The Arm Prime Factors Decomposition
|
|
- Thomas Ward
- 6 years ago
- Views:
Transcription
1 The Arm Prime Factors Decomosition Boris Arm To cite this version: Boris Arm. The Arm Prime Factors Decomosition HAL Id: hal htts://hal.archives-ouvertes.fr/hal Submitted on 10 Ar 2013 HAL is a multi-discilinary oen access archive for the deosit and dissemination of scientific research documents, whether they are ublished or not. The documents may come from teaching and research institutions in France or abroad, or from ublic or rivate research centers. L archive ouverte luridiscilinaire HAL, est destinée au déôt et à la diffusion de documents scientifiques de niveau recherche, ubliés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires ublics ou rivés.
2 The Arm Prime Factors Decomosition Arm Boris Nima Abstract We introduce the Arm rime factors decomosition which is the equivalent of the Taylor formula for decomosition of integers on the basis of rime numbers. We make the link between this decomosition and the -adic norm known in the -adic numbers theory. To see how it works, we give examles of these two formulas.
3 Introduction The Arm theory [1] gives the decomosition of functions on each function basis. Also, because the fundamental arithmetic theorem tells us each integers can be decomose in rime factors, I wondered if it was ossible to build the decomosition of integers on the basis of rime integers. As a matter of fact, this is ossible and the answer of this question is the Arm rime factors decomosition. To build an equivalent of the Taylor formula for the rime numbers basis, we need to find a good scalar roduct on this basis. In first lace, I remarked that if a rime number P divise an integer n N + then the difference between it and its integer art would be zero whereas that if does not divise n then the same difference would be ositive. In mathematical words it means : [ ] n n if n then = 0 otherwise n ] [ n > However, we need to build a Kronecker which is one when n is why we take the exonential minus 0.1 multily by x : n δ n = lim ex is an integer and zero otherwise. This [ ] n x 0.2 which is one when divise n and zero otherwhise. For all that, it still remains the roblem of the multilicity m i of each rime number i because 0.2 tells us only if a rime number is in the rime factors decomosition of an integer n. Thus we have to sum all the ower of if we want to know the multilicity of each factor : δ m n = m i 0.3 With all these ingredients, we build the final Arm rime factors decomosition formula 1.5 which is nothing else that the multilication of 0.3 by the logarithm of all rime numbers. In this case the formula 0.3 gives a -adic valuation in the -adic number theory. Thus we can give an exlicit exression for the well-known -adic norm of rational numbers used in the -adic numbers theory : a = δ m b δ m a 0.4 b for each rime numbers P. 1
4 In the first section, we introduce the Arm rime factors decomosition formula which gives the decomosition of each integer in the rime numbers basis. After describing the scalar roduct, we give in the second section a full examle of rime factors decomosition with the number which is nothing else that Next in the third section, we give the formula of the -adic norm and, in the fourth section, we calculate all -adic norm of the rational which is
5 1 The Arm Prime Factors Decomosition Formula We give the rojection on the rime integers basis of each ositive integer n Theorem 1. n N + the Arm rime factors decomosition is given by lnn = [ ] n n lim ex m m x P where [ ] is the integer art and P is the set of all rime numbers. ln 1.5 Proof : The main idea here is that if m n i.e. m divise n then n N + and n m Q + \ N +. In other m words, we have that if m n then n is an integer so it is equal to its integer arts. m Because n [ ] n m 0, we can construct the Kronecker m N m δ m n : [ ] n n lim ex m m x = 1 if m n [ ] n n lim ex m m x = 0 otherwise 1.6 If we consider the usual rime factors decomosition showed in the fundamental theorem of arithmetic: n = i m i 1.8 i=1 where m i is the multilicity of each rime factors i P. IntheArmrimefactors decomosition formula, themultilicity m i of each rimefactor i is obtained by summing the Kronecker : [ ] n n lim ex m m x With 1.9, we can find the Arm rime factors decomosition formula 1.5 : which is the final result. lnn = i = i = P lnn = P m i ln i lim n lim ex lim ex ex m i n m [ n n m m i [ n m 1.7 = m i 1.9 [ n m ] x ln i ] x ln ] x ln
6 Remark 1. We can deduce of the Arm rime factors decomosition formula 1.5 that the scalar roduct of the logarithm of each integer n N + on the basis {ln} P is given by < lnn,ln > = lim which the multilicity of each rime factor. [ ] n n ex m m x 1.11 Corollary 1. Each integer n N + can be decomosed in : n = [ lim ex n m n ]x m P 1.12 Proof : We just take the exonential of Examle Of Arm Prime Factors decomosition HerewealytheArmrimefactorsdecomostion formulatofindtherimefactors oftheinteger : n = The formula 1.5 gives : lnn = ln2 lim e n 2 [n 2 ]x +e n 2 2[ n 2 2]x +e n 2 3[ n 2 3]x ln3 lim e n 3 [n 3 ]x +e n 3 2[ n 3 2]x +e n 3 3[ n 3 3]x +e n 3 4[ n 3 4]x ln5 lim e n 5 [n 5 ]x +e n 5 2[ n 5 2]x +e n 5 3[ n 5 3]x +e n 5 4[ n 5 4]x +e n 5 5[ n 5 5]x +e n 5 6[ n 5 6]x ln7 lim e n 7 [n 7 ]x +e n 7 2[ n 7 2]x +e n 7 3[ n 7 3]x +e n 7 4[ n 7 4]x +e n 7 5[ n 7 5]x +e n 7 6[ n 7 6]x +e n 7 7[ n 7 7]x +e n 7 8[ n 7 8]x
7 which is with the value of n : lnn = ln2 lim e [ ]x +e [ ]x +e [ ]x ln3 lim e [ ]x +e [ ]x +e [ ]x +e [ ]x ln5 lim e [ ]x +e [ ]x +e [ ]x +e [ ]x +e [ ]x +e [ ]x ln7 lim e [ ]x +e [ ]x +e [ ]x +e [ ]x +e [ ]x +e [ ]x +e [337500]x +e [ ]x When we evaluate, it becomes : lnn = ln2 lim 1+1+e x ln3 lim e x ln5 lim e 0.8x ln7 lim e 0.3x +... So we have the decomosition of lnn in rime factors : lnn = 2ln2+3ln3+5ln5+7ln Hence If we define the integer function n = = Υ Υi = k k 2.20 k P;k i 5
8 3 Link with the -adic numbers The formula 1.9 of an integer n gives the multilicity of an rime factor. This multilicity is called the -adic valuation in the -adic numbers theory. We give here its exlicit exression Proosition 1. The -adic valuation of a rime factor i of an integer n is given by [ ] n n v n = lim ex m m x Proof : See 1.9. Now, with the -adic valuation, we can define the corresonding -adic norm Proosition 2. The -adic norm of a rational number a b Q, where a and b are corime, is given by a = lim [ [ ex b m b ]x m ex a m a ]x m 3.22 b or its logarithm is : a ln = b lim Proof : The -adic norm of an integer a : [ ] [ ] b b a a ex m m x ex m m x a = i ln 3.23 i mi 3.24 as in 1.8, where the rime factor i P and m i is the multilicity of each i, is defined as a i = m i i 3.25 However we know from 1.9 that the multilicity of each rime factor is given by i [ ] a a lim ex m m x = m i 3.26 Hence the -adic norm of n 3.25 is given by [ a i = lim ex a m a ]x m i 3.27 And so the -adic norm of a rational a b Q is given by a [ b = lim ex b m b ]x m i i which gives the formula ex [ a m a ]x m
9 4 Examle of -adic norm As examle, we consider the rational : a = 4.29 b With the formula 3.22, we can first calculate the 2-adic norm [ ] [ ] ln = lim ex 2 2 m 2 m x ex 2 m 2 m x ln 2 [ ] [ ] = lim ex 2 x ex 2 2 x ln 2 2 ln = ln or in the exonential form : = Now we calculate the 3-adic norm ln = lim 3 = lim + ln 3 or in the exonential form : lim Now we calculate the 5-adic norm ln = lim 5 = lim ex ex ex [ 3 m 3 m [ ] 3 x ex 3 [ ] 9 x ex 9 ] x ex [ ] 3 m 3 m x ln 3 [ ] 3 x ln 3 3 [ ] 9 x ln 3 9 = 2 ln ln 5 or in the exonential form : lim ex ex = ex [ 5 m 5 m [ ] 5 x ex 5 [ ] 25 x ex 25 ] x ex 4.33 [ ] 5 m 5 m x ln 5 [ ] 5 x ln 5 5 [ ] 25 x ln 5 25 = 2 ln =
10 Now we calculate the 7-adic norm ln = lim 7 ln 7 = or in the exonential form : lim ex Now we calculate the 11-adic norm ln = lim 11 ln 11 ex 7 [ 7 m 7 m [ ] x 7 ] x ex ex 7 [ 7 m 7 m [ ] x 7 ] x ln 7 ln 7 = ln = or in the exonential form : lim ex = ex 11 [ 11 m 11 m [ ] x 11 ] x ex ex [ ] 11 m 11 m x ] x ln 11 [ 11 ln 11 = ln = And we have that = {2,3,5,7,11}. So we have the rime factors decomosition of a b =
11 Discussion Maybe the Arm rime factors formula 1.5 is too simle but it gives a ractical way to calculate the decomosition of every logarithms of integers on the basis of the logarithm of rime numbers. However, the Arm rime factors decomosition formula 1.5 is not efficient when it is rogrammed on comuters because it does the same work as the traditional algorithm it checks if the division is an integer or not. In addition, the traditional algorithm which do the rime factorization is faster than this one. The only utility of my formula is that it gives a ractical formula in the theory. Furthermore in the formula 1.5 there is summation over ositive integers and we have to sto it until a big value if we want the algorithm to be finish. Besides there is an other summation over rime numbers and the algorithm needs to calculate all the rime numbers so it takes a lot of time for calculating. After all, I ve decided to write this article even if the algorithm is not efficient because the formulas are right and give the results. 9
12 Références [1] Arm B. N., The Arm Theory 10
The Arm Prime Factors Decomposition
The Arm Prime Factors Decomosition Arm Boris Nima arm.boris@gmail.com Abstract We introduce the Arm rime factors decomosition which is the equivalent of the Taylor formula for decomosition of integers
More informationA filter-based computational homogenization method for handling non-separated scales problems
A filter-based comutational homogenization method for handling non-searated scales roblems Julien Yvonnet, Amen Tognevi, Guy Bonnet, Mohamed Guerich To cite this version: Julien Yvonnet, Amen Tognevi,
More informationThe sum of digits function in finite fields
The sum of digits function in finite fields Cécile Dartyge, András Sárközy To cite this version: Cécile Dartyge, András Sárközy. The sum of digits function in finite fields. Proceedings of the American
More informationA new simple recursive algorithm for finding prime numbers using Rosser s theorem
A new simple recursive algorithm for finding prime numbers using Rosser s theorem Rédoane Daoudi To cite this version: Rédoane Daoudi. A new simple recursive algorithm for finding prime numbers using Rosser
More informationA construction of bent functions from plateaued functions
A construction of bent functions from lateaued functions Ayca Cesmelioglu, Wilfried Meidl To cite this version: Ayca Cesmelioglu, Wilfried Meidl. A construction of bent functions from lateaued functions.
More informationMethylation-associated PHOX2B gene silencing is a rare event in human neuroblastoma.
Methylation-associated PHOX2B gene silencing is a rare event in human neuroblastoma. Loïc De Pontual, Delphine Trochet, Franck Bourdeaut, Sophie Thomas, Heather Etchevers, Agnes Chompret, Véronique Minard,
More informationBonding a linearly piezoelectric patch on a linearly elastic body
onding a linearly iezoelectric atch on a linearly elastic body Christian Licht, omsak Orankitjaroen, Patcharakorn Viriyasrisuwattana, Thibaut Weller To cite this version: Christian Licht, omsak Orankitjaroen,
More informationPublic Key Cryptosystems RSA
Public Key Crytosystems RSA 57 17 Receiver Sender 41 19 and rime 53 Attacker 47 Public Key Crytosystems RSA Comute numbers n = * 2337 323 57 17 Receiver Sender 41 19 and rime 53 Attacker 2491 47 Public
More informationA new approach of the concept of prime number
A new approach of the concept of prime number Jamel Ghannouchi To cite this version: Jamel Ghannouchi. A new approach of the concept of prime number. 4 pages. 24. HAL Id: hal-3943 https://hal.archives-ouvertes.fr/hal-3943
More informationAN OPTIMAL CONTROL CHART FOR NON-NORMAL PROCESSES
AN OPTIMAL CONTROL CHART FOR NON-NORMAL PROCESSES Emmanuel Duclos, Maurice Pillet To cite this version: Emmanuel Duclos, Maurice Pillet. AN OPTIMAL CONTROL CHART FOR NON-NORMAL PRO- CESSES. st IFAC Worsho
More informationEaster bracelets for years
Easter bracelets for 5700000 years Denis Roegel To cite this version: Denis Roegel. Easter bracelets for 5700000 years. [Research Report] 2014. HAL Id: hal-01009457 https://hal.inria.fr/hal-01009457
More informationSmart Bolometer: Toward Monolithic Bolometer with Smart Functions
Smart Bolometer: Toward Monolithic Bolometer with Smart Functions Matthieu Denoual, Gilles Allègre, Patrick Attia, Olivier De Sagazan To cite this version: Matthieu Denoual, Gilles Allègre, Patrick Attia,
More informationCase report on the article Water nanoelectrolysis: A simple model, Journal of Applied Physics (2017) 122,
Case report on the article Water nanoelectrolysis: A simple model, Journal of Applied Physics (2017) 122, 244902 Juan Olives, Zoubida Hammadi, Roger Morin, Laurent Lapena To cite this version: Juan Olives,
More informationUnderstanding Big Data Spectral Clustering
Understanding Big Data Sectral Clustering Romain Couillet, Florent Benaych-Georges To cite this version: Romain Couillet, Florent Benaych-Georges. Understanding Big Data Sectral Clustering. IEEE 6th International
More informationOn Newton-Raphson iteration for multiplicative inverses modulo prime powers
On Newton-Raphson iteration for multiplicative inverses modulo prime powers Jean-Guillaume Dumas To cite this version: Jean-Guillaume Dumas. On Newton-Raphson iteration for multiplicative inverses modulo
More informationPasserelle entre les arts : la sculpture sonore
Passerelle entre les arts : la sculpture sonore Anaïs Rolez To cite this version: Anaïs Rolez. Passerelle entre les arts : la sculpture sonore. Article destiné à l origine à la Revue de l Institut National
More informationCan we reduce health inequalities? An analysis of the English strategy ( )
Can we reduce health inequalities? An analysis of the English strategy (1997-2010) Johan P Mackenbach To cite this version: Johan P Mackenbach. Can we reduce health inequalities? An analysis of the English
More informationSoundness of the System of Semantic Trees for Classical Logic based on Fitting and Smullyan
Soundness of the System of Semantic Trees for Classical Logic based on Fitting and Smullyan Shahid Rahman To cite this version: Shahid Rahman. Soundness of the System of Semantic Trees for Classical Logic
More informationExact Comparison of Quadratic Irrationals
Exact Comparison of Quadratic Irrationals Phuc Ngo To cite this version: Phuc Ngo. Exact Comparison of Quadratic Irrationals. [Research Report] LIGM. 20. HAL Id: hal-0069762 https://hal.archives-ouvertes.fr/hal-0069762
More informationFrom Unstructured 3D Point Clouds to Structured Knowledge - A Semantics Approach
From Unstructured 3D Point Clouds to Structured Knowledge - A Semantics Approach Christophe Cruz, Helmi Ben Hmida, Frank Boochs, Christophe Nicolle To cite this version: Christophe Cruz, Helmi Ben Hmida,
More informationNew estimates for the div-curl-grad operators and elliptic problems with L1-data in the half-space
New estimates for the div-curl-grad operators and elliptic problems with L1-data in the half-space Chérif Amrouche, Huy Hoang Nguyen To cite this version: Chérif Amrouche, Huy Hoang Nguyen. New estimates
More informationNumerical Exploration of the Compacted Associated Stirling Numbers
Numerical Exploration of the Compacted Associated Stirling Numbers Khaled Ben Letaïef To cite this version: Khaled Ben Letaïef. Numerical Exploration of the Compacted Associated Stirling Numbers. 2017.
More informationEvolution of the cooperation and consequences of a decrease in plant diversity on the root symbiont diversity
Evolution of the cooperation and consequences of a decrease in plant diversity on the root symbiont diversity Marie Duhamel To cite this version: Marie Duhamel. Evolution of the cooperation and consequences
More informationAnalysis of Boyer and Moore s MJRTY algorithm
Analysis of Boyer and Moore s MJRTY algorithm Laurent Alonso, Edward M. Reingold To cite this version: Laurent Alonso, Edward M. Reingold. Analysis of Boyer and Moore s MJRTY algorithm. Information Processing
More informationMATH342 Practice Exam
MATH342 Practice Exam This exam is intended to be in a similar style to the examination in May/June 2012. It is not imlied that all questions on the real examination will follow the content of the ractice
More informationThere are infinitely many twin primes 30n+11 and 30n+13, 30n+17 and 30n+19, 30n+29 and 30n+31
There are infinitely many twin primes 30n+11 and 30n+13, 30n+17 and 30n+19, 30n+29 and 30n+31 Sibiri Christian Bandre To cite this version: Sibiri Christian Bandre. There are infinitely many twin primes
More informationDispersion relation results for VCS at JLab
Dispersion relation results for VCS at JLab G. Laveissiere To cite this version: G. Laveissiere. Dispersion relation results for VCS at JLab. Compton Scattering from Low to High Momentum Transfer, Mar
More informationL institution sportive : rêve et illusion
L institution sportive : rêve et illusion Hafsi Bedhioufi, Sida Ayachi, Imen Ben Amar To cite this version: Hafsi Bedhioufi, Sida Ayachi, Imen Ben Amar. L institution sportive : rêve et illusion. Revue
More informationVibro-acoustic simulation of a car window
Vibro-acoustic simulation of a car window Christophe Barras To cite this version: Christophe Barras. Vibro-acoustic simulation of a car window. Société Française d Acoustique. Acoustics 12, Apr 12, Nantes,
More informationA numerical approach of Friedrichs systems under constraints in bounded domains
A numerical aroach of Friedrichs systems under constraints in bounded domains Clément Mifsud, Bruno Desrés To cite this version: Clément Mifsud, Bruno Desrés. A numerical aroach of Friedrichs systems under
More informationEntropies and fractal dimensions
Entropies and fractal dimensions Amelia Carolina Sparavigna To cite this version: Amelia Carolina Sparavigna. Entropies and fractal dimensions. Philica, Philica, 2016. HAL Id: hal-01377975
More informationOn size, radius and minimum degree
On size, radius and minimum degree Simon Mukwembi To cite this version: Simon Mukwembi. On size, radius and minimum degree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no.
More informationb-chromatic number of cacti
b-chromatic number of cacti Victor Campos, Claudia Linhares Sales, Frédéric Maffray, Ana Silva To cite this version: Victor Campos, Claudia Linhares Sales, Frédéric Maffray, Ana Silva. b-chromatic number
More informationAlgebraic Parameter Estimation of Damped Exponentials
Algebraic Parameter Estimation of Damed Exonentials Aline Neves, Maria Miranda, Mamadou Mbou To cite this version: Aline Neves, Maria Miranda, Mamadou Mbou Algebraic Parameter Estimation of Damed Exonentials
More informationA remark on a theorem of A. E. Ingham.
A remark on a theorem of A. E. Ingham. K G Bhat, K Ramachandra To cite this version: K G Bhat, K Ramachandra. A remark on a theorem of A. E. Ingham.. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2006,
More informationStickelberger s congruences for absolute norms of relative discriminants
Stickelberger s congruences for absolute norms of relative discriminants Georges Gras To cite this version: Georges Gras. Stickelberger s congruences for absolute norms of relative discriminants. Journal
More informationThomas Lugand. To cite this version: HAL Id: tel
Contribution à la Modélisation et à l Optimisation de la Machine Asynchrone Double Alimentation pour des Applications Hydrauliques de Pompage Turbinage Thomas Lugand To cite this version: Thomas Lugand.
More informationOn the longest path in a recursively partitionable graph
On the longest path in a recursively partitionable graph Julien Bensmail To cite this version: Julien Bensmail. On the longest path in a recursively partitionable graph. 2012. HAL Id:
More informationCompleteness of the Tree System for Propositional Classical Logic
Completeness of the Tree System for Propositional Classical Logic Shahid Rahman To cite this version: Shahid Rahman. Completeness of the Tree System for Propositional Classical Logic. Licence. France.
More informationOn Symmetric Norm Inequalities And Hermitian Block-Matrices
On Symmetric Norm Inequalities And Hermitian lock-matrices Antoine Mhanna To cite this version: Antoine Mhanna On Symmetric Norm Inequalities And Hermitian lock-matrices 015 HAL Id: hal-0131860
More informationOn the performance of greedy algorithms for energy minimization
On the erformance of greedy algorithms for energy minimization Anne Benoit, Paul Renaud-Goud, Yves Robert To cite this version: Anne Benoit, Paul Renaud-Goud, Yves Robert On the erformance of greedy algorithms
More informationOptimizing Power Allocation in Interference Channels Using D.C. Programming
Otimizing Power Allocation in Interference Channels Using D.C. Programming Hussein Al-Shatri, Tobias Weber To cite this version: Hussein Al-Shatri, Tobias Weber. Otimizing Power Allocation in Interference
More informationOn path partitions of the divisor graph
On path partitions of the divisor graph Paul Melotti, Eric Saias To cite this version: Paul Melotti, Eric Saias On path partitions of the divisor graph 018 HAL Id: hal-0184801 https://halarchives-ouvertesfr/hal-0184801
More informationHook lengths and shifted parts of partitions
Hook lengths and shifted parts of partitions Guo-Niu Han To cite this version: Guo-Niu Han Hook lengths and shifted parts of partitions The Ramanujan Journal, 009, 9 p HAL Id: hal-00395690
More informationAll Associated Stirling Numbers are Arithmetical Triangles
All Associated Stirling Numbers are Arithmetical Triangles Khaled Ben Letaïef To cite this version: Khaled Ben Letaïef. All Associated Stirling Numbers are Arithmetical Triangles. 2017.
More informationSolution to Sylvester equation associated to linear descriptor systems
Solution to Sylvester equation associated to linear descriptor systems Mohamed Darouach To cite this version: Mohamed Darouach. Solution to Sylvester equation associated to linear descriptor systems. Systems
More informationThe FLRW cosmological model revisited: relation of the local time with th e local curvature and consequences on the Heisenberg uncertainty principle
The FLRW cosmological model revisited: relation of the local time with th e local curvature and consequences on the Heisenberg uncertainty principle Nathalie Olivi-Tran, Paul M Gauthier To cite this version:
More informationA Simple Proof of P versus NP
A Simple Proof of P versus NP Frank Vega To cite this version: Frank Vega. A Simple Proof of P versus NP. 2016. HAL Id: hal-01281254 https://hal.archives-ouvertes.fr/hal-01281254 Submitted
More informationTorsion subgroups of quasi-abelianized braid groups
Torsion subgrous of quasi-abelianized braid grous Vincent Beck, Ivan Marin To cite this version: Vincent Beck, Ivan Marin. Torsion subgrous of quasi-abelianized braid grous. 2017. HAL Id:
More informationA non-commutative algorithm for multiplying (7 7) matrices using 250 multiplications
A non-commutative algorithm for multiplying (7 7) matrices using 250 multiplications Alexandre Sedoglavic To cite this version: Alexandre Sedoglavic. A non-commutative algorithm for multiplying (7 7) matrices
More informationOn a series of Ramanujan
On a series of Ramanujan Olivier Oloa To cite this version: Olivier Oloa. On a series of Ramanujan. Gems in Experimental Mathematics, pp.35-3,, . HAL Id: hal-55866 https://hal.archives-ouvertes.fr/hal-55866
More informationA note on the computation of the fraction of smallest denominator in between two irreducible fractions
A note on the computation of the fraction of smallest denominator in between two irreducible fractions Isabelle Sivignon To cite this version: Isabelle Sivignon. A note on the computation of the fraction
More informationThe Riemann Hypothesis Proof And The Quadrivium Theory
The Riemann Hypothesis Proof And The Quadrivium Theory Thierno M. Sow To cite this version: Thierno M. Sow. The Riemann Hypothesis Proof And The Quadrivium Theory. 2017. HAL Id: hal-01513658 https://hal.archives-ouvertes.fr/hal-01513658
More informationNumerical Modeling of Eddy Current Nondestructive Evaluation of Ferromagnetic Tubes via an Integral. Equation Approach
Numerical Modeling of Eddy Current Nondestructive Evaluation of Ferromagnetic Tubes via an Integral Equation Approach Anastassios Skarlatos, Grégoire Pichenot, Dominique Lesselier, Marc Lambert, Bernard
More informationSolving the neutron slowing down equation
Solving the neutron slowing down equation Bertrand Mercier, Jinghan Peng To cite this version: Bertrand Mercier, Jinghan Peng. Solving the neutron slowing down equation. 2014. HAL Id: hal-01081772
More informationOn The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method
On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method S. Salman Nourazar, Mohsen Soori, Akbar Nazari-Golshan To cite this version: S. Salman Nourazar, Mohsen Soori,
More informationTowards an active anechoic room
Towards an active anechoic room Dominique Habault, Philippe Herzog, Emmanuel Friot, Cédric Pinhède To cite this version: Dominique Habault, Philippe Herzog, Emmanuel Friot, Cédric Pinhède. Towards an active
More informationPractice Final Solutions
Practice Final Solutions 1. Find integers x and y such that 13x + 1y 1 SOLUTION: By the Euclidean algorithm: One can work backwards to obtain 1 1 13 + 2 13 6 2 + 1 1 13 6 2 13 6 (1 1 13) 7 13 6 1 Hence
More informationFORMAL TREATMENT OF RADIATION FIELD FLUCTUATIONS IN VACUUM
FORMAL TREATMENT OF RADIATION FIELD FLUCTUATIONS IN VACUUM Frederic Schuller, Renaud Savalle, Michael Neumann-Spallart To cite this version: Frederic Schuller, Renaud Savalle, Michael Neumann-Spallart.
More informationNonlocal computational methods applied to composites structures
Nonlocal computational methods applied to composites structures Norbert Germain, Frédéric Feyel, Jacques Besson To cite this version: Norbert Germain, Frédéric Feyel, Jacques Besson. Nonlocal computational
More informationOn Symmetric Norm Inequalities And Hermitian Block-Matrices
On Symmetric Norm Inequalities And Hermitian lock-matrices Antoine Mhanna To cite this version: Antoine Mhanna On Symmetric Norm Inequalities And Hermitian lock-matrices 016 HAL Id: hal-0131860
More informationA Slice Based 3-D Schur-Cohn Stability Criterion
A Slice Based 3-D Schur-Cohn Stability Criterion Ioana Serban, Mohamed Najim To cite this version: Ioana Serban, Mohamed Najim. A Slice Based 3-D Schur-Cohn Stability Criterion. ICASSP 007, Apr 007, Honolulu,
More informationFull-order observers for linear systems with unknown inputs
Full-order observers for linear systems with unknown inputs Mohamed Darouach, Michel Zasadzinski, Shi Jie Xu To cite this version: Mohamed Darouach, Michel Zasadzinski, Shi Jie Xu. Full-order observers
More informationCharacterization of the local Electrical Properties of Electrical Machine Parts with non-trivial Geometry
Characterization of the local Electrical Properties of Electrical Machine Parts with non-trivial Geometry Laure Arbenz, Abdelkader Benabou, Stéphane Clenet, Jean Claude Mipo, Pierre Faverolle To cite this
More informationSound intensity as a function of sound insulation partition
Sound intensity as a function of sound insulation partition S. Cvetkovic, R. Prascevic To cite this version: S. Cvetkovic, R. Prascevic. Sound intensity as a function of sound insulation partition. Journal
More informationPractice Final Solutions
Practice Final Solutions 1. True or false: (a) If a is a sum of three squares, and b is a sum of three squares, then so is ab. False: Consider a 14, b 2. (b) No number of the form 4 m (8n + 7) can be written
More informationOn sl3 KZ equations and W3 null-vector equations
On sl3 KZ equations and W3 null-vector equations Sylvain Ribault To cite this version: Sylvain Ribault. On sl3 KZ equations and W3 null-vector equations. Conformal Field Theory, Integrable Models, and
More informationWater Vapour Effects in Mass Measurement
Water Vapour Effects in Mass Measurement N.-E. Khélifa To cite this version: N.-E. Khélifa. Water Vapour Effects in Mass Measurement. Measurement. Water Vapour Effects in Mass Measurement, May 2007, Smolenice,
More informationAxiom of infinity and construction of N
Axiom of infinity and construction of N F Portal To cite this version: F Portal. Axiom of infinity and construction of N. 2015. HAL Id: hal-01162075 https://hal.archives-ouvertes.fr/hal-01162075 Submitted
More informationVarious Proofs for the Decrease Monotonicity of the Schatten s Power Norm, Various Families of R n Norms and Some Open Problems
Int. J. Oen Problems Comt. Math., Vol. 3, No. 2, June 2010 ISSN 1998-6262; Coyright c ICSRS Publication, 2010 www.i-csrs.org Various Proofs for the Decrease Monotonicity of the Schatten s Power Norm, Various
More informationFactorisation of RSA-704 with CADO-NFS
Factorisation of RSA-704 with CADO-NFS Shi Bai, Emmanuel Thomé, Paul Zimmermann To cite this version: Shi Bai, Emmanuel Thomé, Paul Zimmermann. Factorisation of RSA-704 with CADO-NFS. 2012. HAL Id: hal-00760322
More informationCutwidth and degeneracy of graphs
Cutwidth and degeneracy of graphs Benoit Kloeckner To cite this version: Benoit Kloeckner. Cutwidth and degeneracy of graphs. IF_PREPUB. 2009. HAL Id: hal-00408210 https://hal.archives-ouvertes.fr/hal-00408210v1
More informationA Study of the Regular Pentagon with a Classic Geometric Approach
A Study of the Regular Pentagon with a Classic Geometric Approach Amelia Carolina Sparavigna, Mauro Maria Baldi To cite this version: Amelia Carolina Sparavigna, Mauro Maria Baldi. A Study of the Regular
More informationSparse multivariate factorization by mean of a few bivariate factorizations
Sparse multivariate factorization by mean of a few bivariate factorizations Bernard Parisse To cite this version: Bernard Parisse. Sparse multivariate factorization by mean of a few bivariate factorizations.
More informationA Simple Model for Cavitation with Non-condensable Gases
A Simple Model for Cavitation with Non-condensable Gases Mathieu Bachmann, Siegfried Müller, Philippe Helluy, Hélène Mathis To cite this version: Mathieu Bachmann, Siegfried Müller, Philippe Helluy, Hélène
More informationThe Zenith Passage of the Sun in the Plan of Brasilia
The Zenith Passage of the Sun in the Plan of Brasilia Amelia Carolina Sparavigna To cite this version: Amelia Carolina Sparavigna. The Zenith Passage of the Sun in the Plan of Brasilia. Philica, Philica,
More informationThe Learner s Dictionary and the Sciences:
The Learner s Dictionary and the Sciences: Geoffrey Williams To cite this version: Geoffrey Williams. The Learner s Dictionary and the Sciences:: Mismatch or no match?. Corpora, Language, Teaching, and
More informationVoltage Stability of Multiple Distributed Generators in Distribution Networks
oltage Stability of Multiple Distributed Generators in Distribution Networks Andi Wang, Chongxin Liu, Hervé Guéguen, Zhenquan Sun To cite this version: Andi Wang, Chongxin Liu, Hervé Guéguen, Zhenquan
More informationChebyshev polynomials, quadratic surds and a variation of Pascal s triangle
Chebyshev polynomials, quadratic surds and a variation of Pascal s triangle Roland Bacher To cite this version: Roland Bacher. Chebyshev polynomials, quadratic surds and a variation of Pascal s triangle.
More informationLorentz force velocimetry using small-size permanent magnet systems and a multi-degree-of-freedom force/torque sensor
Lorentz force velocimetry using small-size permanent magnet systems and a multi-degree-of-freedom force/torque sensor D Hernández, C Karcher To cite this version: D Hernández, C Karcher. Lorentz force
More informationUnbiased minimum variance estimation for systems with unknown exogenous inputs
Unbiased minimum variance estimation for systems with unknown exogenous inputs Mohamed Darouach, Michel Zasadzinski To cite this version: Mohamed Darouach, Michel Zasadzinski. Unbiased minimum variance
More informationThe Accelerated Euclidean Algorithm
The Accelerated Euclidean Algorithm Sidi Mohamed Sedjelmaci To cite this version: Sidi Mohamed Sedjelmaci The Accelerated Euclidean Algorithm Laureano Gonzales-Vega and Thomas Recio Eds 2004, University
More informationMultiple sensor fault detection in heat exchanger system
Multiple sensor fault detection in heat exchanger system Abdel Aïtouche, Didier Maquin, Frédéric Busson To cite this version: Abdel Aïtouche, Didier Maquin, Frédéric Busson. Multiple sensor fault detection
More informationOn production costs in vertical differentiation models
On production costs in vertical differentiation models Dorothée Brécard To cite this version: Dorothée Brécard. On production costs in vertical differentiation models. 2009. HAL Id: hal-00421171
More informationEddy-Current Effects in Circuit Breakers During Arc Displacement Phase
Eddy-Current Effects in Circuit Breakers During Arc Displacement Phase Olivier Chadebec, Gerard Meunier, V. Mazauric, Yann Le Floch, Patrice Labie To cite this version: Olivier Chadebec, Gerard Meunier,
More informationOn Poincare-Wirtinger inequalities in spaces of functions of bounded variation
On Poincare-Wirtinger inequalities in spaces of functions of bounded variation Maïtine Bergounioux To cite this version: Maïtine Bergounioux. On Poincare-Wirtinger inequalities in spaces of functions of
More informationFast Computation of Moore-Penrose Inverse Matrices
Fast Computation of Moore-Penrose Inverse Matrices Pierre Courrieu To cite this version: Pierre Courrieu. Fast Computation of Moore-Penrose Inverse Matrices. Neural Information Processing - Letters and
More informationConfluence Algebras and Acyclicity of the Koszul Complex
Confluence Algebras and Acyclicity of the Koszul Complex Cyrille Chenavier To cite this version: Cyrille Chenavier. Confluence Algebras and Acyclicity of the Koszul Complex. Algebras and Representation
More informationNorm Inequalities of Positive Semi-Definite Matrices
Norm Inequalities of Positive Semi-Definite Matrices Antoine Mhanna To cite this version: Antoine Mhanna Norm Inequalities of Positive Semi-Definite Matrices 15 HAL Id: hal-11844 https://halinriafr/hal-11844v1
More informationComparison of Harmonic, Geometric and Arithmetic means for change detection in SAR time series
Comparison of Harmonic, Geometric and Arithmetic means for change detection in SAR time series Guillaume Quin, Béatrice Pinel-Puysségur, Jean-Marie Nicolas To cite this version: Guillaume Quin, Béatrice
More informationDetermination of absorption characteristic of materials on basis of sound intensity measurement
Determination of absorption characteristic of materials on basis of sound intensity measurement R. Prascevic, A. Milosevic, S. Cvetkovic To cite this version: R. Prascevic, A. Milosevic, S. Cvetkovic.
More informationExogenous input estimation in Electronic Power Steering (EPS) systems
Exogenous input estimation in Electronic Power Steering (EPS) systems Valentina Ciarla, Carlos Canudas de Wit, Franck Quaine, Violaine Cahouet To cite this version: Valentina Ciarla, Carlos Canudas de
More informationParallel Repetition of entangled games on the uniform distribution
Parallel Repetition of entangled games on the uniform distribution André Chailloux, Scarpa Giannicola To cite this version: André Chailloux, Scarpa Giannicola. Parallel Repetition of entangled games on
More informationTheoretical calculation of the power of wind turbine or tidal turbine
Theoretical calculation of the power of wind turbine or tidal turbine Pierre Lecanu, Joel Breard, Dominique Mouazé To cite this version: Pierre Lecanu, Joel Breard, Dominique Mouazé. Theoretical calculation
More informationSome diophantine problems concerning equal sums of integers and their cubes
Some diophantine problems concerning equal sums of integers and their cubes Ajai Choudhry To cite this version: Ajai Choudhry. Some diophantine problems concerning equal sums of integers and their cubes.
More informationTeaching Reitlinger Cycles To Improve Students Knowledge And Comprehension Of Thermodynamics
Teaching Reitlinger Cycles To Improve Students Knowledge nd Comprehension Of Thermodynamics melia Carolina Sparavigna To cite this version: melia Carolina Sparavigna. Teaching Reitlinger Cycles To Improve
More informationBasic concepts and models in continuum damage mechanics
Basic concepts and models in continuum damage mechanics Djimedo Kondo, Hélène Welemane, Fabrice Cormery To cite this version: Djimedo Kondo, Hélène Welemane, Fabrice Cormery. Basic concepts and models
More informationWidely Linear Estimation with Complex Data
Widely Linear Estimation with Complex Data Bernard Picinbono, Pascal Chevalier To cite this version: Bernard Picinbono, Pascal Chevalier. Widely Linear Estimation with Complex Data. IEEE Transactions on
More informationParticle-in-cell simulations of high energy electron production by intense laser pulses in underdense plasmas
Particle-in-cell simulations of high energy electron production by intense laser pulses in underdense plasmas Susumu Kato, Eisuke Miura, Mitsumori Tanimoto, Masahiro Adachi, Kazuyoshi Koyama To cite this
More informationSTATISTICAL ENERGY ANALYSIS: CORRELATION BETWEEN DIFFUSE FIELD AND ENERGY EQUIPARTITION
STATISTICAL ENERGY ANALYSIS: CORRELATION BETWEEN DIFFUSE FIELD AND ENERGY EQUIPARTITION Thibault Lafont, Alain Le Bot, Nicolas Totaro To cite this version: Thibault Lafont, Alain Le Bot, Nicolas Totaro.
More information