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Добірка наукової літератури з теми "Kato square root problem"

Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Kato square root problem"

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Arlinskiĭ, Yury. "On the Kato square root problem." Journal of Mathematical Analysis and Applications 505, no. 2 (January 2022): 125501. http://dx.doi.org/10.1016/j.jmaa.2021.125501.

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2

Morris, Andrew J. "The Kato square root problem on submanifolds." Journal of the London Mathematical Society 86, no. 3 (August 10, 2012): 879–910. http://dx.doi.org/10.1112/jlms/jds039.

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3

Escauriaza, Luis, and Steve Hofmann. "Kato square root problem with unbounded leading coefficients." Proceedings of the American Mathematical Society 146, no. 12 (September 17, 2018): 5295–310. http://dx.doi.org/10.1090/proc/14224.

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4

AXELSSON, ANDREAS, STEPHEN KEITH, and ALAN McINTOSH. "THE KATO SQUARE ROOT PROBLEM FOR MIXED BOUNDARY VALUE PROBLEMS." Journal of the London Mathematical Society 74, no. 01 (August 2006): 113–30. http://dx.doi.org/10.1112/s0024610706022873.

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Bechtel, Sebastian, Moritz Egert, and Robert Haller-Dintelmann. "The Kato square root problem on locally uniform domains." Advances in Mathematics 375 (December 2020): 107410. http://dx.doi.org/10.1016/j.aim.2020.107410.

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6

Egert, Moritz, Robert Haller-Dintelmann, and Patrick Tolksdorf. "The Kato Square Root Problem for mixed boundary conditions." Journal of Functional Analysis 267, no. 5 (September 2014): 1419–61. http://dx.doi.org/10.1016/j.jfa.2014.06.003.

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7

Bandara, Lashi, and Alan McIntosh. "The Kato Square Root Problem on Vector Bundles with Generalised Bounded Geometry." Journal of Geometric Analysis 26, no. 1 (January 27, 2015): 428–62. http://dx.doi.org/10.1007/s12220-015-9557-y.

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8

Skubachevskii, A. L. "Elliptic differential‐difference operators with degeneration and the Kato square root problem." Mathematische Nachrichten 291, no. 17-18 (August 31, 2018): 2660–92. http://dx.doi.org/10.1002/mana.201700475.

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Zhang, Junqiang, Dachun Yang, and Sibei Yang. "Kato square root problem for degenerate elliptic operators on bounded Lipschitz domains." Journal of Differential Equations 353 (April 2023): 1–62. http://dx.doi.org/10.1016/j.jde.2022.12.039.

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Egert, M., R. Haller-Dintelmann, and P. Tolksdorf. "The Kato Square Root Problem follows from an extrapolation property of the Laplacian." Publicacions Matemàtiques 60 (July 1, 2016): 451–83. http://dx.doi.org/10.5565/publmat_60216_05.

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Дисертації з теми "Kato square root problem"

1

Ndikintum, Nfii Kangong. "A Special Inference Problem in Repeated Measures Design with Applications to Pulse Oximetry." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1177418766.

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Bandara, Lashi. "Geometry and the Kato square root problem." Phd thesis, 2013. http://hdl.handle.net/1885/10690.

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The primary focus of this thesis is to consider Kato square root problems for various divergence-form operators on manifolds. This is the study of perturbations of second-order differential operators by bounded, complex, measurable coefficients. In general, such operators are not self-adjoint but uniformly elliptic. The Kato square root problem is then to understand when the square root of such an operator, which exists due to uniform ellipticity, is comparable to its unperturbed counterpart. A remarkably adaptable operator-theoretic framework due to Axelsson, Keith and McIntosh sits in the background of this work. This framework allows us to take a powerful first-order perspective of the problems which we consider in a geometric setting. Through a well established procedure, we reduce these problems to the study of quadratic estimates. Under a set of natural conditions, we prove quadratic estimates for a class of operators on vector bundles over complete measure metric spaces. The first kind of estimates we prove are global, and we establish them on trivial vector bundles when the underlying measure grows at most polynomially. The second kind are local, and there, we allow the vector bundle to be non-trivial but bounded in an appropriate sense. Here, the measure is allowed to grow exponentially. An important consequence of obtaining quadratic estimates on measure metric spaces is that it allows us to consider subelliptic operators on Lie groups. The first-order perspective allows us to reduce the subelliptic problem to a fully elliptic one on a sub-bundle. As a consequence, we are able to solve a homogeneous Kato square root problem for perturbations of subelliptic operators on nilpotent Lie groups. For general Lie groups we solve a similar inhomogeneous problem. In the situation of complete Riemannian manifolds, we consider uniformly elliptic divergence-form operators arising from connections on vector bundles. Under a set of assumptions, we show that the Kato square root problem can be solved for such operators. As a consequence, we solve this problem on functions under the condition that the Ricci curvature and injectivity radius are bounded. Assuming an additional lower bound for the curvature endomorphism on forms, we solve a similar problem for perturbations of inhomogeneous Hodge-Dirac operators. A theorem for tensors is obtained by additionally assuming boundedness of a second-order Riesz transform. Motivated by the study of these Kato problems, where for technical reasons it is useful to know the density of compactly supported functions in the domains of operators, we study connections and their divergence on a vector bundle. Through a first-order formulation, we show that this density property holds for the domains of these operators if the metric and connection are compatible and the underlying manifold is complete. We also show that compactly supported functions are dense in the second-order Sobolev space on complete manifolds under the sole assumption that the Ricci curvature is bounded below, improving a result that previously required an additional lower bound on the injectivity radius.
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Bailey, Julian. "Schrodinger Operators and the Kato Square Root Problem." Phd thesis, 2020. http://hdl.handle.net/1885/198780.

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The general theme of this thesis is the harmonic analysis of Schr¨odinger operators and its applications. We will focus on two distinct but related open problems in this field. The first problem is the construction of potential dependent averaging operators and will be primarily considered in the first part of this thesis. Here, a Hardy-Littlewood type maximal operator adapted to the Schrodinger operator L := −∆ + |x| 2 and acting on L 2 (R n ) is constructed. This is achieved through the use of the Gaussian grid ∆γ 0 , constructed in [42] with the Ornstein-Uhlenbeck operator in mind. At the scale of this grid, the maximal operator will resemble the classical Hardy-Littlewood operator. At a larger scale, the constituent averaging operators of the maximal function are decomposed over the cubes from ∆γ 0 and weighted appropriately. Through this maximal function, a new class of weights is defined, A+ p , with the property that for any w ∈ A+ p the heat maximal operator associated with L is bounded from L p (w) to itself. This class contains any other known class that possesses this property and contains weights of exponential growth. In particular, it is strictly larger than Ap. The second problem that we consider is the Kato square root problem for divergence form elliptic operators with potential V : R n → C. This is the equivalence statement (L + V ) 1 2 u L2(Rn) ' k∇ukL2(Rn) + V 1 2 u L2(Rn) , where L + V := −div (A∇) + V and the perturbation A is an L ∞ complex matrix-valued function satisfying an ellipticity condition. One possible path to a solution for this problem is by proving square function estimates for perturbations of associated non-homogeneous Dirac-type operators. At present, there is no general method to obtain such square function estimates other than for potentials bounded both from above and below (cf. [10]). We develop such a method by adapting the homogeneous framework introduced by A. Axelsson, S. Keith and A. McIntosh in their seminal paper [11]. Two distinct approaches will be considered when adapting this framework. The second such approach will yield a satisfying solution to the potential dependent Kato problem for a large class of potentials. This class will include any potential V with range contained in some sector of angle ωV ∈ [0, π 2 ) and for which |V | belongs either to the reverse H¨older class RH2 in any dimension or L n 2 (R n ) for n > 4.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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Helfgott, Harald Andres. "Root numbers and the parity problem." Phd thesis, 2003. http://tel.archives-ouvertes.fr/tel-00010129.

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Let E be a one-parameter family of elliptic curves over a number field. It is natural to expect the average root number of the curves in the family to be zero. All known counterexamples to this folk conjecture occur for families obeying a certain degeneracy condition. We prove that the average root number is zero for a large class of families of elliptic curves of fairly general type. Furthermore, we show that any non-degenerate family E has average root number 0, provided that two classical arithmetical conjectures hold for two homogeneous polynomials with integral coefficients constructed explicitly in terms of E.
The first such conjecture -- commonly associated with Chowla -- asserts the equidistribution of the parity of the number of primes dividing the integers represented by a polynomial. We prove the conjecture for homogeneous polynomials of degree 3.
The second conjecture used states that any non-constant homogeneous polynomial yields to a square-free sieve. We sharpen the existing bounds on the known cases by a sieve refinement and a new approach combining height functions, sphere packings and sieve methods.
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6

McCarthy, Christabel. "Investigating the use of dasymetric techniques for assessing employment containment in Melbourne, Australia." Master's thesis, 2012. http://hdl.handle.net/10362/8307.

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Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.
This project studies employment containment in Melbourne, Australia. Employment containment is a measure of the proportion of people that work in a location close to their home. Recent urban planning policies in Melbourne have aimed to improve employment containment in the city’s suburbs. While there has been analysis of the rates at which people both live and work within broadly defined ‘local areas’, little work has been done to investigate employment containment using smaller and more uniform catchment areas as the unit of analysis. This research attempts such a finer scale analysis using dasymetric downscaling techniques. A regression modelling approach supported by land use data, alongside a binary dasymetric method, is used to develop fine scale estimates of employment distribution, while binary and populationdensity weighted methods are used to develop a fine scale estimate of working population distribution. For the employment distribution estimate, the Poisson model that distributed employment to employment-related land use classes produced the smallest error. However, the error produced by this model is still high. For the working population distribution estimate, the population-density weighted estimate is the more accurate of the approaches, and overall produced low error. For the employment containment analysis, a number of employment centres were randomly selected and an employment containment catchment has been derived from a 5 km2 commuting distance catchment. Commuting flows from an origin-destination matrix were areaweighted to estimate flows into the employment centre from the 5 km2 catchment. The method is found to be potentially useful; however inspecting the results of this employment containment calculation highlighted flaws in the current estimates that should be addressed before the measures can be used to further analyse employment containment in Melbourne. Improvements to this method would support urban strategic and transport planning analyses at a metropolitan-wide scale.
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Книги з теми "Kato square root problem"

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Auscher, Pascal. Square root problem for divergence operators and related topics. [Paris]: Société mathématique de France, 1998.

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Частини книг з теми "Kato square root problem"

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McIntosh, Alan. "The square root problem for elliptic operators a survey." In Lecture Notes in Mathematics, 122–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0084902.

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Zhang, Fangguo, and Ping Wang. "On Relationship of Computational Diffie-Hellman Problem and Computational Square-Root Exponent Problem." In Lecture Notes in Computer Science, 283–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20901-7_19.

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3

Egudo, R. R. "A Duality Theorem for a Fractional Multiobjective Problem with Square Root Terms." In Recent Developments in Mathematical Programming, 101–13. London: CRC Press, 2022. http://dx.doi.org/10.1201/9780429333439-7.

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"Chapter Eight. A Review of the Kato Square Root Problem." In Analysis of Heat Equations on Domains. (LMS-31), 253–64. Princeton University Press, 2009. http://dx.doi.org/10.1515/9781400826483.253.

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"Positive Operators. Square Root." In An Operator Theory Problem Book, 123–42. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813236264_0005.

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Tapley, Byron D., Bob E. Schutz, and George H. Born. "Square Root Solution Methods for the Orbit Determination Problem." In Statistical Orbit Determination, 285–386. Elsevier, 2004. http://dx.doi.org/10.1016/b978-012683630-1/50024-2.

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Van Loi, Nguyen, Tran Quoc Tuan, Tran Trung Kien, Tran Van Truong, and Tran Vu Hop. "Performance Evaluation of Radar Range-Bearing Centroid Processing Using Time Series Analysis." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2021. http://dx.doi.org/10.3233/faia210201.

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The paper deals with a problem of performance evaluation of the range-bearing centroid processing for a surveillance radar. First, we review several techniques for centroid processing that are Moving window estimator, Beam shape centroid estimator, Center of mass correlation and Recursive least-squares centroid estimator. Then we point out that the range root-mean-square error (RMSE) and bearing RMSE are not sufficient for performance evaluation of the range-bearing centroid processing. Further, a new parameter using time series analysis for evaluation of structural stability of the centroid processing is proposed. As an illustration, a test with data from an X-band coastal surveillance radar is given.
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Dhupia, Bhawna, and M. Usha Rani. "Assessment of Electric Consumption Forecast Using Machine Learning and Deep Learning Models for the Industrial Sector." In Advances in Wireless Technologies and Telecommunication, 206–18. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-7685-4.ch016.

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Power demand forecasting is one of the fields which is gaining popularity for researchers. Although machine learning models are being used for prediction in various fields, they need to upgrade to increase accuracy and stability. With the rapid development of AI technology, deep learning (DL) is being recommended by many authors in their studies. The core objective of the chapter is to employ the smart meter's data for energy forecasting in the industrial sector. In this chapter, the author will be implementing popular power demand forecasting models from machine learning and compare the results of the best-fitted machine learning (ML) model with a deep learning model, long short-term memory based on RNN (LSTM-RNN). RNN model has vanishing gradient issue, which slows down the training in the early layers of the network. LSTM-RNN is the advanced model which take care of vanishing gradient problem. The performance evaluation metric to compare the superiority of the model will be R2, mean square error (MSE), root means square error (RMSE), and mean absolute error (MAE).
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Aggarwal, Ritu, and Suneet Kumar. "Missing Value Imputation and Estimation Methods for Arrhythmia Feature Selection Classification Using Machine Learning Algorithms." In Machine Learning Methods for Engineering Application Development, 145–63. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9879815079180122010013.

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 Electrocardiogram signal analysis is very difficult to classify cardiac arrhythmia using machine learning methods. The ECG datasets normally come with multiple missing values. The reason for the missing values is the faults or distortion. When performing data mining, missing value imputation is the biggest task for data preprocessing. This problem could arise due to incomplete medical datasets if the incomplete missing values and cases were removed from the original database. To produce a good quality dataset for better analyzing the clinical trials, the suitable missing value imputation method is used. In this paper, we explore the different machine-learning techniques for the computed missing value in the electrocardiogram dataset. To estimate the missing imputation values, the collected data contains feature dimensions with their attributes. The experiments to compute the missing values in the dataset are carried out by using the four feature selection methods and imputation methods. The implemented results are shown by combined features using IG (information gain), GA (genetic algorithm) and the different machine learning classifiers such as NB (naïve bayes), KNN (K-nearest neighbor), MLP (Multilayer perception), and RF (Random forest). The GA (genetic algorithm) and IG (information gain) are the best suitable methods for obtaining the results on lower dimensional datasets with RMSE (Root mean square error. It efficiently calculates the best results for missing values. These four classifiers are used to analyze the impact of imputation methods. The best results for missing rate 10% to 40% are obtained by NB that is 0.657, 0.6541, 0.66, 0.657, and 0.657, as computed by RMSE (Root mean Square error). It means that error will efficiently reduced by naïve bayes classifier.
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Mansouri, Majdi, Hazem Numan Nounou, and Mohamed Numan Nounou. "Modeling and Monitoring of Chemical System." In Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics, 835–58. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9644-0.ch032.

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This chapter addresses the problem of time-varying nonlinear modeling and monitoring of a continuously stirred tank reactor (CSTR) process using state estimation techniques. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently the variational Bayesian filter (VBF). The objectives of this chapter are threefold. The first objective is to use the variational Bayesian filter with better proposal distribution for nonlinear states and parameters estimation. The second objective is to extend the state and parameter estimation techniques to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. The third objective is to apply the state estimation techniques EKF, PF and VBF for time-varying nonlinear modeling and monitoring of CSTR process. The estimation performance is evaluated on a synthetic example in terms of estimation accuracy, root mean square error and execution times.
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Тези доповідей конференцій з теми "Kato square root problem"

1

Ankishan, H., and F. Ari. "Square root unscented filter based FastSLAM approach for SLAM problem solution." In 2013 21st Signal Processing and Communications Applications Conference (SIU). IEEE, 2013. http://dx.doi.org/10.1109/siu.2013.6531206.

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Sutikno, Tole, Aiman Zakwan Jidin, Nik Rumzi Nik Idris, and Auzani Jidin. "A simple strategy to solve complicated square root problem in DTC for FPGA implementation." In 2010 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2010). IEEE, 2010. http://dx.doi.org/10.1109/isiea.2010.5679378.

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3

Ihn, Yong Seok, Sae Whan Park, and Ja Choon Koo. "Position Alignment of Micro Manipulator Using Root Mean Square Errors for Maskless Lithography System." In ASME 2013 Conference on Information Storage and Processing Systems. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/isps2013-2943.

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A precision optical exposure process of lithography has become one of the essential processes to manufacture and develop micro electro mechanical system (MEMS) devices, flat panel display (FPD), and semiconductor. For a typical exposure process for the lithography, a photomask that is often very expensive is required to generate patterns[1]. So it is very inefficient not only in terms of cost but also the time due to the reliance on the photomasks in development. The alternative solution is the maskless lithography system, which does not use photomasks since the patterns are generated by using a digital mirror device (DMD). The unit mirror of a digital mirror device has two kinds of status which are on and off, then the status of unit mirrors configures a pattern called point array method. The maskless lithography system can reduce the amount of work forces significantly and save money as well. However, the maskless lithography system has a critical drawback, which is a low throughput since the patterns are generated in a line. This is an intrinsic problem of point array method. So in most volume production processes of maskless lithography system, a number of optical heads are used in order to maximize throughput of the expositing process. And to guarantee the exposure quality, multiple numbers of optical heads should be accurately aligned to each other, and then the focal plane of each optical head is also well aligned with chuck.
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4

Anderson, Rodger O., and Fred T. Willett. "A Repair Alternative for Worn Square-Base Compressor Vanes." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-53484.

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Square base compressor vanes are a simple time-tested design and are in use in hundreds of large industrial gas turbines throughout the world. The square base of the vane fits inside a carrier slot machined into the compressor casing. Over time, the motion of the vane base, during operation and due to start-stop cycles, results in wear of both the vane base and the compressor casing. The classic solution to this wear problem is vane replacement and extensive repair of the casing either by welding or remachining and adding a patch ring. The square base compressor vane design is described, along with exemplary evidence of the wear problem. An alternative to the expensive repair is presented. The alternative approach addresses the root cause of the wear, i.e., the sliding motion at the vane base–casing interface. The vane contact is modeled with and without the solution to show, analytically, the benefit of the alternative approach. Successful field experience is also presented and discussed.
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5

Esmailzadeh, Mitra, and Aouni A. Lakis. "Turbulence-Induced Vibration Analysis of an Open Curved Thin Shell." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30383.

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A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of the structure in terms of the cross-spectral density of random pressure fields. The cross-spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis et al.
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Coquard, Typhaine, Bruno Camassel, and Marc Prat. "Evaporation in Capillary Tubes of Square Cross Section." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72452.

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Анотація:
Modeling of evaporation of a pure liquid within a capillary tube of circular cross section is a classic problem which has been the subject of many studies. Here we consider the case of tubes of polygonal cross section. This case leads to much greater evaporation rates owing to the liquid flow along the tube edges induced by the capillary forces. We concentrate on slow evaporation situations for which evaporation is controlled by mass transfer. Various evaporation regimes are distinguished depending on the competition between capillary, gravity and viscous forces. When the capillary forces are dominant, it is shown that the position of the bulk meniscus scales linearly with time (and not as the square root of time as in a capillary tube of circular cross section). The effect of viscous or gravity forces is to thin out the corner liquid fingers as the bulk meniscus recedes into the tube. This contributes to reduce the evaporation rate compared to the capillarity dominated regime. Then the case of faster evaporations inducing significant temperature variations is briefly discussed.
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7

Kozhemyak, Olesya A., and Oleg V. Stukach. "Reducing the Root-Mean-Square Error at Signal Restoration using Discrete and Random Changes in the Sampling Rate for the Compressed Sensing Problem." In 2021 International Siberian Conference on Control and Communications (SIBCON). IEEE, 2021. http://dx.doi.org/10.1109/sibcon50419.2021.9438937.

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8

Makaryan, Vahagn, Michael Sutton, Gurgen Chlingaryan, Davresh Hasanyan, and Xiaomin Deng. "Some Boundary Value Problems of Elastic Media Containing Rigid Inclusions Under Compressive Mechanical Loads." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11843.

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In this work we discuss some 2D boundary-value problems related to an elastic medium containing a thin rigid inclusion with general geometrical shape located in the interface between two separate elastic half-planes and subjected to compressive loading. Assuming perfect bonding between the inclusion and elastic medium, Fourier and Henkel integral transformation techniques are used to obtain the exact solution for the problem. Explicit forms are presented for arbitrary forms of thin inclusions, demonstrating that the tangent shear stress at the end-points of the inclusion has a square-root singularity. It is also shown that the normal stress has a logarithmic singularity when the end-points of the inclusion are approached from the inside of the inclusion and a square-root singularity when the end-points of the inclusion are approached from the outside of the inclusion. For special, extreme cases the solutions for anti-cracks are also presented.
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9

Yang, R. J., N. Wang, C. H. Tho, J. P. Bobineau, and B. P. Wang. "Metamodeling Development for Vehicle Frontal Impact Simulation." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21012.

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Abstract Response surface methods or metamodels are commonly used to approximate large engineering systems. This paper presents a new metric for evaluating a response surface method or a metamodeling technique. Five response surface methods are studied: Stepwise Regression, Moving Least Square, Kriging, Multiquadratic, and Adaptive and Interactive Modeling System. A real world frontal impact design problem is used as an example, which is a complex, highly nonlinear, transient, dynamic, large deformation finite element model. The optimal Latin Hypercube Sampling method is used to distribute the sampling points uniformly over the entire design space. The Root Mean Square Error is used as the error indicator to study the accuracy and convergence rate of the metamodels for this vehicle impact analysis. A hybrid approach/strategy for selecting the best metamodels of impact responses is proposed.
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10

Crepeau, John C., and Ali Siahpush. "Effects of Internal Heat Generation on Solidification." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72079.

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We present solutions for solid-liquid phase change in materials that generate internal heat. This problem is solved for both cylindrical and semi-infinite geometries. The analysis assumes a temperature profile in the solid phase and constant temperature boundary conditions on the exposed surfaces. We derive differential equations governing the solidification thickness for both geometries as functions of the Stefan number and the internal heat generation (IHG). For the cylindrical geometry, the solidification layer obtains a steady-state value which is related to the inverse of the square root of the IHG. The solutions to the semi-infinite geometry problem show that when the surface is cooled to below the freezing point, a solidification layer forms along the edge and begins to grow until it reaches a maximum, then begins remelt.
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