On the definition of the cross-product

2001 ◽  
Vol 32 (4) ◽  
pp. 585-587
Author(s):  
H. Azad
Keyword(s):  
Cross Product ◽  
The Cross ◽  
Definition Of

scholarly journals Angular Vectors in the Theory of Vectors

2017 ◽  
Vol 9 (5) ◽  
pp. 71
Author(s):  
Yevhen Mykolayovych Kharchenko
Keyword(s):  
Angular Velocity ◽  
Cross Product ◽  
Vector Form ◽  
Coordinate Vector ◽  
The Cross ◽  
Definition Of ◽  
Physical Quantities

The theory of angular vectors, which allows modelling of the properties of angular physical quantities, is considered. The meaning of the cross product of vectors was radically revised and changed. Formulas for finding torque and angular velocity in a coordinate-vector form with a correct mapping of their directions were deduced. Described definition of the inverse vector and its properties. The inversed vector allows us to perform vector division operations.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

Confidence Estimation of the Cross-Product Ratio of Binomial Proportions under Different Sampling Schemes

2021 ◽  
Vol 42 (2) ◽  
pp. 435-450
Author(s):  
Chanakan Sungboonchoo ◽  
Thuntida Ngamkham ◽  
Wararit Panichkitkosolkul ◽  
Andrei Volodin
Keyword(s):  
Cross Product ◽  
Confidence Estimation ◽  
Sampling Schemes ◽  
Product Ratio ◽  
Binomial Proportions ◽  
The Cross

scholarly journals The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group

2003 ◽  
Vol 2003 (38) ◽  
pp. 2425-2445 ◽  
Author(s):  
Heath Emerson
Keyword(s):  
Free Group ◽  
Homology Class ◽  
Hyperbolic Group ◽  
Cross Product ◽  
Direct Connection ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Duality Map ◽  
The Cross ◽  
Gromov Boundary

For every hyperbolic groupΓwith Gromov boundary∂Γ, one can form the cross productC∗-algebraC(∂Γ)⋊Γ. For each such algebra, we construct a canonicalK-homology class. This class induces a Poincaré duality mapK∗(C(∂Γ)⋊Γ)→K∗+1(C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case ofΓ=𝔽2, the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes conjecture and eventually use the latter to deduce our result.

scholarly journals KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE

EDUPEDIA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 161
Author(s):  
Febriyana Putra Pratama ◽  
Julan Hernadi
Keyword(s):  
Half Plane ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Cross Ratio ◽  
Literature Study ◽  
Disk Model ◽  
Non Euclidean Geometry ◽  
The Cross ◽  
Definition Of ◽  
Poincaré Disk

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History)  by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of   . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from  to  is , where  is cross-ratio defined by  . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

Personality Assessment

2016 ◽  
pp. 134-146
Author(s):  
Dragos Iliescu ◽  
Dan Ispas
Keyword(s):  
South African ◽  
Personality Assessment ◽  
Factor Model ◽  
Five Factor Model ◽  
Personality Assessment Inventory ◽  
Cross Cultural ◽  
International Context ◽  
Two Measures ◽  
The Cross ◽  
Definition Of

The chapter focuses on the assessment of personality in an international context. Starting from the definition of personality, the chapter discusses the way culture and personality are mixed and sets then out to explain the emic (indigenous) versus etic (universal) debate in personality assessment. The combined emic-etic approach is outlined as an interesting evolution in cross-cultural personality assessment, and two measures based on this approach are discussed, the Cross-Cultural Personality Assessment Inventory (CPAI) and the South African Personality Inventory (SAPI). Finally, the chapter discusses the currently dominant model of personality used in assessment internationally, the five-factor model, outlining some of the dilemmas still being debated related to this model, such as the broad versus narrow debate, the cross-cultural replicability issue, and the bandwidth-fidelity dilemma.

Evaluation of Tumor Measurements in Oncology: Use of Film-Based and Electronic Techniques

2000 ◽  
Vol 18 (10) ◽  
pp. 2179-2184 ◽  
Author(s):  
Lawrence H. Schwartz ◽  
Michelle S. Ginsberg ◽  
Douglas DeCorato ◽  
Lawrence N. Rothenberg ◽  
Steven Einstein ◽  
...  
Keyword(s):  
Coefficient Of Variation ◽  
Interobserver Variability ◽  
Tumor Therapy ◽  
Measurement Techniques ◽  
Cross Product ◽  
Ct Images ◽  
Coefficients Of Variation ◽  
Significant Difference ◽  
The Cross ◽  
Tumor Measurements

PURPOSE: To evaluate the variability in bidimensional computed tomography (CT) measurements obtained of actual tumors and of tumor phantoms by use of three measurement techniques: hand-held calipers on film, electronic calipers on a workstation, and an autocontour technique on a workstation. MATERIALS AND METHODS: Three radiologists measured 45 actual tumors (in the lung, liver, and lymph nodes) on CT images, using each of the three techniques. Bidimensional measurements were recorded, and their cross-products calculated. The coefficient of variation was calculated to assess interobserver variability. CT images of 48 phantoms were measured by three radiologists with each of the techniques. In addition to the coefficient of variation, the differences between the cross-product measurements of tumor phantoms themselves and the measurements obtained with each of the techniques were calculated. RESULTS: The differences between the coefficients of variation were statistically significantly different for the autocontour technique, compared with the other techniques, both for actual tumors and for tumor phantoms. There was no statistically significant difference in the coefficient of variation between measurements obtained with hand-held calipers and electronic calipers. The cross-products for tumor phantoms were 12% less than the actual cross-product when calipers on film were used, 11% less using electronic calipers, and 1% greater using the autocontour technique. CONCLUSION: Tumor size is obtained more accurately and consistently between readers using an automated autocontour technique than between those using hand-held or electronic calipers. This finding has substantial implications for monitoring tumor therapy in an individual patient, as well as for evaluating the effectiveness of new therapies under development.

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