accomplished under an applied research program to develop a thermionic converter module suitable for liquid metal heating. The A1198B converter, designed for operation in a liquid metal loop, was operated for more than 2400 hours during life test. A technique for bonding the converter to the liquid metal tubing was developed. Design and fabrication methods perfected in the development of the A1198B led to the production of the first multipleunit thermionic energy module. Designated the A1274, the module consisted of three seriesconnected converters in a single vacuumtight envelope using a common cesium reservoir. Modular techniques were extended with the production of a 10converter unit, a complex structure containing many ceramictometal and metaltometal seals. During the program, a number of detailed evaluations of techniques and materials, including cesium compatibility studies, were also made. (Author)
2 editions published in 1963 in English and held by 1 WorldCat member library worldwide
This report describes the continuation of work accomplished under an applied research program to develop a thermionic converter module suitable for liquid metal heating. The A1198B converter, designed for operation in a liquid metal loop, was operated for more than 2400 hours during life test. A technique for bonding the converter to the liquid metal tubing was developed. Design and fabrication methods perfected in the development of the A1198B led to the production of the first multipleunit thermionic energy module. Designated the A1274, the module consisted of three seriesconnected converters in a single vacuumtight envelope using a common cesium reservoir. Modular techniques were extended with the production of a 10converter unit, a complex structure containing many ceramictometal and metaltometal seals. During the program, a number of detailed evaluations of techniques and materials, including cesium compatibility studies, were also made. (Author)
GRADIENT PROJECTION IN HILBERT SPACE(
Book
)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
This note embroiders two simple ideas. The first is a natural generalization of constructive tech niques employed by Kantorovich and Altman for the minimization of quadratic functionals defined on a real Hilbert space H. The extension below is for the minimization of a twice differentiable functional defined on a closed linear manifold in H. Such an extension may appear superfluous because functionals arising in applications are often not even oncerentiable. However, sometimes we can approximate well behaved non differentiable functionals by a differentiable functional. This is the second idea. (Author)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
This note embroiders two simple ideas. The first is a natural generalization of constructive tech niques employed by Kantorovich and Altman for the minimization of quadratic functionals defined on a real Hilbert space H. The extension below is for the minimization of a twice differentiable functional defined on a closed linear manifold in H. Such an extension may appear superfluous because functionals arising in applications are often not even oncerentiable. However, sometimes we can approximate well behaved non differentiable functionals by a differentiable functional. This is the second idea. (Author)
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Languages