scholarly journals A note on the refinement of Hermite-Hadamard inequality

2021 ◽  
Vol 2106 (1) ◽  
pp. 012006
Author(s):  
Mochammad Idris
Keyword(s):  
Convex Function ◽  
Maximum Error ◽  
Mean Value ◽  
Hadamard Inequality ◽  
The Mean ◽  
Dyadic Decomposition

Abstract In this paper, we give the sharper bounds for the mean value of a convex function using dyadic decomposition. Our result is related with classical Hermite-Hadamard inequality. Moreover, using the result, we can determine the maximum error before calculating the numerical (trapezoidal) integral of the convex function.

scholarly journals KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES

2012 ◽  
Vol 4 (1) ◽  
pp. 59
Author(s):  
Denny Ivanal Hakim ◽  
Hendra Gunawan
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Closed Interval ◽  
Mean Value ◽  
Stieltjes Integral ◽  
Power Mean ◽  
Real Numbers ◽  
Positive Real ◽  
Hadamard Inequality

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value.  An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral  for estimating the power mean of   positive real numbers by the aritmethic mean is given at the end of discussion.

scholarly journals Some Remarks on Results Related to ∇-Convex Function

2021 ◽  
Vol 53 (1) ◽  
pp. 67-85
Author(s):  
Asif Raza Khan ◽  
Faraz Mehmood ◽  
Faisal Nawaz ◽  
Aamna Nazir
Keyword(s):  
Convex Function ◽  
Present Article ◽  
Divided Difference ◽  
Mean Value ◽  
Higher Order ◽  
Two Dimensions ◽  
Mean Value Theorem ◽  
New Techniques ◽  
Differentiable Functions ◽  
The Mean

In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented.

REFINING RECURSIVELY THE HERMITE–HADAMARD INEQUALITY ON A SIMPLEX

2015 ◽  
Vol 92 (1) ◽  
pp. 57-67 ◽  
Author(s):  
MUSTAPHA RAÏSSOULI ◽  
SEVER S. DRAGOMIR
Keyword(s):  
Convex Function ◽  
Upper Bounds ◽  
Mean Value ◽  
Lower And Upper Bounds ◽  
Hadamard Inequality

In the present paper, a coupled algorithm refining recursively the Hermite–Hadamard inequality on a simplex is investigated. Our approach allows us to express the integral mean value $M_{f}$ of a convex function $f$ on a simplex as both the limit of sequences and sum of series involving iterative lower and upper bounds of $M_{f}$. Two examples of interest are discussed.

scholarly journals Some Remarks on Results Related to ∇-Convex Function

2021 ◽  
Vol 53 (1) ◽  
pp. 67-85
Author(s):  
Asif Raza Khan ◽  
Faraz Mehmood ◽  
Faisal Nawaz ◽  
Aamna Nazir
Keyword(s):  
Convex Function ◽  
Present Article ◽  
Divided Difference ◽  
Mean Value ◽  
Higher Order ◽  
Two Dimensions ◽  
Mean Value Theorem ◽  
New Techniques ◽  
Differentiable Functions ◽  
The Mean

In the present article, we give new techniques for proving general identities of the Popoviciu type for discrete cases of sums for two dimensions using higher-order ∇-divided difference. Also, integral cases are deduced by different methods for differentiable functions of higher-order for two variables. These identities are a generalization of various previously established results. An application for the mean value theorem is also presented.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

Detection of Soluble Fibrin Monomer Complexes in Blood by Means of Protamine Sulphate Test

1968 ◽  
Vol 20 (01/02) ◽  
pp. 044-049 ◽  
Author(s):  
B Lipiński ◽  
K Worowski
Keyword(s):  
Human Subjects ◽  
Coronary Thrombosis ◽  
Mean Value ◽  
Healthy Human ◽  
Protamine Sulphate ◽  
Soluble Fibrin ◽  
Fibrin Monomer ◽  
Dog Plasma ◽  
The Mean ◽  
Precipitable Protein

SummaryIn the present paper described is a simple test for detecting soluble fibrin monomer complexes (SFMC) in blood. The test consists in mixing 1% protamine sulphate with diluted oxalated plasma or serum and reading the optical density at 6190 Å. In experiments with dog plasma, enriched with soluble fibrin complexes, it was shown that OD read in PS test is proportional to the amount of fibrin recovered from the precipitate. It was found that SFMC level in plasma increases in rabbits infused intravenously with thrombin and decreases after injection of plasmin with streptokinase. In both cases PS precipitable protein in serum is elevated indicating enhanced fibrinolysis. In healthy human subjects the mean value of OD readings in plasma and sera were found to be 0.30 and 0.11, while in patients with coronary thrombosis they are 0.64 and 0.05 respectively. The origin of SFMC in circulation under physiological and pathological conditions is discussed.

Detection of Circulating Tissue Factor and Factor VII in a Normal Population

1996 ◽  
Vol 75 (05) ◽  
pp. 772-777 ◽  
Author(s):  
Sybille Albrecht ◽  
Matthias Kotzsch ◽  
Gabriele Siegert ◽  
Thomas Luther ◽  
Heinz Großmann ◽  
...  
Keyword(s):  
Tissue Factor ◽  
Normal Population ◽  
Mean Value ◽  
Factor Vii ◽  
Significant Difference ◽  
Age Dependent ◽  
The Mean ◽  
Highly Correlated ◽  
And Gender

SummaryThe plasma tissue factor (TF) concentration was correlated to factor VII concentration (FVIIag) and factor VII activity (FVIIc) in 498 healthy volunteers ranging in age from 17 to 64 years. Immunoassays using monoclonal antibodies (mAbs) were developed for the determination of TF and FVIIag in plasma. The mAbs and the test systems were characterized. The mean value of the TF concentration was 172 ± 135 pg/ml. TF showed no age- and gender-related differences. For the total population, FVIIc, determined by a clotting test, was 110 ± 15% and the factor VIlag was 0.77 ± 0.19 μg/ml. FVII activity was significantly increased with age, whereas the concentration demonstrated no correlation to age in this population. FVII concentration is highly correlated with the activity as measured by clotting assay using rabbit thromboplastin. The ratio between FVIIc and FVIIag was not age-dependent, but demonstrated a significant difference between men and women. Between TF and FVII we could not detect a correlation.

Determination of Plasminogen in Clots and Thrombi

1966 ◽  
Vol 16 (01/02) ◽  
pp. 038-050 ◽  
Author(s):  
Ulla Hedner ◽  
Inga Marie Nilsson ◽  
B Robertson
Keyword(s):  
Mean Value ◽  
Main Mechanism ◽  
Clot Lysis ◽  
Post Mortem ◽  
Digestion Time ◽  
Normal Volunteers ◽  
Casein Solution ◽  
The Mean

SummaryThe plasminogen content was determined by a casein method in plasma and serum from 20 normal volunteers. The mean plasminogen content was found to be 10.1 ACU (the arbitrary caseinolytic unit defined in such a way that using a 3% casein solution and a digestion time of 20 min. at 37°C, 10 ACU gave an extinction of 0.300). No difference between serum and plasma regarding the plasminogen content was found.Plasminogen was determined in drained and drained plus washed clots prepared from 2 ml plasma. The highest values found in the drained clots were 0.9 ACU/clot and 0.2 ACU/clot in the drained plus washed clots.Plasminogen was also determined in drained and drained plus washed clots prepared from plasma with added purified plasminogen. The plasminogen was recovered in the washing fluid. According to these tests, then, purified added plasminogen is washed out of the clots.The plasminogen content of 20 thrombi obtained post mortem was also determined. The mean value was found to be 0.7 ACU/cm thrombus. Judging from our results, the “intrinsic clot lysis theory” is not the main mechanism of clot dissolution.

Perbedaan Pengetahuan Siswa Tentang Penyakit Hepatitis A Sebelum Dan Sesudah Penyuluhan Di MTsN 02 Bondowoso Tahun 2015

2017 ◽  
Vol 4 (2) ◽  
pp. 14
Author(s):  
Putri Megasari
Keyword(s):  
Hepatitis A ◽  
Hepatitis Virus ◽  
Sampling Technique ◽  
Mean Value ◽  
Test Design ◽  
The World ◽  
Before And After ◽  
Post Test ◽  
The Mean ◽  
Paired T Test

Hepatitis has become a health problem in the world. The hepatitis virus infected many people. According to the teacher of MTsN 02 Bondowoso more than 20 students have hepatitis A viral infection. The purpose of this research was to know the differences of students' knowledge about hepatitis A before and after counseling in MTsN 02 Bondowoso 2015. This study used pre-experimental (pre-post test design). This study used stratified random sampling technique, 127 students from 270 sample involved this research,and 143 students was excluded. We used questionnaires to collect data. The results showed that the mean value of the students 'knowledge about hepatitis A before counseling in MTsN 02 Bondowoso 2015 was 83.96 with the lowest value of 37.5 and the highest value was 100. The mean value of the students' knowledge about hepatitis A after counseling in MTsN 02 Bondowoso 2015 was 93.21 with the lowest value waf 62.5 and the highest value was 100. Paired t test showed that t (-9.07) > t table (1.98), the null hypothesis (H0) was rejected. There was a difference between students' knowledge about hepatitis A before and after counseling in MTsN 02 Bondowoso 2015. This study showed that routine counseling by healthcare provider was important to prevent hepatitis A infection.; Keywords: counseling, knowledge of students, hepatitis

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