Browsing Mathematics by Title
Now showing items 233-252 of 263
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Tate's and Yoshida's theorems on control of transfer for fusion systems
(2010-03)We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of p-group residuals and transfer maps in cohomology for fusion systems. As a corollary, we obtain a ... -
Temperature effects on brain tissue in compression
(2012)Extensive research has been carried out for at least 50 years to understand the mechanical properties of brain tissue in order to understand the mechanisms of traumatic brain injury (TBI). The observed large variability ... -
Tension lines of the skin
(Springer, Cham, 2019-05-29)Skin tension lines are natural lines of tension that occur within the skin as a result of growth and remodeling mechanisms. Researchers have been aware of their existence and their surgical implications for over 150 years. ... -
Third and fourth-order elasticity of biological soft tissues
(Acoustical Society of America, 2010-01-24)In the theory of weakly nonlinear elasticity, Hamilton et al. [J. Acoust. Soc. Am. 116, 41-44 (2004)] identified W = -I2+(A/3)I3+DI22 as the fourth-order expansion of the strain-energy density for incompressible isotropic ... -
Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect.
(Acoustical Society of America, 2010-02)Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination ... -
Torsion instability of soft solid cylinders
(Oxford Open Journals, 2013-12-10)The application of pure torsion to a long and thin cylindrical rod is known to provoke a twisting instability, evolving from an initial kink to a knot. In the torsional parallel-plate rheometry of stubby cylinders, the ... -
Torus Chiral n-Point Functions for Free Boson and Lattice Vertex Operator Algebras
(2002)We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions. -
Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
(2007)We consider genus one n-point functions for a vertex operator superalgebra with a real grading. We compute all n-point functions for rank one and rank two fermion vertex operator superalgebras. In the rank two fermion case, ... -
Toward a predictive assessment of stab-penetration forces
(Lippincott, Williams & Wilkins, 2015-09)Collaborative research between the disciplines of forensic pathology and biomechanics was undertaken to investigate the hyperelastic properties of human skin, to determine the force required for sharp instrument penetration ... -
Towards understanding the role of viscoelasticity in microstructural buckling in soft particulate composites
(Elsevier, 2023)This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain ... -
Transverse waves in nonlinearly elastic solids and the Milne-Pinney equation
(SAGE Journals, 2011-08-17)We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc Amer Math Soc 1950; 1: 681]. As a starting point, we use the exact ... -
Tuning the pull-in instability of soft dielectric elastomers through loading protocols
(Elsevier, 2019-03-22)Pull-in (or electro-mechanical) instability occurs when a drastic decrease in the thickness of a dielectric elastomer results in electrical breakdown, which limits the applications of dielectric devices. Here we derive the ... -
A two-weight scheme for a time-dependent advection-diffusion problem
(2011)We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion parameters, ... -
An ultrasonic method to measure stress without calibration: The angled shear wave identity.
(Acoustical Society of America, 2020-12-03)Measuring stress levels in loaded structures is crucial to assess and monitor structure health and to predict the length of remaining structural life. Many ultrasonic methods are able to accurately predict in-plane stresses ... -
Uniform transmural strain in pre-stressed arteries occurs at physiological pressure
(Elsevier, 2012-06-21)Residual deformation (strain) exists in arterial vessels, and has been previously proposed to induce homogeneous transmural strain distribution. In this work, we present analytical formulations that predict the existence ... -
The Varchenko determinant of a Coxeter arrangement
(De Gruyter, 2018)The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization ... -
Vertex algebras according to Isaac Newton
(IOP Publishing, 2017-09-08)We give an introduction to vertex algebras using elementary forward difference methods originally due to Isaac Newton. -
Vertex Operators and Modular Forms
(2009)The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite ... -
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
(2006)We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series ... -
Virasoro Correlation Functions for Vertex Operator Algebras
(2011)We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially ...