Chernoff, Paul R. 1942
Overview
Works:  19 works in 79 publications in 2 languages and 1,555 library holdings 

Genres:  Personal narrativesâ€ˇvAmerican Interviews History Biography 
Roles:  Author, Other 
Classifications:  QA3, 515 
Publication Timeline
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Most widely held works by
Paul R Chernoff
Properties of infinite dimensional Hamiltonian systems by
Paul R Chernoff(
Book
)
23 editions published between 1974 and 2006 in English and German and held by 619 WorldCat member libraries worldwide
23 editions published between 1974 and 2006 in English and German and held by 619 WorldCat member libraries worldwide
Geometry and probability in Banach spaces by
Laurent Schwartz(
Book
)
15 editions published between 1981 and 2006 in English and German and held by 602 WorldCat member libraries worldwide
15 editions published between 1981 and 2006 in English and German and held by 602 WorldCat member libraries worldwide
Product formulas, nonlinear semigroups, and addition of unbounded operators by
Paul R Chernoff(
Book
)
13 editions published in 1974 in English and Undetermined and held by 251 WorldCat member libraries worldwide
This work deals with the general theory, both linear and nonlinear, of operator semigroup product formulas of the type lim [over] n[right arrow][infinity] F(t/n) [superscript]n = G(t). The principal application is the use of the TrotterLie product formula e [superscript]tC = lim [over] n[right arrow][infinity] (e [superscript]t/nA e [superscript]t/nB) [superscript]n to define a generalized addition of semigroup generators, and selfadjoint operators in particular. The properties of generalized addition, both regular and pathological, are discussed
13 editions published in 1974 in English and Undetermined and held by 251 WorldCat member libraries worldwide
This work deals with the general theory, both linear and nonlinear, of operator semigroup product formulas of the type lim [over] n[right arrow][infinity] F(t/n) [superscript]n = G(t). The principal application is the use of the TrotterLie product formula e [superscript]tC = lim [over] n[right arrow][infinity] (e [superscript]t/nA e [superscript]t/nB) [superscript]n to define a generalized addition of semigroup generators, and selfadjoint operators in particular. The properties of generalized addition, both regular and pathological, are discussed
Properties of infinite dimensional Hamiltonian systems by
Paul R Chernoff(
Book
)
1 edition published in 1974 in English and held by 31 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 31 WorldCat member libraries worldwide
Lectures on topology and analysis, and Notes on measure and integration in locally compact spaces by
Paul R Chernoff(
Book
)
4 editions published in 1993 in English and held by 15 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 15 WorldCat member libraries worldwide
Elementary classical analysis by
Jerrold E Marsden(
Book
)
1 edition published in 1974 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 1974 in English and held by 11 WorldCat member libraries worldwide
Lectures on topology and analysis by
Paul R Chernoff(
Book
)
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
The Hopf bifurcation and its applications by
Jerrold E Marsden(
Book
)
4 editions published in 1976 in English and Undetermined and held by 4 WorldCat member libraries worldwide
The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their coworkers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare AndronovHopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper
4 editions published in 1976 in English and Undetermined and held by 4 WorldCat member libraries worldwide
The goal of these notes is to give a reasonahly com plete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to spe cific problems, including stability calculations. Historical ly, the subject had its origins in the works of Poincare [1] around 1892 and was extensively discussed by Andronov and Witt [1] and their coworkers starting around 1930. Hopf's basic paper [1] appeared in 1942. Although the term "Poincare AndronovHopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it. Hopf's crucial contribution was the extension from two dimensions to higher dimensions. The principal technique employed in the body of the text is that of invariant manifolds. The method of Ruelle Takens [1] is followed, with details, examples and proofs added. Several parts of the exposition in the main text come from papers of P. Chernoff, J. Dorroh, O. Lanford and F. Weissler to whom we are grateful. The general method of invariant manifolds is common in dynamical systems and in ordinary differential equations: see for example, Hale [1,2] and Hartman [1]. Of course, other methods are also available. In an attempt to keep the picture balanced, we have included samples of alternative approaches. Specifically, we have included a translation (by L. Howard and N. Kopell) of Hopf's original (and generally unavailable) paper
Product formulas, nonlinear semigroups, and addition of unbouded operators by
Paul R Chernoff(
Book
)
2 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 4 WorldCat member libraries worldwide
Lectures on topology and analysis and Notes on measure and integration in locally compact spaces / William Arveson by
Paul R Chernoff(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Inertial, viscous, and plastic effects in high speed impact by
Thomas David Riney(
Book
)
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
A viscoplastic model for hypervelocity impact is proposed which takes into account inertial, viscous, and plastic effects. This is accomplished by introducing a viscosity factor, a dynamic yield stress, and incorporating these into the compressible fluid equations. From an examination of the resulting system of equations several dimensionless parameters are found which control the relative importance of the three effects at the various stages of the cratering process. The inertial effect is important throughout the early stages while the strength of the medium is dominant during final stages. Immediately after impact the viscous effect is large in the zone near contact interface. Its magnitude decreases as the strainrate gradient decreases, but it may remain important throughout the flow process. In the absence of definitive data in the hypervelocity impact regime, computations are performed on a onedimensional model in which the values of the viscosity factor and yield stress are varied. The above qualitative conclusions are verified, amplified, and related to the qualitative model of crater formation that has evolved from experimental studies in which the actual cratering process has been remonitored. It is found that all three effects are significant. (Author)
2 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
A viscoplastic model for hypervelocity impact is proposed which takes into account inertial, viscous, and plastic effects. This is accomplished by introducing a viscosity factor, a dynamic yield stress, and incorporating these into the compressible fluid equations. From an examination of the resulting system of equations several dimensionless parameters are found which control the relative importance of the three effects at the various stages of the cratering process. The inertial effect is important throughout the early stages while the strength of the medium is dominant during final stages. Immediately after impact the viscous effect is large in the zone near contact interface. Its magnitude decreases as the strainrate gradient decreases, but it may remain important throughout the flow process. In the absence of definitive data in the hypervelocity impact regime, computations are performed on a onedimensional model in which the values of the viscosity factor and yield stress are varied. The above qualitative conclusions are verified, amplified, and related to the qualitative model of crater formation that has evolved from experimental studies in which the actual cratering process has been remonitored. It is found that all three effects are significant. (Author)
Lectures in probability in Banach spaces (Berkeley, spring 1978) by
Laurent Schwartz(
Book
)
1 edition published in 1978 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 2 WorldCat member libraries worldwide
Newton Talks, an oral history project(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Paul Chernoff enlisted in the U.S. Coast and Geodetic Survey (USC & GS) [which became the Environmental Science Services Administration (ESSA Corps) in 1965] in 1961. He underwent Naval officer training at Naval Base Norfolk in Norfolk, VA. He served on the USS Pathfinder, a converted destroyer escort at the Naval Reserve facility in Seattle and at the Pearl Harbor Naval Base in Hawaii. Chernoff was later assigned to the minesweeper vessel, USS Bowie (CSS 27), out of Anchorage, Alaska serving in the Cook Inlet. He ended his service as a Naval Lieutenant in 1964. He discusses the last hydrogen bomb test on Christmas Island, serving as a courier, lessons he learned in the military, and his work with veterans
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Paul Chernoff enlisted in the U.S. Coast and Geodetic Survey (USC & GS) [which became the Environmental Science Services Administration (ESSA Corps) in 1965] in 1961. He underwent Naval officer training at Naval Base Norfolk in Norfolk, VA. He served on the USS Pathfinder, a converted destroyer escort at the Naval Reserve facility in Seattle and at the Pearl Harbor Naval Base in Hawaii. Chernoff was later assigned to the minesweeper vessel, USS Bowie (CSS 27), out of Anchorage, Alaska serving in the Cook Inlet. He ended his service as a Naval Lieutenant in 1964. He discusses the last hydrogen bomb test on Christmas Island, serving as a courier, lessons he learned in the military, and his work with veterans
Geometry and Probalility in Banach Spaces Notes by Laurent Schwartz(
Book
)
1 edition published in 1981 in German and held by 1 WorldCat member library worldwide
1 edition published in 1981 in German and held by 1 WorldCat member library worldwide
Asthma by
Paul R Chernoff(
Book
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Lectures on real analysis by
Paul R Chernoff(
Book
)
3 editions published between 1999 and 2008 in English and German and held by 1 WorldCat member library worldwide
3 editions published between 1999 and 2008 in English and German and held by 1 WorldCat member library worldwide
Praxiswissen der chemischen verfahrenstechnik : handbuch fur chemiker und by
Paul R Chernoff(
Book
)
1 edition published in 2009 in German and held by 1 WorldCat member library worldwide
1 edition published in 2009 in German and held by 1 WorldCat member library worldwide
Semigroup product formulas and addition of unbounded operators by
Paul R Chernoff(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
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Banach spaces Bifurcation theory Bombardment of Nagasakishi (Japan : 1945) Canada Collisions (Physics) Differentiable dynamical systems Differential equations Differential equations, Partial Distribution (Probability theory) Dynamics Functional analysis Geometry Hamiltonian systems ImpactTesting Interviews JapanNagasakishi Linear operators Locally compact spaces MassachusettsNewton Mathematical analysis Mathematicians Mathematics Measure theory Oral history Probabilities Product formulas (Operator theory) Scientists Selfadjoint operators Semigroups Semigroups of operators Stability Topology United States United States.Army Veterans Vietnam War (19611975)