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Generic degrees are complemented

Masahiro Kumabe
1993 Annals of Pure and Applied Logic  
For a degree a, we say D(%z) is complemented if for every b < a there is a c such that b fl c = 0 and b U c = a. We prove that D(<u) is complemented for any 2-generic degree a.  ...  For each n a 2, any n-generic degree a, and any nonrecursive degree b < a, there are n-generic degree c < a and n-generic degree d < b such that e U f = a and e tl f = 0 for any nonrecursive degree e s  ... 
doi:10.1016/0168-0072(93)90096-v fatcat:l533jd3bkbdoxkcireg46avnku

Reformulated Reciprocal Degree Distance and Reciprocal Degree Distance of the Complement of the Mycielskian Graph and Generalized Mycielskian

Feifei Zhao, Hong Bian, Haizheng Yu, Min Liu
2019 Mathematical Problems in Engineering  
In this paper, we present the reciprocal degree distance index of the complement of Mycielskian graph and generalize the corresponding results to the generalized Mycielskian graph.  ...  The reformulated reciprocal degree distance is defined for a connected graph G as R¯t(G)=(1/2)∑u,υ∈VG((dG(u)+dG(υ))/(dG(u,υ)+t)),t≥0, which can be viewed as a weight version of the t-Harary index; that  ...  Complement of the Generalized Mycielskian Graph In this section, we obtain the reformulated reciprocal degree distance and reciprocal degree distance of the graph ( ).  ... 
doi:10.1155/2019/3764981 fatcat:itji4ewr45ah3kpenjysdk6dwm

Ideals of curves given by points [article]

E. Fortuna, P. Gianni, B. Trager
2012 arXiv   pre-print
In particular if I can be generated by polynomials of degree at most m and we are given md + 1 points on C, then we can find a set of generators for I.  ...  We wish to compute generators for I, assuming we are given sufficiently many points on the curve C.  ...  In particular if I can be generated by polynomials of degree at most m and we are given at least md+ 1 points on C, then we can find a set of generators for I.  ... 
arXiv:1202.6493v1 fatcat:6o3y6hlkebhlld6whnt6yjcwse

Properties of the jump classes

A. E. M. Lewis
2010 Journal of Logic and Computation  
All generalized high degrees satisfy the complementation property.  ...  While it is immediately clear that no ∆ 0 2 degree can complement all other nonzero and incomplete ∆ 0 2 degrees, one might hope that some version of this theorem might hold for the ∆ 0 2 degrees in general  ... 
doi:10.1093/logcom/exq047 fatcat:xapd32zx3fbonpqyupmvvb3udi

Lattice Complements and the Subadditivity of Syzygies of Simplicial Forests [article]

Sara Faridi
2016 arXiv   pre-print
For such an ideal I, if the i-th Betti number is nonzero and i=a+b, we show that there are monomials in the lcm lattice of I that are complements in part of the lattice, each supporting a nonvanishing  ...  We prove the subadditivity property for the maximal degrees of the syzygies of facet ideals simplicial forests.  ...  1, 2, 3 for a monomial ideal generated in degree 2 (Abedelfatah and Nevo [AN] ).  ... 
arXiv:1605.07727v1 fatcat:5fbjjzfckbhqxaxeib2adeglyu

Hyperbolic surfaces in P^3: examples [article]

Mikhail Zaidenberg
2004 arXiv   pre-print
This is a recent conference report on the Kobayashi Problem on hyperbolicity of generic projective hypersurfaces.  ...  Thus the hyperbolicity of the complement of a generic plane curve of degree d is still to be established for 5 ≤ d ≤ 12.  ...  THEOREM , d ≥ 10 6 ; El Goul [EG] ): For a very generic curve C ⊂ P 2 of degree d ≥ 13 the complement P 2 \ C is hyperbolic.  ... 
arXiv:math/0311394v3 fatcat:enh3kehhrjgk5kfbyhw45b6goy

Obstructions on fundamental groups of plane curve complements [article]

Constance Leidy, Laurentiu Maxim
2007 arXiv   pre-print
Also included are some new computations of higher-order degrees of curves, which are invariants defined in a previous paper of the authors.  ...  We survey various Alexander-type invariants of plane curve complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to complex plane curves  ...  It follows that all higher-order degrees are trivial for curves whose complements have the above fundamental groups.  ... 
arXiv:math/0703008v1 fatcat:qxcpdxmpznfahcrmjr6aq4xfnu

A Modified Intuitionistic Fuzzy Clustering Approach for Sclera Segmentation

M. S. Maheshan, B. S. Harish
2021 SN Computer Science  
How legitimate these transactions are, is the question of the hour. Biometric-enabled transactions have gained popularity.  ...  The experimentation results reveal that the proposed work complements the other existing methods and variants of Fuzzy C-Means.  ...  In literature, there are two widely used intuitionistic fuzzy complement generators namely Sugeno's [17] and Yager's [18] .  ... 
doi:10.1007/s42979-021-00722-5 fatcat:iap3mi3ltbbhfl5hnccs6ka3ka

The syntactic flexibility of adverbs: French degree adverbs

Anne Abeillé, Danièle Godard
2003 Proceedings of the International Conference on Head-Driven Phrase Structure Grammar  
While French degree words in French have been assigned several syntactic categories, we show that they are rather highy polymorphic adverbs (they occur in all syntactic domains), which select the expression  ...  Like French adverbs in general, they occur both to the left and to the right of the head they modify.  ...  adverbs The lightness constraint on ordering applies to complements in general.  ... 
doi:10.21248/hpsg.2003.2 fatcat:p6mh3amh6jhgxm3dg4eghli52y

Higher-order Alexander invariants of plane algebraic curves

C. Leidy, L. Maxim
2006 International mathematics research notices  
We show that for curves in general position at infinity, the higherorder degrees are finite.  ...  We define new higher-order Alexander modules A n (C) and higher-order degrees δ n (C) which are invariants of the algebraic planar curve C.  ...  The degrees δ n (C) are integral invariants of the fundamental group G of the complement. Indeed, we have (cf.  ... 
doi:10.1155/imrn/2006/12976 fatcat:7jk4w5rgi5cpxc7cbkfsvklzsy

Familial occurrence of complement dysfunction in Crohn's disease: correlation with intestinal symptoms and hypercatabolism of complement

J Elmgreen, H Both, V Binder
1985 Gut  
Complement was studied in Crohn's disease probands with early onset and in their first degree relatives.  ...  As previously shown in patients with Crohn's disease, the subnormal generation was related to decreased utilisation of complement C3 in relatives.  ...  A similar defect of complement was revealed in six of their 33 first degree relatives.  ... 
doi:10.1136/gut.26.2.151 pmid:3967833 pmcid:PMC1432432 fatcat:dihdtr62knegpn4douvf7zd55i

On the Complements of Partial k-Trees [chapter]

Arvind Gupta, Damon Kaller, Thomas Shermer
1999 Lecture Notes in Computer Science  
In particular, we show that the complements of partial k-trees provide an intuitively-appealing characterization of partial k-tree obstructions.  ...  k + 4-Obstructions In dealing with complements and witnesses for cowidth 4, it is useful to de ne low-degree as degree 2 or less, and high-degree as degree 3 or more.  ...  It is straightforward to show that these obstruction complements contain no degreezero or degree-one vertices; the low-degree vertices must therefore have degree two.  ... 
doi:10.1007/3-540-48523-6_35 fatcat:x7zgclwgcfh2jftmqhbzvbamli

Excessive Extent in Cognition—A Contrastive Study on Mandarin and English

Hsiu-Ying Liu, Cheng-Chung Kuo
2011 Journal of Language Teaching and Research  
Afterwards, English excessive degree adverbs would be examined to see if the generation works universally.  ...  Coping with Mandarin excessive construction, the present paper first tries to figure out the possible generation linking excessive complements with excessive extent.  ...  The aim of the study is to find out the features shared by the lexical terms which are further grammaticalized to excessive complements, so the degree of generalization is not influential. IV.  ... 
doi:10.4304/jltr.2.5.1015-1022 fatcat:5f3jobjyzfh67gmkreqhhgiz2u

Hyperbolic hypersurfaces in $\mathbb P^n$ of Fermat-Waring type

Bernard Shiffman, Mikhail Zaidenberg
2001 Proceedings of the American Mathematical Society  
Moreover, there are hyperbolic Fermat-Waring hypersurfaces in P n of degree 4n 2 − 2n + 1 possessing complete hyperbolic, hyperbolically embedded complements.  ...  In this note we show that there are algebraic families of hyperbolic, Fermat-Waring type hypersurfaces in P n of degree 4(n−1) 2 , for all dimensions n ≥ 2.  ...  Kobayashi that generic hypersurfaces in P n of (presumably) degree 2n − 1 are hyperbolic (for n = 3, see [DeEl] and [Mc] ).  ... 
doi:10.1090/s0002-9939-01-06417-6 fatcat:dh4vicpfprfjdhl2jb34breuki

Higher-order Alexander invariants of plane algebraic curves [article]

Constance Leidy, Laurentiu Maxim
2005 arXiv   pre-print
We show that for curves in general position at infinity, the higher-order degrees are finite.  ...  We define new higher-order Alexander modules A_n(C) and higher-order degrees δ_n(C) which are invariants of the algebraic planar curve C.  ...  The degrees δ n (C) are integral invariants of the fundamental group G of the complement.  ... 
arXiv:math/0509462v2 fatcat:kx2ijccbvnhzjm32dbsb2yo4q4
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