scholarly journals A parametric version of the Hilbert-Hurwitz theorem using hypercircles

2017 ◽  
Vol 86 (308) ◽  
pp. 3001-3018
Author(s):  
Luis Felipe Tabera
Keyword(s):  
Parametric Version ◽  
Hurwitz Theorem

scholarly journals HURWITZ THEOREM AND PARALLELIZABLE SPHERES FROM TENSOR ANALYSIS

2001 ◽  
Vol 16 (25) ◽  
pp. 4207-4222 ◽  
Author(s):  
J. A. NIETO ◽  
L. N. ALEJO-ARMENTA
Keyword(s):  
Clifford Algebra ◽  
Point Of View ◽  
Tensor Analysis ◽  
Tensor Algebra ◽  
Normed Algebra ◽  
Curved Spaces ◽  
Hurwitz Theorem ◽  
Analysis Point

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S 1, S 3 and S 7. In this process, we discovered the analog of Hurwitz theorem for curved spaces and a geometrical unified formalism for the metric and the torsion. In order to achieve these goals we first develop a proof of Hurwitz theorem based on tensor analysis. It turns out that in contrast to the doubling procedure and Clifford algebra mechanism, our proof is entirely based on tensor algebra applied to the normed algebra condition. From the tersor analysis point of view our proof is straightforward and short. We also discuss a possible connection between our formalism and the Cayley–Dickson algebras and Hopf maps.

scholarly journals Non-pharmacological motor-cognitive treatment to improve the mental health of elderly adults

2019 ◽  
Vol 65 (3) ◽  
pp. 394-403 ◽  
Author(s):  
Javiera Ponce ◽  
Claudia Latín ◽  
Víctor Leiva ◽  
Guillermo Cortés ◽  
Fernando Rodríguez ◽  
...  
Keyword(s):  
Dual Task ◽  
Low Cost ◽  
Wilcoxon Test ◽  
P Value ◽  
Elderly Adults ◽  
Cognitive Level ◽  
Post Intervention ◽  
Institutionalized Elderly ◽  
Paired Samples ◽  
Parametric Version

SUMMARY OBJECTIVE: To propose a program of physical-cognitive dual task and to measure its impact in Chilean institutionalized elderly adults. METHOD: Experimental design study with pre and post-intervention evaluations, measuring the cognitive and depressive levels by means of the Pfeiffer test and the Yesavage scale, respectively. The program was applied for 12 weeks to adults between 68 and 90 years old. The statistical analysis was based on the nonparametric Wilcoxon test for paired samples and was contrasted with its parametric version. The statistical software R was used. RESULTS: Statistically significant differences were obtained in the cognitive level (p-value < 0.05) and highly significant (p-value < 0.001) in the level of depression with both tests (parametric and nonparametric). CONCLUSION: Due to the almost null evidence of scientific interventions of programs that integrate physical activity and cognitive tasks together in Chilean elderly adults, a program of physical-cognitive dual task was proposed as a non-pharmacological treatment, easy to apply and of low cost to benefit their integral health, which improves significantly the cognitive and depressive levels of institutionalized elderly adults.

scholarly journals A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic

2017 ◽  
Vol 60 (3) ◽  
pp. 490-509
Author(s):  
Andrew Fiori
Keyword(s):  
Euler Characteristic ◽  
Euler Characteristics ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Irreducible Components ◽  
Arbitrary Dimensions ◽  
Smooth Projective Varieties ◽  
Ramification Locus ◽  
Hurwitz Theorem

AbstractWe prove an analogue of the Riemann–Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties in arbitrary dimensions, subject only to the condition that the irreducible components of the branch and ramification locus have simple normal crossings.

Dislocation mobility and the concept of flow stress

1975 ◽  
Vol 344 (1638) ◽  
pp. 375-385 ◽  
Keyword(s):  
Shear Stress ◽  
Flow Stress ◽  
First Principles ◽  
Unstable State ◽  
Burgers Vector ◽  
Applied Shear Stress ◽  
Set Up ◽  
The Stability ◽  
Definition Of ◽  
Hurwitz Theorem

A formal definition of the flow stress of a metal is established rigorously from first principles for a certain model by studying the stability of equilibrium of the leader in a group of n ( n large) coplanar screw dislocations with Burgers vector b, moving on a plane a distance h from a non-coplanar locked dislocation with Burgers vector mb ( m < n ) under the action of an applied shear stress p yz = o.A ‘ characteristic equation’ of the model is set up and the onset of instability of the leader is identified with the bifurcation of its equilibrium state, which is predicted by the Routh-Hurwitz theorem, well-known in the theory of stability. As an aid in simplifying this process recourse is had to another well-known the orem -that due to Liénard & Chipart. The applied shear stress required to achieve this unstable state is specified within certain bounds. Since these bounds are very close to each other, especially for small m , the critical flow stress can be estimated accurately. It is shown that the flow stress is closer to the lower bound obtained previously and that the superdislocation approach overestimates the critical stress. The paper also discusses certain implications of the present work.

scholarly journals Introduction to Diophantine Approximation. Part II

2017 ◽  
Vol 25 (4) ◽  
pp. 283-288
Author(s):  
Yasushige Watase
Keyword(s):  
Diophantine Approximation ◽  
Irrational Number ◽  
Basic Result ◽  
Formal Proof ◽  
Integer Solution ◽  
Linear Forms ◽  
Diophantine Approximations ◽  
Integer Solutions ◽  
System 1 ◽  
Hurwitz Theorem

SummaryIn the article we present in the Mizar system [1], [2] the formalized proofs for Hurwitz’ theorem [4, 1891] and Minkowski’s theorem [5]. Both theorems are well explained as a basic result of the theory of Diophantine approximations appeared in [3], [6]. A formal proof of Dirichlet’s theorem, namely an inequation |θ−y/x| ≤ 1/x2has infinitely many integer solutions (x, y) where θ is an irrational number, was given in [8]. A finer approximation is given by Hurwitz’ theorem: |θ− y/x|≤ 1/√5x2. Minkowski’s theorem concerns an inequation of a product of non-homogeneous binary linear forms such that |a1x + b1y + c1| · |a2x + b2y + c2| ≤ ∆/4 where ∆ = |a1b2− a2b1| ≠ 0, has at least one integer solution.

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