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On the Accepting Power of 2-Tape Büchi Automata
[chapter]

2006
*
Lecture Notes in Computer Science
*

We show that, from a topological point

doi:10.1007/11672142_24
fatcat:h5bs3qyzv5bv7kw7i7jhvkx2ru
*of*view,*2*-tape Büchi automata have*the*same accepting*power*than Turing machines equipped with a Büchi acceptance condition. ... This surprising result gives answers to questions*of*Simonnet [Sim92] and*of*Lescow and Thomas [Tho90, LT94] . ... Thanks to*the*anonymous referees for useful comments*on*a preliminary version*of*this paper. ...##
###
An unsolved problem on the powers of 3/2

1968
*
Journal of the Australian Mathematical Society
*

[5] An unsolved problem

doi:10.1017/s1446788700005371
fatcat:w6fe2afgvrhhrdv4b5my5q6bnu
*on**the**powers**of*| 317 We shall use*the*notation*2*a \\H to denote that H is divisible by*2*°, but not by*2*a+1 . 6 Put (15) a k = m k+1 -rn k -l, H k = -^-. ... This formula may be written as By*the*binomial theorem, it implies that T(t)-\-l is*the*coefficient*of*z* in*the**power*series in*powers**of*z for and hence T(t)-\-l is also*the*coefficient*of*z* in*the*...##
###
On the Accepting Power of 2-Tape Büchi Automata
[article]

2007
*
arXiv
*
pre-print

We show that, from a topological point

arXiv:0712.0165v1
fatcat:vokth7s2dvbltpvrlxtqdirf6q
*of*view,*2*-tape B\"uchi automata have*the*same accepting*power*than Turing machines equipped with a B\"uchi acceptance condition. ... Thesis, Universit\'e Paris 7, March 1992], and*of*H. Lescow and W. Thomas [Logical Specifications*of*Infinite Computations, In: "A Decade*of*Concurrency", LNCS 803, Springer, 1994, p. 583-621]. ... Thanks to*the*anonymous referees for useful comments*on*a preliminary version*of*this paper. ...##
###
Reflections on the Power of the Pen – Issue 2 Editorial

2022
*
International Journal of Disability and Social Justice
*

*The*following people deserve particular thanks for their work

*on*this edition: David Abbott (for guiding authors through

*the*process

*of*preparing plain English/lay summaries

*of*their articles); Simon T.M ... We note, in particular,

*the*time and care colleagues have been taking to provide constructive feedback, especially (but not only) when they are alerted that

*the*author(s) are early-career. ... Particular attention is given to

*the*relationship between Paralympics

*on*

*the*

*one*hand and accessibility and awareness, particularly

*of*

*the*social model

*of*disability,

*on*

*the*other. ...

##
###
On the Power Functions of the $E^2$-Test and the $T^2$-Test

1945
*
The Annals of Mathematical Statistics
*

*ON*

*THE*

*POWER*FUNCTIONS

*OF*

*THE*E?-TEST AND

*THE*7°-TEST By P. L. Hsu National University

*of*Peking 1.

*The*general linear hypothesis. ...

*The*author has proved [3] that

*of*all

*the*critical regions which satisfy (5) and whose

*power*function is a function

*of*an,, alone,

*the*region w is

*the*uniformly most

*powerful*

*one*. ...

##
###
Remarks on the symmetric powers of cusp forms on GL(2)
[article]

2009
*
arXiv
*
pre-print

Moreover, sym^6(pi) is Eisenteinian iff sym^5(pi) is an abelian twist

arXiv:0710.0676v2
fatcat:kyjolwexqva6hjnvtnqgs66doy
*of**the*functorial product*of*pi with*the*symmetric square*of*a cusp form pi'*on*GL(*2*)/F. ... Assume that all*the*symmetric*powers*sym^m(pi) are modular, i.e., define automorphic forms*on*GL(m+1)/F. If sym^6(pi) is cuspidal, then all*the*symmetric*powers*are cuspidal, for all m. ... Forms*on*adele groups, and his expository papers, Automorphic forms and Artin's conjecture and Elliptic curves and automorphic representations, as well as his seminal ...##
###
On the $2$-class group of some number fields of $2$-power degree

2022
*
Turkish Journal of Mathematics
*

In this paper, we compute

doi:10.55730/1300-0098.3287
fatcat:zctmzlegkrfp7naelynpgvczzu
*the*rank*of**the**2*-class group*of*K * n*the*n -th layer*of**the*cyclotomic Z2 -extension*of*K * . ... Let K be an imaginary cyclic quartic number field whose*2*-class group is isomorphic to Z/2Z × Z/2Z , and let K * denote*the*genus field*of*K . ... This section is*one**of**the*steps*of**the*proof*of*Theorem 4.2, in which we shall determine*the*structure*of**the**2*-class group*of*K * 1 = K( √ q, ζ 8 )*of*degree 32 over Q. ...##
###
On the power of unique 2-prover 1-round games

2002
*
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02
*

We make

doi:10.1145/510014.510017
fatcat:v6b6shr4hbcb5cga27p2osbtxu
*the*following conjecture regarding*the**power**of*unique*2*-prover games, which we call*the*Unique Games Conjecture : ... A*2*-prover game is called unique if*the*answer*of**one*prover uniquely determines*the*answer*of**the*second prover and vice versa (we implicitly assume games to be*one*round games). ... Proceedings*of**the*17th IEEE Annual Conference*on*Computational Complexity (CCC'02) 1093-0159/02 $17.00 © 2002 IEEE ...##
###
On Lie powers of the augmentation ideal in characteristic 2

2011
*
Journal of Algebra
*

In this article we concentrate

doi:10.1016/j.jalgebra.2011.06.015
fatcat:pq7ge7ai6rachfw5wlvsjrsig4
*on*Lie*powers*L n ( )*of*, and describe*the*module decomposition*of*L 16 ( ), a module*of*dimension 2690010. In particular, I(L 16 ( )) = {D, V 1 , V*2*, V 3 , * }. ... Write L(V ) for*the*free Lie algebra*on*V .*The*action*of*G*on*V extends naturally to L(V ), so it becomes a K Gmodule which is direct sum*of*finite-dimensional submodules. ... Bryant for his invaluable advice, suggestions and comments, and*the*referee for*the*suggestion*on**the*proof*of*Lemma 3.1. ...##
###
On the power of unique 2-prover 1-round games

2002
*
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing - STOC '02
*

We make

doi:10.1145/509907.510017
dblp:conf/stoc/Khot02a
fatcat:72sdsghnnba57byrvfqrtamjye
*the*following conjecture regarding*the**power**of*unique*2*-prover games, which we call*the*Unique Games Conjecture : ... A*2*-prover game is called unique if*the*answer*of**one*prover uniquely determines*the*answer*of**the*second prover and vice versa (we implicitly assume games to be*one*round games). ... Proceedings*of**the*17th IEEE Annual Conference*on*Computational Complexity (CCC'02) 1093-0159/02 $17.00 © 2002 IEEE ...##
###
On the Expressive Power of 2-Stack Visibly Pushdown Automata

2008
*
Logical Methods in Computer Science
*

Finally, we discuss

doi:10.2168/lmcs-4(4:16)2008
fatcat:3qd2cy6o2vh7valxxjqe3jsghq
*the*expressive*power**of*Büchi*2*-stack visibly pushdown automata running*on*infinite (nested) words. ... even express properties beyond*the*class*of*context-free languages. ... Acknowledgment We thank*the*anonymous referees for their careful reading and many useful remarks. ...##
###
On the fields of $2$-power torsion of certain elliptic curves

2004
*
Mathematical Research Letters
*

Let µ

doi:10.4310/mrl.2004.v11.n4.a10
fatcat:qub5qyg4iza7jph6rowl5ufgze
*2*∞ denote*the*group*of**2*-*power*roots*of*unity. ...*The*outer pro-*2*Galois representation*on**the*projective line minus three points has a kernel whose fixed field, Ω*2*, is a pro-*2*extension*of*Q (µ*2*∞), unramified away from*2*. ... This research was supported by*the*University*of*Arizona's NSF VIGRE Grant #9977116. ...##
###
On the symmetric powers of cusp forms on GL (2) of icosahedral type
[article]

2003
*
arXiv
*
pre-print

In this note we study

arXiv:math/0301074v3
fatcat:64tbea5535h6xf5ho6anabzxxq
*the*symmetric*powers**of*strongly modular icosahedral representations ρ*of*Gal (F̅/F), F a number field, and their twisted L--functions. ... paper, which may be*of*independent interest, for*the*Kim--Shahidi automorphic tensor product π sym^*2*(π'), where π and π' are cuspidal automorphic representations*of*GL (*2*) / F. ... In*the*Theorem below, sym m (ρ) denotes*the*symmetric m-th*power**of*ρ, i.e.,*the*composition*of*ρ with*the*symmetric m-th*power*representation*of*GL*2*(C) into GL m+1 (C). ...##
###
On the Differential Properties of the Power Mapping x^p^m+2
[article]

2022
*
arXiv
*
pre-print

In this paper, we investigate

arXiv:2204.08118v1
fatcat:blj626h3x5ghjcuurzcnm2huru
*the*differential properties*of**the**power*mapping x^p^m+*2*over 𝔽_p^n, where n=2m or n=2m-1. ... For*the*case n=2m, by transforming*the*derivative equation*of*x^p^m+*2*and studying some related equations, we completely determine*the*differential spectrum*of*this*power*mapping. ... Moreover, by Lemma*2*,*one*can easily compute*the*differential spectrum*of**the**power*mapping x p t +1 over F p n for any odd prime p. 3.2*The*differential spectrum*of*x p m +*2*for p = 3 In this subsection ...##
###
Impact of the economic recession on the European power sector's CO 2 emissions

2011
*
Energy Policy
*

This paper investigates

doi:10.1016/j.enpol.2010.12.043
fatcat:qss2lvtbirc6njqclnzd5jezqm
*the*impact*of**the*economic recession*on*CO*2*emissions in*the*European*power*sector, during*the*years 2008 and 2009. ... Three main determinants*of**the**power*sector's emissions are identified:*the*demand for electricity,*the*CO*2*price, and fuel prices (especially gas and coal prices). ... However, in*the*summer*of*2008,*the*economy was hit by a severe recession.*The*focus*of*this paper is*on*CO*2*emission in*the**power*sector, in*the*years 2008 and 2009. ...
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