A characterization of uniformly bounded cosine functions generators

1989 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Ioana Cioranescu ◽  
Pedro Ubilla
Keyword(s):  
Cosine Functions ◽  
Uniformly Bounded

Chronobiological analysis techniques. Application to blood pressure

2008 ◽  
Vol 367 (1887) ◽  
pp. 431-445 ◽  
Author(s):  
J.R Fernández ◽  
R.C Hermida ◽  
A Mojón
Keyword(s):  
Blood Pressure ◽  
Circadian Variation ◽  
Activity Cycle ◽  
Multiple Components ◽  
Noisy Time Series ◽  
Clinical Interest ◽  
Components Analysis ◽  
Periodic Components ◽  
Cosine Functions

Most variables of clinical interest show predictable changes with different frequencies, mainly, but not exclusively, along the rest–activity cycle (circadian variation). Methods of linear least-squares estimation have been designed for the detection of periodic components in sparse and noisy time series (as they are usually present in clinical situations). They include the single and population-mean cosinor methods. In cases where more than one period is statistically significant over the span of time investigated, or when the waveform is non-sinusoidal, the use of multiple components analysis to fit a model consisting of several cosine functions (harmonics or not from a given fundamental period) is recommended. We describe these methods, from the characterization of the underlying models to the process of parameter estimation. As an application example, we describe the modelling of the circadian variation of blood pressure (BP). In most individuals, BP presents a morning increase, a small postprandial valley and a deeper descent during nocturnal rest. This pattern can be easily modelled by means of a model with periods of 24 and 12 hours. Individuals that differ from this model might be considered to present increased cardiovascular risk.

A characterization of the sine function

1980 ◽  
Vol 87 (1) ◽  
pp. 69-73 ◽  
Author(s):  
J. Roe
Keyword(s):  
Sine Function ◽  
Uniformly Bounded

AbstractIf a function and all its derivatives and integrals are absolutely uniformly bounded, then the function is a sine function with period 2π.

scholarly journals Anisotropic Hardy Spaces of Musielak-Orlicz Type with Applications to Boundedness of Sublinear Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baode Li ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Orlicz Function ◽  
Real Variable ◽  
Sublinear Operator ◽  
Atomic Decompositions ◽  
Anisotropic Hardy Space ◽  
Sublinear Operators ◽  
Uniformly Bounded

Letφ:ℝn×[0,∞)→[0,∞)be a Musielak-Orlicz function andAan expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type,HAφ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations ofHAφ(ℝn)in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaceHAp(ℝn)withp∈(0,1]and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization ofHAφ(ℝn), and, as an application, the authors prove that, for a given admissible triplet(φ,q,s), ifTis a sublinear operator and maps all(φ,q,s)-atoms withq<∞(or all continuous(φ,q,s)-atoms withq=∞) into uniformly bounded elements of some quasi-Banach spacesℬ, thenTuniquely extends to a bounded sublinear operator fromHAφ(ℝn)toℬ. These results are new even for anisotropic Orlicz-Hardy spaces onℝn.

Sequences characterizing the sine function

1981 ◽  
Vol 89 (1) ◽  
pp. 71-77 ◽  
Author(s):  
H. Burkill
Keyword(s):  
Fourier Transforms ◽  
Generalized Functions ◽  
Sine Function ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Recently J. Roe(1) established the striking characterization of the sine and cosine functions given in Theorem 1 (below). His proof was an ingenious application of Fourier transforms of generalized functions.

scholarly journals A characterization of the grim reaper cylinder

2019 ◽  
Vol 2019 (746) ◽  
pp. 209-234 ◽  
Author(s):  
Francisco Martín ◽  
Jesús Pérez-García ◽  
Andreas Savas-Halilaj ◽  
Knut Smoczyk
Keyword(s):  
Compact Sets ◽  
Translating Soliton ◽  
Grim Reaper ◽  
Uniformly Bounded

Abstract In this article we prove that a connected and properly embedded translating soliton in {{\mathbb{R}^{3}}} with uniformly bounded genus on compact sets which is {C^{1}} -asymptotic to two planes outside a cylinder, either is flat or coincide with the grim reaper cylinder.

scholarly journals Periodic point free homeomorphisms and irrational rotation factors

2020 ◽  
pp. 1-37
Author(s):  
ALEJANDRO KOCSARD
Keyword(s):  
Periodic Point ◽  
Periodic Points ◽  
Complete Characterization ◽  
Irrational Rotation ◽  
Skew Product ◽  
Circle Rotation ◽  
Rational Direction ◽  
Precise Study ◽  
Uniformly Bounded

Abstract We provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uniformly bounded rotational deviations with respect to a rational direction, we show that annularity and the geometry of its non-wandering set are the only possible obstructions for the existence of an irrational circle rotation as topological factor. Through a very precise study of the dynamics of the induced $\rho $ -centralized skew-product, we extend and generalize considerably previous results of Jäger.

Convex Models of Vehicle Response to Unknown but Bounded Terrain

1991 ◽  
Vol 58 (2) ◽  
pp. 354-361 ◽  
Author(s):  
Yakov Ben-Haim ◽  
Isaac Elishakoff
Keyword(s):  
Design Guidelines ◽  
Vehicle Design ◽  
Maximum Acceleration ◽  
Bounded Motion ◽  
Vibrational Acceleration ◽  
Standard Design ◽  
Vehicle Response ◽  
Range Of Variation ◽  
Uniformly Bounded

This study presents a nonprobabilistic set theoretical approach to analyzing uncertainty in vehicle vibrations arising from motion along imperfectly known terrain. The uncertainty in the substrate is described by a set of allowed substrate profile functions. The analysis of the vehicle response consists in determining the range of variation of performance parameters, as the substrate profile varies over the set of allowed functions. This enables characterization of the uncertain but bounded motion of the vehicle as well as optimization of the vehicle design with respect to uncertainty in the substrate. Maximum acceleration during motion on an imperfectly known surface is determined and related to standard design guidelines for limiting exposure to vibrational acceleration. A method is developed for determining the greatest lower bound of the number of sign changes per second of the vibrational acceleration when moving over an irregular and incompletely specified substrate. Motion along uniformly bounded substrates is studied, as well as traversal of barriers.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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