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)}.

scholarly journals Integrals of subharmonic functions and their differences with weight over small sets on a ray

2020 ◽  
Vol 54 (2) ◽  
pp. 162-171
Author(s):  
B.N. Khabibullin
Keyword(s):  
Characteristic Function ◽  
Lebesgue Measure ◽  
Real Axis ◽  
Complex Plane ◽  
Measurable Subset ◽  
Positive Part ◽  
Subharmonic Functions ◽  
The Real ◽  
The Difference

Let $E$ be a measurable subset in a segment $[0,r]$ in the positive part of the real axis in the complex plane, and $U=u-v$ be the difference of subharmonic functions $u\not\equiv -\infty$ and $v\not\equiv -\infty$ on the complex plane. An integral of the maximum on circles centered at zero of $U^+:=\sup\{0,U\} $ or $|u|$ over $E$ with a function-multiplier $g\in L^p(E) $ in the integrand is estimated, respectively, in terms of the characteristic function $T_U$ of $U$ or the maximum of $u$ on circles centered at zero, and also in terms of the linear Lebesgue measure of $E$ and the $ L^p$-norm of $g$. Our main theorem develops the proof of one of the classical theorems of Rolf Nevanlinna in the case $E=[0,R]$, given in the classical monograph by Anatoly A. Goldberg and Iossif V. Ostrovsky, and also generalizes analogs of the Edrei\,--\,Fuchs Lemma on small arcs for small intervals from the works of A.\,F.~Grishin, M.\,L.~Sodin, T.\,I.~Malyutina. Our estimates are uniform in the sense that the constants in these estimates do not depend on $U$ or $u$, provided that $U$ has an integral normalization near zero or $u(0)\geq 0$, respectively.

scholarly journals Majorization and Coefficient Problems for a General Class of Starlike Functions

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 476 ◽  
Author(s):  
Nak Eun Cho ◽  
Zahra Oroujy ◽  
Ebrahim Analouei Adegani ◽  
Ali Ebadian
Keyword(s):  
Real Axis ◽  
General Class ◽  
Symmetric Functions ◽  
Starlike Functions ◽  
Current Paper ◽  
General Category ◽  
Coefficient Bounds ◽  
The Real ◽  
Coefficient Problems

In the current paper, we study a majorization issue for a general category S * ( ϑ ) of starlike functions, the region of which is often symmetric with respect to the real axis. For various special symmetric functions ϑ , corresponding consequences of the main result are also presented with some relevant connections of the outcomes rendered here with those obtained in recent research. Moreover, coefficient bounds for some majorized functions are estimated.

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.

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

Interaction between a nanocrack with surface elasticity and a screw dislocation

2016 ◽  
Vol 22 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Xu Wang ◽  
Hui Fan
Keyword(s):  
Screw Dislocation ◽  
Real Axis ◽  
Analytical Study ◽  
Logarithmic Singularity ◽  
Surface Elasticity ◽  
Spontaneous Generation ◽  
The Real ◽  
Crack Tips ◽  
Interaction Problem ◽  
The Continuum

In the present analytical study, we consider the problem of a nanocrack with surface elasticity interacting with a screw dislocation. The surface elasticity is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. By considering both distributed screw dislocations and line forces on the crack, we reduce the interaction problem to two decoupled first-order Cauchy singular integro-differential equations which can be numerically solved by the collocation method. The analysis indicates that if the dislocation is on the real axis where the crack is located, the stresses at the crack tips only exhibit the weak logarithmic singularity; if the dislocation is not on the real axis, however, the stresses exhibit both the weak logarithmic and the strong square-root singularities. Our result suggests that the surface effects of the crack will make the fracture more ductile. The criterion for the spontaneous generation of dislocations at the crack tip is proposed.

scholarly journals Zeros of Dirichlet L-functions near the Real Axis and Chebyshev's Bias

2001 ◽  
Vol 87 (1) ◽  
pp. 54-76 ◽  
Author(s):  
Carter Bays ◽  
Kevin Ford ◽  
Richard H Hudson ◽  
Michael Rubinstein
Keyword(s):  
Real Axis ◽  
The Real

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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