scholarly journals A Two-parameter Family of Exponentially-fitted Obrechkoff Methods for Second-order Boundary Value Problems

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ashiribo Wusu
Keyword(s):  
Parameter Family ◽  
Single Frequency ◽  
Frequency Method ◽  
New Methods ◽  
New Family ◽  
Obrechkoff Methods ◽  
Periodic Behaviour ◽  
Leading Term ◽  
Exponentially Fitted ◽  
Two Parameter

Generally, classical numerical methods may not be well suited for problems with oscillatory or periodic behaviour. To overcome this deficiency, they are modified using a technique called exponential fittings. The modification makes it possible to construct new methods suitable for the efficient integration of oscillatory or periodic problems from classical ones.In this work, a two--parameter family of exponentially--fitted Obrechkoff methods for approaching problems that exhibit oscillatory or periodic behaviour is constructed. The construction is based on a six-step flowchart described in [13]. Unlike the single--frequency method in [21], the constructed methods depend upon two frequencies which can be tuned to solve the problem at hand more accurately. The leading term of the local truncation error of the new family of method can also be easily obtained from the given general expression. The efficiency of the new methods is demonstrated on some numerical examples. This work is related to [20,21] and provides extension to the results obtained in [21]

A new family of life distributions

1969 ◽  
Vol 6 (02) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

Summary A new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

A new family of life distributions

1969 ◽  
Vol 6 (2) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

SummaryA new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter

Airborne resistivity and susceptibility mapping in magnetically polarizable areas

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 502-511 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Half Space ◽  
Magnetic Permeability ◽  
Apparent Resistivity ◽  
Dynamic Range ◽  
Single Frequency ◽  
Measured Signal ◽  
Apparent Permeability ◽  
Quadrature Component ◽  
New Methods ◽  
Quadrature Response

The apparent resistivity technique using half‐space models has been employed in helicopter‐borne resistivity mapping for twenty years. These resistivity algorithms yield the apparent resistivity from the measured in‐phase and quadrature response arising from the flow of electrical conduction currents for a given frequency. However, these algorithms, which assume free‐space magnetic permeability, do not yield a reliable value for the apparent resistivity in highly magnetic areas. This is because magnetic polarization also occurs, which modifies the electromagnetic (EM) response, causing the computed resistivity to be erroneously high. Conversely, the susceptibility of a magnetic half‐space can be computed from the measured EM response, assuming an absence of conduction currents. However, the presence of conduction currents will cause the computed susceptibility to be erroneously low. New methods for computing the apparent resistivity and apparent magnetic permeability have been developed for the magnetic conductive half‐space. The in‐phase and quadrature responses at the lowest frequency are first used to estimate the apparent magnetic permeability. The lowest frequency should be used to calculate the permeability because this minimizes the contribution to the measured signal from conduction currents. Knowing the apparent magnetic permeability then allows the apparent resistivity to be computed for all frequencies. The resistivity can be computed using different methods. Because the EM response of magnetic permeability is much greater for the in‐phase component than for the quadrature component, it may be better in highly magnetic environments to derive the resistivity using the quadrature component at two frequencies (the quad‐quad algorithm) rather than using the in‐phase and quadrature response at a single frequency (the in‐phase‐quad algorithm). However, the in‐phase‐quad algorithm has the advantage of dynamic range, and it gives credible resistivity results when the apparent permeability has been obtained correctly.

scholarly journals Three-Stage Two-Parameter Symplectic, Symmetric Exponentially-Fitted Runge-Kutta Methods of Gauss Type

2010 ◽  
Author(s):  
M. Van Daele ◽  
D. Hollevoet ◽  
G. Vanden Berghe ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Gauss Type ◽  
Exponentially Fitted ◽  
Runge Kutta ◽  
Two Parameter

scholarly journals An Initial Assessment of the Surface Reference Technique Applied to Data from the Dual-Frequency Precipitation Radar (DPR) on the GPM Satellite

2015 ◽  
Vol 32 (12) ◽  
pp. 2281-2296 ◽  
Author(s):  
Robert Meneghini ◽  
Hyokyung Kim ◽  
Liang Liao ◽  
Jeffrey A. Jones ◽  
John M. Kwiatkowski
Keyword(s):  
Cross Section ◽  
Radar Data ◽  
Single Frequency ◽  
Initial Assessment ◽  
Dual Frequency ◽  
Precipitation Radar ◽  
Frequency Method ◽  
Ka Band ◽  
Spaceborne Radar ◽  
Ku Band

AbstractIt has long been recognized that path-integrated attenuation (PIA) can be used to improve precipitation estimates from high-frequency weather radar data. One approach that provides an estimate of this quantity from airborne or spaceborne radar data is the surface reference technique (SRT), which uses measurements of the surface cross section in the presence and absence of precipitation. Measurements from the dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement (GPM) satellite afford the first opportunity to test the method for spaceborne radar data at Ka band as well as for the Ku-band–Ka-band combination.The study begins by reviewing the basis of the single- and dual-frequency SRT. As the performance of the method is closely tied to the behavior of the normalized radar cross section (NRCS or σ0) of the surface, the statistics of σ0 derived from DPR measurements are given as a function of incidence angle and frequency for ocean and land backgrounds over a 1-month period. Several independent estimates of the PIA, formed by means of different surface reference datasets, can be used to test the consistency of the method since, in the absence of error, the estimates should be identical. Along with theoretical considerations, the comparisons provide an initial assessment of the performance of the single- and dual-frequency SRT for the DPR. The study finds that the dual-frequency SRT can provide improvement in the accuracy of path attenuation estimates relative to the single-frequency method, particularly at Ku band.

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