scholarly journals Restricted mean value theorems and the metric theory of restricted Weyl sums

2020 ◽  
Author(s):  
Changhao Chen ◽  
Igor E Shparlinski
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Square Root ◽  
Mean Values ◽  
Line Segments ◽  
Exceptional Sets ◽  
Natural Measure ◽  
Measure Spaces ◽  
The Mean ◽  
Almost All

Abstract We study the behaviour of Weyl sums on a subset ${\mathcal X}\subseteq [0,1)^d$ with a natural measure µ on ${\mathcal X}$. For certain measure spaces $({\mathcal X}, \mu),$ we obtain non-trivial bounds for the mean values of the Weyl sums, and for µ-almost all points of ${\mathcal X}$ the Weyl sums satisfy the square root cancellation law. Moreover, we characterize the size of the exceptional sets in terms of Hausdorff dimension. Finally, we derive variants of the Vinogradov mean value theorem averaging over measure spaces $({\mathcal X}, \mu)$. We obtain general results, which we refine for some special spaces ${\mathcal X}$ such as spheres, moment curves and line segments.

scholarly journals The effect of bright light on fatigue and sleepiness of shift work nurses

2019 ◽  
Author(s):  
Maghsoudipour M ◽  
Hosseinzadeh S ◽  
Parkhoo M ◽  
Ansari M ◽  
Karbasi A
Keyword(s):  
Shift Work ◽  
Opposite Direction ◽  
Light Exposure ◽  
Intervention Group ◽  
Bright Light ◽  
Mean Value ◽  
Control Group ◽  
Mean Values ◽  
The Mean ◽  
Almost All

Introduction: In this study, we assessed the effect of bright light emitted by light box on fatigue, and sleepiness of nurses. Methods: Forty four healthy female shift work nurses were allocated into two groups of intervention and control. In the first stage, bright light was emitted to the nurses in the intervention group by the light box, and bright light was not emitted to the control group. In the next stage (one month later), we emitted bright light to the control group in the first stage (cross- over design). Main outcome measures assessed were fatigue and sleepiness. We used Visual Analogue Scale (VAS) of fatigue, and, Karolinska Sleepiness Scale (KSS). Fatigue and sleepiness were assessed every hour, during next 24 hours. Results: During 24 hours of the assessment of fatigue (VAS), the trend of changes in two groups were in opposite direction and almost all the time of 24 hours, the mean value of two groups were significantly different.  In addition, the effect of intervention on the mean values of KSS during 24 hours was significant and the mean values in two groups were significantly different and the trend of changes in two groups were in opposite direction. Conclusion: The bright light exposure in nurses resulted in changing the trend of fatigue and sleepiness in opposite directions compared to the controls. The minimum of fatigue occurred at 4 am which was time of maximum fatigue in the controls. Also, minimum sleepiness in the cases who were exposed to the bright light was at 4 am.  

Seasonal trends in the stable isotopic composition of snow and meltwater runoff in a subarctic catchment at Okstindan, Norway

2004 ◽  
Vol 35 (2) ◽  
pp. 119-137 ◽  
Author(s):  
S.D. Gurney ◽  
D.S.L. Lawrence
Keyword(s):  
Isotopic Composition ◽  
Mean Value ◽  
Mean Values ◽  
Stable Isotopic Composition ◽  
Meltwater Runoff ◽  
Stable Isotopic ◽  
The Mean ◽  
The Difference ◽  
Δ18o And Δd

Seasonal variations in the stable isotopic composition of snow and meltwater were investigated in a sub-arctic, mountainous, but non-glacial, catchment at Okstindan in northern Norway based on analyses of δ18O and δD. Samples were collected during four field periods (August 1998; April 1999; June 1999 and August 1999) at three sites lying on an altitudinal transect (740–970 m a.s.l.). Snowpack data display an increase in the mean values of δ18O (increasing from a mean value of −13.51 to −11.49‰ between April and August), as well as a decrease in variability through the melt period. Comparison with a regional meteoric water line indicates that the slope of the δ18O–δD line for the snowpacks decreases over the same period, dropping from 7.49 to approximately 6.2.This change points to the role of evaporation in snowpack ablation and is confirmed by the vertical profile of deuterium excess. Snowpack seepage data, although limited, also suggest reduced values of δD, as might be associated with local evaporation during meltwater generation. In general, meltwaters were depleted in δ18O relative to the source snowpack at the peak of the melt (June), but later in the year (August) the difference between the two was not statistically significant. The diurnal pattern of isotopic composition indicates that the most depleted meltwaters coincide with the peak in temperature and, hence, meltwater production.

scholarly journals Survey of Phenolic Acids, Flavonoids and In Vitro Antioxidant Potency Between Fig Peels and Pulps: Chemical and Chemometric Approach

Molecules ◽  
2021 ◽  
Vol 26 (9) ◽  
pp. 2574
Author(s):  
Lahcen Hssaini ◽  
Francisca Hernandez ◽  
Manuel Viuda-Martos ◽  
Jamal Charafi ◽  
Rachid Razouk ◽  
...  
Keyword(s):  
Phenolic Acids ◽  
Radical Scavenging ◽  
Fruit Peel ◽  
Mean Values ◽  
Local Cultivar ◽  
Ic50 Values ◽  
The Mean ◽  
Lipid Peroxidation Inhibition ◽  
Almost All

In the present study, chromatic coordinates, phenolic acids, flavonoids and antioxidant capacity assessed by 1,1-diphenyl-2-picrylhydrazyl (DPPH), 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulfonate (ABTS) and lipid peroxidation inhibition capacity (LPIC) essays and their relative IC50 were investigated in 25 fig cultivars growing in Morocco. The aims of this study were to determine (i) the variation in these compounds among light and dark-colored cultivars, (ii) their partitioning between fruit peel and pulp and (iii) to display network connections among these variables. Twelve phenolic compounds (PCs) were isolated in peel extract versus eight in pulp samples. Anthocyanins, mainly cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the predominant compounds in peels, where the mean concentrations were 75.90 ± 18.76 and 77.97 ± 18.95 µg/g dw, respectively. On the other hand, (−)-epicatechin and cyanidin-3-O-rutinoside were the major compounds in the pulp extracts, where the mean values were 5.23 ± 4.03 and 9.01 ± 5.67 µg/g dw, respectively. A two-dimensional hierarchically clustered heatmap was applied to the dataset to explore correlations in the dataset and similarities between cultivars, without dimensionality reduction. Results showed that anthocyanins, particularly pelargonidin-3-O-rutinoside, cyanidin-3,5-diglucoside and cyanidin-3-O-rutinoside, were the main contributors to the peels’ free radical scavenging capacity. This capacity was particularly higher in the peel of dark-colored figs compared to the fruit pulp. The local cultivar “INRA 1301” showed the most promising phenolic profile due to its very high levels of almost all detected PCs, especially (−)-epicatechin, quercetin-3-O-rutinoside, quercetin-3-O-glucoside, cyanidine-3,5-diglucoside, cyanidine-3-O-rutinoside and pelargonidin-3-O-rutinoside (54.66, 141.08, 35.48, 494.08, 478.66, 12.56 µg/g dw, respectively). Having the darkest figs in the collection (L* = 25.72, c* = 22.09 and h° = 20.99), this cultivar has also combined promising IC50 values, which were of 19.85, 40.58 and 124.78 µg/mL for DPPH, ABTS and LPIC essays, respectively.

scholarly journals On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1303
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Kadir Hamasalh
Keyword(s):  
Time Scale ◽  
Initial Value Problems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Forward Difference ◽  
The Mean ◽  
Monotonicity Analysis ◽  
Monotonicity Results

Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and then, we can show that y(z) is υ-increasing on Ma+υh,h, where the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) for each z∈Ma+h,h. Conversely, if y(a+υh) is greater or equal to zero and y(z) is increasing on Ma+υh,h, we show that the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) on Ma,h. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale hZ utilizing the monotonicity results.

A new simpler approach to measure the strength of toe plantar flexion requiring no mechanical restraint with a light-weight device

2021 ◽  
pp. 095441192110029
Author(s):  
Yuko Komuro ◽  
Yuji Ohta
Keyword(s):  
Plantar Flexion ◽  
Mean Value ◽  
Simple Approach ◽  
Light Weight ◽  
New Approach ◽  
Mean Values ◽  
Mechanical Restraint ◽  
Significant Difference ◽  
Ankle Joints ◽  
The Mean

Conventionally, the strength of toe plantar flexion (STPF) is measured in a seated position, in which not only the target toe joints but also the knee and particularly ankle joints, are usually restrained. We have developed an approach for the measurement of STPF which does not involve restraint and considers the interactions of adjacent joints of the lower extremities. This study aimed to evaluate this new approach and comparing with the seated approach. A thin, light-weight, rigid plate was attached to the sole of the foot in order to immobilize the toe area. Participants were 13 healthy young women (mean age: 24 ± 4 years). For measurement of STPF with the new approach, participants were instructed to stand, raise the device-wearing leg slightly, plantar flex the ankle, and push the sensor sheet with the toes to exert STPF. The sensor sheet of the F-scan II system was inserted between the foot sole and the plate. For measurement with the seated approach, participants were instructed to sit and push the sensor with the toes. They were required to maintain the hip, knee, and ankle joints at 90°. The mean values of maximum STPF of the 13 participants obtained with each approach were compared. There was no significant difference in mean value of maximum STPF when the two approaches were compared (new: 59 ± 23 N, seated: 47 ± 33 N). The coefficient of variation of maximum STPF was smaller for data obtained with the new approach (new: 39%, seated: 70%). Our simple approach enables measurement of STPF without the need for the restraints that are required for the conventional seated approach. These results suggest that the new approach is a valid method for measurement of STPF.

scholarly journals On Fourier Coefficients of the Symmetric Square L-Function at Piatetski-Shapiro Prime Twins

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1254
Author(s):  
Xue Han ◽  
Xiaofei Yan ◽  
Deyu Zhang
Keyword(s):  
Asymptotic Formula ◽  
Fourier Coefficient ◽  
Cusp Form ◽  
Riemann Hypothesis ◽  
Modular Group ◽  
Fourier Coefficients ◽  
Mean Value ◽  
Symmetric Square ◽  
The Mean ◽  
Almost All

Let Pc(x)={p≤x|p,[pc]areprimes},c∈R+∖N and λsym2f(n) be the n-th Fourier coefficient associated with the symmetric square L-function L(s,sym2f). For any A>0, we prove that the mean value of λsym2f(n) over Pc(x) is ≪xlog−A−2x for almost all c∈ε,(5+3)/8−ε in the sense of Lebesgue measure. Furthermore, it holds for all c∈(0,1) under the Riemann Hypothesis. Furthermore, we obtain that asymptotic formula for λf2(n) over Pc(x) is ∑p,qprimep≤x,q=[pc]λf2(p)=xclog2x(1+o(1)), for almost all c∈ε,(5+3)/8−ε, where λf(n) is the normalized n-th Fourier coefficient associated with a holomorphic cusp form f for the full modular group.

scholarly journals On a sum analogous to Dedekind sum and its mean square value formula

2002 ◽  
Vol 32 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Zhang Wenpeng
Keyword(s):  
Asymptotic Property ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Mean Square ◽  
Dedekind Sum ◽  
The Mean

The main purpose of this paper is using the mean value theorem of DirichletL-functions to study the asymptotic property of a sum analogous to Dedekind sum, and give an interesting mean square value formula.

scholarly journals AB0101 THE IMPACT OF TIME SPAN TO ACHIEVE BOOLEAN REMISSION FOR MAINTAINING DISEASE ACTIVITY AFTER ACQUISITION IN RHEUMATOID ARTHRITIS PATIENT

2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 1079.1-1079
Author(s):  
I. Yoshii
Keyword(s):  
Rheumatoid Arthritis ◽  
Disease Activity ◽  
Disease Duration ◽  
Remission Rate ◽  
Mean Value ◽  
Time Span ◽  
Mean Values ◽  
The Mean ◽  
The Relationship

Background:Boolean remission criteria is one most popular and stringent criteria in treating patient with rheumatoid arthritis (RA), because it may guarantees a stable clinical course after attaining remission.Objectives:Impact of time span from initiation to achieving Boolean remission on maintaining disease activity, daily activities, and quality of life after attaining Boolean remission was investigated from daily clinical practice data.Methods:685 patients with RA since August 2010 under the T2T strategy were treated. They were monitored for their TJC, SJC, PGA, EGA, CRP, and disease activity indices such as CDAI, SDAI, DAS28, and Boolean criteria at every visit. HAQ-DI score, pain score using visual analog scale (PS-VAS), and EQ-5D were also monitored, and the quality of life score (QOLS) calculated from EQ-5D was determined at every visit from the time of diagnosis (baseline).Of 685 patients, 465 patients had achieved Boolean remission >1 times, and were consecutively followed up for >3 years. These patients were enrolled in the study. Time span from the first visit to first Boolean remission was calculated. The relationship between the time span and each of background parameters, and the relationship between the time span and each of the mean values of the SDAI score, HAQ score, PS-VAS, SHS, and QOLS at the first Boolean remission and thereafter was evaluated statistically.Patients were subsequently divided into the G ≤ 6 and G > 6 groups based on the achievement of first Boolean remission within two groups: time span G ≤ 6 months and G > 6 months. The two groups were compared with regard to the SDAI score, HAQ score, PS-VAS, SHS, and QOLS at first visit and at the time of first Boolean remission, and the mean values of these parameters after remission were evaluated statistically. Moreover, changes of these parameters and the mean Boolean remission rate after the first remission, and SDAI remission rate at the first Boolean remission to thereafter were compared between the two groups statistically.Results:Out of 465 patients, females comprised 343 (73.7%), and the mean age was 67.8 years (range, from 21–95 years). The mean disease duration at first visit was 6.1 years (range, from 1 months–45 years). The mean follow up length was 88.1 months (range: 36–122 months; median: 85 months) and mean time span from the first visit to the first Boolean remission was 8.1 months. The mean SDAI score, HAQ score, PS-VAS, and the QOLS at first visit were 13.3, 0.467, 33.2, and 0.834, respectively. Among the study parameters, PS-VAS and QOLS were significantly correlated with the time span. For parameters at the first Boolean remission, HAQ-DI score, PS-VAS, and QOLS demonstrated significant correlation with the time span, whereas SDAI, HAQ-DI score, PS-VAS, SHS, and QOLS after the Boolean remission demonstrated significant correlation with the time span.The comparison between the G ≤ 6 and the G > 6 groups revealed that the disease duration, HAQ score, and PS-VAS at baseline in the G > 6 were significantly higher than that in the G ≤ 6 group, and QOLS in the G ≤ 6 group was significantly higher than that in the G > 6 group at baseline. Similarly, the HAQ score and PS-VAS at the first Boolean remission in the G > 6 group were significantly higher than that in the G ≤ 6 group, whereas QOLS in the G ≤ 6 group demonstrated no significant difference compared with that in the G > 6 group.The mean value of the SDAI score after the first Boolean remission in the G > 6 group was significantly higher than that in the G ≤ 6 group. Similarly, the SDAI score, HAQ score, and PS-VAS after the first Boolean remission in the G > 6 group were also significantly higher than those in the G ≤ 6 group, and the mean value of the QOLS in the G ≤ 6 group were significantly higher than that in the G > 6 group. The Boolean remission rate and SDAI remission rate after the first Boolean remission were significantly higher in the G ≤ 6 group than those in the G > 6 group.Conclusion:Attaining Boolean remission ≤ 6 months for RA has significant benefit for more stable disease control, that leads good maintenance of ADL.Disclosure of Interests:None declared

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