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On a Formula for the Product-Moment Coefficient of any Order of a Normal Frequency Distribution in any Number of Variables

L. Isserlis
1918 Biometrika  
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.  ...  We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. .  ...  for a normal frequency distribution in any number of variables. 2.  ... 
doi:10.2307/2331932 fatcat:chq3gohngjha3bhdtn6qge3c6q

Geometric classification of 4d N = 2 $$ \mathcal{N}=2 $$ SCFTs

Matteo Caorsi, Sergio Cecotti
2018 Journal of High Energy Physics  
The number N(k) of dimensions allowed in rank k is given by a certain sum of the Erdös-Bateman Number-Theoretic function (sequence A070243 in OEIS) so that for large k N(k)=2 ζ(2) ζ(3)/ζ(6) k^2+o(k^2).  ...  In the special case k=2 our dimension formula reproduces a recent result by Argyres et al. Class Field Theory implies a subtlety: certain dimension k-tuples {Δ_1,...  ...  Acknowledgments We thank Michele Del Zotto for several interesting discussions about the classification of SCFT which prompted this project.  ... 
doi:10.1007/jhep07(2018)138 fatcat:2quy4tbwirhh5hcqpktn7qljii

Squares in (2^2-1)...(n^2-1) and p-adic valuation [article]

Shaofang Hong, Xingjiang Liu
2009 arXiv   pre-print
We also give a formula for the p-adic valuation of the terms in this sequence.  ...  In this paper, we determine all the squares in the sequence {∏_k=2^n(k^2-1)}_n=2^∞ . From this, one deduces that there are infinitely many squares in this sequence.  ...  The authors would like to thank the referee for helpful comments.  ... 
arXiv:0810.3366v3 fatcat:narmq6eflveazmzg5yr3z5mtfq

O(N/sup 2/log/sub 2/N) filtered backprojection reconstruction algorithm for tomography

S. Basu, Y. Bresler
2000 IEEE Transactions on Image Processing  
Comparisons with Fourier reconstruction algorithms and a recent multilevel inversion algorithm by Brandt et al., both of which also have ( 2 log 2 ) cost, suggest that the proposed hierarchical scheme  ...  We present a new fast reconstruction algorithm for parallel beam tomography.  ...  O(N 2 log 2 N) Filtered Backprojection I.  ... 
doi:10.1109/83.869187 pmid:18262914 fatcat:cntj72ld4vgo3htktepjscuwl4

$(4+2\log n)\Delta G$ Parallel Prefix Modulo- $(2^n-3)$ Adder via Double Representation of Residues in [0, 2]

Ghassem Jaberipur, Seyed Hamed Fatemi Langroudi
2015 IEEE Transactions on Circuits and Systems - II - Express Briefs  
The most popular modulus in residue number systems (RNS), next to power-of-two modulus, are those of the form (2 n − 1).  ...  However, in RNS applications that require a larger dynamic range, without increasing the n parameter, modulus of the form (2 n − 3) are gaining popularity.  ...  Digital Object Identifier 10.1109/TCSII.2015.2407772 Fig. 1 . 1 (a) RPP and (b) TPP adders of [4] and the (c) constituent elements. Fig. 2 . 2 Two-stage modulo-(2 n − 3) adder [7] .  ... 
doi:10.1109/tcsii.2015.2407772 fatcat:6clhvdl6rzferpapxlho22ar3i

Asymptotics for the number of directions determined by [n] × [n] in 𝔽_p^2 [article]

Greg Martin, Ethan Patrick White, Chi Hoi Yip
2021 arXiv   pre-print
For any arithmetic progression A of length n in 𝔽_p, we establish an asymptotic formula for the number of directions determined by A × A ⊂𝔽_p^2.  ...  The key idea is to reduce the problem to counting the number of solutions to the bilinear Diophantine equation ad+bc=p in variables 1≤ a,b,c,d≤ n; our asymptotic formula for the number of solutions is  ...  The research of the third author was supported in part by a Four Year Doctoral Fellowship from the University of British Columbia.  ... 
arXiv:2107.01311v1 fatcat:7zpaf4kgqjgohbqkzn7pnxxymy

T, Q and periods in SU(3) N$$ \mathcal{N} $$ = 2 SYM

Davide Fioravanti, Hasmik Poghosyan, Rubik Poghossian
2020 Journal of High Energy Physics  
We consider the third order differential equation derived from the deformed Seiberg-Witten differential for pure N = 2 SYM with gauge group SU(3) in Nekrasov-Shatashvili limit of Ω-background.  ...  We show that this is the same differential equation that emerges in the context of Ordinary Differential Equation/Integrable Models (ODE/IM) correspondence for 2d A 2 Toda CFT with central charge c = 98  ...  D.F. thanks the GGI for Theoretical Physics for invitation to the workshop 'Supersymmetric Quantum Field Theories in the Non-perturbative Regime'.  ... 
doi:10.1007/jhep03(2020)049 fatcat:knzt3qdjtnglvjeqos7x2wnkp4

Rank-2 attractors and Fermat type CY n-folds [article]

Wenzhe Yang
2020 arXiv   pre-print
For n=3,4,6,8,10, we have numerically found that the value of the mirror map t for the Fermat pencil at the Fermat point ψ=0 is of the form t|_ψ=0=1/2+ξ i, where ξ is a real algebraic number that intuitively  ...  Furthermore, we have also numerically found that the quotient c^+(𝐇^n_a,1)/c^-(𝐇^n_a,1) of the Deligne's periods of 𝐇^n_a,1 is an algebraic number for the cases where n=3,4,6,8,10, and in fact we will  ...  Here we list the first dozens digits of them . The charges for the split at the Fermat point.  ... 
arXiv:2005.06722v2 fatcat:b4wakkgdira3xffxihnbmczg2e

Arithmetic properties of coefficients of power series expansion of $$\prod _{n=0}^{\infty }\left( 1-x^{2^{n}}\right) ^{t}$$ ∏ n = 0 ∞ 1 - x 2 n t (with an appendix by Andrzej Schinzel)

Maciej Gawron, Piotr Miska, Maciej Ulas
2017 Monatshefte für Mathematik (Print)  
For t ∈ Z <0 the n-th term of the sequence ( f n (t)) nN counts the number of representations of the number n as a sum of powers of 2 where each summand can have one among −t colors.  ...  Next, we present the exact value of the 2-adic valuation of the number f n (1 − 2 m )-a result which generalizes the well known expression concerning the 2-adic valuation of the values of the binary partition  ...  Acknowledgements The authors are grateful to the referee for a careful reading of the manuscript and valuable suggestions, which improved the quality of the paper.  ... 
doi:10.1007/s00605-017-1041-2 fatcat:g77mnk3b4jgx3hp5w7jdfbrpze

AUSTRAL: v.2, n.3 (2013)

Paulo Visentini
2013 Austral  
All of the contributions will be subjected to a scientific review.  ...  the debate and the diffusion of the knowledge produced in these regions.  ...  the Digital Age.  ... 
doi:10.22456/2238-6912.37107 fatcat:z3didvoykvagrkrzql5qzet7lu

Modeling of wave driven molecular (H/sub 2/, N/sub 2/, A/sub 2/-Ar) discharges as atomic sources

C.M. Ferreira, E. Tatarova, V. Guerra, B.F. Gordiets, J. Henriques, F.M. Dias, M. Pinheiro
2003 IEEE Transactions on Plasma Science  
The kinetics of N( 4 S) and metastable N( 2 D) and N( 2 P) atoms and of the molecular N 2 (A 3 6 + ) metastable state in a pure N 2 discharge are shown to be strongly coupled.  ...  The dissociation kinetics is discussed in the framework of theoretical models based on a self-consistent treatment of the main discharge balances, wave electrodynamics and plasma-wall interactions.  ...  Digital Object Identifier 10.1109/TPS.2003.815481 the conditions at the end of the source determine the initial conditions for the postdischarge. Fig. 1 . 1 Experimental setup.  ... 
doi:10.1109/tps.2003.815481 fatcat:dazkz6feb5andmmrzaoghkmxri

On Families Of 2^N-Dimensional Hypercomplex Algebras Suitable For Digital Signal Processing

Daniel Alfsmann
2006 Zenodo  
Publication in the conference proceedings of EUSIPCO, Florence, Italy, 2006  ...  In doing so, the objective is to translate well-known algebra properties from mathematics to the engineering community in a systematic manner by constituting families of 2 N -dimensional algebras.  ...  In general, there are options for both the decomposition level d (the number of orthogonal components) and the choice of the orthogonal base, resulting in an associated subalgebra E of dimension h = n  ... 
doi:10.5281/zenodo.52940 fatcat:sifslhxlkjdrxb4dq77adnykny

Synthesis, Molecular Docking Studies, In Vitro Antimicrobial and Antifungal Activities of Novel Dipeptide Derivatives Based on N-(2-(2-Hydrazinyl-2-oxoethylamino)-2-oxoethyl)-Nicotinamide

Gaber Moustafa, Hemat Khalaf, Ahmed Naglah, Asma Al-Wasidi, Nawal Al-Jafshar, Hassan Awad
2018 Molecules  
A series of linear dipeptide derivatives (4-10) were prepared and evaluated as antimicrobial agents via the synthesis of N-(2-(2-hydrazinyl-2-oxoethylamino)-2-oxoethyl) nicotinamide (4).  ...  Compounds 4, 5, and 9 gave the most promising activity in this study. Most of the tested compounds possessed MIC values ranging from 50 to 500 µg/mL.  ...  Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/molecules23040761 pmid:29584635 fatcat:e67fgxvhvfavnciynf6ocitqka

An $O(N^2 )$ Method for Computing the Eigensystem of $N \times N$ Symmetric Tridiagonal Matrices by the Divide and Conquer Approach

Doron Gill, Eitan Tadmor
1990 SIAM Journal on Scientific and Statistical Computing  
It exploits the fact that by O(N 2 ) of DC operations, one can compute the eigenvalues of N x N ST matrix and a finite number of pairs of successive rows of its eigenvector matrix.  ...  We conclude with numerical examples, which demonstrate the superiority of the proposed method .. by saving an order of magnitude in execution time at the expense of sacrificing a few orders of accuracy  ...  A serial implementation of this algorithm, described in Section 2, requires the same number of operations.  ... 
doi:10.1137/0911010 fatcat:wmppm3miyfdd7m3fpmsemefhyy

Critical behavior ofO(2)⊗O(N)symmetric models

Pasquale Calabrese, Pietro Parruccini, Andrea Pelissetto, Ettore Vicari
2004 Physical Review B  
The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion  ...  In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models.  ...  ACKNOWLEDGMENTS We thank Maurizio Davini for his indispensable technical assistance to manage the computer cluster where the MC simulations have been done.  ... 
doi:10.1103/physrevb.70.174439 fatcat:lax22kaaarh6rcmp6glbununfm
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