scholarly journals Matrix theory of correlations in a lattice. Part I

1944 ◽  
Vol 182 (990) ◽  
pp. 244-259 ◽  
Keyword(s):  
Probability Distribution ◽  
Statistical Mechanics ◽  
Matrix Theory ◽  
The Other ◽  
Infinite Matrices ◽  
Statistical Correlations ◽  
Unit Cells ◽  
The Mean ◽  
A Chain ◽  
Lattice Part

The statistical mechanics of some crystalline systems may be reduced to statistical correlations between objects which are the unit cells of a fictitious lattice. The correlations are deduced from postulates according to which some configurations of the cells are incompatible with some configurations of the neighbouring cells; if, on the other hand, configurations of neighbours are compatible with each other, their probabilities are to combine by multiplication. By these postulates matrices are implicitly defined such that the probability distribution for a chain of cells is found by forming the powers of a matrix. A similar approach to the statistics of a lattice involves infinite matrices. It does not seem practicable to give explicit expressions for these matrices. If appropriate conditions are complied with, the correlations in a chain are accounted for by adjusting the mean probability coefficients of the cells and for the rest regarding the cells as statistically independent. In this case the infinite matrices may be replaced by the outer power of finite matrices. As result an equation is given by means of which the thermodynamical energy may be calculated as function of temperature.

On the wind resource in Algeria: Probability distributions evaluation

2020 ◽  
pp. 095765092097588
Author(s):  
Houdayfa Ounis ◽  
Nawel Aries
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Resource Assessment ◽  
Descriptive Statistics ◽  
The Other ◽  
Wind Speeds ◽  
Wind Resource Assessment ◽  
The Mean ◽  
Wind Resource

The present study aims to present a contribution to the wind resource assessment in Algeria using ERA-Interim reanalysis. Firstly, the ERA-Interim reanalysis 10 m wind speed data are considered for the elaboration of the mean annual 10 m wind speed map for a period starting from 01-01-2000 to 31-12-2017. Moreover, the present study intends to highlight the importance of the descriptive statistics other than the mean in wind resource assessment. On the other hand, this study aims also to select the proper probability distribution for the wind resource assessment in Algeria. Therefore, nine probability distributions were considered, namely: Weibull, Gamma, Inverse Gaussian, Log Normal, Gumbel, Generalized Extreme Value (GEV), Nakagami, Generalized Logistic and Pearson III. Furthermore, in combination with the distribution, three parameter estimation methods were considered, namely, Method of Moment, Maximum Likelihood Method and L-Moment Method. The study showed that Algeria has several wind behaviours due to the diversified topographic, geographic and climatic properties. Moreover, the annual mean 10 m wind speed map showed that the wind speed varies from 2.3 to 5.3 m/s, where 73% of the wind speeds are above 3 m/s. The map also showed that the Algerian Sahara is windiest region, while, the northern fringe envelopes the lowest wind speeds. In addition, it has been shown that the study of the mean wind speeds for the evaluation of the wind potential alone is not enough, and other descriptive statistics must be considered. On the other hand, among the nine considered distribution, it appears that the GEV is the most appropriate probability distribution. Whereas, the Weibull distribution showed its performance only in regions with high wind speeds, which, implies that this probability distribution should not be generalized in the study of the wind speed in Algeria.

scholarly journals 3,3,3′,3′-Tetramethyl-6,6′-bis[(pyridin-4-yl)methoxy]-1,1′-spirobiindane monohydrate

2012 ◽  
Vol 68 (6) ◽  
pp. o1763-o1764
Author(s):  
Ya-Jie Zhang ◽  
Yan Sun ◽  
Shu-Mei Gao ◽  
Xiao-Qing Jiang ◽  
Yu-Heng Deng
Keyword(s):  
Water Molecule ◽  
Pyridine Ring ◽  
The Other ◽  
Stacking Interactions ◽  
Asymmetric Unit ◽  
Solvent Water ◽  
Compound C ◽  
Centroid Distance ◽  
The Mean ◽  
A Chain

The asymmetric unit in the title compound, C33H34N2O2·H2O, consists of a V-shaped molecule and a water molecule to which it is hydrogen bonded. The angle between the mean planes of the two spiro-connected indane groups is 77.06 (5)°. The two five-membered rings of the indane groups have envelope conformations with the methylene atoms adjacent to the spiro C atom forming the flaps. They have deviations from the mean plane of the other four atoms in the rings of 0.374 (4) and 0.362 (4) Å. In the crystal, molecules are linked to form inversion dimers via O—H...N hydrogen bonds involving the pyridine N atoms and the solvent water molecule. The dimers are linked into a chain along the b axis by π–π stacking interactions between a pyridine ring and its centrosymmetrically related ring in an adjacent dimer. The centroid–centroid distance between the planes is 3.7756 (17) Å, the perpendicular distance is 3.4478 (11) Å and the offset is 1.539 Å.

scholarly journals Properties of quantum stochastic walks from the asymptotic scaling exponent

2018 ◽  
Vol 18 (3&4) ◽  
pp. 181-197
Author(s):  
Krzysztof Domino ◽  
Adam Glos ◽  
Mateusz Ostaszewski ◽  
Lukasz Pawela ◽  
Przemyslaw Sadowski
Keyword(s):  
Probability Distribution ◽  
Random Walks ◽  
Quantum Walks ◽  
The Other ◽  
Scaling Exponent ◽  
Continuous Change ◽  
Ballistic Regime ◽  
Second Moment ◽  
The Mean ◽  
Asymptotic Scaling

This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, \ie unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic scaling exponent of the second moment of the walk \ie of the mean squared distance covered by a walk. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the asymptotic scaling exponent. Moreover this model allows for behavior which is not found in any of the previously mentioned model -- a model with global dissipation. We derive the probability distribution for the walker, and determine the asymptotic scaling exponent analytically, showing that ballistic regime of the walk is maintained even at large dissipation strength.

Multi-Center Study of Thromboplastin Calibration Precision – Influence of Reagent Species, Composition, and International Sensitivity Index (ISI)

1993 ◽  
Vol 69 (01) ◽  
pp. 035-040 ◽  
Author(s):  
A M H P van den Besselaar ◽  
R M Bertina
Keyword(s):  
Oral Anticoagulants ◽  
International Normalized Ratio ◽  
The Other ◽  
World Health ◽  
Rabbit Brain ◽  
Sensitivity Index ◽  
Bovine Plasma ◽  
Significant Difference ◽  
The Mean ◽  
International Sensitivity Index

SummaryFour thromboplastin reagents were tested by 18 laboratories in Europe, North-America, and Australasia, according to a detailed protocol. One thromboplastin was the International Reference Preparation for ox brain thromboplastin combined with adsorbed bovine plasma (coded OBT/79), and the second was a certified reference material for rabbit brain thromboplastin, plain (coded CRM 149R). The other two thromboplastin reagents were another rabbit plain brain thromboplastin (RP) with a lower ISI than CRM 149R and a rabbit brain thromboplastin combined with adsorbed bovine plasma (RC). Calibration of the latter two reagents was performed according to methods recommended by the World Health Organization (W. H. O.).The purpose of this study was to answer the following questions: 1) Is the calibration of the RC reagent more precise against the bovine/combined (OBT/79) than against the rabbit/plain reagent (CRM 149R)? 2) Is the precision of calibration influenced by the magnitude of the International Sensitivity Index (ISI)?The lowest inter-laboratory variation of ISI was observed in the calibration of the rabbit/plain reagent (RP) against the other rabbit/plain reagent (CRM 149R) (CV 1.6%). The highest interlaboratory variation was obtained in the calibration of rabbit/plain (RP) against bovine/combined (OBT/79) (CV 5.1%). In the calibration of the rabbit/combined (RC) reagent, there was no difference in precision between OBT/79 (CV 4.3%) and CRM 149R (CV 4.2%). Furthermore, there was no significant difference in the precision of the ISI of RC obtained with CRM 149R (ISI = 1.343) and the rabbit/plain (RP) reagent with ISI = 1.14. In conclusion, the calibration of RC could be performed with similar precision with either OBT/79 or CRM 149R, or RP.The mean ISI values calculated with OBT/79 and CRM 149R were practically identical, indicating that there is no bias in the ISI of these reference preparations and that these reference preparations have been stable since their original calibration studies in 1979 and 1987, respectively.International Normalized Ratio (INR) equivalents were calculated for a lyophilized control plasma derived from patients treated with oral anticoagulants. There were small but significant differences in the mean INR equivalents between the bovine and rabbit thromboplastins. There were no differences in the interlaboratory variation of the INR equivalents, when the four thromboplastins were compared.

Prothrombin Time Standardization: Report of the Expert Panel on Oral Anticoagulant Control

1979 ◽  
Vol 42 (04) ◽  
pp. 1073-1114 ◽  
Keyword(s):  
Prothrombin Time ◽  
Expert Panel ◽  
The Other ◽  
Rabbit Brain ◽  
Calibration Constant ◽  
Freeze Dried ◽  
The Mean ◽  
Point Of Intersection ◽  
And Control ◽  
Standardization Report

SummaryIn collaborative experiments in 199 laboratories, nine commercial thromboplastins, four thromboplastins held by the National Institute for Biological Standards and Control (NIBS & C), London and the British Comparative Thromboplastin were tested on fresh normal and coumarin plasmas, and on three series of freeze-dried plasmas. One of these was made from coumarin plasmas and the other two were prepared from normal plasmas; in each series, one plasma was normal and the other two represented different degrees of coumarin defect.Each thromboplastin was calibrated against NIBS&C rabbit brain 70/178, from the slope of the line joining the origin to the point of intersection of the mean ratios of coumarin/normal prothrombin times when the ratios obtained with the two thromboplastins on the same fresh plasmas were plotted against each other. From previous evidence, the slopes were calculated which would have been obtained against the NIBS&C “research standard” thromboplastin 67/40, and termed the “calibration constant” of each thromboplastin. Values obtained from the freeze-dried coumarin plasmas gave generally similar results to those from fresh plasmas for all thromboplastins, whereas values from the artificial plasmas agreed with those from fresh plasmas only when similar thromboplastins were being compared.Taking into account the slopes of the calibration lines and the variation between laboratories, precision in obtaining a patient’s prothrombin time was similar for all thromboplastins.

Platelet Suruival and Function in Rats with Enhanced Thrombotic Tendency

1985 ◽  
Vol 54 (04) ◽  
pp. 739-743 ◽  
Author(s):  
Federica Delaini ◽  
Elisabetta Dejana ◽  
Ine Reyers ◽  
Elisa Vicenzi ◽  
Germana De Bellis Vitti ◽  
...  
Keyword(s):  
Arachidonic Acid ◽  
Nephrotic Syndrome ◽  
Platelet Function ◽  
Laboratory Tests ◽  
Thrombus Formation ◽  
The Other ◽  
Mean Survival Time ◽  
The Mean ◽  
And Function ◽  
Thrombotic Tendency

SummaryWe have investigated the relevance of some laboratory tests of platelet function in predicting conditions of thrombotic tendency. For this purpose, we studied platelet survival, platelet aggregation in response to different stimuli, TxB2 and 6-keto-PGFlα production in serum of rats bearing a nephrotic syndrome induced by adriamycin. These animals show a heavy predisposition to the development of both arterial and venous thrombosis. The mean survival time was normal in nephrotic rats in comparison to controls. As to aggregation tests, a lower aggregating response was found in ADR-treated rats using ADP or collagen as stimulating agents. With arachidonic acid (AA) we observed similar aggregating responses at lower A A concentrations, whereas at higher AA concentrations a significantly lower response was found in nephrotic rats, despite their higher TxB2 production. Also TxB2 and 6-keto-PGFlα levels in serum of nephrotic rats were significantly higher than in controls. No consistent differences were found in PGI2-activity generated by vessels of control or nephrotic rats.These data show that platelet function may appear normal or even impaired in rats with a markedly increased thrombotic tendency. On the other hand, the significance of high TxB2 levels in connection with mechanisms leading to thrombus formation remains a controversial issue.

Voronoi Analysis of a Soccer Game

2004 ◽  
Vol 9 (3) ◽  
pp. 233-240 ◽  
Author(s):  
S. Kim
Keyword(s):  
Collective Behavior ◽  
Quantitative Assessment ◽  
The Other ◽  
Analysis Method ◽  
Random System ◽  
Soccer Game ◽  
Voronoi Polygons ◽  
The Mean

This paper describes a Voronoi analysis method to analyze a soccer game. It is important for us to know the quantitative assessment of contribution done by a player or a team in the game as an individual or collective behavior. The mean numbers of vertices are reported to be 5–6, which is a little less than those of a perfect random system. Voronoi polygons areas can be used in evaluating the dominance of a team over the other. By introducing an excess Voronoi area, we can draw some fruitful results to appraise a player or a team rather quantitatively.

Determination of the Probability Distribution of the Mean Sound Level

2010 ◽  
Vol 35 (4) ◽  
pp. 543-550 ◽  
Author(s):  
Wojciech Batko ◽  
Bartosz Przysucha
Keyword(s):  
Probability Distribution ◽  
Probability Distribution Function ◽  
Mean Value ◽  
Sound Level ◽  
Function Form ◽  
Noise Levels ◽  
Logarithmic Mean ◽  
The Mean ◽  
Estimation Of Uncertainty

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

Solid, slightly soluble phosphorus compounds as nutrient source in activated sludge treatment of forest industry wastewaters

1997 ◽  
Vol 35 (2-3) ◽  
pp. 131-138 ◽  
Author(s):  
Pirjo-Riitta Rantala ◽  
Hannu Wirola
Keyword(s):  
Activated Sludge ◽  
The Other ◽  
Phosphorus Compounds ◽  
Forest Industry ◽  
Phosphorus Concentration ◽  
Nutrient Source ◽  
Sludge Treatment ◽  
Grain Sizes ◽  
Soluble Phosphorus ◽  
The Mean

The aim of the study was to determine if solid, slightly soluble compounds can be used as nutrient source in activated sludge treatment plants instead of liquid phosphoric acid. Four different solid materials were tested in lab-scale solubility tests to find compounds which are least soluble. Two materials were chosen for further studies: apatite and raw phosphate. The use of apatite and raw phosphate as nutrient source was studied in lab-scale activated sludge reactors along with a control reactor where phosphorus was added in liquid form. The phosphorus dosage, measured as elementary phosphorus, was the same for all three reactors. The reactors were fed with pre-clarified chemi-thermomechanical pulp mill (CTMP) wastewater. There were no significant differences in the reductions of organic matter between the three reactors. The mean effluent concentration of total phosphorus was 3 mg P/l in the control reactor and less than 1 mg P/1 in the other two reactors. The soluble phosphorus concentration was more than 2 mg P/l in the control reactor and less than 0.5 mg P/l in the other two. Apatite was an even better nutrient source than raw phosphate. Further lab-scale tests were conducted using two different grain sizes of apatite. No significant differences were found between the studied grain sizes (&lt;0.074 mm and 0.074 mm-0.125 mm). Apatite was then used in full-scale at a CTMP-mill two different times. The experiments showed that the mean concentrations of phosphorus can be reduced radically by using apatite as a nutrient source instead of liquid phosphorus. Solid phosphorus compounds are a viable alternative to reduce the phosphorus load from forest industry wastewater treatment plants.

scholarly journals Probability Characteristics, Area Reduction, and Wind Directionality Effects of Extreme Pressure Coefficients of High-Rise Buildings

2021 ◽  
Vol 11 (15) ◽  
pp. 7121
Author(s):  
Shouke Li ◽  
Feipeng Xiao ◽  
Yunfeng Zou ◽  
Shouying Li ◽  
Shucheng Yang ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Pressure Coefficient ◽  
Wind Pressure ◽  
Extreme Pressure ◽  
Distribution Law ◽  
Distribution Fitting ◽  
Pressure Coefficients ◽  
High Rise ◽  
Area Reduction ◽  
The Mean

Wind tunnel tests are carried out for the Commonwealth Advisory Aeronautical Research Council (CAARC) high-rise building with a scale of 1:400 in exposure categories D. The distribution law of extreme pressure coefficients under different conditions is studied. Probability distribution fitting is performed on the measured area-averaged extreme pressure coefficients. The general extreme value (GEV) distribution is preferred for probability distribution fitting of extreme pressure coefficients. From the comparison between the area-averaged coefficients and the value from GB50009-2012, it is indicated that the wind load coefficients from GB50009-2012 may be non-conservative for the CAARC building. The area reduction effect on the extreme wind pressure is smaller than that on the mean wind pressure from the code. The recommended formula of the area reduction factor for the extreme pressure coefficient is proposed in this study. It is found that the mean and the coefficient of variation (COV) for the directionality factors are 0.85 and 0.04, respectively, when the orientation of the building is given. If the uniform distribution is given for the building’s orientation, the mean value of the directionality factors is 0.88, which is close to the directionality factor of 0.90 given in the Chinese specifications.

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