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"Finite, The."
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Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster
For a finite group
eBook
The Bounded and Precise Word Problems for Presentations of Groups
We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining
relations. For example, for every finitely presented group, the bounded word problem is in
eBook
Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups
A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only
several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle
exceptional Lie type or orthogonal of minus type. The characterization is then applied to study
eBook
Hypergeometric functions over finite fields
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we
consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions
over finite fields in a manner that is parallel to that of the classical hypergeometric functions. Using a comparison between the
classical gamma function and its finite field analogue the Gauss sum, we give a systematic way to obtain certain types of hypergeometric
transformation and evaluation formulas over finite fields and interpret them geometrically using a Galois representation perspective. As
an application, we obtain a few finite field analogues of algebraic hypergeometric identities, quadratic and higher transformation
formulas, and evaluation formulas. We further apply these finite field formulas to compute the number of rational points of certain
hypergeometric varieties.
eBook
Robust hybrid/mixed finite elements for rubber-like materials under severe compression
A new family of hybrid/mixed finite elements optimized for numerical stability is introduced. It comprises a linear hexahedral and quadratic hexahedral and tetrahedral elements. The element formulation is derived from a consistent linearization of a well-known three-field functional and related to Simo–Taylor–Pister (STP) elements. For the quadratic hexahedral and tetrahedral elements we derive (static reduced) discontinuous hybrid elements, as well as continuous mixed finite elements with additional primary unknowns for the hydrostatic pressure and the dilation, whereas the linear hexahedral element is of the discontinuous type. The elements can readily be used in combination with any isotropic, invariant-based hyperelastic material model and can be considered as being locking-free. In a representative numerical benchmark test the elements numerical stability is assessed and compared to STP-elements and the family of discontinuous hybrid elements implemented in the commercial finite element code Abaqus/Standard. The new elements show a significant advantage concerning the numerical robustness.
Journal Article
Symbolic Extensions of Amenable Group Actions and the Comparison Property
In topological dynamics, the
Of course, the statement is preceded by the
presentation of the concepts of an entropy structure and its superenvelopes, adapted from the case of
eBook
Leaflet stress and strain distributions following incomplete transcatheter aortic valve expansion
Transcatheter aortic valve replacement (TAVR) is an established treatment alternative to surgical valve replacement in high-risk patients with severe symptomatic aortic stenosis. The current guidelines for TAVR are to upsize transcatheter aortic valve (TAV) relative to the native annulus to secure the device and minimize paravalvular leakage. Unlike surgical stented bioprosthetic valves where leaflets are attached to a rigid frame, TAVs must expand to fit within the native annulus. Fully-expanded circular TAVs have consistent leaflet kinematics; however, subtle variations in the degree of stent expansion may affect leaflet coaptation. The objective of this study was to determine the impact of incomplete TAV expansion on leaflet stress and strain distributions. In this study, we developed finite element models of a 23mm homemade TAV expanded to diameters ranging from 18 to 23mm in 1mm increments. Through dynamic finite element simulations, we found that leaflet stress and strain distributions were dependent on the diameter of the inflated TAV. After complete expansion of the TAV to 23mm, high stress and strain regions were observed primarily in the commissures during diastole. However, 2–3mm incomplete TAV stent expansion induced localized high stress regions within the TAV commissures, while 4–5mm incomplete stent expansion induced localized high stress regions within the belly of the TAV leaflets during the diastolic phase of the cardiac cycle. Increased mechanical stress and flexural deformation on TAV leaflets due to incomplete stent expansion may lead to accelerated tissue degeneration and diminished long-term valve durability.
Journal Article
Population-specific material properties of the implantation site for transcatheter aortic valve replacement finite element simulations
Patient-specific computational models are an established tool to support device development and test under clinically relevant boundary conditions. Potentially, such models could be used to aid the clinical decision-making process for percutaneous valve selection; however, their adoption in clinical practice is still limited to individual cases. To be fully informative, they should include patient-specific data on both anatomy and mechanics of the implantation site. In this work, fourteen patient-specific computational models for transcatheter aortic valve replacement (TAVR) with balloon-expandable Sapien XT devices were retrospectively developed to tune the material parameters of the implantation site mechanical model for the average TAVR population.
Pre-procedural computed tomography (CT) images were post-processed to create the 3D patient-specific anatomy of the implantation site. Balloon valvuloplasty and device deployment were simulated with finite element (FE) analysis. Valve leaflets and aortic root were modelled as linear elastic materials, while calcification as elastoplastic. Material properties were initially selected from literature; then, a statistical analysis was designed to investigate the effect of each implantation site material parameter on the implanted stent diameter and thus identify the combination of material parameters for TAVR patients.
These numerical models were validated against clinical data. The comparison between stent diameters measured from post-procedural fluoroscopy images and final computational results showed a mean difference of 2.5 ± 3.9%. Moreover, the numerical model detected the presence of paravalvular leakage (PVL) in 79% of cases, as assessed by post-TAVR echocardiographic examination.
The final aim was to increase accuracy and reliability of such computational tools for prospective clinical applications.
Journal Article