Addition formula for Kodaira dimensions of analytic fibre bundles

1975 ◽  
pp. 172-187
Author(s):  
Kenji Ueno
Keyword(s):  
Addition Formula ◽  
Fibre Bundles

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals Development of Permeability Models for Saturated Fluid Flow across Arrays of Fibre Clusters

2002 ◽  
Vol 11 (3) ◽  
pp. 096369350201100
Author(s):  
E.M. Gravel ◽  
T.D. Papathanasiou
Keyword(s):  
Analytical Models ◽  
Dual Porosity ◽  
Hydraulic Permeability ◽  
Fibrous Media ◽  
Fibre Bundles ◽  
Hexagonal Packing ◽  
Composites Manufacturing ◽  
Starting Point ◽  
Wide Range ◽  
Flow Through

Dual porosity fibrous media are important in a number of applications, ranging from bioreactor design and transport in living systems to composites manufacturing. In the present study we are concerned with the development of predictive models for the hydraulic permeability ( Kp) of various arrays of fibre bundles. For this we carry out extensive computations for viscous flow through arrays of fibre bundles using the Boundary Element Method (BEM) implemented on a multi-processor computer. Up to 350 individual filaments, arranged in square or hexagonal packing within bundles, which are also arranged in square of hexagonal packing, are included in each simulation. These are simple but not trivial models for fibrous preforms used in composites manufacturing – dual porosity systems characterised by different inter- and intra-tow porosities. The way these porosities affect the hydraulic permeability of such media is currently unknown and is elucidated through our simulations. Following numerical solution of the governing equations, ( Kp) is calculated from the computed flowrate through Darcy's law and is expressed as function of the inter- and intra-tow porosities (φ, φt) and of the filament radius ( Rf). Numerical results are also compared to analytical models. The latter form the starting point in the development of a dimensionless correlation for the permeability of such dual porosity media. It is found that the numerically computed permeabilities follow that correlation for a wide range of φ i, φt and Rf.

scholarly journals A New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles

2016 ◽  
Vol 40 ◽  
pp. 1660098
Author(s):  
K. Heinemann ◽  
D. P. Barber ◽  
J. A. Ellison ◽  
M. Vogt
Keyword(s):  
Normal Form ◽  
Spin Dynamics ◽  
Invariant Sets ◽  
Spin Orbit ◽  
Spin Tensor ◽  
Spin Vector ◽  
Spin Motion ◽  
New Formalism ◽  
Fibre Bundles ◽  
Ongoing Work

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties invariant fields with the notion of normal form, the second allows comparison of different invariant fields and the two others tie the existence of invariant fields to the existence of certain invariant sets. We explain how the theorems apply to the spin dynamics of spin-[Formula: see text] and spin-[Formula: see text] particles. Our approach elegantly unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics and suggests an avenue for addressing the question of the existence of the invariant spin field.

Fibre bundles in the human extensor carpi ulnaris tendon are arranged in a spiral

2011 ◽  
Vol 37 (6) ◽  
pp. 550-554 ◽  
Author(s):  
N. S. Kalson ◽  
P. S. C. Malone ◽  
R. S. Bradley ◽  
P. J. Withers ◽  
V. C. Lees
Keyword(s):  
Polarized Light ◽  
Clinical Importance ◽  
Longitudinal Axis ◽  
Distal Radioulnar Joint ◽  
Forearm Rotation ◽  
Fibre Bundles ◽  
Extensor Carpi Ulnaris ◽  
Dart Throwing ◽  
Dynamic Stabilizer ◽  
Antagonist Action

The extensor carpi ulnaris musculotendinous unit has important agonist and antagonist action in wrist motion, including the dart-throwing action, and is a dynamic stabilizer of the distal radioulnar joint during forearm rotation. Despite its functional and clinical importance, little is known about its internal structure. Investigation of the ultrastructure of the human extensor carpi ulnaris (ECU) tendon was undertaken using plane polarized light microscopy and microcomputer tomography with 3D reconstruction. The study demonstrates that the tendon comprises fibre bundles (fascicles) approximately 0.1 mm in diameter that are arranged in a gradual spiral. The spiralling fibres make an angle of 8º to the longitudinal axis of the tendon. The spiral structure of the human ECU tendon has important biomechanical implications, allowing fascicular sliding during forearm rotation. The observed features may prevent injury.

Effect of strain rate, off-axis loading and high-velocity impact damage on the compressive strength of C/SiC composite

2018 ◽  
Vol 53 (4) ◽  
pp. 535-546 ◽  
Author(s):  
M Altaf ◽  
S Singh ◽  
VV Bhanu Prasad ◽  
Manish Patel
Keyword(s):  
Compressive Strength ◽  
Strain Rate ◽  
High Velocity ◽  
Impact Damage ◽  
The Other ◽  
High Velocity Impact ◽  
Fibre Bundles ◽  
Velocity Impact ◽  
Kink Bands ◽  
Other Hand

The compressive strength of C/SiC composite at different strain rates, off-axis orientations and after high-velocity impact was studied. The compressive strength was found to be 137 ± 23, 130 ± 46 and 162 ± 33 MPa at a strain rate of 3.3 × 10−5, 3.3 × 10−3, 3.3 × 10−3 s−1, respectively. On the other hand, the compressive strength was found to be 130 ± 46, 99 ± 23 and 87 ± 9 MPa for 0°/90°, 30°/60° and 45°/45° fibre orientations to loading direction, respectively. After high-velocity impact, the residual compressive strength of C/SiC composite was found to be 58 ± 26, 44 ± 18 and 36 ± 3.5 MPa after impact with 100, 150 and 190 m/s, respectively. The formation of kink bands in fibre bundles was found to be dominant micro-mechanism for compressive failure of C/SiC composite for 0°/90° orientation. On the other hand, delamination and the fibre bundles rotation were found to be the dominant mechanism for off-axis failure of composite.

Testing E-glass fibre bundles using acoustic emission

1991 ◽  
Vol 26 (5) ◽  
pp. 1301-1310 ◽  
Author(s):  
A. Cowking ◽  
A. Attou ◽  
A. M. Siddiqui ◽  
M. A. S. Sweet ◽  
R. Hill
Keyword(s):  
Acoustic Emission ◽  
Glass Fibre ◽  
Fibre Bundles
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