scholarly journals Antipowers in Uniform Morphic Words and the Fibonacci Word

2021 ◽  
Vol vol. 23, no. 3 (Combinatorics) ◽  
Author(s):  
Swapnil Garg
Keyword(s):  
Finite Size ◽  
Equal Length ◽  
Block Length

Fici, Restivo, Silva, and Zamboni define a $k$-antipower to be a word composed of $k$ pairwise distinct, concatenated words of equal length. Berger and Defant conjecture that for any sufficiently well-behaved aperiodic morphic word $w$, there exists a constant $c$ such that for any $k$ and any index $i$, a $k$-antipower with block length at most $ck$ starts at the $i$th position of $w$. They prove their conjecture in the case of binary words, and we extend their result to alphabets of arbitrary finite size and characterize those words for which the result does not hold. We also prove their conjecture in the specific case of the Fibonacci word.

The partial realization theory of finite size two-dimensional arrays

1981 ◽  
Vol 64 (10) ◽  
pp. 1-8
Author(s):  
Tsuyoshi Matsuo ◽  
Yasumichi Hasegawa ◽  
Yoshikuni Okada
Keyword(s):  
Finite Size ◽  
Two Dimensional ◽  
Realization Theory

Autoradiography of Incorporated Leucine-H3 in the Enamel Matrix and Enamel Organ of the Upper Incisor of the Rat

1964 ◽  
Vol 04 (02) ◽  
pp. 186-192
Author(s):  
Leonel Costacurta
Keyword(s):  
Amino Acid ◽  
Blood Vessels ◽  
Tooth Germ ◽  
Longitudinal Section ◽  
Equal Length ◽  
Enamel Organ ◽  
Enamel Matrix ◽  
Distal Extremity ◽  
Old Rats ◽  
Thin Band

SummaryDental germs of the upper incisors of six-days old rats were studied for the uptake of leucine-H3 by different layers of the enamel organ in correlation to the various stages of the development of enamel.The longitudinal section of the tooth germ was divided into 15 zones of about equal length in order to facilitate the description and interpretation of results. Autoradiographic images of the histologic preparations from rats sacrificed 30 minutes, 1 hour, 1 day and 3 days after the injection were made. The strongest reactions were observed in dental germs of rats sacrificed 1 hour, and particularly one day, after the leucine-H3 injection.The uptake of this compound by the enamel matrix increases progressively up to the young enamel and then decreases to the distal extremity; the greatest quantity of this labeled amino-acid was observed in the primary and young enamel. The reactions were present in the transitional enamel only along a thin band close to the dentine-enamel junction.In the enamel organ leucine-H3 incorporation was greatest in the three layers, the zones corresponding to primary and young enamel. In zones corresponding to transitional enamel, the inner epithelium showed a small quantity, and the stellate reticulum a blackening only in its superficial part, were the blood vessels reach the enamel organ.

Finite-size instabilities in finite-range forces

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
C. Gonzalez-Boquera ◽  
M. Centelles ◽  
X. Viñas ◽  
L. M. Robledo
Keyword(s):  
Finite Size ◽  
Finite Range

scholarly journals Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Zhengwen Liu ◽  
Rafael A. Porto ◽  
Zixin Yang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Scattering Problem ◽  
Finite Size ◽  
Effective Field ◽  
Compact Objects ◽  
Scattering Data ◽  
Theory Approach ◽  
Spin Effects ◽  
Radial Action

Abstract Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

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