least square fitting method
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2020 ◽  
Vol 65 (2) ◽  
pp. 120
Author(s):  
F. M. A. Al-Jomaily ◽  
M. I. Khalil

The half-lives for the even–even (e–e), even–odd (e–o), odd–even (o–e) and odd–odd (o–o) nuclei in the range 100 < Z < 120 have been tested within the Viola–Seaborg formula (VSF) and within the analytical formula of Royer (RF). We proposed another formula (Present Work Formula or PWF) with regard for the effect of angular momentum of the alpha decay particle and with the use of the relative neutron excess (︀(N−Z)/A)︀. Our formula includes a new set of parameters found by the least square fitting method of alpha decays of 128 nuclei. We obtained the standard deviations for each of the formulas for comparison. The results show an acceptable agreement with available data. The values of the suggested theoretical coefficient (K) for the PWF show a similar behavior of half-lives with a-decay, which can be used to predict the new superheavy nuclei.


2018 ◽  
Vol 59 (9) ◽  
pp. 1731-1762 ◽  
Author(s):  
S Braunger ◽  
M A W Marks ◽  
B F Walter ◽  
R Neubauer ◽  
R Reich ◽  
...  

Abstract The Miocene Kaiserstuhl Volcanic Complex (Southwest Germany) consists largely of tephritic to phonolitic rocks, accompanied by minor nephelinitic to limburgitic and melilititic to haüynitic lithologies associated with carbonatites. Based on whole-rock geochemistry, petrography, mineralogy and mineral chemistry, combined with mineral equilibrium calculations and fractional crystallization models using the Least Square Fitting Method, we suggest that the Kaiserstuhl was fed by at least two distinct magma sources. The most primitive rock type of the tephritic to phonolitic group is rare monchiquite (basanitic lamprophyre) evolving towards tephrite, phonolitic tephrite, phonolitic noseanite, nosean phonolite and tephritic phonolite by fractional crystallization of variable amounts of clinopyroxene, amphibole, olivine, spinel/magnetite, garnet, titanite, plagioclase and nosean. During this evolution, temperature and silica activity (aSiO2) decrease from about 1100°C and aSiO2 = 0·6–0·8 to 880°C and aSiO2 = ∼0·2. At the same time, oxygen fugacity (fO2) increases from ΔFMQ* = +2–3 to ΔFMQ* = +3–5, with ΔFMQ* being defined as the log fO2 deviation from the silica activity-corrected FMQ buffer curve. Nephelinitic rocks probably derive by fractionation of mostly olivine, spinel/magnetite, melilite, perovskite and nepheline from an olivine melilititic magma. The nephelinitic rocks were formed at similarly high crystallization temperatures (&gt;1000°C) and evolve towards limburgite (hyalo-nepheline basanite) by an increase of silica activity from about aSiO2 = 0·4–0·5 to aSiO2 = 0·5–0·9, whilst redox conditions are buffered to ΔFMQ* values of around +3. Haüyne melilitite and the more evolved (melilite) haüynite may equally be derived from an olivine melilitite by more intense olivine and less melilite fractionation combined with the accumulation of haüyne, clinopyroxene and spinel. These rocks were crystallized at very low silica activities (aSiO2 ≤0·2) and highly oxidized conditions (ΔFMQ* = +4–6). Even higher oxygen fugacities (ΔFMQ* = +6–7) determined for the carbonatite suggests a close genetic relation between these two groups. The assemblage of carbonatites with highly oxidized silicate rocks is typical of many carbonatite occurrences worldwide, at least for those associated with melilititic to nephelinitic silicate rocks. Therefore, we suggest that the existence of highly oxidized carbonate-bearing sublithospheric mantle domains is an important prerequisite to form such complexes.


2015 ◽  
Vol 3 (Suppl 1) ◽  
pp. A319
Author(s):  
S Spadaro ◽  
S Grasso ◽  
V Cricca ◽  
F Dalla Corte ◽  
R Di Mussi ◽  
...  

2014 ◽  
Vol 590 ◽  
pp. 651-655
Author(s):  
Yun Cheng Li ◽  
Yong Zhi Liang ◽  
Xi Sheng Ma ◽  
Wen Pei Jia

This paper presents a structural design of a methane sensor based on the principle of infrared detection, and designs a program of the experimental calibration. In the conditions of laboratory, different concentrations of methane gas were detected. A concentration inversion formula was proposed by the segmented least-square fitting method. The sensor can measure concentrations of methane in a real-time and accurate way, it contains the functions that digital display and sound and light alarm. The results show that a full-scale concentrations of methane gas can be detected, when the concentration range is in 0-10%, the absolute error is less than 0.09%; when it is more than 10%, the absolute error is less than 0.2%, the response time is less than 15s.


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