scholarly journals Continuous functions of bounded nth variation

1969 ◽  
Vol 16 (3) ◽  
pp. 205-214
Author(s):  
Gavin Brown
Keyword(s):  
Continuous Function ◽  
Positive Integer ◽  
Decomposition Theorem ◽  
Continuous Functions ◽  
Unit Interval ◽  
Jordan Decomposition ◽  
The Real ◽  
Elementary Construction ◽  
The Difference

Let n be a positive integer. We give an elementary construction for the nth variation, Vn(f), of a real valued continuous function f and prove an analogue of the classical Jordan decomposition theorem. In fact, let C[0, 1] denote the real valued continuous functions on the closed unit interval, let An denote the semi-algebra of non-negative functions in C[0, 1] whose first n differences are non-negative, and let Sn denote the difference algebra An - An. We show that Sn is precisely that subset of C[0, 1] on which Vn(f)<∞. (Theorem 1).

scholarly journals Examples of expanding maps with some special properties

1987 ◽  
Vol 36 (3) ◽  
pp. 469-474 ◽  
Author(s):  
Bau-Sen Du
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Periodic Point ◽  
Topological Entropy ◽  
Real Line ◽  
Periodic Points ◽  
Unit Interval ◽  
Expanding Maps ◽  
The Real ◽  
Piecewise Monotonic

Let I be the unit interval [0, 1] of the real line. For integers k ≥ 1 and n ≥ 2, we construct simple piecewise monotonic expanding maps Fk, n in C0 (I, I) with the following three properties: (1) The positive integer n is an expanding constant for Fk, n for all k; (2) The topological entropy of Fk, n is greater than or equal to log n for all k; (3) Fk, n has periodic points of least period 2k · 3, but no periodic point of least period 2k−1 (2m+1) for any positive integer m. This is in contrast to the fact that there are expanding (but not piecewise monotonic) maps in C0(I, I) with very large expanding constants which have exactly one fixed point, say, at x = 1, but no other periodic point.

scholarly journals Chaotic difference equations are dense

1976 ◽  
Vol 15 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Peter E. Kloeden
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Difference Equations ◽  
Real Line ◽  
Dense Subset ◽  
Structural Instability ◽  
Compact Interval ◽  
The Real ◽  
Continuous Mappings ◽  
The Difference

A continuous function mapping a compact interval of the real line into itself is called chaotic if the difference equation defined in terms of it behaves chaotically in the sense of Li and Yorke. The set of all such chaotic functions is shown to toe a dense subset of the space of continuous mappings of that interval into itself with the max norm. This result indicates the structural instability of nonchaotic difference equations with respect to chaotic behaviour.

An extension of Šarkovskiư's Theorem to the n-od

1991 ◽  
Vol 11 (2) ◽  
pp. 249-271 ◽  
Author(s):  
Stewart Baldwin
Keyword(s):  
Positive Integer ◽  
Real Number ◽  
Continuous Functions ◽  
Complete Characterization ◽  
Unit Interval ◽  
Central Point ◽  
Complex Numbers

AbstractThe n-od is defined to be the set of all complex numbers z such that zn is a real number in the interval [0,1], i.e., a central point with n copies of the unit interval attached at their endpoints. Given a space X and a function f:X → X, Per (f) is defined to be the set {k: f has for a point of (least) period k, k a positive integer}. The main result of this paper is to give, for each n, a complete characterization of all possible sets Per (f), where f ranges over all continuous functions on the n-od.

scholarly journals Harmonic numbers, harmonic series and zeta function

2018 ◽  
Vol 4 (2) ◽  
pp. 122-157
Author(s):  
Ahmed Sebbar
Keyword(s):  
Continuous Function ◽  
Positive Integer ◽  
Real Line ◽  
Prime Numbers ◽  
Bernoulli Numbers ◽  
The Other ◽  
Harmonic Series ◽  
Harmonic Numbers ◽  
The Real ◽  
Points Of View

AbstractThis paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. Robin, as formulated by J. Lagarias. The other parts are devoted to the series $\mathcal{M}{i_s}(z) = \sum\limits_{n = 1}^\infty {{{\mu (n)} \over {{n^s}}}{z^n}} $. A significant result is that the real part f of$$\sum {{{\mu (n)} \over n}{e^{2in\pi \theta }}}$$is an example of a non-trivial real-valued continuous function f on the real line which is 1-periodic, is not odd and has the property $\sum\nolimits_{h = 1}^n {f(h/k) = 0}$ for every positive integer k.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

ANALYTICAL INDICATOR. ANALYSIS OF THE REAL STATE OF DYNAMICS OF MORTALITY OF THE POPULATION OF RUSSIA FROM MALIGNANT TUMORS AND CHANGES IN ITS STRUCTURE

2019 ◽  
Vol 65 (2) ◽  
pp. 205-219 ◽  
Author(s):  
V. Merabishvili
Keyword(s):  
Malignant Tumors ◽  
Specific Weight ◽  
Mortality Rates ◽  
Retirement Age ◽  
Medium Term ◽  
Age Composition ◽  
The Real ◽  
Indicator Analysis ◽  
The Difference ◽  
Real State

The mortality rate is one of the most important criteria for assessing the health of the population. However, it is important to use analytical indicators correctly, especially when evaluating time series. The value of the “gross” mortality is closely linked with a specific weight of persons of elderly and senile ages. All international publications (WHO, IARC, territorial cancer registers) assess the dynamics of morbidity and mortality only by standardized indicators that eliminate the difference in the age composition of the compared population groups. In Russia, from 1960 to 2017, the share of people of retirement age has increased more than 2 times. The structure of mortality from malignant tumors has changed dramatically. The paper presents the dynamics of gross and standardized mortality rates from malignant tumors in Russia and in all administrative territories. Shows the real success of the Oncology service. The medium-term interval forecast until 2025 has been calculated.

scholarly journals Wirtinger integral inequalities for pseudo-integrals and pseudo-additive measure

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Guo ◽  
Xianjun Zhu
Keyword(s):  
Continuous Function ◽  
Integral Inequalities ◽  
Additive Measure ◽  
The Real ◽  
First Case ◽  
Interval Valued

AbstractThe main purpose of this paper is to show Wirtinger type inequalities for the pseudo-integral. We are concerned with pseudo-integrals based on the following three canonical cases: in the first case, the real semiring with pseudo-operation is generated by a strictly monotone continuous function g; in the second case, the pseudo-operations include a pseudo-multiplication and a power arithmetic addition; in the last case, ⊕-measures are interval-valued. Examples are given to illustrate these equalities.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

The feasibility and validity of using a real time location system (RTLS) to measure bedside contact time

2021 ◽  
pp. 174498712110161
Author(s):  
Ann-Marie Cannaby ◽  
Vanda Carter ◽  
Thomas Hoe ◽  
Stephenson Strobel ◽  
Elena Ashtari Tafti ◽  
...  
Keyword(s):  
Real Time ◽  
Contact Time ◽  
Measured Data ◽  
Complete Agreement ◽  
Observation Data ◽  
The Real ◽  
Measured Time ◽  
The Difference ◽  
Hospital Wards ◽  
Location Systems

Background The association between the nurse-to-patient ratio and patient outcomes has been extensively investigated. Real time location systems have the potential capability of measuring the actual amount of bedside contact patients receive. Aims This study aimed to determine the feasibility and accuracy of real time location systems as a measure of the amount of contact time that nurses spent in the patients’ bed space. Methods An exploratory, observational, feasibility study was designed to compare the accuracy of data collection between manual observation performed by a researcher and real time location systems data capture capability. Four nurses participated in the study, which took place in 2019 on two hospital wards. They were observed by a researcher while carrying out their work activities for a total of 230 minutes. The amount of time the nurses spent in the patients’ bed space was recorded in 10-minute blocks of time and the real time location systems data were extracted for the same nurse at the time of observation. Data were then analysed for the level of agreement between the observed and the real time location systems measured data, descriptively and graphically using a kernel density and a scatter plot. Results The difference (in minutes) between researcher observed and real time location systems measured data for the 23, 10-minute observation blocks ranged from zero (complete agreement) to 5 minutes. The mean difference between the researcher observed and real time location systems time in the patients’ bed space was one minute (10% of the time). On average, real time location systems measured time in the bed space was longer than the researcher observed time. Conclusions There were good levels of agreement between researcher observation and real time location systems data of the time nurses spend at the bedside. This study confirms that it is feasible to use real time location systems as an accurate measure of the amount of time nurses spend at the patients’ bedside.

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