scholarly journals Panaitopol-Bandila-Lascu Type Inequalities for Generalized Hyperbolic Functions

2020 ◽  
pp. 30-36
Author(s):  
Kwara Nantomah ◽  
Osman Kasimu
Keyword(s):  
Geometric Mean ◽  
Schwarz Inequality ◽  
Hyperbolic Functions ◽  
Classical Arithmetic

In this paper, we establish Panaitopol-Bandila-Lascu type inequalities for some generalized hyperbolic functions. The established results extend and generalize some earlier results due Barbu and Piscoran. The procedure makes use of the classical arithmetic-geometric mean inequality and the Cauchy-Schwarz inequality.

scholarly journals Buzano inequality in inner product C*-modules via the operator geometric mean

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1689-1694
Author(s):  
Jun Fujii ◽  
Masatoshi Fujii ◽  
Yuki Seo
Keyword(s):  
Geometric Mean ◽  
Type Inequality ◽  
Schwarz Inequality ◽  
Inner Product

In this paper, by means of the operator geometric mean, we show a Buzano type inequality in an inner product C*-module, which is an extension of the Cauchy-Schwarz inequality in an inner product C*-module.

On a class of inequalities

1963 ◽  
Vol 3 (4) ◽  
pp. 442-448 ◽  
Author(s):  
B. C. Rennie
Keyword(s):  
General Theory ◽  
Geometric Mean ◽  
Schwarz Inequality ◽  
Image Position

First consider some familiar results, the inequality of the arithmetic and geometric mean is: Kantorovich's inequality (reference [1]) asserts that if 0 < A ≦f(x) ≦ B then: The Cauchy-Schwarz inequality is: This paper discusses a certain class of inequalities which includes the three above. Three theorems are proved which apply to any inequality of this class; then follow some examples. They are mainly to show how the general theory helps in the finding of inequalities, but the result of Example 1 seems worth reporting for its own sake.

Radiation synovectomy of the knee joint

2006 ◽  
Vol 45 (01) ◽  
pp. 57-61
Author(s):  
M. Puille ◽  
D. Steiner ◽  
R. Bauer ◽  
R. Klett
Keyword(s):  
Knee Joint ◽  
Lymph Nodes ◽  
Geometric Mean ◽  
Radiation Synovectomy ◽  
Real Activity ◽  
Anterior View ◽  
Inguinal Lymph Nodes ◽  
The Real ◽  
Therapeutic Modalities ◽  
Real Value

Summary Aim: Multiple procedures for the quantification of activity leakage in radiation synovectomy of the knee joint have been described in the literature. We compared these procedures considering the real conditions of dispersion and absorption using a corpse phantom. Methods: We simulated different distributions of the activity in the knee joint and a different extra-articular spread into the inguinal lymph nodes. The activity was measured with a gammacamera. Activity leakage was calculated by measuring the retention in the knee joint only using an anterior view, using the geometric mean of anterior and posterior views, or using the sum of anterior and posterior views. The same procedures were used to quantify the activity leakage by measuring the activity spread into the inguinal lymph nodes. In addition, the influence of scattered rays was evaluated. Results: For several procedures we found an excellent association with the real activity leakage, shown by an r² between 0.97 and 0.98. When the real value of the leakage is needed, e. g. in dosimetric studies, simultaneously measuring of knee activity and activity in the inguinal lymph nodes in anterior and posterior views and calculation of the geometric mean with exclusion of the scatter rays was found to be the procedure of choice. Conclusion: When measuring of activity leakage is used for dosimetric calculations, the above-described procedure should be used. When the real value of the leakage is not necessary, e. g. for comparing different therapeutic modalities, several of the procedures can be considered as being equivalent.

DMSA-scintigraphy in paediatrics: Is the evaluation of the geometric mean necessary for the calculation of the differential renal function?

2001 ◽  
Vol 40 (04) ◽  
pp. 107-110 ◽  
Author(s):  
B. Roßmüller ◽  
S. Alalp ◽  
S. Fischer ◽  
S. Dresel ◽  
K. Hahn ◽  
...  
Keyword(s):  
Renal Function ◽  
Geometric Mean ◽  
Region Of Interest ◽  
Posterior View ◽  
Renal Abnormality ◽  
Anterior View ◽  
Differential Renal Function ◽  
The Mean ◽  
The Right ◽  
To Receive

SummaryFor assessment of differential renal function (PF) by means of static renal scintigraphy with Tc-99m-dimer-captosuccinic acid (DMSA) the calculation of the geometric mean of counts from the anterior and posterior view is recommended. Aim of this retrospective study was to find out, if the anterior view is necessary to receive an accurate differential renal function by calculating the geometric mean compared to calculating PF using the counts of the posterior view only. Methods: 164 DMSA-scans of 151 children (86 f, 65 m) aged 16 d to 16 a (4.7 ± 3.9 a) were reviewed. The scans were performed using a dual head gamma camera (Picker Prism 2000 XP, low energy ultra high resolution collimator, matrix 256 x 256,300 kcts/view, Zoom: 1.6-2.0). Background corrected values from both kidneys anterior and posterior were obtained. Using region of interest technique PF was calculated using the counts of the dorsal view and compared with the calculated geometric mean [SQR(Ctsdors x Ctsventr]. Results: The differential function of the right kidney was significantly less when compared to the calculation of the geometric mean (p<0.01). The mean difference between the PFgeom and the PFdors was 1.5 ± 1.4%. A difference > 5% (5.0-9.5%) was obtained in only 6/164 scans (3.7%). Three of 6 patients presented with an underestimated PFdors due to dystopic kidneys on the left side in 2 patients and on the right side in one patient. The other 3 patients with a difference >5% did not show any renal abnormality. Conclusion: The calculation of the PF from the posterior view only will give an underestimated value of the right kidney compared to the calculation of the geometric mean. This effect is not relevant for the calculation of the differntial renal function in orthotopic kidneys, so that in these cases the anterior view is not necesssary. However, geometric mean calculation to obtain reliable values for differential renal function should be applied in cases with an obvious anatomical abnormality.

On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Log Ratio

Milk acetone determination by the photometrical method after microdiffusion and via FT infra-red spectroscopy

2011 ◽  
Vol 28 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Oto Hanuš ◽  
Václava Genčurová ◽  
Yunhai Zhang ◽  
Pavel Hering ◽  
Jaroslav Kopecký ◽  
...  
Keyword(s):  
Infrared Spectroscopy ◽  
Indirect Method ◽  
Geometric Mean ◽  
Mid Infrared ◽  
Subclinical Ketosis ◽  
Infra Red ◽  
Variation Range ◽  
Ft Ir ◽  
Infrared Method ◽  
Photometrical Method

Milk acetone determination by the photometrical method after microdiffusion and via FT infra-red spectroscopyMilk acetone (AC) and betahydroxybutyrate (BHB) are important indicators of the energy metabolism of cows (ketosis occurrence) and an effective method for their determination, with reliable results, is of great importance. The goal of this work was to investigate the infrared method MIR-FT in terms of its calibration for milk AC and to develop a usable procedure. The microdiffusion photometric (485 nm; Spekol 11) method was used with salicylaldehyde as a reference (Re) and mid infrared spectroscopy FT (MIR-FT: Lactoscope FT-IR, Delta; MilkoScan FT 6000, M-Sc) as an indirect method. The acetone addition to milk had no recovery using MIR-FT (Delta). The reference AC set must have acceptable statistics for good MIR-FT calibration (M-Sc) and they were: 10.1 ± 9.74 at a geometric mean of 7.26 mg l-1, and a variation range from 1.98 to 33.66 mg l-1. The AC correlation between Re and MIR-FT (Delta) was low at 0.32 (P>0.05 but the Log AC relationship between Re and MIR-FT (M-Sc) was markedly better at 0.80 (P<0.01). The conversion of >10 mg l-1 as an AC subclinical ketosis limit could be > -0.80 (feedback 0.158 mmol l-1 = 9.25 mg l-1) and > -1.66. This could be important for ketosis monitoring (using M-Sc).

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