Psychotherapy beyond all the words: Dyadic expansion, vagal regulation, and biofeedback in psychotherapy.

2019 ◽  
Vol 29 (4) ◽  
pp. 412-425 ◽  
Author(s):  
Charlotte Fiskum
Keyword(s):  
Dyadic Expansion

EXCEPTIONAL SETS RELATED TO THE RUN-LENGTH FUNCTION OF BETA-EXPANSIONS

Fractals ◽  
2018 ◽  
Vol 26 (04) ◽  
pp. 1850049 ◽  
Author(s):  
LULU FANG ◽  
KUNKUN SONG ◽  
MIN WU
Keyword(s):  
Limit Theorem ◽  
Hausdorff Dimension ◽  
Maximal Length ◽  
Length Function ◽  
Run Length ◽  
Exceptional Sets ◽  
Consecutive Zero ◽  
Dyadic Expansion ◽  
Almost All ◽  
Increasing Function

Let [Formula: see text] and [Formula: see text] be real numbers. The run-length function of [Formula: see text]-expansions denoted by [Formula: see text] is defined as the maximal length of consecutive zeros in the first [Formula: see text] digits of the [Formula: see text]-expansion of [Formula: see text]. It is known that for Lebesgue almost all [Formula: see text], [Formula: see text] increases to infinity with the logarithmic speed [Formula: see text] as [Formula: see text] goes to infinity. In this paper, we calculate the Hausdorff dimension of the subtle set for which [Formula: see text] grows to infinity with other speeds. More precisely, we prove that for any [Formula: see text], the set [Formula: see text] has full Hausdorff dimension, where [Formula: see text] is a strictly increasing function satisfying that [Formula: see text] is non-increasing, [Formula: see text] and [Formula: see text] as [Formula: see text]. This result significantly extends the existing results in this topic, such as the results in [J.-H. Ma, S.-Y. Wen and Z.-Y. Wen, Egoroff’s theorem and maximal run length, Monatsh. Math. 151(4) (2007) 287–292; R.-B. Zou, Hausdorff dimension of the maximal run-length in dyadic expansion, Czechoslovak Math. J. 61(4) (2011) 881–888; J.-J. Li and M. Wu, On exceptional sets in Erdős–Rényi limit theorem, J. Math. Anal. Appl. 436(1) (2016) 355–365; J.-J. Li and M. Wu, On exceptional sets in Erdős–Rényi limit theorem revisited, Monatsh. Math. 182(4) (2017) 865–875; Y. Sun and J. Xu, A remark on exceptional sets in Erdős–Rényi limit theorem, Monatsh. Math. 184(2) (2017) 291–296; X. Tong, Y.-L. Yu and Y.-F. Zhao, On the maximal length of consecutive zero digits of [Formula: see text]-expansions, Int. J. Number Theory 12(3) (2016) 625–633; J. Liu, and M.-Y. Lü, Hausdorff dimension of some sets arising by the run-length function of [Formula: see text]-expansions, J. Math. Anal. Appl. 455(1) (2017) 832–841; L.-X. Zheng, M. Wu and B. Li, The exceptional sets on the run-length function of [Formula: see text]-expansions, Fractals 25(6) (2017) 1750060; X. Gao, H. Hu and Z.-H. Li, A result on the maximal length of consecutive 0 digits in [Formula: see text]-expansions, Turkish J. Math. 42(2) (2018) 656–665, doi: 10.3906/mat-1704-119].

scholarly journals Weighted normal numbers

1995 ◽  
Vol 52 (2) ◽  
pp. 177-181
Author(s):  
Geon H. Choe
Keyword(s):  
Normal Numbers ◽  
Fixed Integer ◽  
Almost Everywhere ◽  
Dyadic Expansion

We show that if {ak}k is bounded then for almost every 0 < x < 1 where is the dyadic expansion of x. It is also shown that almost everywhere where p > 1 is any fixed integer.

scholarly journals A note on immersing manifolds in euclidean spaces

1987 ◽  
Vol 36 (2) ◽  
pp. 215-226
Author(s):  
Ng Tze Beng
Keyword(s):  
Normal Bundle ◽  
Euclidean Spaces ◽  
Thom Class ◽  
Dyadic Expansion ◽  
Cohomology Operations ◽  
General Manifold

Let M be a closed, connected smooth and 3-connected mod 2 (that is Hi(M;ℤ2) = 0, 0 < i ≤ 3) manifold of dimension n = 7 + 8k. Using a combination of cohomology operations on certain cohomology classes of M and on the Thom class of the stable normal bundle of M we show that under certain conditions M immerses in R2n−8. This extends previously known results for such a general manifold when the number of 1's in the dyadic expansion of n is less than 8.

scholarly journals USING THE ATTACHMENT LENS AND THE DYADIC EXPANSION OF CONSCIOUSNESS APPROACH TO INCREASE SCHOOL ADJUSTMENT

2020 ◽  
pp. 349-358
Author(s):  
Oana Dănilă ◽  
Keyword(s):  
Human Brain ◽  
Student Teacher ◽  
School Adjustment ◽  
Social Competencies ◽  
Student Teacher Relationship ◽  
The Social ◽  
Dyadic Expansion ◽  
The Brain ◽  
Attachment Strategies

When in danger, either we refer to menaces or just novel situations, the brain needs firstly to connect to another human brain in order to coregulate; only after, can that brain continue process/ learn, regulate behaviors and thus adjust to the environment. The purpose of this study was to explore the connection between the quality of the pupil-teacher relationship, assessed from the attachment perspective and different school adjustment aspects. A sample of 40 educators were invited to evaluate their attachment strategies and then assess at least 3children from their current classes(primary school); results for a total of 121pupils were collected. First of all, educators assessed the pupil’s attachment needs using the Student-Teacher Relationship Scale; then, they were asked to assess social competencies using the Social Competence Scaleand the Engagementversus Disaffection with Learning Scale, as facets of school adjustment. Results show that the strength of the pupil-teacher relationship is influenced by the particularities of the attachment strategies of both parties, and, in turn, this relationship, with its 3 dimensions (closeness, conflict and dependence)impacts adjustment. Results are discussed in the light of the Dyadic Expansion of Consciousnesshypothesis–in a safe relationship, both the teacherand the pupil significantly expand the learning possibilities.

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