scholarly journals A Fourier inversion method for the estimation of a density and its derivatives

1977 ◽  
Vol 23 (2) ◽  
pp. 166-171 ◽  
Author(s):  
J. Blum ◽  
V. Susarla
Keyword(s):  
Almost Sure Convergence ◽  
Characteristic Functions ◽  
Inversion Method ◽  
Fourier Inversion ◽  
Bivariate Normal ◽  
Unknown Density ◽  
The Mean ◽  
Image Position ◽  
Almost All ◽  
Derivatives Of

During the last two decades a variety of methods have been developed for the problem of estimation of unknown density f wrt Lebesgue measure and its vth dervative g(= f(v)) using i.i.d random variables X1, …, Xn when X1 ∼ f. For example, see Wegman (1972). In almost all the papers on the estimation of f(x) or g(x), various authors assumed the existence of derivatives of f of order r(>v) at x to obtain rates for the mean-square convergences and other desirable properties for their estimators. Here it is shown that ifthen estimators gˇ(x) can be constructed for which E[(gˇ(x)-g(x))2] = O(n−(2a-δ)/(2a+2v+1)) for anygiveng δ > 0. Simiar statements hold for almost sure convergence of gˇ(x). It can also be shown that (gˇ(x1), gˇ(x2)) is asymptotically bivariate normal under certain conditions for x1, ≠ x2. If (Al) is satisfied with a ≦ l, then our estimators have all the desirable properties while other methods are not applicable in this situation since they require differentiability conditions on g. (For example, see Susarla and Kumar (1975) and its references.) Our estimators are defined by using the inversion theorem for some absolutely integrable characteristic functions. The motivation for our estimators is given in O'Bryan and Susarla (1975, 76) and Susarla and O'Bryan (1975).

scholarly journals New Determination of the Polar Motion from 1890 to 1969

1972 ◽  
Vol 48 ◽  
pp. 12-13 ◽  
Author(s):  
E. P. Fedorov ◽  
A. A. Rorsun ◽  
S. P. Major ◽  
N. T. Panchenko ◽  
V. K. Tarady ◽  
...  
Keyword(s):  
Polar Motion ◽  
Normal Values ◽  
Mean Value ◽  
Polar Coordinates ◽  
Periodic Part ◽  
Equal Weight ◽  
The Mean ◽  
Image Position ◽  
Almost All ◽  
Academy Of Sciences

To obtain the coordinates of the Earth's pole almost all series of systematic latitude observations that continued for more than two years have been utilized. They are listed in Table I which comprises 92 series of observation at 72 observatories.Computation was made by the following stages. As initial data we used normal values of latitude φ1, φ2, ……. φn, i.e. the means of instantaneous latitudes over successive intervals of time. These values were smoothed using Whittaker's numerical method which is capable of giving the most probable curve of latitude variation. The smoothed values φ′ satisfy the following condition where hi is a measure of precision, λ2 an arbitrary number by means of which the degree of smoothing is set, and Δ3 designates the third difference of φ′. Whittaker's method was applied in different modifications according to whether or not the normal values of φ′i had an equal weight and were given at equidistant moments of time.For the origin of the system of coordinates we adopted the mean pole of the epoch of observation. Because of this the data given in Table II represent only the periodic part of the polar motion in the region of frequency from 0.77 to 2 cycles per year. In this connection the sequence of φ′ was subjected to filtration in order to eliminate variation of the mean latitude.Coordinates of the pole were computed in two approximations. First, it was assumed that all the series are of the same accuracy and so they were taken with an equal weight.The polar coordinates obtained on this assumption are denoted by x1, y1 and shown in the second and third columns of Table II. The divergences of the smoothed values φ′i from the latitudes computed with x1, y1 were denoted by zκi where the index κ designates the number of a series. Then for the second approximation each series of observation was taken with the weight inversely proportional to the mean value of for this series. The polar coordinates obtained in the second approximation are denoted by x2, y2 and given in the last two columns of Table II.The full paper with the tables will be published by the Ukrainian Academy of Sciences as a separate book.

Evaluation of Low-Dose Gentamicin Once Daily Dosing Regimen at A General Hospital in Malaysia

2018 ◽  
Vol 9 (01) ◽  
Author(s):  
Ab Rahman A F ◽  
Md Sahak N. ◽  
Ali A. M.
Keyword(s):  
Medical Records ◽  
Public Hospital ◽  
Low Dose ◽  
Dosing Regimen ◽  
Once Daily ◽  
Neutropenic Sepsis ◽  
Wide Acceptance ◽  
The Mean ◽  
Initiation Of Therapy ◽  
Almost All

Objective: Once daily dosing (ODD) aminoglycoside is gaining wide acceptance as an alternative way of dosing. In our setting it is the regimen of choice whenever gentamicin is indicated. The objective of this study was to evaluate the practice of gentamicin ODD in a public hospital in Malaysia. Methods: We conducted a retrospective review of medical records of patients on gentamicin ODD who were admitted to Hospital Melaka during January 2002 until March 2010. All adult patients who were on ODD gentamicin with various level of renal function were included in the study. Patients on gentamicin less than 72 hours and pregnant women were excluded. Results: From 110 patients, 75 (68.2%) were male and 35 (31.8%) were female. Indications for ODD gentamicin included pneumonia, 34 (31.0%) neutropenic sepsis, 27 (24.5%) and sepsis, 11 (10.0%). The mean dose and duration of gentamicin was 3.2 mg/kg/day and 7 days, respectively. Almost all patients were on gentamicin combined with other antibiotics. Clinical cure based on fever resolution was found in 89.1% of patients treated with ODD. Resolution of fever took an average of 48 hours after initiation of therapy. The evaluation for bacteriologic cure could not be performed because of insufficient data on culture and sensitivity. Out of 38 patients with analyzable serum creatinine data, four patients might have developed nephrotoxicity. Conclusion: In our setting, lower dosages of ODD gentamicin when used in combination with other antibiotics seemed to be effective and safe in treating most gram negative infections.

DFT Benchmark Study of the O--O Bond Dissociation Energy in Peroxides Validated with High-Level Ab-Initio Calculations

2019 ◽  
Author(s):  
Danilo Carmona ◽  
Pablo Jaque ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Reference Value ◽  
Basis Set ◽  
Basis Sets ◽  
Mean Deviation ◽  
Bond Dissociation ◽  
Dissociation Energies ◽  
The Mean ◽  
Experimental Values ◽  
High Level ◽  
Almost All

<div><div><div><p>Peroxides play a central role in many chemical and biological pro- cesses such as the Fenton reaction. The relevance of these compounds lies in the low stability of the O–O bond which upon dissociation results in radical species able to initiate various chemical or biological processes. In this work, a set of 64 DFT functional-basis set combinations has been validated in terms of their capability to describe bond dissociation energies (BDE) for the O–O bond in a database of 14 ROOH peroxides for which experimental values ofBDE are available. Moreover, the electronic contributions to the BDE were obtained for four of the peroxides and the anion H2O2− at the CBS limit at CCSD(T) level with Dunning’s basis sets up to triple–ζ quality provid- ing a reference value for the hydrogen peroxide anion as a model. Almost all the functionals considered here yielded mean absolute deviations around 5.0 kcal mol−1. The smallest values were observed for the ωB97 family and the Minnesota M11 functional with a marked basis set dependence. Despite the mean deviation, order relations among BDE experimental values of peroxides were also considered. The ωB97 family was able to reproduce the relations correctly whereas other functionals presented a marked dependence on the chemical nature of the R group. Interestingly, M11 functional did not show a very good agreement with the established order despite its good performance in the mean error. The obtained results support the use of similar validation strategies for proper prediction of BDE or other molecular properties by DF Tmethods in subsequent related studies.</p></div></div></div>

scholarly journals Pilonidal sinus disease on the rise: a one-third incidence increase in inpatients in 13 years with substantial regional variation in Germany

2021 ◽  
Author(s):  
Christina Oetzmann von Sochaczewski ◽  
Jan Gödeke
Keyword(s):  
Pilonidal Sinus ◽  
Regional Variation ◽  
Disease Incidence ◽  
Age Groups ◽  
Pilonidal Sinus Disease ◽  
National Guidelines ◽  
Reconstructive Procedures ◽  
Sinus Disease ◽  
The Mean ◽  
Almost All

Abstract Purpose Collective evidence from single-centre studies suggests an increasing incidence of pilonidal sinus disease in the last decades, but population-based data is scarce. Methods We analysed administrative case–based principal diagnoses of pilonidal sinus disease and its surgical therapy between 2005 and 2017 in inpatients. Changes were addressed via linear regression. Results The mean rate of inpatient episodes of pilonidal sinus disease per 100,000 men increased from 43 in 2005 to 56 in 2017. In females, the mean rate of inpatient episodes per 100,000 women rose from 14 in 2005 to 18 in 2017. In the whole population, for every case per 100,000 females, there were 3.1 cases per 100,000 males, but the numbers were highly variable between the age groups. There was considerable regional variation within Germany. Rates of inpatient episodes of pilonidal sinus disease were increasing in almost all age groups and both sexes by almost a third. Surgery was dominated by excision of pilonidal sinus without reconstructive procedures, such as flaps, whose share was around 13% of all procedures, despite recommendations of the national guidelines to prefer flap procedures. Conclusion Rates of inpatient episodes of pilonidal sinus disease in Germany rose across almost all age groups and both sexes with relevant regional variation. The underlying causative factors are unknown. Thus, patient-centred research is necessary to explore them. This should also take cases into account that are solely treated office-based in order to obtain a full-spectrum view of pilonidal sinus disease incidence rates.

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 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.

Quantitative analysis of static equilibrium in women after mastectomy

2014 ◽  
Vol 14 (1) ◽  
pp. 81-87
Author(s):  
Maciej Rachwał ◽  
Justyna Drzał-Grabiec ◽  
Katarzyna Walicka-Cupryś ◽  
Aleksandra Truszczyńska
Keyword(s):  
Mean Amplitude ◽  
Control Group ◽  
Foot Pressure ◽  
Locomotor System ◽  
Center Of Foot Pressure ◽  
The Mean ◽  
Almost All ◽  
Posture Stability ◽  
Mastectomy Group ◽  
Better Than

Abstract Background: The post-mastectomy changes to the locomotor system are related to the scar and adhesion or to the lymphatic edema after amputation which, in turn, lead to local and global distraction of the work of the muscles. These changes lead to body statics disturbance that changes the projection of the center of gravity and worsens motor response due to changing of the muscle sensitivity. Objective: The aim of the study was to evaluate the static balance of women after undergoing mastectomy. Methods: The study included 150 women, including 75 who underwent mastectomy (mean age: 60±7.6) years, mean body mass index (BMI): 26 (±3.6) kg/m2) and 75 who were placed in the control group with matched age and BMI. The study was conducted using a tensometric platform. Results: Statistically significant differences were found for almost all parameters between the post-mastectomy group and group of healthy women, regarding center of foot pressure (COP) path length in the Y and X axes and the mean amplitude of COP. Conclusions: First, the findings revealed that balance in post-mastectomy women is significantly better than in the control group. Second, physiotherapeutic treatment of post-mastectomy women may have improved their posture stability compared with their peers.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

Characteristics and attitudes of family planners in Khartoum, Sudan

1982 ◽  
Vol 14 (1) ◽  
pp. 7-16 ◽  
Author(s):  
M. A. Khalifa
Keyword(s):  
Family Planning ◽  
Birth Control ◽  
Early Stage ◽  
Significant Proportion ◽  
Large Family ◽  
Capital City ◽  
Age Group ◽  
African Countries ◽  
The Mean ◽  
Almost All

SummaryIn a survey of 1475 urban Moslem wives in the age group 15–49 living in the capital city of the Sudan, knowledge of birth control was reported by almost all respondents while a significant proportion had used contraception at least once. The mean age of the users was 32·8 years, their duration of marriage was 15·1 years and their mean number of surviving children was 4·6. Those who had never used contraception had a higher mean age, a longer duration of marriage and more surviving children. Most of the users had an urban residential background and belonged to the high socioeconomic class. They held favourable attitudes to family planning. Although they thought that having a large family (more than five children) was not desirable, their mean preferred family size was no different from that of the never users.The results indicate that contraception is used for the purpose of spacing births rather than limiting their ultimate number. At this early stage of contraceptive adoption in Sudan, the characteristics of the pioneer acceptors are similar to those observed in other African countries.

Sign in / Sign up

Export Citation Format

Share Document