Finite measures. Medical search. Frequent questions

If X {\displaystyle X} is a Hausdorff space and A {\displaystyle {\mathcal {A}}} contains the Borel σ {\displaystyle \sigma } -algebra then every finite measure is also a locally finite Borel measure. (wikipedia.org)
If X {\displaystyle X} is a metric space and the A {\displaystyle {\mathcal {A}}} is again the Borel σ {\displaystyle \sigma } -algebra, the weak convergence of measures can be defined. (wikipedia.org)

Important subsets of the finite measures are the sub-probability measures, which form a convex subset, and the probability measures, which are the intersection of the unit sphere in the normed space of signed measures and the finite measures. (wikipedia.org)

In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values. (wikipedia.org)
Vitali D. Milman and Gideon Schechtman , Asymptotic theory of finite-dimensional normed spaces , Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986. (ams.org)

Someone knows of some definition or reference of how to define conditional expectation for a measure space with $\sigma$-finite measure. (mathoverflow.net)

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. (ams.org)
We consider both finite sample and asymptotic points of view. (lu.se)

Nack, W., "Brake Squeal Analysis by Finite Elements," SAE Technical Paper 1999-01-1736, 1999, https://doi.org/10.4271/1999-01-1736 . (sae.org)
Geometric measure theory, real analysis. (warwick.ac.uk)
The implant models were developed using computer-aided design (CAD) software and all models were analyzed via finite element analysis (FEA) software. (researchgate.net)
4.1 Finite element analysis is a valuable tool for evaluating the performance of metallic stents and in estimating quantities such as stress, strain, and displacement due to applied external loads and boundary conditions. (astm.org)
A finite element analysis is especially valuable in determining quantities that cannot be readily measured. (astm.org)
1.2 Limitations- The analysis technique discussed in this guide is restricted to structural analysis using the finite element method. (astm.org)
Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. (hindawi.com)
We compared equivalent stress and strain energy density (SED) to bone mineral density (BMD) in the femur after total hip arthroplasty (THA) using subject-specific finite element analysis (FEA). (intechopen.com)
This study aims to assess the feasibility of a safe entry anchor point retrofit by using finite element analysis. (cdc.gov)
Finite element analysis (FEA) is useful to predict if the structure will withstand when subjected to stress. (cdc.gov)
The measured deflections compared well to defections predicted by finite element analysis. (cdc.gov)
Although commercial laboratories commonly measure the submitted hair sample in bulk, the methodology is sufficiently sensitive to allow investigators to yield segmental analysis (³ 1 cm) on bundles of hair for which information on the alignment and distance from the root has been preserved. (cdc.gov)
Finite Element Analysis (FEA) has been widely used through numerical analysis that has been successfully applied in many engineering and bioengineering areas since the 1960s. (bvsalud.org)
For each 5 min time-series of RR intervals we then calculated Shannon entropy, high spectral entropy, high spectral Detrended Fluctuation Analysis, spectral Multi-Taper Method as well as the standard deviation and two commonly used complexity measures: Approximate Entropy and Sample Entropy. (bvsalud.org)
For each subject and HRV measure, we performed regression analysis with respect to gestational age. (bvsalud.org)

with positive measure essentially contains a measurable set with finite positive measure. (ncatlab.org)

In a highly influential work in geometric measure theory, Marstrand [ 18 ] related the Hausdorff dimension of a Borel set $E \subseteq \mathbb {R}^2$ , $\dim _{\text {H}}E$ , to the Hausdorff dimension of its images under orthogonal projections and its intersections with lines. (springer.com)
The classical Minkowski problem asks for the existence, uniqueness, and regularity of a convex body whose surface area measure is equal to a pre-given spherical Borel measure. (degruyter.com)
The surface area measure of a convex body in Euclidean space is a Borel measure on the unit sphere, which was introduced by Aleksandrov-Fenchel-Jessen in the 1930s. (degruyter.com)

The functional form of the strain energy of a general anisotropic nonlinear elastic material may then be expressed in terms of these directional strain measures. (asme.org)
Next, we consider general nonlinear isotropic response by developing explicit functional forms for three independent strain invariants in terms of these directional strain measures. (asme.org)
This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. (hindawi.com)

Report of the Focussed Research Group Residually finite groups, graph limits and dynamics (09frg147), Banff International Research Station, April 2009. (ams.org)
and ignores the natural limits of a finite planet. (yesmagazine.org)

One can define a reasonable notion of conditional expectation for arbitrary localizable measurable spaces, not necessarily σ-finite. (mathoverflow.net)
It is a theorem, I believe, that every localizable measurable space is capable of supporting a semifinite, hence localizable, measure with the same full/null sets. (ncatlab.org)

More consistency among tissue selection, preparation, and testing protocols must be attained before an accurate 3-dimensional finite-element model of an equine foot can be constructed. (avma.org)
derived the one-dimensional (1D) finite strain consolidation equation which was called the Gibson equation [ 12 ]. (hindawi.com)
We define a family of one-parameter compensators and prove that this family is unique in some sense and characterizes the finite dimensional distributions of a totally ordered point process. (projecteuclid.org)
A calibrated three-dimensional finite element model, developed in conjunction with an underground test area, provided the critical components and design principals for a comprehensive parametric study. (cdc.gov)

The finite element method has been used to develop computational models of the human carpus. (avma.org)
Finite element simulation can integrate computational fluid dynamics techniques to analyze and optimize fluid behavior in engineering applications. (verdict.co.uk)
Introduction: The finite element method (FEM) involves a series of computational procedures to calculate the stress in each element, which performs a model solution. (bvsalud.org)

When the given measure has a positive continuous density, the Minkowski problem is also known as the problem of prescribing the Gauss curvature in differential geometry. (degruyter.com)
Another family of geometric measures associated with quermassintegrals is the curvature measures of Federer. (degruyter.com)
Area measures and curvature measures are fundamental concepts in the classical Brunn-Minkowski theory. (degruyter.com)
Their discovery of dual curvature measures gives dual concepts to Federer's curvature measures. (degruyter.com)
Dual curvature measures are differentials of the dual quermassintegrals. (degruyter.com)

Finite element simulation refers to a numerical approach employed for addressing intricate engineering challenges. (verdict.co.uk)
The finite element method (FEM) is a numerical procedure for analyzing structures. (bvsalud.org)

In fact, they hold for localizable measures, and this fact characterizes the localizable measures. (ncatlab.org)
I don't know if it characterizes localizable measures. (ncatlab.org)

The sumset conjecture ( 1.1 ) was resolved by Hochman and Shmerkin [ 12 ], who proved a more general result concerning the dimension of sums of invariant measures. (springer.com)

Finite gap Jacobi matrices, II. (crossref.org)

Two of the most frequently used methods are based on measuring the attenuation of a beam of electromagnetic radiation or ultrasound when it passes through the bone. (medscape.com)
The electromagnetic cor- rections are particularly problematic due to the systematic effects coming from the finite-volume approximation on the lattice, and in order to provide useful input for the SM prediction these must be well under control. (lu.se)
The finite-size effects from electromagnetic (EM) corrections to the above quantity can be obtained using effective field theory techniques, see e.g. (lu.se)

Sofic measure entropy via finite partitions. (ams.org)

Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. (hindawi.com)
Results indicated that the finite-element design method provided reasonable comparisons with both the anticipated regional stress regime and the measured deformational response of the underground accessways. (cdc.gov)
These include the finite limitations of the assay method (ideal method recovery and precision), and the variability associated with within-run and day to day operation of the assay (actual method recovery and precision). (cdc.gov)
This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. (bvsalud.org)
Literature review: This paper shows the basic concept, advances, advantages, limitations and applications of finite element method (FEM) in dentistry. (bvsalud.org)

begingroup$ Someone (Gustaf Soderlind) has finally proposed a quantitative measure of stiffness that experts are beginning to agree on. (stackexchange.com)

With Finite-difference time-domain simulations we show that these dynamics differences between similarly sized. (lu.se)
With Finite-difference time-domain simulations we show that these dynamics differences between similarly sized antennas can be due to small lateral shape variations generally induced during the fabrication. (lu.se)

A Finite Element (FE) model which can precisely predict the actual dynamic responses of a bridge is necessary for accurate condition assessment and health monitoring purposes. (scsolutions.com)
This document is not intended to cover all aspects of developing a finite element model of radial deformation of a stent. (astm.org)
We provide a mathematical model of the problem and algorithms that are guaranteed to learn the underlying spatial configuration for a given class of environments with probability 1 - 5 in time polynomial in l/S and some measure of the structural complexity of the environment and the robot's ability to discern that structure. (aaai.org)
presented a coupling model for 1D finite strain primary-secondary consolidation [ 21 ]. (hindawi.com)
The FEA model results were compared to the experimental measured results. (cdc.gov)

Who are the leading innovators in finite element simulation for the technology industry? (verdict.co.uk)
In the last three years alone, there have been over 4.1 million patents filed and granted in the technology industry, according to GlobalData's report on Artificial intelligence in technology: finite element simulation . (verdict.co.uk)
Within the emerging innovation stage, GenAI for design, finite element simulation and deep reinforcement learning are disruptive technologies that are in the early stages of application and should be tracked closely. (verdict.co.uk)
According to GlobalData, there are 390 companies, spanning technology vendors, established technology companies, and up-and-coming start-ups engaged in the development and application of finite element simulation. (verdict.co.uk)

It is a conservative measure for stability evaluation. (sae.org)
As part of safety and stability studies at three underground mines in the United States, researchers installed earth pressure cells and embedment strain gauges in cemented rockfill to measure stress and strain changes as mining progressed and the rockfi. (cdc.gov)

Motivated by studies of low-density materials and fiber-dominated composites, we consider an elastic material whose strain energy function depends only on a finite number of directional strain measures, which correspond to the strains of material fibers in specific material directions. (asme.org)
Using these base tensors and their reciprocal tensors we develop a representation for the strain tensor in terms of six directional strain measures. (asme.org)
Finally, with reference to previous work, we discuss isotropy of specific functional forms of directional strain measures associated with up to 15 directions in space. (asme.org)
Many scholars carried in-depth researches on finite strain consolidation [ 16 - 18 ]. (hindawi.com)
However, the secondary consolidation behavior is not considered in the majority of existing finite strain consolidation theories. (hindawi.com)
So it is necessary to consider the secondary consolidation behavior in the study of finite strain consolidation. (hindawi.com)

For other important geometric measures of convex bodies, similar Minkowski problems have been studied in convex geometry, differential geometry, and partial differential equations. (degruyter.com)
The finite-size effects are then, for a lattice of geometry T × L3, given by an inverse polynomial in L where the first a priori possible term is of order 1/L2. (lu.se)

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n , in addition to Aleksandrov-Fenchel-Jessen's area measures. (degruyter.com)
However, what acts as the dual counterpart of the geometric measures in the Brunn-Minkowski theory was not clear until the work of Huang et al. (degruyter.com)

In this talk, we first discuss the influence of IP on common realized measures for integrated daily volatility from a theoretical perspective. (lu.se)

1.1 Purpose- This guide establishes recommendations and considerations for the development, verification, validation, and reporting of structural finite element models used in the evaluation of the performance of a metallic vascular stent design undergoing uniform radial loading. (astm.org)

This requires introducing QED on the lattice, and the associated finite-size effects are potentially large due to the absence of a mass gap. (lu.se)

J.F. Bonnans, G. Bonnet and J.-M. Mirebeau, Second order monotone finite differences discretization of linear anisotropic differential operators. (esaim-cocv.org)

Many of the important theorems of measure theory fail to hold in full generality. (ncatlab.org)
Signed and complex measures, Radon-Nikodym theorem, decomposition theorems. (sc.edu)

For any measurable space, the finite measures form a convex cone in the Banach space of signed measures with the total variation norm. (wikipedia.org)

Using NAA to measure 7 elements in a single specimen of hair, the coefficient of variation ranged from 5.92% in the case of Mn (mean concentration 1.65 ppm) to 15.7% in the case of Sb (mean concentration 0.18 ppm) (Cornelius, 1973). (cdc.gov)

When does $U\subset V$ induce maps on homology of finite rank? (stackexchange.com)

If our priority is to meet the essential needs for food, water, shelter, and other basics for all the world's people, then we must measure for those results so that we can get the outcomes we really want. (yesmagazine.org)
I imagine that by coming into contact of the two measuring devices by starting to share the same lightcone(s) (for instance, if measurement results are being compared on macro-level, the devices have a long time to exchange information by, for instance, EM radiation), that the measuring devices assimilate, among other information, also information about their respective measurements. (physicsforums.com)

In some cases, discrete variables can take on only a finite number of values. (stattrek.com)

Lewis Bowen , Measure conjugacy invariants for actions of countable sofic groups , J. Amer. Math. (ams.org)
finite only on a countable set ). (ncatlab.org)

M[/itex], then this set has to have null measure, because either the functions doesn't converge here or they're not finite. (physicsforums.com)

The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. (ams.org)

MAIN MEASURES: Annual per capita adjusted visit rate ratios (ARRs) comparing visit rates by LEP and EP persons to individual specialties, and to three categories of specialties: (1) primary care (internal or family medicine, geriatrics, general practice, or obstetrics/gynecology), (2) medical-subspecialties, or (3) surgical specialties. (bvsalud.org)

This means that the finite-size effects scale as an inverse polynomial in L rather than be- ing exponentially suppressed. (lu.se)

Different dynamics are, as expected, measured for antennas of different sizes. (lu.se)

Random Measures, Theory and Applications. (wikipedia.org)
Application diversity' measures the number of applications identified for each patent. (verdict.co.uk)

The finite measures are often easier to handle than more general measures and show a variety of different properties depending on the sets they are defined on. (wikipedia.org)
First, one doesn't really need a measure μ to talk about conditional expectations, only a measure class [μ], or equivalently, a σ-ideal N of negligible sets (alias sets of measure 0). (mathoverflow.net)
In particular, in the notation of the original post, one uses the morphism (X,B,N)→(X,F,N), where N is the σ-ideal of sets with ν-measure zero. (mathoverflow.net)
ideal of null sets), without equipping it with the measure of any other set. (ncatlab.org)
Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. (sc.edu)

This document provides specific guidance for verification and validation (V&V) of finite element (FE) models of vascular stents subjected to uniform radial loading using ASME V&V40 as the basis for developing and executing risk-informed V&V plans. (astm.org)

Twenty two Narada wireless sensing units were installed on the bridge to measure the ambient-induced vibration responses of the bridge. (scsolutions.com)
The modal frequencies and modal shapes were extracted from the measured vibration responses. (scsolutions.com)

This study has now rejected the hypothesis that the spectral complexity measures outperform those applied previously. (bvsalud.org)

Estimates of majority of the data considered were measures of reactivity, the uncertainty, as well as average values of the epidermal both purely chemical and in vitro cell based, whereas epidermal disposition kinetics parameters, were made by fitting to the time disposition was simply represented by the octanol-water course skin permeation data from individual skin donors. (cdc.gov)

Many already measure their "scope 1" direct emissions. (theconversation.com)
A smaller number measure "scope 2" emissions (from things such as electricity used by the firm). (theconversation.com)
A much smaller number measure " scope 3 " emissions (from sources they do not own, such as air travel, waste and water). (theconversation.com)

With the advent of a novel H1N1 influenza outbreak in spring 2009 and the expectation of a second wave during the 2009-2010 flu season, there has been considerable interest in the use of surgical masks (facemasks) and respirators as infection control measures. (cdc.gov)
The CDC guidance can be found in Interim Guidance on Infection Control Measures for 2009 H1N1 Influenza in Healthcare Settings . (cdc.gov)

If X {\displaystyle X} is Polish, then the set of all finite measures with the weak topology is Polish too. (wikipedia.org)

The most accurate way to diagnose osteoporosis is by measuring bone mass. (medscape.com)
Bone mineral density (BMD) is determined by measuring the amount of bone mineral (calcium hydroxyapatite) per unit volume of bone tissue. (medscape.com)

independently presented random normed modules and first applied them to the study of conditional risk measures. (hindawi.com)

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