Gauss and the Mathematical Background to Standardisation

AbstractOur aim is to explore the links between standardisation, the quantifying spirit, and the discipline mathematics. To do so, we consider the work of Gauss, renowned as a pure mathematician, but professionally an astronomer, and one heavily engaged with all kinds of measuring and precision initiatives. He contributed to the mathematical correction of data with the method of least squares; to observations of high precision in his geodetic work; to the introduction of absolute measures in his collaborations with Weber on terrestrial magnetism; and to the rationalisation of weights and measures in the state of Hannover. Ultimately, the question is to what extent such precision and standardisation activities may have been rooted in the mathematical way of thinking. Mathematics in our tradition has had a strong contemplative bias (theory, theorein in Greek means to contemplate), but it’s a fact that mathematics has always had a non-eliminable technical side.

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Linear Modelling of The State-Wise Yield of Principal Crops in India

Mathematical Journal of Interdisciplinary Sciences ◽

10.15415/mjis.2019.72009 ◽

2019 ◽

Vol 7 (2) ◽

pp. 69-76

Author(s):

P Gayathri ◽

K R Subramanian

Keyword(s):

Time Series ◽

Time Series Analysis ◽

Least Squares ◽

Tamil Nadu ◽

Linear Equations ◽

The State ◽

Average Yield ◽

Method Of Least Squares ◽

Linear Modelling ◽

Modelling Techniques

Modelling techniques are applied in agriculture field. Yield of rice is modelled using the method of least squares in Time Series Analysis and linear equations are fitted for the state-wise average yield of crops in kg per hectare in India and also for the average yield of various principal crops in Tamil Nadu.

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A Re-Appraisal of the Role of Blood Coagulation and Platelets in the Generalized Shwartzman Phenomenon

Thrombosis and Haemostasis ◽

10.1055/s-0038-1649455 ◽

1966 ◽

Vol 15 (03/04) ◽

pp. 519-538 ◽

Cited By ~ 10

Author(s):

J Levin ◽

E Beck

Keyword(s):

Blood Coagulation ◽

The State ◽

Coagulation System ◽

Renal Lesions ◽

Intravascular Coagulation ◽

Renal Glomeruli ◽

Coagulation Mechanism ◽

Shwartzman Phenomenon ◽

Do So

SummaryThe role of intravascular coagulation in the production of the generalized Shwartzman phenomenon has been evaluated. The administration of endotoxin to animals prepared with Thorotrast results in activation of the coagulation mechanism with the resultant deposition of fibrinoid material in the renal glomeruli. Anticoagulation prevents alterations in the state of the coagulation system and inhibits development of the renal lesions. Platelets are not primarily involved. Platelet antiserum produces similar lesions in animals prepared with Thorotrast, but appears to do so in a manner which does not significantly involve intravascular coagulation.The production of adrenal cortical hemorrhage, comparable to that seen in the Waterhouse-Friderichsen syndrome, following the administration of endotoxin to animals that had previously received ACTH does not require intravascular coagulation and may not be a manifestation of the generalized Shwartzman phenomenon.

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The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.1.05 ◽

2020 ◽

pp. 60-73

Author(s):

Yu V Nemirovskii ◽

S V Tikhonov

Keyword(s):

General Solution ◽

Least Squares ◽

Nonlinear Differential Equations ◽

Limit State ◽

Algebraic Equations ◽

Method Of Least Squares ◽

Elasticity Limit ◽

Limit Values ◽

Symbolic Calculations ◽

Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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Functional ratings in sports

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2020-0001 ◽

2020 ◽

Vol 16 (3) ◽

pp. 183-191

Author(s):

Brad Lowery ◽

Abigail Slater ◽

Kaison Thies

Keyword(s):

Least Squares ◽

Method Of Least Squares ◽

Sports Teams ◽

New Model ◽

College Basketball ◽

Division 1

AbstractIn this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a team average point differential adjusted for strength of schedule. Using two team’s functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018–2019 NCAA Division 1 men’s college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

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On the Appropriate Measure to Estimate Hyperbolic Discounting Rate (K) using the Method of Least Squares

Perspectives on Behavior Science ◽

10.1007/s40614-021-00306-x ◽

2021 ◽

Author(s):

Harli R. Berk ◽

Tanya A. Gupta ◽

Federico Sanabria

Keyword(s):

Least Squares ◽

Hyperbolic Discounting ◽

Method Of Least Squares

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Reconceptualizing Clans: Kinship Networks and Statehood in Kazakhstan

Nationalities Papers ◽

10.1080/00905990500088594 ◽

2005 ◽

Vol 33 (2) ◽

pp. 231-254 ◽

Cited By ~ 30

Author(s):

Edward Schatz

Keyword(s):

Recent Work ◽

Comparative Politics ◽

Sustained Attention ◽

The State ◽

Political Life ◽

Kinship Networks ◽

State Apparatus ◽

Do So

What role, if any, does kinship play in modern political life? Recent work in comparative politics has focused on a variety of informal relationships. It is striking that kinship has not received similar, sustained attention. The broad assumption of most theoretically-driven work is that kinship is the domain of the anthropologist; to the extent that political scientists consider kinship, they do so as something for modern institutions to overcome, as something in fundamental opposition to the state apparatus.

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