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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
1918
Biometrika
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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
2018
Journal of High Energy Physics
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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]
2009
arXiv
pre-print
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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
2000
IEEE Transactions on Image Processing
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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]
2015
IEEE Transactions on Circuits and Systems - II - Express Briefs
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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]
2021
arXiv
pre-print
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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
2020
Journal of High Energy Physics
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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]
2020
arXiv
pre-print
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2020 pre-print arXiv:2005.06722v1 fatcat:v6odieabfffcvapt6r3lhxyzr4
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)
2017
Monatshefte für Mathematik (Print)
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For t ∈ Z <0 the n-th term of the sequence ( f n (t)) n∈N 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)
2013
Austral
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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
2003
IEEE Transactions on Plasma Science
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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
2006
Zenodo
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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
2018
Molecules
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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
1990
SIAM Journal on Scientific and Statistical Computing
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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
2004
Physical Review B
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2004 accepted arXiv:cond-mat/0405667v3 fatcat:tq6257r2hzdwhphrxrwjqehb6mOther Versions
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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