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Higher-Order Distributions for Differential Linear Logic [chapter]

Marie Kerjean, Jean-Simon Pacaud Lemay
2019 Green Chemistry and Sustainable Technology  
This extends what was done previously by Kerjean for first order Differential Linear Logic without promotion.  ...  Concretely, we follow the previous idea of interpreting the exponential of Differential Linear Logic as a space of higher-order distributions with compact-support, which is constructed as an inductive  ...  Differential Linear Logic (DiLL) [7] is a refinement of Linear Logic which allows for a notion of linear approximation of non-linear proofs.  ... 
doi:10.1007/978-3-030-17127-8_19 dblp:conf/fossacs/KerjeanL19 fatcat:dgkvio2mnrdsbl2hm6sh4pbyw4

Book announcements

1991 Discrete Applied Mathematics  
Continuity, consistency, and completeness properties for logic programs (L. Cavedon). A deduction procedure for first order programs (D. Lugiez).  ...  Chapter 11: Techniques of differentiation. Maximum and minimum values of a function. Higher derivatives. Curvature. Chapter 13: Non-Linear Equations. Location of roots.  ... 
doi:10.1016/0166-218x(91)90051-w fatcat:oqpbdxzpljcihecb5tgyinpmva

High Speed Serial Link Transmitter for 10Gig Ethernet Applications

Navin K. Ramamoorthy, Jayabharath Reddy M, Vishwanath Muniyappa
2010 2010 23rd International Conference on VLSI Design  
This paper presents a Current Mode Logic (CML) transmitter circuit that forms part of a Serializer/ Deserializer IP core used in a high speed I/O links targeted for 10+ Gbps Ethernet applications.  ...  The paper also discusses on the design optimization implemented using hybrid segmentation of driver segments which results in improved control on the step sizes variations, Differential Non Linearity (  ...  Fishkill, New York for valuable technical guidance, insights and managerial support of this project. References  ... 
doi:10.1109/vlsi.design.2010.51 dblp:conf/vlsid/RamamoorthyMM10 fatcat:rwzxnhmjazcz3g4hf6h7f4gycq

FASiM: A Framework for Automatic Formal Analysis of Simulink Models of Linear Analog Circuits [article]

Adnan Rashid, Ayesha Gauhar, Osman Hasan
2020 arXiv   pre-print
Higher-order-logic theorem proving is a formal verification method that has been recently proposed to overcome these limitations for the modeling and the Laplace transform based analysis of linear analog  ...  Moreover, due to the undecidable nature of higher-order logic, the analysis generally requires a significant amount of user guidance in the manual proof process.  ...  Higher-order-logic theorem proving has also been used for formally analyzing the Simulink models. Chen et al.  ... 
arXiv:2001.06702v1 fatcat:pvhvnadd2bggzg57cs47j3cn34

Book reports

1999 Computers and Mathematics with Applications  
Some remarks on the distribution of subsequences of second order linear recurrences (John R. Burke).  ...  Optimization techniques for stable reduced order controllers for partial differential equations (Belinda B. King and Ekkehard W. Sachs).  ... 
doi:10.1016/s0898-1221(99)90501-1 fatcat:bruc2kcm5zgfvnvygclnl3we6m

On the formal analysis of Gaussian optical systems in HOL

Umair Siddique, Sofiène Tahar
2016 Formal Aspects of Computing  
This paper provides a higher-order-logic formalization of fractional calculus based on the Riemann-Liouville approach using the HOL theorem prover.  ...  To overcome this limitation, we propose to leverage upon the high expressiveness of higher-order logic to formalize the theory of fractional calculus, which is the foremost mathematical concept in analyzing  ...  of the given system in higher-order logic.  ... 
doi:10.1007/s00165-016-0367-1 fatcat:env7aa6ivzbojly4pr4rwcgj2e

Page 2074 of Mathematical Reviews Vol. , Issue 98C [page]

1998 Mathematical Reviews  
order logics ........... *68024 Tokyo, 1994 * 65005 Topics in complex analysis, differential geometry and mathematical physics Topological social choice Toronto, ON, 1996 Townsville, 1997  ...  ordinary differential equations * 82001 * 81004 Harmonic analysis and nonlinear differential equations Hauptvermutung book Higher-dimensional complex varieties Honolulu, HI, 1995 Human-like systems using  ... 

Jets and differential linear logic [article]

James Wallbridge
2019 arXiv   pre-print
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic.  ...  The exponential modality is modelled by composing the jet comonad, whose Kleisli category has linear differential operators as morphisms, with the more familiar distributional comonad, whose Kleisli category  ...  Acknowledgements The author would like to thank Kazuo Yano and Daniel Murfet for comments. We also thank the anonymous referees whose comments led to significant improvements to the paper.  ... 
arXiv:1811.06235v2 fatcat:6dudi3zffjdhzi4isvfqteh2qm

Book reports

2005 Computers and Mathematics with Applications  
A.1 Second-order partial differential equations. A.2 Systems of first-order PDEs. Appendix B Elements of linear algebra. B.1 Eigenvalues and eigenvectors. B.2 Vector and matrix norms. Bibliography.  ...  logic. 2.6 Expressiveness of predicate logic. 2.6.1 Existential second-order logic. 2.6.2 Universal second-order logic. 2.7 Micromodels of software. 2.7.1 State machines. 2.7.2 Alma -re-visited. 2.7.3  ... 
doi:10.1016/j.camwa.2005.04.001 fatcat:melc2iqigrh6tn37ldct5k73jm

Page 7397 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
(P-INIC-AM; Lisbon) The linear Cauchy problem for a class of differential equations with distributional coefficients. (English summary) Portugal. Math. 52 (1995), no. 4, 379-390.  ...  second-order ordinary differential equations.  ... 

Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light [chapter]

Syeda Hira Taqdees, Osman Hasan
2013 Lecture Notes in Computer Science  
In particular, we use integral, differential, transcendental and topological theories of multivariable calculus to formally define Laplace transform in higher-order logic and reason about the correctness  ...  of Laplace transform properties, such as existence, linearity, frequency shifting and differentiation and integration in time domain.  ...  This work was supported by the National Research Program for Universities grant (number 1543) of Higher Education Commission (HEC), Pakistan.  ... 
doi:10.1007/978-3-642-45221-5_50 fatcat:fks2jihksrfalktlbopv5weapy

Page 325 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 67, Issue 3 [page]

1961 American Mathematical Society. Bulletin of the American Mathematical Society  
Lytle, New York University, February, Differentiators for linear second order elliptic partial differential equations. E. B.  ...  McKay, University of Buffalo, February, minor in Philos- ophy, An extension of the Staudt-Clausen and Kummer congruences for the Bernoulli numbers of higher order. D. R.  ... 

Differential Learning Algorithm for Artificial Neural Networks

R Manjunath, Shyam vasudev, Narendranath Udupa
2010 International Journal of Computer Applications  
The different orders of differential feed back form a manifold of hyperplanes. Interesting properties of this differentially fed ANN (DANN) are derived through these hyperplanes.  ...  Various architectures are available for the ANNs to speedup the training period and reduce the square error. In this paper, new classes of neural networks with differential feedback are presented.  ...  The error distribution is assumed to be Gaussian distributed since a large number of additions are involved with the higher order differential feedback.  ... 
doi:10.5120/381-571 fatcat:nwccpb3etrhbha3omidflchhhi

Page 540 of Applied Mechanics Reviews Vol. 13, Issue 8 [page]

1960 Applied Mechanics Reviews  
In this case, however, paper is a trivial application, in bad notation, of well-known fact that the Fourier transform of a linear differential equation with linear coefficients is a linear, first-order  ...  Vague comments are made about generalizations to higher-order polynomials, but the fact is that, in general, only when the polynomials are linear can the method be of any real value, since only in this  ... 

Design And Implementation Of A Cyclic ADC For CMOS Image Sensors

O. Venkata Kris hna, CVR College of Engineering/EIE, Hyderabad, India, B. Janardhana Rao, CVR College of Engineering/ECE, Hyderabad, India
2014 CVR Journal of Science & Technology  
The improvement of lithography and solid-state technologies provide the possibility of manufacturing higher resolution image sensors, as they provide possibilities for reduced power consumption and integration  ...  In this paper a 12-bit Cyclic ADC (CADC) is designed and implemented in 180nm CMOS technology aimed for column-parallel readout implementation in CMOS image sensors.  ...  Figure 10 : 10 A principal logic diagram of the implemented Sub-AD encoding control logic. Figure 11 . 11 Differential Non-Linearity deviation distribution.  ... 
doi:10.32377/cvrjst0604 fatcat:hotwo2tsizhkhgm4zpi52q5tum
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