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Analytic cohomology groups in top degrees of Zariski open sets in $${\mathbb{P}^n}$$

2009
*
Mathematische Zeitschrift
*

Matsumoto [13] in the study

doi:10.1007/s00209-009-0484-0
fatcat:xtr6wxwbanfr7hr72xwgqrdrw4
*of*cohomologic convexity*of*some open*sets*in complex manifolds which are finite intersection*of*q-complete open*sets*. ... It follows from Proposition 1 that the canonical comparison map in*degree*n − 2, between the algebraic and*analytic*cohomology, is surjective. ...##
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Are the Validities of Modal Logic Analytic? Or Analyticity Again, through Information, Proof, Modal Logic and Hintikka

2015
*
Philosophia Scientiæ
*

Hence, for each basic maximal consistent

doi:10.4000/philosophiascientiae.1110
fatcat:5cigo4ctmnejhgmebtojwfd3pa
*set*, there is exactly one modal constituent*of**degree*1 that is a logical consequence*of*it. ...*sets*. ...##
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A Duality in Interpolation to Analytic Functions by Rational Functions

1933
*
Proceedings of the National Academy of Sciences of the United States of America
*

However, the prospects

doi:10.1073/pnas.19.12.1049
pmid:16587824
pmcid:PMC1086281
fatcat:p745x7thpzf4ngfaxrfcbo4uiu
*of*carrying this treatment to a higher*degree**of*approximation are not very favorable. ... If the function f(z) is*analytic*for z I < R, then the sequence*of*VOL. 19, 1933VOL. 19, 1049 ... (z), and that a function q(t)*analytic*on the complementary*set*can be developed in terms*of*the q. (t). ...##
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On semialgebraic points of definable sets

1998
*
Banach Center Publications
*

We prove that the semialgebraic, algebraic, and algebraic nonsingular points

doi:10.4064/-44-1-189-193
fatcat:iywvqe6ufbdxhep6lg5cipivd4
*of*a definable*set*in o-minimal structure with*analytic*cell decomposition are definable. ... Moreover, the operation*of*taking semialgebraic points is idempotent and the*degree**of*complexity*of*semialgebraic points is bounded. ... Krzysztof Kurdyka, Janusz Gwoździewicz, Andrzej Lenarcik and Wies law Paw lucki for their valuable remarks, and The Fields Institute for invitation and supporting his stay in Toronto, where definability*of*...##
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On Compact Complex Analytic Varieties

1949
*
American Journal of Mathematics
*

Each copy

doi:10.2307/2372375
fatcat:mfvjxyufavggnho27rlwcnrkuu
*of*any part*of*a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page*of*such transmission. ... The Johns Hopkins University Press is collaborating with JSTOR to digitize, preserve and extend access to American Journal*of*Mathematics. ... Since, according to Theorem I, each*set*U(I) is an everywhere dense open*set*in P, it follows that (2 is also an everywhere dense*set*in P. J=1 evidently the*degree**of*the*analytic*cycle Zr. ...##
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Representations of Analytic Functions and Weihrauch Degrees
[chapter]

2016
*
Lecture Notes in Computer Science
*

-Dbnd C ω (D) , that is: Given an

doi:10.1007/978-3-319-34171-2_26
fatcat:aukiezj5obew7cm5htanszvziy
*analytic*function which is a polynomial, find an upper bound*of*its*degree*. deg C ω (D) : Given an*analytic*function which is a polynomial, find its*degree*. Proof. ... -Dbnd C(D) : Given an*analytic*function which is a polynomial, find an upper bound*of*its*degree*. ...##
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Page 495 of Mathematical Reviews Vol. , Issue 80B
[page]

1980
*
Mathematical Reviews
*

This relationship, the boldface version

*of*Kleene’s relative re- cursiveness, defines a*degree*structure on the*analytic**sets*, and the equivalence classes are called S-*degrees*. ... The author’s main theorem is that if S and‘T are*analytic**sets*with S<T then there are 2°*analytic*non-Borel*sets*whose S-de- grees are intermediate between the S-*degrees**of*S and T and which are pairwise ...##
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Page 82 of Mathematical Reviews Vol. 37, Issue 1
[page]

1969
*
Mathematical Reviews
*

Let M be a

*set**of*type (A). Consider a function f(z) which is continuous on M and*analytic*in the interior*of*M. ... If P is effective and if f is*analytic*on #,, then the co- efficients A, in (*) are unique. Let {S,} be a sequence*of*polynomials (S,, is*of**degree*n). ...##
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Optical in-band crosstalk monitor placement using Partial Set Cover model

2012
*
IEICE Communications Express
*

The numerical results showed that heuristic parameters, Interference Rate (IR) and Highest Crosstalk

doi:10.1587/comex.1.78
fatcat:btukzwm72zckfffzf77koxvpga
*Analytical*Value which are computed during network operation, outperform parameters, highest*degree*... In this paper, switch induced in-band crosstalk impairment is used for evaluating the number*of*monitoring devices with respect to the amount*of*reported monitoring information in items*of*optical signal ... Given*set**of*node's Crosstalk*Analytical*Value as input, the algorithm returns a covering*set*whose elements have highest Crosstalk*Analytical*Value. ...##
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Page 1622 of Neural Computation Vol. 8, Issue 8
[page]

1996
*
Neural Computation
*

As expected, the cell has a CD

*of*1*degree*, which is marked by the vertical line in the figure. The above*set**of*parameters was chosen for illustrative purposes. ... Other*sets**of*parameters work equally well. For example, to model a parafoveal cell with small RFs, we could scale down the above*set**of*parameters by a factor*of*, say, 10. ...##
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Page 673 of Annals of Mathematics Vol. 37, Issue 3
[page]

1936
*
Annals of Mathematics
*

Given any function f

*of*class C’ in R,*set*(29.1) ey(c)= DO a (x — a); Zz. kl This is the polynomial*of**degree*S s approximating to f most closely at a. ... Then there is an*analytic*linear (R, Ey, r, A, ¢)- functional &; moreover, & is defined for any polynomial P*of**degree*< s, and ep = P. ...##
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Dominating Scale-Free Networks Using Generalized Probabilistic Methods

2014
*
Scientific Reports
*

We analyze both

doi:10.1038/srep06308
pmid:25200937
pmcid:PMC4158322
fatcat:edwcb5ivl5dx5kdlfh6tufcd4e
*analytical*upper bounds*of*dominating*sets*and numerical realizations for applications. ... One*of*them obtains the smallest probabilistic dominating*set*and also outperforms the deterministic*degree*-ranked method. ... Nguyen for preparing the network-structure files used in this research from the Flickr and Foursquare data*sets*. This work was supported in part by grant No. ...##
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Factoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables
[article]

2022
*
arXiv
*
pre-print

at most 2d_2

arXiv:1811.06005v3
fatcat:isrcirgqdvg6bg2syv4f2qhvai
*analytic*polynomials with*degrees*at most (d_1, 2d_2-1). ... It is shown using Schur complement techniques that a non-negative operator valued trigonometric polynomial in two variables with*degree*(d_1,d_2) can be written as a finite sum*of*hermitian squares*of*... ) is an outer*analytic*operator*of*the same*degree*d as T . ...##
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Rational interpolation and best rational approximation

1976
*
Journal of Mathematical Analysis and Applications
*

A relation between the

doi:10.1016/0022-247x(76)90143-8
fatcat:di7e6zchv5hmvdft5dn2ns3otq
*degree**of*convergence (in capacity)*of*Pad& approximants and the*degree**of*best rational approximation is derived for functions in GonEar's class R, . ... THEOREM 1 . 1 Let f E R,@(n)) and let f be*analytic*on a compact*set*E somewhere in the domain*of*generalized*analytic*continuation off. ... As we have already pointed out, the class R, contains all functions*analytic*except on a*set**of*zero capacity. ...##
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On Convergence of Interpolation to Analytic Functions

2002
*
Journal of Approximation Theory
*

In the present paper, both the perfect convergence for the Lagrange interpolation

doi:10.1006/jath.2001.3633
fatcat:oqn75xzzmfbyfbit5chty4cwte
*of**analytic*functions on [ − 1, 1] and the perfect convergence for the trigonometric interpolation*of**analytic*functions ... n , where T n f is the Taylor polynomial*of**degree*(n − 1)*of*f at the point x 0 . ... ||L P n f − T n f||=0 where T n f is the Taylor polynomial*of**degree*(n − 1)*of*f at x 0 , then f| [ − 1, 1) has an*analytic*continuation into B(x 0 , 1+|x 0 |) for x 0 ¥ [ − 1, 0), f| (−1, 1] has an*analytic*...
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