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Higher-Order Linearisability [article]

Andrzej S. Murawski, Nikos Tzevelekos
2016 arXiv   pre-print
In this paper we extend linearisability to the general higher-order setting: methods can be passed as arguments and returned as values. A library may also depend on abstract methods of any order.  ...  We use this generalised notion to show correctness of several higher-order example libraries.  ...  In this paper, we make a further step forward and present linearisability for general higher-order concurrent libraries, where methods can be of arbitrary higher-order types.  ... 
arXiv:1610.07965v1 fatcat:su7ul5qppngv5o3npxtd4s5gmu

Higher-Order Linearisability

Andrzej S. Murawski, Nikos Tzevelekos
2019 Journal of Logical and Algebraic Methods in Programming  
In this paper we extend linearisability to the general higher-order setting, where methods of arbitrary type can be passed as arguments and returned as values, and establish its soundness.  ...  In our framework (higher-order computation with state) specifications are necessarily close to implementations.  ...  Acknowledgements We thank the authors of [3] for bringing the higher-order linearisability problem to our attention.  ... 
doi:10.1016/j.jlamp.2019.01.002 fatcat:2mksk2lghvaondfoeq3bbvko5u

Efficient linearisation of sigma-delta modulators using single-bit dither

C. Dunn, M. Sandler
1995 Electronics Letters  
Idle tones and noise modulation in higher-order sigma-delta modulators (SDMs) can be eliminated using single-bit dither signals, with no additional reduction in dynamic range compared to multilevel dither  ...  For higher-order systems (order > 2), single-bit (BPD) dither can successfully linearise sigmadelta modulators with no significant additional SNR penalty compared to RPD-dithered systems.  ...  For higher-order systems, the SNR penalty for linearisation with single-bit dither is no greater than that paid when using multilevel dither. Fig. 1 . 1 General sigma-delta modulator.  ... 
doi:10.1049/el:19950687 fatcat:7z5cn2scmrc2rpk2siy47b373y

Adaptive Lineariser for RF Wideband Power Amplifier

Prabhat Singh Lakhwal, Maninder Pal, Vijay Kumar
2012 International Journal of Advances in Computing and Information Technology  
This helps reducing the distortion in power amplifiers, resulting in a better linearised output.  ...  The characteristics of this non-linear adaptive lineariser are represented by an analogue polynomial.  ...  (Ideally, the adaptive linearizer polynomia1 should comprises of the infinite number of the higher order terms, but in practise the effects of the higher order terms (above 7th order term) is very less  ... 
doi:10.6088/ijacit.12.14004 fatcat:fcenon34srb77bgyqldhjgi5fy

Improved TPWL Based Nonlinear MOR For Fast Simulation Of Large Circuits

Ammu Chathukulam, Debashree Sarkar, Shifali Kalra, M. Nabi
2018 ECMS 2018 Proceedings edited by Lars Nolle, Alexandra Burger, Christoph Tholen, Jens Werner, Jens Wellhausen  
Trajectory Piecewise Linearisation(TPWL) is one of the nonlinear Model Order Reduction(MOR) techniques that involves multiple linearisations around suitably selected linearisation points(LPs).  ...  Selection of linearisation points play a major role in the accuracy of the reduced order model in TPWL technique.  ...  TRAJECTORY PIECEWISE LINEARISATION The TPWL process includes the following steps: • The higher order system is simulated for a training input to obtain the nonlinear system trajectory. • Location of suitable  ... 
doi:10.7148/2018-0293 dblp:conf/ecms/ChathukulamSKN18 fatcat:524sb6ptizd3fcgqjjtvcihypa

Gauge symmetry of linearised Nordström gravity and the dual spin two field theory [article]

V. A. Abakumova, D. Frolovsky, H.-C. Herbig, S. L. Lyakhovich
2022 arXiv   pre-print
The starting point of the construction is the linearised system of Einstein equations which includes the Nordström equation.  ...  We find the sequence of the reducible gauge transformations for the linearised Nordström equation, with the hook tensor being the initial gauge symmetry parameter.  ...  If the original system is linearised, the inclusion of Stueckelberg fields terminates at squares. In the non-linear case it continues to the higher orders.  ... 
arXiv:2206.07891v1 fatcat:syk2erxg3rckpga6jn6tkk5su4

The Linear Stability of the Schwarzschild Solution to Gravitational Perturbations in the Generalised Wave Gauge

Thomas William Johnson
2019 Annals of PDE  
to gravitational perturbations in the generalised wave gauge, arXiv: 1803.04012, 2018) by modifying the generalised wave gauge employed therein so as to establish asymptotic flatness of the associated linearised  ...  The higher order cases then follow by an inductive procedure and Lemma 3.1, noting that commuting with higher order derivatives generates positively signed lower order terms.  ...  Higher Order Estimates With the key ingredients for the proving the n = 0 case of the Theorem understood we turn now to the higher order cases.  ... 
doi:10.1007/s40818-019-0069-0 fatcat:wgambihaebdlncokqusswfrb6q

Do All Integrable Evolution Equations Have the Painlevé Property?

K.M. Tamizhmani
2007 Symmetry, Integrability and Geometry: Methods and Applications  
We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the Painleve property.  ...  The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional  ...  It suffices to start from a linearisable equation for v of higher order (of which several examples do exist).  ... 
doi:10.3842/sigma.2007.073 fatcat:cndvbayo4nesdnwlkre36tudgu

Comment on the formation of black holes in nonsymmetric gravity [article]

N. J. Cornish, J. W. Moffat
1995 arXiv   pre-print
THE LINEARISED THEORY We shall first consider the lowest-order linearised NGT field equations used to study black hole formation in Ref. [4] .  ...  For weak fields, the higher-order massive modes are suppressed and can be neglected.  ... 
arXiv:gr-qc/9506055v1 fatcat:tezrgbm76vamfgeer2rc3j57pm

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge [article]

Thomas William Johnson
2018 arXiv   pre-print
In particular we improve on our recent work Johnsonlinstabschwarzold by modifying the generalised wave gauge employed therein so as to establish asymptotic flatness of the associated linearised system.  ...  The higher order cases then follow by an inductive procedure and Lemma 3.1, noting that commuting with higher order derivatives generates positively signed lower order terms.  ...  Higher order estimates With the key ingredients for the proving the n = 0 case of the Theorem understood we turn now to the higher order cases.  ... 
arXiv:1810.01337v2 fatcat:zle34emdebgffctfn6s2o4pnkm

Adaptive IIR blind algorithms

Fang-Biau Ueng, Y.T. Su
1995 Electronics Letters  
Simulations: 64-times oversampled modulators with noise-shaping orders between 2 and 5 and with a range of dither amplitudes, were individually optimised to yield maximum dynamic range, using the approach  ...  For higher-order systems, the SNR penalty for linearisation with single-bit dither is no greater than that paid when using multilevel dither.  ...  For higher-order systems (order > 2), single-bit (BPD) dither can successfully linearise sigma-delta modulators with no significant additional SNR penalty compared Proc. 1992 IEEE Int. Symp.  ... 
doi:10.1049/el:19950688 fatcat:ihf4omjirbew5iwbvu5sxm7hvq

The evolution of free and bound waves during dispersive focusing in a numerical and physical flume

Thomas Vyzikas, Dimitris Stagonas, Eugeny Buldakov, Deborah Greaves
2018 Coastal Engineering  
The propagation of such wave groups is associated with high order nonlinearities that can cause considerable deviations from linear and 2 nd order predictions.  ...  The rapid growth of 3 rd and 4 th harmonics near focusing as well as the evolution of the free-wave spectrum, cause departures of up to 29% and 22% from analytic linear and 2 nd order predictions.  ...  It must be noted that the correction of only the linearised part should be the natural choice, since the 2 nd order bound waves (Sharma and Dean, 1981) and the 3 rd order and higher harmonics are uniquely  ... 
doi:10.1016/j.coastaleng.2017.11.003 fatcat:vvhz6aorundyhmpybg2rfcdqdy

Linearization with cosmological perturbation theory

Francisco-Shu Kitaura, Raul E. Angulo
2012 Monthly notices of the Royal Astronomical Society  
We propose a new method to linearise cosmological mass density fields using higher order Lagrangian perturbation theory (LPT).  ...  In addition, we note that this method opens the possibility of use directly higher order LPT on nonlinear fields.  ...  In order to improve this one has to make higher order expansions. The importance of computing the mean field µ was especially emphasized in Kitaura et al. (2010) .  ... 
doi:10.1111/j.1365-2966.2012.21614.x fatcat:33qsw5757zcofkpq3mecjnpqmu

Prediction of the aerodynamic effect of model deformation during transonic wind tunnel tests

Sylvain Mouton, Yves Le Sant, Marianne Lyonnet
2013 International Journal of Engineering Systems Modelling and Simulation  
This illustrates again the non-linear behaviour of the flow field around this flight point and the dominance of higher order terms over the first order ones.  ...  can be added to the first order term computed by adjoint / linearised computation.  ... 
doi:10.1504/ijesms.2013.052371 fatcat:ezgu32xvmbgbjmf4use4s3g2va

On linearisation of microwave-transmitter solid-state power amplifiers

M. O'Droma, E. Bertran, J. Portilla, N. Mgebrishvili, S. Donati Guerrieri, G. Montoro, T. J. Brazil, G. Magerl
2005 International Journal of RF and Microwave Computer-Aided Engineering  
The issues addressed include feedforward, digital, and analog predistortion; feedback (at both circuit and system levels); and context-based bounds for linearisation benefits.  ...  Developments in new and classical RF solid-state power amplifier (SSPA) linearisation techniques, within the context of the EU TARGET ("Top Amplifier Research Groups in a European Team") Network of Excellence's  ...  to achieve a higher degree of linearisation.  ... 
doi:10.1002/mmce.20114 fatcat:eaaloqepdffu3jt54mzuncf5re
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