The VM/SP System Editor XEDIT is used to edit APL objects. Two approaches are possible: with an A... more The VM/SP System Editor XEDIT is used to edit APL objects. Two approaches are possible: with an APL function, or with an exec written in REXX (the new VM/SP System Interpreter). The advantages of the latter are that nothing need be copied into the user's workspace, and that APL code can be executed from XEDIT, and XEDIT commands from APL No new Auxiliary Processor is needed. The technique is in use at IBM Yorktown.
IEEE Transactions on Acoustics, Speech, and Signal Processing, Jun 1, 1976
An alternative form of the fast Fourier transform @ET) is developed. The new algorithm has the pe... more An alternative form of the fast Fourier transform @ET) is developed. The new algorithm has the peculiarity that none of the multiplying constants required are complex-most are pure imaginary.
APL includes a few primitives to permit searching of strings for single characters, principally t... more APL includes a few primitives to permit searching of strings for single characters, principally the dyadic iota. APL2 adds iota underline. This latter function will find all occurrences of a given string in a longer string. Sometimes, however, more elaborate searching is needed; for example, searching for strings of variable length, searching for any of several alternate strings and avoiding of particular strings. In this paper, we describe two APL functions which permit very general string searching and substitution. Patterns describing the search to be done are written in APL with extended syntax. They are converted into a mixture of standard APL and defined functions and executed. The facility described is in experimental use as part of a macro language for the experimental full-screen editor ED3 [1].
Submittal of an algorithm for consideration for publication in Communications of the ACM implies ... more Submittal of an algorithm for consideration for publication in Communications of the ACM implies unrestricted use of the algorithm within a computer is permissible.
This note describes and lists three programs, all written in USASI Basic Fortran, which perform t... more This note describes and lists three programs, all written in USASI Basic Fortran, which perform the discrete Fourier transform upon a multidimensional array of floating point data. The data may be either real or complex, with a savings in running time for real over complex. The transform values are always complex and are returned in the array used to carry the original data. The running time is much shorter than that of any program performing a direct summation, even when sine and cosine values are precalculated and stored in a table. For example, on a CDC 3300 with floating point add time of six microseconds, a complex array of size 80 X 80 can be transformed in 19«2 seconds. Besides the main array, only a working storage array of size l6o need be supplied.
Publisher Summary This chapter discusses application of fast Fourier transform (FFT) in radio ast... more Publisher Summary This chapter discusses application of fast Fourier transform (FFT) in radio astronomy. The Fourier transform is a particularly useful computational technique in radio astronomy. The essence of the FFT technique is that it is possible to treat the one-dimensional DFT as though it were a pseudo-two-dimensional one, and then reduce the running time by performing the inner and outer summations separately. The basic idea behind the FFT is discussed and it is shown how this algorithm is programmed on a digital computer. Because of the requirement for computational speed, a number of programs are given. These include short, moderately efficient subroutines for the transform of one-dimensional, complex data (FOURG and FOURI). With the addition of a subroutine (FXRLI) to either of the above routines, real, one-dimensional data may be transformed in half the time with half the memory storage. Additional subroutines (CFFT2, RFFT2, and HFFT2) permit the transform of two-dimensional data. A program is also given for transforming real, symmetric data for which only the cosine (or sine) transform is desired (FORSI).
Telephone 914-945-1276 (BRENNER at YKTVMX) An experimental full screen editor has been written in... more Telephone 914-945-1276 (BRENNER at YKTVMX) An experimental full screen editor has been written in APL for IBM 3270 display terminals, based on the following principles: a small command repertoire, based on APL syntax an undo facility for correcting mistakes internal dependence upon a small number of editing primitives As written, the editor contains two major commands, thirteen minor commands, and permits all of APL for a macro language. The internal primitives are Erase, Insert Gap, Overlay and Find.
Previous investigations of the evolution of the 3:2 spinorbit resonance state of the planet Mercu... more Previous investigations of the evolution of the 3:2 spinorbit resonance state of the planet Mercury have used simplified mathematical models in which the rotation axis of the planet has been assumed to remain perpendicular to the orbital plane. This thesis investigates the evolution of both the spin rate and the orientation of the rotation axis under tidal and permanentasymmetry torques applied by the Sun. It is found that as the spin rate decreases, the inclination of the equatorial to the orbital plane increases. For initial inclinations of less than 500, the maximum inclination is never greater than 600, and is attained when the spin rate is about three times the orbital mean motion. The effect of such a substantial inclination upon the resonance capture probability depends upon the tidal-friction model. For a viscous friction model, the capture probability is less at each resonance for non-zero inclination than for the previously studied, zero inclination, case. However, for a model in which the tidal torque undergoes a discrete change with passage through the resonant rotation rate, the capture probability is less for non-zero inclination for the odd-halfinteger resonances (3:2, 5:2, etc.), and larger for the even resonances (2:1, 3:1, etc.). Also, the capture probabilities for the discrete-change model are consistently larger (approximately one) than probabilities for the viscous model.
This paper describes my reactions to teaching Visual Basic .NET in an intermediate programming co... more This paper describes my reactions to teaching Visual Basic .NET in an intermediate programming course and lists the new features I have found helpful or confusing.
WITHDRAWN AR IES ACKNOWLEDGEMENTS I would like to thank my two advisors, Professors Shapiro and C... more WITHDRAWN AR IES ACKNOWLEDGEMENTS I would like to thank my two advisors, Professors Shapiro and Counselman, for their assistance in choosing and in carrying out this thesis research. I would also like to thank my wife, but this is impossible, as I am single. ABSTRACT Previous investigations of the evolution of the 3:2 spin-orbit resonance state of the planet Mercury have used simplified mathematical models in which the rotation axis of the planet has been assumed to remain perpendicular to the orbital plane. This thesis investigates the evolution of both the spin rate and the orientation of the rotation axis under tidal and permanent-asymmetry torques applied by the Sun. It is found that as the spin rate decreases, the inclination of the equatorial to the orbital plane increases. For initial inclinations of less than 500, the maximum inclination is never greater than 600, and is attained when the spin rate is about three times the orbital mean motion. The effect of such a substantia...
The programming languages in Microsoft's .NET framework share a common set of constructs for ... more The programming languages in Microsoft's .NET framework share a common set of constructs for building new variable types. Two of them are Class and Structure. They are nearly identical in capability and syntax, except that one creates a reference type object and the other a value type object. Confusion over the difference between them is a fruitful source of programming errors. This paper clearly presents the advantages and the disadvantages of both, for the benefit of improved teaching.
The VM/SP System Editor XEDIT is used to edit APL objects. Two approaches are possible: with an A... more The VM/SP System Editor XEDIT is used to edit APL objects. Two approaches are possible: with an APL function, or with an exec written in REXX (the new VM/SP System Interpreter). The advantages of the latter are that nothing need be copied into the user's workspace, and that APL code can be executed from XEDIT, and XEDIT commands from APL No new Auxiliary Processor is needed. The technique is in use at IBM Yorktown.
IEEE Transactions on Acoustics, Speech, and Signal Processing, Jun 1, 1976
An alternative form of the fast Fourier transform @ET) is developed. The new algorithm has the pe... more An alternative form of the fast Fourier transform @ET) is developed. The new algorithm has the peculiarity that none of the multiplying constants required are complex-most are pure imaginary.
APL includes a few primitives to permit searching of strings for single characters, principally t... more APL includes a few primitives to permit searching of strings for single characters, principally the dyadic iota. APL2 adds iota underline. This latter function will find all occurrences of a given string in a longer string. Sometimes, however, more elaborate searching is needed; for example, searching for strings of variable length, searching for any of several alternate strings and avoiding of particular strings. In this paper, we describe two APL functions which permit very general string searching and substitution. Patterns describing the search to be done are written in APL with extended syntax. They are converted into a mixture of standard APL and defined functions and executed. The facility described is in experimental use as part of a macro language for the experimental full-screen editor ED3 [1].
Submittal of an algorithm for consideration for publication in Communications of the ACM implies ... more Submittal of an algorithm for consideration for publication in Communications of the ACM implies unrestricted use of the algorithm within a computer is permissible.
This note describes and lists three programs, all written in USASI Basic Fortran, which perform t... more This note describes and lists three programs, all written in USASI Basic Fortran, which perform the discrete Fourier transform upon a multidimensional array of floating point data. The data may be either real or complex, with a savings in running time for real over complex. The transform values are always complex and are returned in the array used to carry the original data. The running time is much shorter than that of any program performing a direct summation, even when sine and cosine values are precalculated and stored in a table. For example, on a CDC 3300 with floating point add time of six microseconds, a complex array of size 80 X 80 can be transformed in 19«2 seconds. Besides the main array, only a working storage array of size l6o need be supplied.
Publisher Summary This chapter discusses application of fast Fourier transform (FFT) in radio ast... more Publisher Summary This chapter discusses application of fast Fourier transform (FFT) in radio astronomy. The Fourier transform is a particularly useful computational technique in radio astronomy. The essence of the FFT technique is that it is possible to treat the one-dimensional DFT as though it were a pseudo-two-dimensional one, and then reduce the running time by performing the inner and outer summations separately. The basic idea behind the FFT is discussed and it is shown how this algorithm is programmed on a digital computer. Because of the requirement for computational speed, a number of programs are given. These include short, moderately efficient subroutines for the transform of one-dimensional, complex data (FOURG and FOURI). With the addition of a subroutine (FXRLI) to either of the above routines, real, one-dimensional data may be transformed in half the time with half the memory storage. Additional subroutines (CFFT2, RFFT2, and HFFT2) permit the transform of two-dimensional data. A program is also given for transforming real, symmetric data for which only the cosine (or sine) transform is desired (FORSI).
Telephone 914-945-1276 (BRENNER at YKTVMX) An experimental full screen editor has been written in... more Telephone 914-945-1276 (BRENNER at YKTVMX) An experimental full screen editor has been written in APL for IBM 3270 display terminals, based on the following principles: a small command repertoire, based on APL syntax an undo facility for correcting mistakes internal dependence upon a small number of editing primitives As written, the editor contains two major commands, thirteen minor commands, and permits all of APL for a macro language. The internal primitives are Erase, Insert Gap, Overlay and Find.
Previous investigations of the evolution of the 3:2 spinorbit resonance state of the planet Mercu... more Previous investigations of the evolution of the 3:2 spinorbit resonance state of the planet Mercury have used simplified mathematical models in which the rotation axis of the planet has been assumed to remain perpendicular to the orbital plane. This thesis investigates the evolution of both the spin rate and the orientation of the rotation axis under tidal and permanentasymmetry torques applied by the Sun. It is found that as the spin rate decreases, the inclination of the equatorial to the orbital plane increases. For initial inclinations of less than 500, the maximum inclination is never greater than 600, and is attained when the spin rate is about three times the orbital mean motion. The effect of such a substantial inclination upon the resonance capture probability depends upon the tidal-friction model. For a viscous friction model, the capture probability is less at each resonance for non-zero inclination than for the previously studied, zero inclination, case. However, for a model in which the tidal torque undergoes a discrete change with passage through the resonant rotation rate, the capture probability is less for non-zero inclination for the odd-halfinteger resonances (3:2, 5:2, etc.), and larger for the even resonances (2:1, 3:1, etc.). Also, the capture probabilities for the discrete-change model are consistently larger (approximately one) than probabilities for the viscous model.
This paper describes my reactions to teaching Visual Basic .NET in an intermediate programming co... more This paper describes my reactions to teaching Visual Basic .NET in an intermediate programming course and lists the new features I have found helpful or confusing.
WITHDRAWN AR IES ACKNOWLEDGEMENTS I would like to thank my two advisors, Professors Shapiro and C... more WITHDRAWN AR IES ACKNOWLEDGEMENTS I would like to thank my two advisors, Professors Shapiro and Counselman, for their assistance in choosing and in carrying out this thesis research. I would also like to thank my wife, but this is impossible, as I am single. ABSTRACT Previous investigations of the evolution of the 3:2 spin-orbit resonance state of the planet Mercury have used simplified mathematical models in which the rotation axis of the planet has been assumed to remain perpendicular to the orbital plane. This thesis investigates the evolution of both the spin rate and the orientation of the rotation axis under tidal and permanent-asymmetry torques applied by the Sun. It is found that as the spin rate decreases, the inclination of the equatorial to the orbital plane increases. For initial inclinations of less than 500, the maximum inclination is never greater than 600, and is attained when the spin rate is about three times the orbital mean motion. The effect of such a substantia...
The programming languages in Microsoft's .NET framework share a common set of constructs for ... more The programming languages in Microsoft's .NET framework share a common set of constructs for building new variable types. Two of them are Class and Structure. They are nearly identical in capability and syntax, except that one creates a reference type object and the other a value type object. Confusion over the difference between them is a fruitful source of programming errors. This paper clearly presents the advantages and the disadvantages of both, for the benefit of improved teaching.
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