Arcs on which a univalent function has small magnitude

1987 ◽  
pp. 131-148
Author(s):  
Carl H. FitzGerald
Keyword(s):  
Univalent Function ◽  
Small Magnitude

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

scholarly journals A novel digital approach to describe real world outcomes among patients with constipation

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Allison Shapiro ◽  
Benjamin Bradshaw ◽  
Sabine Landes ◽  
Petra Kammann ◽  
Beatrice Bois De Fer ◽  
...  
Keyword(s):  
Heart Rate ◽  
Prospective Study ◽  
Real World ◽  
Symptom Severity ◽  
Interaction Analysis ◽  
Behavioral Activity ◽  
Patient Centered ◽  
Small Magnitude ◽  
Digital Devices ◽  
Bowel Movements

AbstractUnderstanding day-to-day variations in symptoms and medication management can be important in describing patient centered outcomes for people with constipation. Patient Generated Health Data (PGHD) from digital devices is a potential solution, but its utility as a tool for describing experiences of people with frequent constipation is unknown. We conducted a virtual, 16-week prospective study of individuals with frequent constipation from an online wellness platform that connects mobile consumer digital devices including wearable monitors capable of passively collecting steps, sleep, and heart rate data. Participants wore a Fitbit monitoring device for the study duration and were administered daily and monthly surveys assessing constipation symptom severity and medication usage. A set of 38 predetermined day-level behavioral activity metrics were computed from minute-level data streams for steps, sleep and heart rate. Mixed effects regression models were used to compare activity metrics between constipation status (irregular or constipated vs. regular day), medication use (medication day vs. non-medication day) and the interaction of medication day with irregular or constipation days, as well as to model likelihood to treat with constipation medications based on daily self-reported symptom severity. Correction for multiple comparisons was performed with the Benjamini–Hochberg procedure for false discovery rate. This study analyzed 1540 enrolled participants with completed daily surveys (mean age 36.6 sd 10.0, 72.8% female, 88.8% Caucasian). Of those, 1293 completed all monthly surveys and 756 had sufficient Fitbit data density for analysis of activity metrics. At a daily-level, 22 of the 38 activity metrics were significantly associated with bowel movement or medication treatment patterns for constipation. Participants were measured to have fewer steps on irregular days compared to regular days (−200 steps, 95% CI [−280, −120]), longer periods of inactivity on constipated days (9.1 min, 95% CI [5.2, 12.9]), reduced total sleep time on irregular and constipated days (−2.4 min, 95% CI [−4.3, −0.4] and −4.0 min, 95% CI [−6.5, −1.4], respectively). Participants reported greater severity of symptoms for bloating, hard stool, difficulty passing, and painful bowel movements on irregular, constipation and medication days compared to regular days with no medication. Interaction analysis of medication days with irregular or constipation days observed small increases in severity compared to non-medication days. Participants were 4.3% (95% CI 3.2, 5.3) more likely to treat with medication on constipated days versus regular. No significant increase in likelihood was observed for irregular days. Daily likelihood to treat increased for each 1-point change in symptom severity of bloating (2.4%, 95% CI [2.0, 2.7]), inability to pass (2.2%, 95% CI [1.4, 3.0]) and incomplete bowel movements (1.3%, 95% CI [0.9, 1.7]). This is the first large scale virtual prospective study describing the association between passively collected PGHD and constipation symptoms and severity at a day-to-day granularity level. Constipation status, irregular or constipated, was associated with a number of activity metrics in steps and sleep, and likelihood to treat with medication increased with increasing severity for a number of constipation symptoms. Given the small magnitude of effect, further research is needed to understand the clinical relevance of these results. PGHD may be useful as a tool for describing real world patient centered experiences for people with constipation.

scholarly journals Perceiving numerosity does not cause automatic shifts of spatial attention

2021 ◽  
Author(s):  
Michele Pellegrino ◽  
Mario Pinto ◽  
Fabio Marson ◽  
Stefano Lasaponara ◽  
Fabrizio Doricchi
Keyword(s):  
Spatial Attention ◽  
Colour Change ◽  
Simultaneous Presentation ◽  
Variable Delay ◽  
Large Magnitude ◽  
Small Magnitude ◽  
Spatial Component ◽  
Speed Up ◽  
The Right

AbstractIt is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space.

Are Firms with Negative Book Equity in Financial Distress?

2015 ◽  
Vol 18 (03) ◽  
pp. 1550016 ◽  
Author(s):  
Tze Chuan Chewie ANG
Keyword(s):  
Failure Rate ◽  
Financial Distress ◽  
Operating Performance ◽  
Large Magnitude ◽  
Small Magnitude ◽  
First Report ◽  
Distress Risk ◽  
Financial Characteristics ◽  
And Control ◽  
Negative Earnings

This study examines whether negative book equity (BE) firms are in financial distress by analyzing their operating performance, financial characteristics, distress risk, and survivability when they first report negative BE. Firms with small magnitude of negative BE (SNBE firms) suffer from persistent negative earnings and financial distress, while firms with large magnitude of negative BE (LNBE firms) experience a temporary non-distress related earnings shock. LNBE firms report consecutive years of negative BE, but have lower distress risk and failure rate than both SNBE and control firms. However, all negative BE stocks have abysmal returns subsequent to their first report of negative BE.

Linear and nonlinear behaviour of two-stream instabilities in collisionless plasmas

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Y. W. Hou ◽  
M. X. Chen ◽  
M. Y. Yu ◽  
B. Wu
Keyword(s):  
Normal Mode Analysis ◽  
System Size ◽  
Point Of View ◽  
Mode Analysis ◽  
Nonlinear Behaviour ◽  
Initial Growth ◽  
Small Magnitude ◽  
Plasma Oscillations ◽  
Numerical Noise ◽  
Growth Properties

The transient, growth and nonlinear saturation stages in the evolution of the electrostatic two-stream instabilities as described by the Vlasov–Poisson system are reconsidered by numerically following the evolution of the total wave energy of the plasma oscillations excited from (numerical) noise. Except for peculiarities related to the necessarily finite (even though very small) magnitude of the perturbations in the numerical simulation, the existence and initial growth properties of the instabilities from the numerical results are found to be consistent with those from linear normal mode analysis and the Penrose criteria. However, contradictory to the traditional point of view, the growth of instability before saturation is not always linear. The initial stage of the growth can exhibit fine structures that can be attributed to the harmonics of the excited plasma oscillations, whose wavelengths are determined by the system size and the numerical noise. As expected, saturation of the unstable oscillations is due to electron trapping when they reach sufficiently large amplitudes.

Framework for a Ground-Motion Model for Induced Seismic Hazard and Risk Analysis in the Groningen Gas Field, The Netherlands

2017 ◽  
Vol 33 (2) ◽  
pp. 481-498 ◽  
Author(s):  
Julian J. Bommer ◽  
Peter J. Stafford ◽  
Benjamin Edwards ◽  
Bernard Dost ◽  
Ewoud van Dedem ◽  
...  
Keyword(s):  
Seismic Hazard ◽  
Ground Motion ◽  
Quantitative Estimation ◽  
Epistemic Uncertainty ◽  
Induced Earthquakes ◽  
Gas Field ◽  
Small Magnitude ◽  
Ground Motion Model ◽  
Hazard And Risk ◽  
Groningen Gas Field

The potential for building damage and personal injury due to induced earthquakes in the Groningen gas field is being modeled in order to inform risk management decisions. To facilitate the quantitative estimation of the induced seismic hazard and risk, a ground motion prediction model has been developed for response spectral accelerations and duration due to these earthquakes that originate within the reservoir at 3 km depth. The model is consistent with the motions recorded from small-magnitude events and captures the epistemic uncertainty associated with extrapolation to larger magnitudes. In order to reflect the conditions in the field, the model first predicts accelerations at a rock horizon some 800 m below the surface and then convolves these motions with frequency-dependent nonlinear amplification factors assigned to zones across the study area. The variability of the ground motions is modeled in all of its constituent parts at the rock and surface levels.

scholarly journals Vertical air motions derived from a descending radiosonde using a lightweight hard ball as the parachute

2013 ◽  
Vol 6 (5) ◽  
pp. 8107-8127 ◽  
Author(s):  
H. Chen ◽  
Y. Zhu ◽  
J. Zhang ◽  
Y. Xuan
Keyword(s):  
Northern China ◽  
Lower Atmosphere ◽  
Radiosonde Data ◽  
Small Magnitude ◽  
Abstract Knowledge ◽  
Launch Site ◽  
Wind Profiler Radar ◽  
Vertical Wind Speed ◽  
The Difference ◽  
Hard Ball

Abstract. Knowledge of vertical air motions in the atmosphere is important for meteorological and climate studies due to its impact on clouds, precipitation and the vertical transport of air masses, heat, momentum, and composition. It is among the most difficult quantities to measure because of its small magnitude. In this study, a descending radiosonde technique has been developed to detect the vertical wind speed (VW) in the atmosphere. The system is composed of a radiosonde and a 0.5-m diameter hard ball made of plastic foam that acts as a parachute. The radiosonde hangs under the hard ball by a string which is then cut when the instrument is elevated into the upper troposphere by a balloon. The VW is derived from the difference between the observed radiosonde descent rate and the calculated radiosonde descent rate in still air based on fluid dynamics. Deduction of the appropriate drag coefficient for the radiosonde is facilitated by the symmetrical shape of the parachute. An intensive radiosonde launch experiment was held in northern China during the summer seasons of 2010 to 2012. This study uses radiosonde data collected during the campaign to retrieve the vertical air velocity within the radiosonde altitude-detecting range. In general, the VW ranges from −1 to 1 m s−1. Strong vertical air motion (~2 m s−1) is seen in a few radiosonde measurements. Although considerable uncertainties exist in measuring weak vertical air motions, a case study shows that there is reasonable agreement between retrievals of VW in the lower atmosphere from the radiosonde and a wind profiler radar located at the launch site.

scholarly journals First-Principles Study of Superlow Friction Between Hydrogenated Diamond Surfaces

2005 ◽  
Author(s):  
S. Ciraci ◽  
S. Dag
Keyword(s):  
First Principles ◽  
Lateral Force ◽  
Repulsive Interaction ◽  
Ambient Conditions ◽  
Small Magnitude ◽  
Diamond Surfaces ◽  
Sliding Surfaces ◽  
Carbon Coated ◽  
Force Variation ◽  
Coated Surfaces

Attractive interaction between two clean diamond(001) slabs turns repulsive upon the hydrogenation of surfaces. Even under high loading forces, this repulsive interaction prevents the sliding surfaces from being closer to each other. As a result, calculated lateral force variation generated during sliding has small magnitude under high constant loading forces. Superlow friction observed earlier between diamond like carbon coated surfaces can be understood by the steady repulsive interaction between sliding surfaces, as well as strong and stiff carbon-carbon and carbon-hydrogen bonds which do not favor energy dissipation. In ambient conditions, the steady repulsive interaction is, however, destroyed by oxygenation of hydrogenated surface.

Abstract P218: The Association Of Mid-life Cumulative Exposure To Systolic Blood Pressure, Myocardial Oxygen Demand, And Hypertension With Later-life Central Arterial Stiffness And Its 5-year Change: The Atherosclerosis Risk In Communities Study - Neurocognitive Study (ARIC-NCS)

Circulation ◽  
2021 ◽  
Vol 143 (Suppl_1) ◽  
Author(s):  
Michelle L Meyer ◽  
Veeral Saraiya ◽  
Hirofumi Tanaka ◽  
Priya Palta ◽  
Timothy M Hughes ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Arterial Stiffness ◽  
Systolic Blood Pressure ◽  
Oxygen Demand ◽  
Later Life ◽  
Cumulative Exposure ◽  
Rate Pressure Product ◽  
Myocardial Oxygen Demand ◽  
Small Magnitude ◽  
Cumulative Exposures

Background: Greater central artery stiffness predicts cardiovascular disease and all-cause mortality, thus understanding arterial stiffness determinants has prevention implications. Reports of the temporal association of blood pressure with arterial stiffness are conflicting and the association with myocardial oxygen demand has not been evaluated. Objective: Characterize the association of mid- to later-life cumulative exposure to systolic blood pressure (SBP), myocardial oxygen demand, and hypertension (HTN) with arterial stiffness and its 5-year change in older adults. Methods: We included 1,975 adults (1151 women; 359 Black; visit 5 mean age 74 years) examined in visits 5 (2011-13) and 6 or 7 (2016-19) of the population-based ARIC-NCS with measures of arterial stiffness (carotid-femoral pulse wave velocity (cfPWV)). Higher cfPWV indicates greater arterial stiffness. We calculated cumulative exposures as the sum of averages from four consecutive visits from 1987-89 to 1996-98 divided by total time. Myocardial oxygen demand was calculated as the rate pressure product (RPP): (SBP x heart rate)/1,000. We derived HTN duration as the time since first HTN detection. Associations of cumulative exposures with visit 5 cfPWV and the 5-year cfPWV change were evaluated by multivariable linear regression adjusted for demographics and cardiometabolic factors. Results: Over the mean 5.7 years between visits 5 and 6 or 7, cfPWV increased by 144.9 cm/s (SD: 276.0; range -680.0, 961.5 cm/s). HTN at any visit, duration, and the time-weighted cumulative measures were associated with higher visit 5 cfPWV (Table). Prevalent HTN was inversely associated with cfPWV change. No statistically significant associations were observed for the other exposures and cfPWV change. Conclusion: Cumulative exposure to SBP, RPP, and HTN are modifiable traits associated with higher cfPWV at later-life, but not with rate of cfPWV change in older adulthood. HTN at visit 5 was associated with lower cfPWV change, albeit the change is of small magnitude.

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