scholarly journals Determination of the Invariant Vector Field in Non-Linear Field

1989 ◽  
Vol 82 (6) ◽  
pp. 1023-1031
Author(s):  
N. Asano
Keyword(s):  
Vector Field ◽  
Invariant Vector ◽  
Invariant Vector Field ◽  
Non Linear ◽  
Linear Field

scholarly journals THE BURNSIDE RING-VALUED MORSE FORMULA FOR VECTOR FIELDS ON MANIFOLDS WITH BOUNDARY

2009 ◽  
Vol 01 (01) ◽  
pp. 13-27 ◽  
Author(s):  
GABRIEL KATZ
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Compact Lie Group ◽  
Manifolds With Boundary ◽  
Burnside Ring ◽  
Polynomial Inequality ◽  
Invariant Vector ◽  
Generic Polynomial ◽  
Invariant Vector Field ◽  
Algebraic Fields

Let G be a compact Lie group and A(G) its Burnside Ring. For a compact smooth n-dimensional G-manifold X equipped with a generic G-invariant vector field v, we prove an equivariant analog of the Morse formula [Formula: see text] which takes its values in A(G). Here Ind G(v) denotes the equivariant index of the field v, [Formula: see text] the v-induced Morse stratification (see [10]) of the boundary ∂X, and [Formula: see text] the class of the (n - k)-manifold [Formula: see text] in A(G). We examine some applications of this formula to the equivariant real algebraic fields v in compact domains X ⊂ ℝn defined via a generic polynomial inequality. Next, we link the above formula with the equivariant degrees of certain Gauss maps. This link is an equivariant generalization of Gottlieb's formulas ([3, 4]).

Homogeneous Finsler spaces with exponential metric

2020 ◽  
Vol 20 (3) ◽  
pp. 391-400
Author(s):  
Gauree Shanker ◽  
Kirandeep Kaur
Keyword(s):  
Vector Field ◽  
Explicit Formula ◽  
Finsler Space ◽  
Finsler Spaces ◽  
Invariant Vector ◽  
Homogeneous Finsler Space ◽  
Invariant Vector Field ◽  
The Mean ◽  
Exponential Metric

AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.

scholarly journals VECTOR FIELDS ON QUANTUM GROUPS

1996 ◽  
Vol 11 (06) ◽  
pp. 1077-1100 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
PETER SCHUPP
Keyword(s):  
Vector Field ◽  
Hopf Algebra ◽  
Quantum Group ◽  
Vector Fields ◽  
Lie Derivative ◽  
Tensor Fields ◽  
Invariant Vector ◽  
Invariant Vector Field ◽  
Left Invariant Vector ◽  
Invariant Vector Fields

We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left-invariant vector fields. We study the duality between vector fields and one-forms and generalize the construction to tensor fields. A Lie derivative along any (also non-left-invariant) vector field is proposed and a puzzling ambiguity in its definition discussed. These results hold for a generic Hopf algebra.

Determination of Concrete Cube Strength from Used Samples / Určení Krychelné Pevnosti Betonu U Použitých Zkušebních Trámců

2012 ◽  
Vol 12 (2) ◽  
pp. 186-194 ◽  
Author(s):  
Oldřich Sucharda ◽  
David Mikolášek ◽  
Jiří Brožovský
Keyword(s):  
Compressive Strength ◽  
Concrete Beams ◽  
Linear Analysis ◽  
Bending Tests ◽  
Cube Strength ◽  
Non Linear ◽  
Compressive Strength Of Concrete ◽  
Concrete Cube

Abstract This paper deals with the determination of compressive strength of concrete. Cubes, cylinders and re-used test beams were tested. The concrete beams were first subjected to three-point or fourpoint bending tests and then used for determination of the compressive strength of concrete. Some concrete beams were reinforced, while others had no reinforcement. Accuracy of the experiments and calculations was verified in a non-linear analysis.

scholarly journals Bias Truck Tire Deformation Analysis with Finite Element Modeling

2020 ◽  
Vol 10 (12) ◽  
pp. 4326
Author(s):  
Józef Pelc
Keyword(s):  
Incompressible Material ◽  
Axisymmetric Deformation ◽  
Thermal Shrinkage ◽  
Deformation Analysis ◽  
Truck Tire ◽  
Non Linear ◽  
Strain Relationship ◽  
Tire Modeling ◽  
Total Lagrangian Formulation

This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.

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