scholarly journals Relative logarithmic cohomology and Nambu structures of maximal degree

2020 ◽  
Vol 144 ◽  
pp. 250-268
Author(s):  
Konstantinos Kourliouros
Keyword(s):  
Maximal Degree

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

scholarly journals Clique coverings of graphs V: maximal-clique partitions

1982 ◽  
Vol 25 (3) ◽  
pp. 337-356 ◽  
Author(s):  
N.J. Pullman ◽  
H. Shank ◽  
W.D. Wallis
Keyword(s):  
Maximal Clique ◽  
Maximal Degree ◽  
Open Problems ◽  
Partition Number

A maximal-clique partition of a graph G is a way of covering G with maximal complete subgraphs, such that every edge belongs to exactly one of the subgraphs. If G has a maximal-clique partition, the maximal-clique partition number of G is the smallest cardinality of such partitions. In this paper the existence of maximal-clique partitions is discussed – for example, we explicitly describe all graphs with maximal degree at most four which have maximal-clique partitions - and discuss the maximal-clique partition number and its relationship to other clique covering and partition numbers. The number of different maximal-clique partitions of a given graph is also discussed. Several open problems are presented.

scholarly journals Improved Resource State for Verifiable Blind Quantum Computation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 996
Author(s):  
Qingshan Xu ◽  
Xiaoqing Tan ◽  
Rui Huang
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Maximal Degree ◽  
Recent Advances ◽  
Quantum Computations ◽  
Blind Quantum Computation ◽  
Computation Graph ◽  
Resource State

Recent advances in theoretical and experimental quantum computing raise the problem of verifying the outcome of these quantum computations. The recent verification protocols using blind quantum computing are fruitful for addressing this problem. Unfortunately, all known schemes have relatively high overhead. Here we present a novel construction for the resource state of verifiable blind quantum computation. This approach achieves a better verifiability of 0.866 in the case of classical output. In addition, the number of required qubits is 2N+4cN, where N and c are the number of vertices and the maximal degree in the original computation graph, respectively. In other words, our overhead is less linear in the size of the computational scale. Finally, we utilize the method of repetition and fault-tolerant code to optimise the verifiability.

scholarly journals On the Rationality of Certain Strata of the Lange Stratification of Stable Vector Bundles on Curves

2001 ◽  
Vol 8 (4) ◽  
pp. 665-668
Author(s):  
E. Ballico
Keyword(s):  
Vector Bundles ◽  
Maximal Degree ◽  
Projective Curve ◽  
Fiber Structure ◽  
Generic Fiber ◽  
Smooth Projective Curve ◽  
Stable Vector Bundles ◽  
Natural Way

Abstract Let 𝑋 be a smooth projective curve of genus 𝑔 ≥ 2 and 𝑆(𝑟, 𝑑) the moduli scheme of all rank 𝑟 stable vector bundles of degree 𝑑 on 𝑋. Fix an integer 𝑘 with 0 < 𝑘 < 𝑟. H. Lange introduced a natural stratification of 𝑆(𝑟, 𝑑) using the degree of a rank 𝑘 subbundle of any 𝐸 ∈ 𝑆(𝑟, 𝑑) with maximal degree. Every non-dense stratum, say 𝑊(𝑘, 𝑟 – 𝑘, 𝑎, 𝑑 – 𝑎), has in a natural way a fiber structure ℎ : 𝑊(𝑘, 𝑟 – 𝑘, 𝑎, 𝑑 – 𝑎) → Pic𝑎(𝑋) × Pic𝑏(𝑋) with ℎ dominant. Here we study the rationality or the unirationality of the generic fiber of ℎ.

scholarly journals The Effects of Valvular Heart Disease on Atrial Conduction During Sinus Rhythm

2019 ◽  
Vol 13 (4) ◽  
pp. 632-639 ◽  
Author(s):  
Lisette J. M. E. van der Does ◽  
Eva A. H. Lanters ◽  
Christophe P. Teuwen ◽  
Elisabeth M. J. P. Mouws ◽  
Ameeta Yaksh ◽  
...  
Keyword(s):  
Sinus Rhythm ◽  
Left Atrium ◽  
Conduction Delay ◽  
Atrial Remodeling ◽  
Strongly Correlated ◽  
Maximal Degree ◽  
Conduction Disorders ◽  
History Of ◽  
Bachmann’S Bundle ◽  
Unipolar Electrogram

AbstractDifferent arrhythmogenic substrates for atrial fibrillation (AF) may underlie aortic valve (AV) and mitral valve (MV) disease. We located conduction disorders during sinus rhythm by high-resolution epicardial mapping in patients undergoing AV (n = 85) or MV (n = 54) surgery. Extent and distribution of conduction delay (CD) and block (CD) across the entire right and left atrial surface was determined from circa 1880 unipolar electrogram recordings per patient. CD and CB were most pronounced at the superior intercaval area (2.5% of surface, maximal degree 6.6%/cm2). MV patients had a higher maximal degree of CD at the lateral left atrium than AV patients (4.2 vs 2.3%/cm2, p = 0.001). A history of AF was most strongly correlated to CD/CB at Bachmann’s bundle and age. Although MV patients have more conduction disorders at the lateral left atrium, disturbed conduction at Bachmann’s bundle during sinus rhythm indicates the presence of atrial remodeling which is related to AF episodes.

scholarly journals Growth of linear semigroups

1996 ◽  
Vol 60 (1) ◽  
pp. 18-30 ◽  
Author(s):  
Jan Okniński
Keyword(s):  
Finite Rank ◽  
Polynomial Growth ◽  
Growth Function ◽  
Unipotent Radical ◽  
Maximal Degree ◽  
Finitely Generated ◽  
Group Of Fractions

AbstractWe show that the growth function of a finitely generated linear semigroup S ⊆ Mn(K) is controlled by its behaviour on finitely many cancellative subsemigroups of S. If the growth of S is polynomially bounded, then every cancellative subsemigroup T of S has a group of fractions G ⊆ Mn (K) which is nilpotent-by-finite and of finite rank. We prove that the latter condition, strengthened by the hypothesis that every such G has a finite unipotent radical, is sufficient for S to have a polynomial growth. Moreover, the degree of growth of S is then bounded by a polynomial f(n, r) in n and the maximal degree r of growth of finitely generated cancellative T ⊆ S.

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