scholarly journals The connections of pseudo-Finsler spaces

2014 ◽  
Vol 11 (07) ◽  
pp. 1460025 ◽  
Author(s):  
E. Minguzzi
Keyword(s):  
General Relativity ◽  
Conservation Law ◽  
Finsler Geometry ◽  
The Other ◽  
Finsler Spaces ◽  
Dynamical Equations ◽  
Nonlinear Connection ◽  
Cartan Torsion ◽  
The Mean ◽  
Mean Cartan Torsion

We give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self-contained proofs. Our study of the Berwald nonlinear connection is framed into the theory of connections over general fibered spaces pioneered by Mangiarotti, Modugno and other scholars. The main identities for the linear Finsler connection are presented in the general case, and then specialized to some notable cases like Berwald's, Cartan's or Chern–Rund's. In this way it becomes easy to compare them and see the advantages of one connection over the other. Since we introduce two soldering forms we are able to characterize the notable Finsler connections in terms of their torsion properties. As an application, the curvature symmetries implied by the compatibility with a metric suggest that in Finslerian generalizations of general relativity the mean Cartan torsion vanishes. This observation allows us to obtain dynamical equations which imply a satisfactory conservation law. The work ends with a discussion of yet another Finsler connection which has some advantages over Cartan's and Chern–Rund's.

scholarly journals On generalized P-reducible Finsler manifolds

2018 ◽  
Vol 16 (1) ◽  
pp. 718-723
Author(s):  
Seyyed Mohammad Zamanzadeh ◽  
Behzad Najafi ◽  
Megerdich Toomanian
Keyword(s):  
Vector Field ◽  
Finsler Geometry ◽  
Finsler Manifolds ◽  
Cartan Torsion ◽  
Mean Cartan Torsion

AbstractThe class of generalized P-reducible manifolds (briefly GP-reducible manifolds) was first introduced by Tayebi and his collaborates [1]. This class of Finsler manifolds contains the classes of P-reducible manifolds, C-reducible manifolds and Landsberg manifolds. We prove that every compact GP-reducible manifold with positive or negative character is a Randers manifold. The norm of Cartan torsion plays an important role for studying immersion theory in Finsler geometry. We find the relation between the norm of Cartan torsion, mean Cartan torsion, Landsberg and mean Landsberg curvatures of the class of GP-reducible manifolds. Finally, we prove that every GP-reducible manifold admitting a concurrent vector field reduces to a weakly Landsberg manifold.

scholarly journals On S-curvature of a homogeneous Finsler space with square metric

2020 ◽  
Vol 17 (02) ◽  
pp. 2050019
Author(s):  
Gauree Shanker ◽  
Sarita Rani
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Finsler Spaces ◽  
Invariant Vector ◽  
Homogeneous Finsler Space ◽  
The Mean ◽  
Invariant Vector Fields

The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.

The spectra of turbulence in a compressible fluid; eddy turbulence and random noise

1952 ◽  
Vol 48 (2) ◽  
pp. 329-344 ◽  
Author(s):  
J. E. Moyal
Keyword(s):  
Incompressible Fluid ◽  
Random Noise ◽  
The Other ◽  
Temperature Fields ◽  
Homogeneous Field ◽  
Dynamical Equations ◽  
Noise Component ◽  
Real Fluid ◽  
The Mean ◽  
Fourier Spectra

AbstractThe state of a real fluid is completely specified by its velocity, density, pressure and temperature fields. When the fluid is in turbulent flow, all these quantities fluctuate in a disordered manner. The method of space Fourier spectra is used to show that these field variables separate into two physically distinct groups, one corresponding to fluctuating acoustical waves, or random noise, and the other to fluctuating vorticity, or eddy turbulence. The corresponding decomposition of the spectral and correlation tensors in a homogeneous field of turbulence is given. The noise Fourier components are shown to be coupled to the eddy Fourier components only through the non-linear inertia terms in the dynamical equations of the fluid; whereas the former propagate as acoustical waves, the wave character of the latter is due entirely to the mean motion of the fluid. The measurement of the noise component, its attenuation through absorption by walls and its effects on the eddy component are discussed. Finally, the dynamical equations for the eddy component of the velocity spectral tensor in a homogeneous field of turbulence are compared with the corresponding equations for an incompressible fluid.

The angular momentum of cylindrical systems in general relativity

1994 ◽  
Vol 446 (1926) ◽  
pp. 57-66 ◽  
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Coordinate System ◽  
Conservation Law ◽  
Energy Transport ◽  
Killing Vector ◽  
The State ◽  
The Other ◽  
Conservation Of Energy ◽  
Conservation Theorem

Though the vanishing of the covariant divergence does not directly imply a conservation law, there is some meaning both to conservation and to non-conservation of energy in General Relativity. In this paper the method of slow changes previously applied to elucidate the conservation of energy is used to study changes in cylindrical systems with rotation. It is shown that in such systems only a single quantity is conserved that can be identified with angular momentum. It corresponds to the symmetry imposed, and agrees with the Killing vector based analysis of J. Winicour. On the other hand, as previously shown, axial energy transport prevents the existence of a conservation theorem for mass. This conserved angular momentum is intrinsic to the system in that its value is unaffected by the state of rotation of the coordinate system used to define it. Machian space drag is also examined. It emerges that angular momentum and space drag behave very differently as thicker and thicker spinning cylinders are studied.

scholarly journals ON $S$-CURVATURE OF A HOMOGENEOUS FINSLER SPACE WITH RANDERS CHANGED SQUARE METRIC

2020 ◽  
pp. 673
Author(s):  
Sarita Rani ◽  
Gauree Shanker
Keyword(s):  
Explicit Formula ◽  
Vector Fields ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Finsler Spaces ◽  
Invariant Vector ◽  
Homogeneous Finsler Space ◽  
The Mean ◽  
Alpha Beta ◽  
Invariant Vector Fields

The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on a homogeneous Finsler space with Randers changed square metric has been proved. Further, an explicit formula for $S$-curvature of Randers changed square metric has been established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(\alpha, \beta)$-metric has been calculated. 

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.

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 (<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.

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