Systolic counters with unique zero state

2004 ◽  
Author(s):  
M.R. Stan
Keyword(s):  
Unique Zero

INVERSE TOPOLOGICAL PRESSURE WITH APPLICATIONS TO HOLOMORPHIC DYNAMICS OF SEVERAL COMPLEX VARIABLES

2004 ◽  
Vol 06 (04) ◽  
pp. 653-679 ◽  
Author(s):  
EUGEN MIHAILESCU ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Technical Condition ◽  
Topological Pressure ◽  
Holomorphic Dynamics ◽  
Critical Set ◽  
Axiom A ◽  
Type Definition ◽  
Basic Set ◽  
Unique Zero ◽  
Stable Dimension ◽  
The One

In this paper, we introduce a few notions of inverse topological pressure [Formula: see text], defined in terms of backward orbits (prehistories) instead of forward orbits. This inverse topological pressure has some properties similar to the regular (forward) pressure but, in general, if the map is not a homeomorphism, they do not coincide. In fact, there are several ways to define inverse topological pressure; for instance, we show that the Bowen type definition coincides with the one using spanning sets. Then we consider the case of a holomorphic map [Formula: see text] which is Axiom A and such that its critical set does not intersect a particular basic set of saddle type Λ. We will prove that, under a technical condition, the Hausdorff dimension of the intersection between the local stable manifold and the basic set is equal to ts, i.e. [Formula: see text], for all points x belonging to Λ. Here ts represents the unique zero of the function t→P-(tϕs), with P- denoting the inverse topological pressure and [Formula: see text], y∈Λ. In general, [Formula: see text] will be estimated above by ts and below by [Formula: see text], where [Formula: see text] is the unique zero of the map t→P_(tϕs). As a corollary we obtain that, if the stable dimension is non-zero, then Λ must be a non-Jordan curve, and also, if f|Λ happens to be a homeomorphism (like in the examples from [13]), then the stable dimension cannot be zero.

scholarly journals Second-order dynamical systems with penalty terms associated to monotone inclusions

2018 ◽  
Vol 16 (05) ◽  
pp. 601-622 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Szilárd Csaba László
Keyword(s):  
Monotone Operator ◽  
Normal Cone ◽  
Maximal Monotone ◽  
Global Solutions ◽  
Second Order ◽  
Step Size ◽  
Continuous Version ◽  
Unique Zero ◽  
The Resolvent Operator ◽  
Cocoercive Operators

In this paper, we investigate in a Hilbert space setting a second-order dynamical system of the form [Formula: see text] where [Formula: see text]image[Formula: see text] is a maximal monotone operator, [Formula: see text] is the resolvent operator of [Formula: see text] and [Formula: see text] are cocoercive operators, and [Formula: see text], and [Formula: see text] are step size, penalization and, respectively, damping functions, all depending on time. We show the existence and uniqueness of strong global solutions in the framework of the Cauchy–Lipschitz–Picard Theorem and prove ergodic asymptotic convergence for the generated trajectories to a zero of the operator [Formula: see text] where [Formula: see text] and [Formula: see text] denotes the normal cone operator of [Formula: see text]. To this end, we use Lyapunov analysis combined with the celebrated Opial Lemma in its ergodic continuous version. Furthermore, we show strong convergence for trajectories to the unique zero of [Formula: see text], provided that [Formula: see text] is a strongly monotone operator.

Traction data analysis in reference to a unique zero condition

1998 ◽  
Vol 35 (3) ◽  
pp. 179-188 ◽  
Author(s):  
Ajay Kumar Sharma ◽  
K.P Pandey
Keyword(s):  
Data Analysis ◽  
Unique Zero ◽  
Zero Condition

scholarly journals Numbers with simply normal β-expansions

2018 ◽  
Vol 167 (01) ◽  
pp. 171-192 ◽  
Author(s):  
SIMON BAKER ◽  
DERONG KONG
Keyword(s):  
Dynamical Systems ◽  
Combinatorics On Words ◽  
Unique Zero ◽  
Made In

AbstractIn [6] the first author proved that for any β ∈ (1, βKL) everyx∈ (0, 1/(β − 1)) has a simply normal β-expansion, where βKL≈ 1.78723 is the Komornik–Loreti constant. This result is complemented by an observation made in [22], where it was shown that whenever β ∈ (βT, 2] there exists anx∈ (0, 1/(β − 1)) with a unique β-expansion, and this expansion is not simply normal. Here βT≈ 1.80194 is the unique zero in (1, 2] of the polynomialx3−x2− 2x+ 1. This leaves a gap in our understanding within the interval [βKL, βT]. In this paper we fill this gap and prove that for any β ∈ (1, βT], everyx∈ (0, 1/(β − 1)) has a simply normal β-expansion. For completion, we provide a proof that for any β ∈ (1, 2), Lebesgue almost everyxhas a simply normal β-expansion. We also give examples ofxwith multiple β-expansions, none of which are simply normal.Our proofs rely on ideas from combinatorics on words and dynamical systems.

scholarly journals Weather Observations of Remote Polar Areas Using an AWS Onboard a Unique Zero-Emissions Polar Vehicle

2019 ◽  
Vol 100 (10) ◽  
pp. 1891-1895 ◽  
Author(s):  
Sergi Gonzalez ◽  
Manuel Bañon ◽  
José V. Albero ◽  
Ramón Larramendi ◽  
Hermenegildo Moreno ◽  
...  
Keyword(s):  
Climate Models ◽  
Weather Forecasting ◽  
Meteorological Data ◽  
Polar Regions ◽  
Large Set ◽  
Antarctic Plateau ◽  
Weather Observations ◽  
Unique Zero ◽  
The Antarctic ◽  
Harsh Conditions

AbstractThe Antarctic Plateau is one of the land areas with the largest gaps in surface weather observations on Earth, gaps that are usually filled with simulations provided by climate models. However, these simulated values must be ground-validated, which is particularly difficult and costly in remote polar regions. We designed and developed a Mobile Automatic Weather Station (M-AWS) which, on board a zero-emissions polar vehicle, recorded a large set of ground measurements that could be used to evaluate numerical weather simulations in an inexpensive way during the Year of Polar Prediction Southern Hemisphere Special Observing Period (YOPP). The M-AWS registered several weather variables over a transect of 2538 km in the East Antarctic Plateau. These meteorological data were also used by other scientific projects that were part of the expedition and for improving weather forecasting during the mission. The innovative design of the M-AWS overcame the main challenges imposed by the harsh conditions of a voyage in one of the world’s most extreme regions.

scholarly journals Random affine code tree fractals: Hausdorff and affinity dimensions and pressure

2016 ◽  
Vol 162 (2) ◽  
pp. 367-382 ◽  
Author(s):  
ESA JÄRVENPÄÄ ◽  
MAARIT JÄRVENPÄÄ ◽  
MENG WU ◽  
WEN WU
Keyword(s):  
Pressure Function ◽  
Box Counting ◽  
Unique Zero ◽  
Additional Assumptions

AbstractWe prove that for random affine code tree fractals the affinity dimension is almost surely equal to the unique zero of the pressure function. As a consequence, we show that the Hausdorff, packing and box counting dimensions of such systems are equal to the zero of the pressure. In particular, we do not presume the validity of the Falconer–Sloan condition or any other additional assumptions which have been essential in all the previously known results.

Existence of a unique zero of nonlinear systems

2007 ◽  
Vol 15 (1) ◽  
pp. 1-6
Author(s):  
P. G. Bao ◽  
F. Anton ◽  
J. G. Rokne
Keyword(s):  
Nonlinear Systems ◽  
Unique Zero
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