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On the existence of distributional potentials [article]

Jürgen Voigt
<span title="2022-04-26">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present proofs for the existence of distributional potentials F∈𝒟'(Ω) for distributional vector fields G∈𝒟'(Ω)^n, i.e. grad F=G, where Ω is an open subset of ℝ^n.  ...  A key ingredient of our treatment is the use of the Bogovskii formula, assigning vector fields v∈𝒟(Ω)^n with div v=φ to functions φ∈𝒟(Ω) with ∫φ(x) dx=0.  ...  The author is grateful to M. Kunzinger (Vienna) for pointing out reference [11] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.09976v6">arXiv:2102.09976v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b6jins5j7nfohfyvgnsd23nrva">fatcat:b6jins5j7nfohfyvgnsd23nrva</a> </span>
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On the existence and non-existence of elliptic pseudoprimes

Siguna Müller
<span title="2009-10-16">2009</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
We derive some criteria for the group structure of CM curves that allow testing for all composites, including N ≡ 3 mod 4 which had been excluded by Gordon.  ...  The challenge was to either prove that a certain composite N ≡ 1 mod 4 did not exist, or to explicitly calculate such a number.  ...  Acknowledgement The author would like to thank the referee for many insightful and helpful remarks that helped improve both the content and presentation of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-09-02275-3">doi:10.1090/s0025-5718-09-02275-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sp3aw2w2zjcvte4ydpazri5wle">fatcat:sp3aw2w2zjcvte4ydpazri5wle</a> </span>
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On the existence of frames

R.C. Mullin, P.J. Schellenberg, S.A. Vanstone, W.D. Wallis
<span title="">1981</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Wallis for the construction of (skew) Room squares, are shown to exist for most orders con_gruent to 1 (mod 4).  ...  This result relies heavily on the existence of PBD's since the set F = {u 1 there is a frame of order u] is shown to be PHD-closed.  ...  Moore's proof [ 121 of the existence of Steirler triple system of order v for every positive integer v = 1, 3 (mod 6) relies heavily on the existence of' triple systems containing subdesigns of order 7  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(81)90142-4">doi:10.1016/0012-365x(81)90142-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r3wjp2eabzcldg7urslwn2rmqy">fatcat:r3wjp2eabzcldg7urslwn2rmqy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922150355/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/033/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDEyMzY1eDgxOTAxNDI0.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e4/c9/e4c931a3397831ae3cf25bbb64abf8578a15df36.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0012-365x(81)90142-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On the existence of flips [article]

Christopher Hacon, James McKernan
<span title="2005-07-28">2005</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.  ...  There are plenty of such examples, even on the curve P 1 .  ...  Let vN R be the vector corresponding to D. Let A be the cyclic subgroup of the torus N R N Z , generated by the image of v.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0507597v1">arXiv:math/0507597v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d6zyia4msnfwbpvjx2spagqree">fatcat:d6zyia4msnfwbpvjx2spagqree</a> </span>
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On the Existence of Similar Sublattices [article]

J.H. Conway, E.M. Rains, N.J.A. Sloane
<span title="2002-07-20">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
When is the sublattice "clean", in the sense that the boundary of the Voronoi cells for Lambda ' do not intersect Lambda?  ...  When does a lattice Lambda contain a sublattice Lambda' of index N that is geometrically similar to Lambda?  ...  Quebbemann for suggesting that the similar sublattice problem is best handled via the Hilbert symbol, and for pointing out an error in the first version of this paper. We also thank V. A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0207177v1">arXiv:math/0207177v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bx2adzg5evcgpfonrqwevesjky">fatcat:bx2adzg5evcgpfonrqwevesjky</a> </span>
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On the Existence of Similar Sublattices

J. H. Conway, E. M. Rains, N. J. A. Sloane
<span title="1999-12-01">1999</span> <i title="Canadian Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/m5ds6a3cpng5df7duilz7mzivi" style="color: black;">Canadian Journal of Mathematics - Journal Canadien de Mathematiques</a> </i> &nbsp;
When is the sublattice "clean", in the sense that the boundary of the Voronoi cells for Λ do not intersect Λ?  ...  When does a lattice Λ contain a sublattice Λ of index N that is geometrically similar to Λ?  ...  Quebbemann for suggesting that the similar sublattice problem is best handled via the Hilbert symbol, and for pointing out an error in the first version of this paper. We also thank V. A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4153/cjm-1999-059-5">doi:10.4153/cjm-1999-059-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wuyokkkxhnaynazctmebnazc2e">fatcat:wuyokkkxhnaynazctmebnazc2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810071148/http://neilsloane.com/doc/sim.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b5/63/b5639fe3971fcdf91e08d75d59d7326ca13f5219.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4153/cjm-1999-059-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

On the existence of integer relative Heffter arrays [article]

Fiorenza Morini, Marco Antonio Pellegrini
<span title="2020-03-19">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we study the existence of an integer H_t(m,n;s,k) when s and k are both even, proving the following results. Suppose that 4≤ s≤ n and 4≤ k ≤ m are such that ms=nk.  ...  Let t be a divisor of 2ms. (a) If s,k ≡ 0 4, there exists an integer H_t(m,n;s,k). (b) If s≡ 2 4 and k≡ 0 4, there exists an integer H_t(m,n;s,k) if and only if m is even.  ...  The same holds also for t = k = 5, as proved in [12] (the existence of an integer H 5 (n; 5) is still an open problem for n ≡ 0 (mod 4)).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.09921v2">arXiv:1910.09921v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qncx46csgrhl7ghnojnu43sobe">fatcat:qncx46csgrhl7ghnojnu43sobe</a> </span>
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On the existence of canonical multi-phase Brakke flows [article]

Salvatore Stuvard, Yoshihiro Tonegawa
<span title="2022-03-22">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
As a consequence of the results recently established by Fischer et al. in arXiv:2003.05478, under suitable assumptions on the initial datum, such additional property resolves the non-uniqueness issue of  ...  This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a BV solution at the same  ...  S.S. is partially supported by the GNAMPA -Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni of INdAM; Y.T. is partially supported by JSPS 18H03670, 19H00639, 17H01092.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.14415v4">arXiv:2109.14415v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/csdr75dwqfdspeqsqutfqf2pmq">fatcat:csdr75dwqfdspeqsqutfqf2pmq</a> </span>
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On the non-existence of conjugate points

G. J. Butler, L. H. Erbe, R. M. Mathsen
<span title="1970-01-01">1970</span> <i title="Canadian Mathematical Society"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/stl7jpkksnhgjaaleuuhox3tou" style="color: black;">Canadian mathematical bulletin</a> </i> &nbsp;
The points a k+l 9 andv > k, or (b) k is even, [i> k, andv > k+l. Proof. Let y be a non-trivial solution to D n on [a 9 b], with a(/)=0 for t=a and t=b.  ...  Hence we have the following corollary to the proof of Theorem 1.1. COROLLARY 1.2. Let f satisfy (1.1) and let n = 2k+l. Then there do not exist points a>k and v>k.  ...  Hence, for k = n-[i = v, (-l) v + v y (n) (a v )>0. But since (-l) v y (il) (a)>0, it follows that (-l) Y y(t) > For the case \i-\-v=n and /x>y, a similar proof holds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4153/cmb-1970-006-x">doi:10.4153/cmb-1970-006-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6n7n44xfrjei3nz5szxkmmvf5y">fatcat:6n7n44xfrjei3nz5szxkmmvf5y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201212041024/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7635B754496CCFB36F10F1AB6FEDFC8D/S0008439500055193a.pdf/div-class-title-on-the-non-existence-of-conjugate-points-div.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c1/c8/c1c87bda7abceb1d1f227ce4011b99de47026771.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4153/cmb-1970-006-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

On the existence of regular approximations

Brendan Cordy, Kai Salomaa
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The degree of approximation is measured, roughly speaking, by counting the number of incorrect answers an automaton gives on inputs of length m and observing how these values behave for large m.  ...  We study closure and decision properties of the approximation measure.  ...  But since, on the other hand w 2 u ∈ L whenever u ∈ {c, d} * , the existence of the above bound n 0 implies that for lengths n = |w 2 | + k, where k ≥ n 0 , the right side of (1) has a lower bound that  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2007.07.032">doi:10.1016/j.tcs.2007.07.032</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cb7mip4ueba2hpccajmax3ijh4">fatcat:cb7mip4ueba2hpccajmax3ijh4</a> </span>
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On the existence of analytic mappings

Mitsuru Ozawa, Nobuyuki Suita
<span title="">1973</span> <i title="Tokyo Institute of Technology, Department of Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zznepipairfrrazmn3azdjt73i" style="color: black;">Kodai Mathematical Seminar Reports</a> </i> &nbsp;
Since ψ(z) has period 1, M(R) is taken by ψ at a point on the arc \z\=R, |9te!^l/2. Further ψ is even. So we evaluate \ψ(z)\ for z=x+iy, I Λ? I ^1/2, y>0.  ...  ON THE EXISTENCE OF ANALYTIC MAPPINGS BY MITSURU OZAWA AND NOBUYUKI SUITA 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2996/kmj/1138846865">doi:10.2996/kmj/1138846865</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dq6vi5i6orfx3irl5rch4hqqz4">fatcat:dq6vi5i6orfx3irl5rch4hqqz4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220302185036/https://projecteuclid.org/journals/kodai-mathematical-seminar-reports/volume-25/issue-4/On-the-existence-of-analytic-mappings/10.2996/kmj/1138846865.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a9/46/a94690686fc24ea56d1b1d48cd89980d17d42ba1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2996/kmj/1138846865"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On the Existence of Epipolar Matrices [article]

Sameer Agarwal, Hon-Leung Lee, Bernd Sturmfels, Rekha R. Thomas
<span title="2015-10-06">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a complete answer for the existence of fundamental matrices for any value of m. Using examples we disprove the widely held beliefs that fundamental matrices always exist whenever m ≤ 7.  ...  We also characterize the six and seven point configurations in two views for which all matrices satisfying the epipolar constraint have rank at most one.  ...  Theorem 1 . 11 . 111 Consider an irreducible projective variety V C ⊆ P C n of dimension d and a linear subspace L ⊆ P C n of dimension l. If d + l = n then V must intersect L.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1510.01401v1">arXiv:1510.01401v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mfktn2vpwbcxlptzsk3rya7zie">fatcat:mfktn2vpwbcxlptzsk3rya7zie</a> </span>
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On the existence of regular vectors [article]

Christoph Zellner
<span title="2015-11-06">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Moreover we show the existence of a dense space of analytic vectors for the class of semibounded representations of Banach-Lie groups.  ...  Here π is called semibounded, if π is smooth and there exists a non-empty open subset U⊂g such that the operators idπ(x) from the derived representation are uniformly bounded from above for x∈ U.  ...  Nevertheless, a proof of the conjecture seems to require new techniques as for x, y ∈ g it is not even clear that dπ(x) and dπ(y) are defined on a common dense domain.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1510.08727v2">arXiv:1510.08727v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3ekdrl2rkrb4xm6rejvxvb47li">fatcat:3ekdrl2rkrb4xm6rejvxvb47li</a> </span>
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The Automorphism Group of the Vertex Operator Algebra V_L^+ for an even lattice L without roots [article]

Hiroki Shimakura
<span title="2004-05-14">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, the shape of the automorphism group of $V_L^+$ is determined when $L$ is isomorphic to an even unimodular lattice without roots, $\sqrt2R$ for an irreducible root lattice $R$ of type $ADE  ...  The automorphism group of the vertex operator algebra $V_L^+$ is studied by using its action on isomorphism classes of irreducible $V_L^+$-modules.  ...  Ivanov for stimulating discussions on orthogonal groups, Professor Satoshi Yoshiara for valuable comments on finite groups, Hiroshi Yamauchi for useful advice on the simple current extension of a simple  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0311141v2">arXiv:math/0311141v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ye5lpbaktngqlcntyei4j4ktr4">fatcat:ye5lpbaktngqlcntyei4j4ktr4</a> </span>
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On the existence of maximal orders [article]

Chia-Fu Yu
<span title="2011-05-14">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We generalize the existence of maximal orders in a semi-simple algebra for general ground rings.  ...  Finally, we show the existence of maximal orders as endomorphism rings of abelian varieties in each isogeny class.  ...  He is grateful to Matsumura and Reiner for their tremendous efforts on writing the great books. He is also grateful to Tse-Chung Yang, and especially to C.-L. Chai for very helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1105.2897v1">arXiv:1105.2897v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6qrk6wvaijavvhzg5iqcsxjsna">fatcat:6qrk6wvaijavvhzg5iqcsxjsna</a> </span>
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