###### Finite Element Analysis

###### Stress, Mechanical

###### Models, Anatomic

###### Biomechanical Phenomena

###### Elastic Modulus

###### Dental Prosthesis Design

###### Dental Stress Analysis

###### Computer Simulation

###### Weight-Bearing

###### Dental Abutments

###### Compressive Strength

###### Dental Implant-Abutment Design

###### Tooth, Nonvital

###### Denture Design

###### Models, Biological

###### Post and Core Technique

###### Alveolar Process

###### Tensile Strength

###### Computer-Aided Design

###### Imaging, Three-Dimensional

The process of generating three-dimensional images by electronic, photographic, or other methods. For example, three-dimensional images can be generated by assembling multiple tomographic images with the aid of a computer, while photographic 3-D images (HOLOGRAPHY) can be made by exposing film to the interference pattern created when two laser light sources shine on an object.

###### Periodontal Ligament

###### Materials Testing

###### Dental Porcelain

A type of porcelain used in dental restorations, either jacket crowns or inlays, artificial teeth, or metal-ceramic crowns. It is essentially a mixture of particles of feldspar and quartz, the feldspar melting first and providing a glass matrix for the quartz. Dental porcelain is produced by mixing ceramic powder (a mixture of quartz, kaolin, pigments, opacifiers, a suitable flux, and other substances) with distilled water. (From Jablonski's Dictionary of Dentistry, 1992)

###### Mandible

###### Crowns

###### Dental Implants

###### Tooth Root

The part of a tooth from the neck to the apex, embedded in the alveolar process and covered with cementum. A root may be single or divided into several branches, usually identified by their relative position, e.g., lingual root or buccal root. Single-rooted teeth include mandibular first and second premolars and the maxillary second premolar teeth. The maxillary first premolar has two roots in most cases. Maxillary molars have three roots. (Jablonski, Dictionary of Dentistry, 1992, p690)

###### Immediate Dental Implant Loading

Endosseous dental implantation where implants are fitted with an abutment or where an implant with a transmucosal coronal portion is used immediately (within 1 week) after the initial extraction. Conventionally, the implantation is performed in two stages with more than two months in between the stages.

###### Pliability

###### Eustachian Tube

###### Denture, Partial, Removable

###### Dental Materials

###### Masticatory Muscles

###### Models, Cardiovascular

###### Maxilla

###### Denture, Partial, Fixed

###### Gold Alloys

###### Equipment Failure Analysis

###### Dental Prosthesis, Implant-Supported

###### Dental Clasps

###### Mechanical Phenomena

###### Dinosaurs

###### Anatomy, Comparative

###### Glass

###### Dental Restoration Failure

###### Shear Strength

The internal resistance of a material to moving some parts of it parallel to a fixed plane, in contrast to stretching (TENSILE STRENGTH) or compression (COMPRESSIVE STRENGTH). Ionic crystals are brittle because, when subjected to shear, ions of the same charge are brought next to each other, which causes repulsion.

###### Dentin

###### Denture, Partial, Fixed, Resin-Bonded

A commonly used prosthesis that results in a strong, permanent restoration. It consists of an electrolytically etched cast-metal retainer that is cemented (bonded), using resins, to adjacent teeth whose enamel was previously acid-treated (acid-etched). This type of bridgework is sometimes referred to as a Maryland bridge.

###### Titanium

###### Genu Valgum

###### Incisor

###### Tomography, X-Ray Computed

###### Intervertebral Disc

###### Lumbar Vertebrae

###### Tooth Preparation, Prosthodontic

The selected form given to a natural tooth when it is reduced by instrumentation to receive a prosthesis (e.g., artificial crown or a retainer for a fixed or removable prosthesis). The selection of the form is guided by clinical circumstances and physical properties of the materials that make up the prosthesis. (Boucher's Clinical Dental Terminology, 4th ed, p239)

###### Bicuspid

###### Molar

The most posterior teeth on either side of the jaw, totaling eight in the deciduous dentition (2 on each side, upper and lower), and usually 12 in the permanent dentition (three on each side, upper and lower). They are grinding teeth, having large crowns and broad chewing surfaces. (Jablonski, Dictionary of Dentistry, 1992, p821)

###### Inlays

###### Pelvic Bones

###### Hardness Tests

###### Hardness

###### Stomatognathic System

###### Osteotomy, Sagittal Split Ramus

###### Prostheses and Implants

Artificial substitutes for body parts, and materials inserted into tissue for functional, cosmetic, or therapeutic purposes. Prostheses can be functional, as in the case of artificial arms and legs, or cosmetic, as in the case of an artificial eye. Implants, all surgically inserted or grafted into the body, tend to be used therapeutically. IMPLANTS, EXPERIMENTAL is available for those used experimentally.

###### Temporomandibular Joint

###### Dental Cements

###### Anatomy, Cross-Sectional

Descriptive anatomy based on three-dimensional imaging (IMAGING, THREE-DIMENSIONAL) of the body, organs, and structures using a series of computer multiplane sections, displayed by transverse, coronal, and sagittal analyses. It is essential to accurate interpretation by the radiologist of such techniques as ultrasonic diagnosis, MAGNETIC RESONANCE IMAGING, and computed tomography (TOMOGRAPHY, X-RAY COMPUTED). (From Lane & Sharfaei, Modern Sectional Anatomy, 1992, Preface)

###### Dental Alloys

###### Surface Properties

###### Models, Theoretical

###### Osseointegration

###### Bone Cements

Adhesives used to fix prosthetic devices to bones and to cement bone to bone in difficult fractures. Synthetic resins are commonly used as cements. A mixture of monocalcium phosphate, monohydrate, alpha-tricalcium phosphate, and calcium carbonate with a sodium phosphate solution is also a useful bone paste.

###### Reproducibility of Results

The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.

###### Bone Plates

###### Dental Occlusion

The relationship of all the components of the masticatory system in normal function. It has special reference to the position and contact of the maxillary and mandibular teeth for the highest efficiency during the excursive movements of the jaw that are essential for mastication. (From Jablonski, Dictionary of Dentistry, 1992, p556, p472)

###### Nonlinear Dynamics

The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.

###### Buttocks

###### Cuspid

###### Tibia

###### Anisotropy

A physical property showing different values in relation to the direction in or along which the measurement is made. The physical property may be with regard to thermal or electric conductivity or light refraction. In crystallography, it describes crystals whose index of refraction varies with the direction of the incident light. It is also called acolotropy and colotropy. The opposite of anisotropy is isotropy wherein the same values characterize the object when measured along axes in all directions.

###### Zygoma

###### Bone and Bones

###### Porosity

###### Bone Density

The amount of mineral per square centimeter of BONE. This is the definition used in clinical practice. Actual bone density would be expressed in grams per milliliter. It is most frequently measured by X-RAY ABSORPTIOMETRY or TOMOGRAPHY, X RAY COMPUTED. Bone density is an important predictor for OSTEOPOROSIS.

###### Transducers

Any device or element which converts an input signal into an output signal of a different form. Examples include the microphone, phonographic pickup, loudspeaker, barometer, photoelectric cell, automobile horn, doorbell, and underwater sound transducer. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed)

###### DNA Transposable Elements

Discrete segments of DNA which can excise and reintegrate to another site in the genome. Most are inactive, i.e., have not been found to exist outside the integrated state. DNA transposable elements include bacterial IS (insertion sequence) elements, Tn elements, the maize controlling elements Ac and Ds, Drosophila P, gypsy, and pogo elements, the human Tigger elements and the Tc and mariner elements which are found throughout the animal kingdom.

###### Pressure

###### Range of Motion, Articular

###### Aortic Rupture

###### Dental Bonding

###### Resin Cements

Dental cements composed either of polymethyl methacrylate or dimethacrylate, produced by mixing an acrylic monomer liquid with acrylic polymers and mineral fillers. The cement is insoluble in water and is thus resistant to fluids in the mouth, but is also irritating to the dental pulp. It is used chiefly as a luting agent for fabricated and temporary restorations. (Jablonski's Dictionary of Dentistry, 1992, p159)

###### Algorithms

###### Image Processing, Computer-Assisted

###### Acetabulum

###### Response Elements

###### Bone Remodeling

The continuous turnover of BONE MATRIX and mineral that involves first an increase in BONE RESORPTION (osteoclastic activity) and later, reactive BONE FORMATION (osteoblastic activity). The process of bone remodeling takes place in the adult skeleton at discrete foci. The process ensures the mechanical integrity of the skeleton throughout life and plays an important role in calcium HOMEOSTASIS. An imbalance in the regulation of bone remodeling's two contrasting events, bone resorption and bone formation, results in many of the metabolic bone diseases, such as OSTEOPOROSIS.

## Balloon-artery interactions during stent placement: a finite element analysis approach to pressure, compliance, and stent design as contributors to vascular injury. (1/1327)

Endovascular stents expand the arterial lumen more than balloon angioplasty and reduce rates of restenosis after coronary angioplasty in selected patients. Understanding the factors involved in vascular injury imposed during stent deployment may allow optimization of stent design and stent-placement protocols so as to limit vascular injury and perhaps reduce restenosis. Addressing the hypothesis that a previously undescribed mechanism of vascular injury during stent deployment is balloon-artery interaction, we have used finite element analysis to model how balloon-artery contact stress and area depend on stent-strut geometry, balloon compliance, and inflation pressure. We also examined superficial injury during deployment of stents of varied design in vivo and in a phantom model ex vivo to show that balloon-induced damage can be modulated by altering stent design. Our results show that higher inflation pressures, wider stent-strut openings, and more compliant balloon materials cause markedly larger surface-contact areas and contact stresses between stent struts. Appreciating that the contact stress and contact area are functions of placement pressure, stent geometry, and balloon compliance may help direct development of novel stent designs and stent-deployment protocols so as to minimize vascular injury during stenting and perhaps to optimize long-term outcomes. (+info)## Diffusion tensor imaging in biomechanical studies of skeletal muscle function. (2/1327)

In numerical simulations of skeletal muscle contractions, geometric information is of major importance. The aim of the present study was to determine whether the diffusion tensor imaging (DTI) technique is suitable to obtain valid input with regard to skeletal muscle fibre direction. The accuracy of the DTI method was therefore studied by comparison of DTI fibre directions in the rat tibialis anterior muscle with fascicle striation patterns visible on high-resolution magnetic resonance imaging (MRI) and with fibre directions in an actual longitudinal section (ALS) through the same muscle. The results showed an excellent qualitative agreement between high-resolution MRI and DTI. Despite less accurate quantitative comparison with ALS, it was concluded that DTI does indeed measure skeletal muscle fibre direction. After the experiment, it was possible to determine an appropriate voxel size (0.9 mm3) that provided enough resolution and acceptable accuracy (5 degrees) to use DTI fibre directions in biomechanical analyses. Muscle deformation during contraction, resulting from a finite element simulation with a mesh that was directly generated from the experimental data, has been presented. (+info)## Red cell distribution and the recruitment of pulmonary diffusing capacity. (3/1327)

The distribution of red blood cells in alveolar capillaries is typically nonuniform, as shown by intravital microscopy and in alveolar tissue fixed in situ. To determine the effects of red cell distribution on pulmonary diffusive gas transport, we computed the uptake of CO across a two-dimensional geometric capillary model containing a variable number of red blood cells. Red blood cells are spaced uniformly, randomly, or clustered without overlap within the capillary. Total CO diffusing capacity (DLCO) and membrane diffusing capacity (DmCO) are calculated by a finite-element method. Results show that distribution of red blood cells at a fixed hematocrit greatly affects capillary CO uptake. At any given average capillary red cell density, the uniform distribution of red blood cells yields the highest DmCO and DLCO, whereas the clustered distribution yields the lowest values. Random nonuniform distribution of red blood cells within a single capillary segment reduces diffusive CO uptake by up to 30%. Nonuniform distribution of red blood cells among separate capillary segments can reduce diffusive CO uptake by >50%. This analysis demonstrates that pulmonary microvascular recruitment for gas exchange does not depend solely on the number of patent capillaries or the hematocrit; simple redistribution of red blood cells within capillaries can potentially account for 50% of the observed physiological recruitment of DLCO from rest to exercise. (+info)## Simulation model of an eyeball based on finite element analysis on a supercomputer. (4/1327)

BACKGROUND/AIMS: A simulation model of the human eye was developed. It was applied to the determination of the physical and mechanical conditions of impacting foreign bodies causing intraocular foreign body (IOFB) injuries. METHODS: Modules of the Hypermesh (Altair Engineering, Tokyo, Japan) were used for solid modelling, geometric construction, and finite element mesh creation based on information obtained from cadaver eyes. The simulations were solved by a supercomputer using the finite element analysis (FEA) program PAM-CRASH (Nihon ESI, Tokyo, Japan). It was assumed that rupture occurs at a strain of 18.0% in the cornea and 6.8% in the sclera and at a stress of 9.4 MPa for both cornea and sclera. Blunt-shaped missiles were shot and set to impact on the surface of the cornea or sclera at velocities of 30 and 60 m/s, respectively. RESULTS: According to the simulation, the sizes of missile above which corneal rupture occurred at velocities of 30 and 60 m/s were 1.95 and 0.82 mm. The missile sizes causing scleral rupture were 0.95 and 0.75 mm at velocities of 30 and 60 m/s. CONCLUSIONS: These results suggest that this FEA model has potential usefulness as a simulation tool for ocular injury and it may provide useful information for developing protective measures against industrial and traffic ocular injuries. (+info)## Abductor weakness and stresses around acetabular components of total hip arthroplasty: a finite element analysis. (5/1327)

Abductor weakness, and the resulting Trendelenburg gait, after total hip arthroplasty is believed to be associated with a poor long-term outcome. We have constructed a two-dimensional finite element analysis using load cases to mimic this abductor weakness. The finite element analysis demonstrates slightly increased stresses, particularly at the bone-cement interface in the DeLee-Charnley zone I, which does not seem sufficient to explain the adverse effect of abductor weakness. (+info)## Determination of the centre of resistance in an upper human canine and idealized tooth model. (6/1327)

The purpose of this investigation was to analyse the influence of geometric and material parameters of a human canine on initial tooth mobility, and the stress and strain profiles in the periodontal ligament. While the material parameters of tooth and bony structures are known within an uncertain limit of approximately a factor of 10, values reported for the elasticity parameters of the periodontal ligament differ significantly. In the course of this study, bilinear behaviour was assumed for the mechanical property of the periodontium. The finite element model of an elliptical paraboloid was created as an approximation to the geometry of a human canine to reduce calculation time and to determine influences of the geometry on numerical results. The results were compared with those obtained for a realistic human canine model. The root length of both models was 19.5 mm. By calculating pure rotational and pure tipping movements, the centre of resistance (CR) was determined for both models. They were located on the long axis of the tooth approximately 7.2 mm below the alveolar crest for the idealized model and 8.2 mm for the canine model. Thus, the centre of resistance of a human canine seems to be located around two-fifths of the root length from the alveolar margin. Using these results, uncontrolled tipping (1 N of mesializing force and 5 Nmm of derotating momentum), as well as pure translation (additionally about 10 Nmm of uprighting momentum) were calculated. Comparing the idealized and the realistic models, the uncontrolled tipping was described by the parabolic-shaped model within an accuracy limit of 10 per cent as compared with the canine model, whereas the results for bodily movement differed significantly showing that it is very difficult to achieve a pure translation with the realistic canine model. (+info)## Wall stress distribution on three-dimensionally reconstructed models of human abdominal aortic aneurysm. (7/1327)

PURPOSE: Abdominal aortic aneurysm (AAA) rupture is believed to occur when the mechanical stress acting on the wall exceeds the strength of the wall tissue. Therefore, knowledge of the stress distribution in an intact AAA wall could be useful in assessing its risk of rupture. We developed a methodology to noninvasively estimate the in vivo wall stress distribution for actual AAAs on a patient-to-patient basis. METHODS: Six patients with AAAs and one control patient with a nonaneurysmal aorta were the study subjects. Data from spiral computed tomography scans were used as a means of three-dimensionally reconstructing the in situ geometry of the intact AAAs and the control aorta. We used a nonlinear biomechanical model developed specifically for AAA wall tissue. By means of the finite element method, the stress distribution on the aortic wall of all subjects under systolic blood pressure was determined and studied. RESULTS: In all the AAA cases, the wall stress was complexly distributed, with distinct regions of high and low stress. Peak wall stress among AAA patients varied from 29 N/cm(2) to 45 N/cm(2) and was found on the posterior surface in all cases studied. The wall stress on the nonaneurysmal aorta in the control subject was relatively low and uniformly distributed, with a peak wall stress of 12 N/cm(2). AAA volume, rather than AAA diameter, was shown by means of statistical analysis to be a better indicator of high wall stresses and possibly rupture. CONCLUSION: The approach taken to estimate AAA wall stress distribution is completely noninvasive and does not require any additional involvement or expense by the AAA patient. We believe that this methodology may allow for the evaluation of an individual AAA's rupture risk on a more biophysically sound basis than the widely used 5-cm AAA diameter criterion. (+info)## Removal of the subchondral plate in acetabular preparation. (8/1327)

Retention of the subchondral plate during acetabular preparation in total hip replacement is believed to be an important part of modern cementing techniques. We have constructed a two-dimensional finite element analysis to assess the effect of retention and removal of this relatively stiff structure. The finite element analysis demonstrates increased stiffness and stress concentrations at the bone-cement interface that may have an adverse effect. Although further study is required, it may be that subchondral bone retention is not advantageous. (+info)###### NAFEMS Practical Introduction to Non-Linear Finite Element Analysis engineering analysis and simulation - FEA, Finite Element...

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**element**concepts were developed based on engineering methods in 1950s. The

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**element**method obtained its real ... The original works such as those by Argyris and Clough became the foundation for today's

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**analysis**... packages Structural

**analysis**Virtual work Interval

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**Analysis**Of Framed Structures, 3rd Edition by Jr. ...

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Widas, P. (1997, April 9). Introduction to

**finite****element****analysis**. Retrieved from "Introduction to**Finite****Element****Analysis**". ... Among the fundamental**elements**of the design process are the establishment of objectives and criteria, synthesis,**analysis**, ... It can also calculate stress and displacement using the**finite****element**method to determine stresses throughout the part. The ... It outlines and**analyses**alternatives or methods of achieving the desired outcome. The feasibility study helps to narrow the ...###### Composite material

Pre-construction testing may adopt

**finite****element****analysis**(FEA) for ply-by-ply**analysis**of curved surfaces and predicting ... What is**Finite****Element****Analysis**? Matzkanin, George A.; Yolken, H. Thomas. "Techniques for the Nondestructive Evaluation of ... Within the finished structure, the individual**elements**remain separate and distinct, distinguishing composites from mixtures ... dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual**elements**. ...###### Emily Rayfield

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Some have involved

**finite****element****analysis**. One of the commonly referenced empirical estimations was published by McKee in 1963 ...###### Ansys

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**finite****element****analysis**software is used to simulate computer models of structures, electronics, or machine ... At the time, engineers performed**finite****element****analysis**(FEA) by hand. Westinghouse rejected Swanson's idea to automate FEA by ... Wahab, M.A. (2014). The Mechanics of Adhesives in Composite and Metal Joints:**Finite****Element****Analysis**with Ansys. Destech ... Reh, Stefan; Beley, Jean-Daniel; Mukherjee, Siddhartha; Khor, Eng Hui (2006). "Probabilistic**finite****element****analysis**using ...###### Baháʼí Institute for Higher Education

"

**Finite****element**for cylindrical thin shells under harmonic forces".**Finite****Elements**in**Analysis**and Design. 52: 83-92. doi: ...###### Absement

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**element**in the Bratland sense ...

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**Elements**in

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ISBN 978-3-540-32612-0. Ferreira, A.J.M. (2009). MATLAB Codes for

**Finite****Element****Analysis**. Springer. ISBN 978-1-4020-9199-5. ... Numerical**analysis**software for Linux, Numerical**analysis**software for macOS, Numerical**analysis**software for Windows, ... The list of**elements**should be surrounded by square brackets []. Parentheses () are used to access**elements**and subarrays (they ... For example, mod(2*J,n) will multiply every**element**in J by 2, and then reduce each**element**modulo n. MATLAB does include ...###### Container compression test

Some have involved

**finite****element****analysis**. One of the commonly referenced empirical estimations was published by McKee in 1963 ... "Box Compression**Analysis**of World Wide Data", Wood and Fiber Science, 2006, [1] Yam, K.L., "Encyclopedia of Packaging ...###### Viscoelasticity

**Finite**

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**Analysis**of Composite Materials. CRC Press, Boca Raton, Florida, 2007. S.A. Baeurle, A. Hotta, A.A. Gusev, ... Wagner, Manfred (1976). "

**Analysis**of time-dependent non-linear stress-growth data for shear and elongational flow of a low- ... Viscoelastic materials have

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**Finite****Elements**for Biomechanics) is a software package for**finite****element****analysis**and was specifically designed for ...**Finite****element**software,**Finite****element**software for Linux). ... Nonlinear Continuum Mechanics for**Finite****Element****Analysis**. ... Maas, SA; Ellis BJ; Ateshian GA; Weiss JA (2012). "FEBio:**Finite****elements**for biomechanics". Journal of Biomechanical ... Solid 3D linear and quadratic**elements**(tetrahedral, hexahedral, pentahedral). Linear and quadratic shell**elements**that can be ...###### Dynamic design **analysis** method

Engineers use

**finite****element**method**analysis**software to verify designs using DDAM computer simulations that model the known ... "Nastran**Finite****Element****Analysis**and Simulation Software". NEi Software. Archived from the original on January 30, 2013. ...**Finite****element**method, Numerical differential equations, Partial differential equations, Structural**analysis**). ... Dynamic Shock**Analysis**, and Dynamic Shock**Analysis**Extension Request. Barber, Pam; Arden, Kevin. "Dynamic Design**Analysis**...###### Leaning Tower of Pisa

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**Analysis**in Geotechnical Engineering: Application. Thomas Telford. p. 254. ISBN 9780727727831. Archived from the ... It was built by Tommaso di Andrea Pisano, who succeeded in harmonizing the Gothic

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**Elements**, History, and Meaning. Routledge. p. 98. ISBN ...

###### Feedback with Carry Shift Registers

This can be solved with a variant of Mahler and De Weger's lattice based

**analysis**of N-adic numbers when N = 2 {\displaystyle N ... is a**finite**state device with a state ( a ; z ) = ( a 0 , a 1 , … , a r − 1 ; z ) {\displaystyle (a;z)=(a_{0},a_{1},\dots ,a_{r ... This is maximized when q is prime and N is a primitive**element**modulo q. In this case, the period is q − 1 {\displaystyle q-1 ... z)} consisting of a vector of**elements**a i {\displaystyle a_{i}} in { 0 , 1 , … , N − 1 } = S {\displaystyle \{0,1,\dots ,N-1 ...###### Uncertainty quantification

... various material properties in a

**finite****element****analysis**for engineering, and multiplier uncertainty in the context of ... For example, the**finite****element**method or**finite**difference method may be used to approximate the solution of a partial ... "Modularization in Bayesian**analysis**, with emphasis on**analysis**of computer models". Bayesian**Analysis**. Institute of ... In regression**analysis**and least squares problems, the standard error of parameter estimates is readily available, which can be ...###### Frame (linear algebra)

Suppose H is a Hilbert space, X a locally compact space, and μ {\displaystyle \mu } is a locally

**finite**Borel measure on X. ... Frames are used in error detection and correction and the design and**analysis**of filter banks and more generally in applied ... without removing**elements**in { e k } {\displaystyle \{\mathbf {e} _{k}\}} . The coefficients c k {\displaystyle c_{k}} will no ... The adjoint operator T ∗ {\displaystyle \mathbf {T} ^{*}} of the**analysis**operator is called the synthesis operator of the ...###### Alexander Kluge

"Öffentlichkeit und Erfahrung" has been translated into English as Public Sphere and Experience: Toward an

**Analysis**of the ... AC with 30**elements**, 1932 births, Living people, People from Halberstadt, Mass media people from Saxony-Anhalt, People from the ... Kluge and his studio are featured in the film**Finite**and Infinite Games by artist Sarah Morris. The film, which focuses around ...**Analysis**of the Bourgeois and Proletarian Public, trans. Peter Labany, Jamie Owen Daniel, and Assenka Oksiloff (Verso Books, ...###### Old English

Questions were usually formed by inverting subject and

**finite**verb, and negatives by placing ne before the**finite**verb, ... independent**elements**, and**element**order Mitchell, Bruce. (1990) A Critical Bibliography of Old English Syntax to the end of ...**Analyses**and Reconstruction). 244 p., in German with English summary, London/Berlin 2013, ISBN 978-3-9812110-7-8. Fulk, R. D. ( ...**Finite**verbs agree with subjects in person and number. The future tense, passive voice, and other aspects are formed with ...###### Josephoartigasia

... and Blanco used

**finite****element****analysis**to estimate the absolute maximum possible bite force of 967-1,850 N (217-416 lbf) at ... "Predicting bite force and cranial biomechanics in the largest fossil rodent using**finite****element****analysis**". Journal of Anatomy ... Carbon isotope**analyses**of the enamel of giant fossil rodents, including J. monesi, report that they ate only C3 plants, such ...###### Binary relation

... which have an n-

**element**set S and a set of k-**element**subsets called blocks, such that a subset with t**elements**lies in just one ... Structural**analysis**of relations with concepts provides an approach for data mining. Proposition: If R is a serial relation and ...**Finite**and infinite projective and affine planes are included. Jakob Steiner pioneered the cataloguing of configurations with ... It encodes the common concept of relation: an**element**x is related to an**element**y, if and only if the pair (x, y) belongs to ...###### Henry T. Yang

... as well as a widely used textbook on

**finite****element**structural**analysis**. He has guided 54 Ph.D. and 20 M.S. recipients. In ... and**finite****elements**, Yang was on the staff of Purdue University for 25 years. He first joined the faculty as an assistant ...###### UML state machine

**Analysis**by hierarchical state decomposition can include the application of the operation 'exclusive-OR' to any given state. ... In other words, these

**elements**of the graphical notation do not add much value in representing flow of control as compared to ... UML state machine, also known as UML statechart, is an extension of the mathematical concept of a

**finite**automaton in computer ... The goal of UML state machines is to overcome the main limitations of traditional

**finite**-state machines while retaining their ...

###### Network synthesis filters

The method can be viewed as the inverse problem of network

**analysis**. Network**analysis**starts with a network and by applying the ... Values of prototype**elements**are published in tables, one of the first being due to Sidney Darlington. Both modern computing ... Otto Brune (1931) "Synthesis of a**finite**two-terminal network whose driving-point impedance is a prescribed function of ... The order of the filter is the number of filter**elements**present in the filter's ladder implementation. Generally speaking, the ...###### Andrew Clennel Palmer

... avoiding the need for numerically-laborious calculation of

**finite****element****analysis**. In 1975, after his engagement with BP, ... He would deploy dimensional**analysis**, which he described as 'a magical way of finding useful results with almost no effort,' as ... as it is being laid by an S-lay barge by building a physical model and dimensional**analysis**, ...###### Suffix automaton

Its

**elements**are called "characters"; "Word" is a**finite**sequence of characters ω = ω 1 ω 2 … ω n {\displaystyle \omega =\omega ... one has to use the methods of amortized**analysis**. The value of l e n ( p ) {\displaystyle len(p)} strictly reduces with each ... In this example, the**element**x = 2 ∈ e n d p o s ( a b ) {\displaystyle x=2\in endpos(ab)} corresponds with the word s 3 s 4 s ... Formally, deterministic**finite**automaton is determined by 5-tuple A = ( Σ , Q , q 0 , F , δ ) {\displaystyle {\mathcal {A}}=(\ ...###### Frank Hawthorne

The

**elements**of the adjacency matrix of this graph form a permutation group that is a subgroup of the symmetric group SN (where ... Infinite arrangements with translational symmetry may be represented by**finite**graphs via wrapping and extends this method to ... Luciano Ungaretti and Giuseppe Rossi in Pavia using large-scale crystal-structure refinement and electron-microprobe**analysis**... Light lithophile**elements**(LLEs) can be important variable components in several groups of rock-forming minerals that were ...###### Asymptotic dimension

As shown by Guoliang Yu, finitely generated groups of

**finite**homotopy type with**finite**asymptotic dimension satisfy the Novikov ... Asymptotic dimension has important applications in geometric**analysis**and index theory. Let X {\displaystyle X} be a metric ... Buyalo, Sergei; Schroeder, Viktor (2007).**Elements**of Asymptotic Geometry. EMS Monographs in Mathematics. European Mathematical ... is a finitely generated group of**finite**homotopy type (that is with a classifying space of the homotopy type of a**finite**CW- ...###### Lumped-**element** model

Another way of viewing the validity of the lumped-

**element**model is to note that this model ignores the**finite**time it takes ... The third assumption is the basis of the lumped-**element**model used in network**analysis**. Less severe assumptions result in the ... distributed**elements**but are often represented to a first-order approximation by lumped**elements**. To account for leakage in ... The lumped-**element**model is valid whenever L c ≪ λ {\displaystyle L_{c}\ll \lambda } , where L c {\displaystyle L_{c}} denotes ...###### Invariant subspace problem

Bernstein & Robinson (1966) proved using non-standard

**analysis**that if the operator T {\displaystyle T} on a Hilbert space is ... is an**element**of the Banach space H {\displaystyle H} , the orbit of x {\displaystyle x} under the action of T {\displaystyle T ... For**finite**-dimensional complex vector spaces, every operator admits an eigenvector, so it has a 1-dimensional invariant ... In the field of mathematics known as functional**analysis**, the invariant subspace problem is a partially unresolved problem ...###### Mark Tomforde

He works in the areas of functional

**analysis**and algebra, and he earned his Ph.D. in mathematics at Dartmouth College in 2002. ... Desingularization allows one to extend many results for row-**finite**graphs to countable graphs, and it has become a standard ... Home page (Articles with short description, Short description matches Wikidata, Articles with hCards, AC with 0**elements**, 20th- ... In his research, Tomforde has connected ideas from Functional**Analysis**and Algebra, and he has used techniques and methods from ...###### Calculation of glass properties

The

**finite****element**method may also be applied to glass forming processes. It is often required to optimize several glass ... In the form of statistical**analysis**glass modeling can aid with accreditation of new data, experimental procedures, and ... For modeling of the glass flow in a glass melting furnace the**finite****element**method is applied commercially, based on data or ... sometimes combined with the**finite****element**method. For estimating the melting enthalpy thermodynamic databases are used. If the ...###### Van der Waals radius

A more recent

**analysis**of the Cambridge Structural Database, carried out by Santiago Alvarez, provided a new set of values for ... Atomic radii of the**elements**(data page) van der Waals force van der Waals molecule van der Waals strain van der Waals surface ... a is a correction for intermolecular forces and b corrects for**finite**atomic or molecular sizes; the value of b equals the van ... "van der Waals Radius of the**elements**". Wolfram. Weast, Robert C., ed. (1981). CRC Handbook of Chemistry and Physics (62nd ed ...###### Homoscedasticity and heteroscedasticity

The existence of heteroscedasticity is a major concern in regression

**analysis**and the**analysis**of variance, as it invalidates ... ISBN 978-0-07-337577-9. Kmenta, Jan (1986).**Elements**of Econometrics (Second ed.). New York: Macmillan. pp. 269-298. ISBN 978-0 ... if all its random variables have the same**finite**variance. This is also known as homogeneity of variance. The complementary ... Thus, regression**analysis**using heteroscedastic data will still provide an unbiased estimate for the relationship between the ...###### Cantor set

As to cardinality, almost all

**elements**of the Cantor set are not endpoints of intervals, nor rational points like 1/4. The ... The ternary representation of these fractions terminates (i.e., is**finite**) or - recall from above that proper ternary fractions ... The "universal" property has important applications in functional**analysis**, where it is sometimes known as the representation ... All these endpoints are proper ternary fractions (**elements**of Z ⋅ 3 − N 0 {\displaystyle \mathbb {Z} \cdot 3^{-\mathbb {N} _{0 ...###### Flip-flop (electronics)

In the special cases of 1-of-3 encoding, or multi-valued ternary logic, such an

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Fourier

**analysis**allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the ... They can also be used in charge pump circuits as the energy storage**element**in the generation of higher voltages than the input ... The capacitor therefore has a**finite**parallel resistance, and slowly discharges over time, which may vary greatly depending on ... The usual methods of network**analysis**can then be applied. In other cases, such as with breakdown voltage, the effect is non- ...###### Modern searches for Lorentz violation

1997). "Bayesian

**analysis**of the polarization of distant radio sources: Limits on cosmological birefringence". Physical Review ... It is generally assumed that neutrino oscillations require a certain**finite**mass. However, oscillations could also occur as a ... level by examining Keplerian orbital**elements**of a test particle acted upon by Lorentz-violating gravitomagnetic accelerations ... method and**analysis**see, discussion e.g.). Besides terrestrial tests also astrometric tests using Lunar Laser Ranging (LLR), i. ...###### Parametric determinism

A synthesis cannot be achieved without a preceding

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**finite****element****analysis**". Paleobiology. 45 (1): 182-200. doi:10.1017/pab.2018.48. S2CID ...###### Real closed field

... such that every

**element**of L is less than every**element**of U, there is an**element**x in F with x larger than every**element**of L ... It is not an ultrapower but it is a hyperreal field, and hence a suitable field for the usages of nonstandard**analysis**. It can ... F is not algebraically closed, but its algebraic closure is a**finite**extension. F is not algebraically closed but the field ... There is a total order on F making it an ordered field such that, in this ordering, every positive**element**of F has a square ...###### Constantine A. Balanis

doi:10.1109/74.997945 A. C. Polycarpou, P. A. Tirkas and C. A. Balanis, "The

**finite**-**element**method for modeling circuits and ... Antenna Theory:**Analysis**and Design (2016, 2005, 1997, 1982), John Wiley & Sons, Publishers, Inc., New York. The book has been ... P. A. Tirkas and C. A. Balanis, "**Finite**-difference time-domain method for antenna radiation," in IEEE Transactions on Antennas ... doi:10.1109/8.135478 S. V. Georgakopoulos, C. R. Birtcher, C. A. Balanis and R. A. Renaut, "Higher-order**finite**-difference ...###### Head-directionality parameter

In more traditional

**analysis**the entire phrase (including any**elements**denoting tense or aspect) is considered to be simply a ... In a**finite**verb phrase (or tense/aspect phrase) the verb (tense/aspect) is initial, although it may move to final position in ... In the following example, the non-**finite**verb phrase es finden is head-final, whereas in the tensed main clause ich werde es ... In the tense phrase in (b), the tense-marking**element**(T) precedes its verb phrase (VP) complement. (The subject of the tense ...###### Robin boundary condition

J. E. Akin (2005).

**Finite****Element****Analysis**with Error Estimators: An Introduction to the FEM and Adaptive Error**Analysis**for ... ISBN 3-540-00889-6. Atkinson, Kendall E.; Han, Weimin (2001). Theoretical numerical**analysis**: a functional**analysis**framework. ... ISBN 0-521-56738-6. Mei, Zhen (2000). Numerical bifurcation**analysis**for reaction-diffusion equations. Berlin; New York: ...###### Global/local **finite** **element** **analysis** for textile composites - NASA Technical Reports Server (NTRS)

Global/local methodology combined with special macro

**elements**is proposed herein as a practical alternative. Initial tests ... Conventional**analysis**of textile composites is impractical because of the complex microstructure. ... Global/local**finite****element****analysis**for textile composites. Conventional**analysis**of textile composites is impractical because ... Global/local methodology combined with special macro**elements**is proposed herein as a practical alternative. Initial tests ...###### "**Finite** **Element** **Analysis** of Compressor Valve Dynamics" by S. Akella, N. J. Rao et al.

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