Relevant bibliographies by topics / R-functions method

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'R-functions method'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "R-functions method"

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Basarab, Mikhail, Alain Giani, and Philippe Combette. "Thermal Accelerometer Simulation by the R‑Functions Method." Applied Sciences 10, no. 23 (November 25, 2020): 8373. http://dx.doi.org/10.3390/app10238373.

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As well as many modern devices, thermal accelerometers (TAs) need a sophisticated mathematical simulation to find the ways for their performance optimization. In the paper, a novel approach for solving computational fluid dynamics (CFD) problems in the TA’s cavity is proposed (MQ-RFM), which is based on the combined use of Rvachev’s R-functions method (RFM) and the Galerkin technique with multiquadric (MQ) radial basis functions (RBFs). The semi-analytical RFM takes an intermediate position between traditional analytical approaches and numerical methods, such as the finite-element method (FEM), belonging to the family of the so-called meshless techniques which became popular in the last decades in solving various CFD problems in complex-shaped cavities. Mathematical simulation of TA by using the MQ-RFM was carried out with the purpose to simulate the temperature response of the device and to study and improve its performance. The results of numerical experiments were compared with well-known analytical and numerical benchmark solutions for the circular annulus geometry and it demonstrated the effectiveness of the MQ-RFM for solving the convective heat-transfer problem in the TA’s cavity. The use of solution structures allows one to take a relatively small number of expansion terms to achieve an appropriate accuracy of the approximate solution satisfying at the same time the given boundary conditions exactly. The application of the MQ-RFM gives the possibility to obtain semi-analytical solutions to the diffusion-convection problems and to identify the main thermal characteristics of the TA, that allows one to improve the device performance.
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Ranenko, A. A., and T. I. Sheiko. "Method of R-functions in problems with natural boundary conditions." Journal of Soviet Mathematics 66, no. 1 (August 1993): 2097–102. http://dx.doi.org/10.1007/bf01097401.

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Miyajima, Keiichi, Takahiro Kato, and Yasunari Shidama. "Riemann Integral of Functions R into C." Formalized Mathematics 18, no. 4 (January 1, 2010): 201–6. http://dx.doi.org/10.2478/v10037-010-0024-8.

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Riemann Integral of Functions R into C In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
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Rvachev, V. L., and T. I. Sheiko. "R-Functions in Boundary Value Problems in Mechanics." Applied Mechanics Reviews 48, no. 4 (April 1, 1995): 151–88. http://dx.doi.org/10.1115/1.3005099.

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Described are the concepts and applications of the R-functions theory in continuum mechanics boundary value problems which model fields of different physical natures. With R-functions there appears the possibility of creating a constructive mathematical tool which incorporates the capabilities of classical continuous analysis and logic algebra. This allows one to overcome the main obstacle which hinders the use of variational methods when solving boundary value problems in domains of complex shape with complex boundary conditions, this obstacle being connected with the construction of so-called coordinate sequences. In contrast to widely used methods of the network type (finite difference, finite and boundary elements), in the R-functions method all the geometric information present in the boundary value problem statement is reduced to analytical form, which allows one to search for a solution in the form of formulae called solution structures containing some indefinite functional components. A method of constructing solution structures satisfying the required conditions of completeness has been developed. The structural formulae include the left-hand sides of the normalized equations of the boundaries of the domains or their regions being considered, thus allowing one to change the solution structure expeditiously when changing the geometric shape. Given in the work is a definition of the basic class of R-functions, solution with their help of the inverse problem of analytical geometry (construction of equations of specified configurations); generalization of the Taylor-Hermite formulae for functional spaces in which points are represented by lines and surfaces; and construction of solution structures of some types of boundary value problems. Shown are the solutions of a number of concrete problems in these application fields with the use of the RL language and POLYE system.
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Chrapoński, Jacek, Marian Maliński, Janusz Szala, and Jan Cwajna. "FGM Structure Characterization by Distance Functions and Systematic Scanning Method." Materials Science Forum 567-568 (December 2007): 153–56. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.153.

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The distance functions such as G(r), K(r), H(r), g(r) and systematic scanning method connected with variance analysis have been used for quantitative characterization of functionally gradient materials structures. The methods have been tested on computer generated 3D model polycrystalline structures with diverse type of gradient function. Usefulness of the presented methods for quantitative description of FGM structures has been evaluated.
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Torres-Hernandez, A., F. Brambila-Paz, U. Iturrarán-Viveros, and R. Caballero-Cruz. "Fractional Newton–Raphson Method Accelerated with Aitken’s Method." Axioms 10, no. 2 (March 31, 2021): 47. http://dx.doi.org/10.3390/axioms10020047.

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In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order α of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.
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Gudmundsson, Sigmundur, and Marko Sobak. "Proper r-harmonic functions from Riemannian manifolds." Annals of Global Analysis and Geometry 57, no. 1 (December 10, 2019): 217–23. http://dx.doi.org/10.1007/s10455-019-09696-3.

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AbstractWe introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups $$\mathbf{SO }(n)$$SO(n), $$\mathbf{SU }(n)$$SU(n), $$\mathbf{Sp }(n)$$Sp(n), $$\mathbf{SL }_{n}({\mathbb {R}})$$SLn(R), $$\mathbf{Sp }(n,{\mathbb {R}})$$Sp(n,R), $$\mathbf{SU }(p,q)$$SU(p,q), $$\mathbf{SO }(p,q)$$SO(p,q), $$\mathbf{Sp }(p,q)$$Sp(p,q), $$\mathbf{SO }^*(2n)$$SO∗(2n) and $$\mathbf{SU }^*(2n)$$SU∗(2n).
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Avramov, K. V. "Nonlinear vibrations of circular plates with notches. Method of R-functions." Journal of Mathematical Sciences 170, no. 6 (October 14, 2010): 708–20. http://dx.doi.org/10.1007/s10958-010-0115-7.

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Stetsyuk, P., V. Stovba, and A. Suprun. "B-FORM OF THE DAVIDON–FLETCHER–POWELL METHOD." Journal of Numerical and Applied Mathematics, no. 2 (136) (2021): 93–110. http://dx.doi.org/10.17721/2706-9699.2021.2.08.

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A special form (B-form) of methods of Quasi-Newton type is discussed, which makes it easy to interpret these methods as gradient in appropriately transformed argument space. B-form of the Davidon–Fletcher–Powell method is given and compared with r-algorithms. To minimize smooth convex functions, a gradient method with space transformation is built, combining properties of both quasi-Newtonian methods and r-algorithms. Possible schemes of this type of methods for minimizing non-smooth convex functions are discussed.
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Bray, William O. "TRANSPLANTATION FORMULAE AND HADAMARD'S METHOD OF DESCENT." Proceedings of the Edinburgh Mathematical Society 50, no. 2 (May 17, 2007): 277–92. http://dx.doi.org/10.1017/s0013091505000933.

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AbstractWe define a partial Radon transform mapping functions on $\mathbb{R}^{n+l}$ to functions on $\mathbb{R}^{n}$ which intertwines the Laplace operator on the two spaces. As a consequence, transplantation formulae relating the radial eigenfunctions of the Laplacian on Euclidean spaces of different dimensions are obtained. Our formulae provide a geometric interpretation of integral formulae for Bessel functions of Abel type, which are found useful in potential theory. The formulae portray a view of Hadamard's method of descent within the realm of harmonic analysis, allowing the transplant of local problems from even dimensions to odd dimensions and unifying the techniques of several authors.
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Dissertations / Theses on the topic "R-functions method"

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Awrejcewicz, Jan, Lidiya Kurpa, and Olga Mazur. "Stability investigation of nonlinear vibrations of plates by R-functions method." Thesis, Wydawnictwo Politechniki Łódzkiej, 2007. http://repository.kpi.kharkov.ua/handle/KhPI-Press/37159.

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The parametric vibrations of plates with cutouts subjected to in-plane periodic and compressive loads, are studied. The proposed approach is based on R-functions method and the classical variational approach. The influence of cutouts parameters, as well as static factors of load on stability regions and nonlinear vibrations are investigated.
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Kurpa, Lidiya, Olga Mazur, and Igor Tsukanov. "Application of R-Functions Theory to Study Parametric Vibrations and Dynamical Stability of Laminated Plates." Thesis, Точка, 2013. http://repository.kpi.kharkov.ua/handle/KhPI-Press/37087.

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The problem of nonlinear parametric vibrations and stability analysis of the symmetric laminated plates is considered. The proposed method is based on multimode approximation of displacements and solving series auxiliary linear tasks. The main feature of the work is the application of the R-functions theory, which allows investigating parametric vibrations of plates with complex shape and different boundary conditions.
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Kurpa, Lidiya, and T. Shmatko. "Investigation of Geometrically Nonlinear Vibrations of Laminated Shallow Shells with Layers of Variable Thickness by Meshless Approach." Thesis, Точка, 2013. http://repository.kpi.kharkov.ua/handle/KhPI-Press/37086.

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Geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness are studied. Nonlinear equations of motion for shells based on the first order shear deformation and classical shells theories are considered. In order to solve this problem we use the numerically-analytical method proposed in work [1]. Accordingly to this approach the initial problem is reduced to consequences of some linear problems including linear vibrations problem, special elasticity ones and nonlinear system of ordinary differential equations in time. The linear problems are solved by the variational Ritz’ method and Bubnov-Galerkin procedure combined with the R-functions theory [2]. To construct the basic functions that satisfy all boundary conditions in case of simply-supported shells we propose new solutions structures. The proposed method is used to solve both test problems and new ones.
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Awrejcewicz, Jan, Lidiya Kurpa, and Olga Mazur. "Investigation of the parametric vibration of the orthotropic plates subjected to periodic in plane forces by multi-modal approximation and R-functions method." Thesis, NTU "KhPI", 2010. http://repository.kpi.kharkov.ua/handle/KhPI-Press/37138.

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The original method of studying parametric vibrations of orthotropic plate with complex shape is proposed. Suggested approach is based on combined application of variational methods and the R-functions theory. Using the proposed method and developed software the regular and chaotic regimes of T-shaped plate are analyzed.
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Mejia, Humberto. "Modeling of a Heat-Induced Buckling of Plates Using the Mesh-free Method." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1512.

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In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.
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Drake, David M. "Method for Identifying Resting State Networks following Probabilistic Independent Component Analysis." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1416231546.

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Nylén, Erik. "An application portfolio management method - for implementation at SCANIA CV AB." Thesis, KTH, Industriella informations- och styrsystem, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-81364.

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Information Technology (IT) has become a vital tool for most industrial businesses and Scania CV AB is no exception. As the importance of IT generally has increased, the usage and number of applications has grown as well. Applications are substantial assets for an organization that is heavily supported by IT. Consequently, a way of managing applications efficiently and sustaining the costs of applications rather low ? doing more with less ? is required. In addition it is also important, from a business perspective, that applications as part of IT are aligned with business strategies and goals. Application Portfolio Management (APM) is a practice and a business-centric activity aimed to allocate IT resources to support business objectives and strategies; it helps determining the impact of applications and the relative importance of each application in the portfolio to the business. APM attempts to justify and measure the financial benefits of each application relative to the costs of the applications? maintenance and operations. Performing APM successfully is nevertheless a complicated issue, and something that many businesses are challenged with on a daily basis. New applications are constantly and regularly added, downloaded, purchased or selfdeveloped ? too often without any further control. In order to regain the control of the software that automates the business, and ensuring that the applications adds value and reliability to the company, Scania CV AB requires a rigorous and comprehensive method for an APM approach. In this master thesis together with Camilla Palomeques?s thesis1, such a method is provided. These two theses also offer a suggestion on how to proceed with the APM effort at Scania CV AB.
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Darbeheshti, Neda. "Modification of the least-squares collocation method for non-stationary gravity field modelling." Curtin University of Technology, Department of Spatial Sciences, 2009. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=120241.

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Geodesy deals with the accurate analysis of spatial and temporal variations in the geometry and physics of the Earth at local and global scales. In geodesy, least-squares collocation (LSC) is a bridge between the physical and statistical understanding of different functionals of the gravitational field of the Earth. This thesis specifically focuses on the [incorrect] implicit LSC assumptions of isotropy and homogeneity that create limitations on the application of LSC in non-stationary gravity field modeling. In particular, the work seeks to derive expressions for local and global analytical covariance functions that account for the anisotropy and heterogeneity of the Earth's gravity field.
Standard LSC assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing, e.g., of the gravity field in mountains and under-smoothing in great plains. The kernel convolution method from spatial statistics is introduced for non-stationary covariance structures, and its advantage in dealing with non-stationarity in geodetic data is demonstrated.
Tests of the new non-stationary solutions were performed over the Darling Fault, Western Australia, where the anomalous gravity field is anisotropic and non-stationary. Stationary and non-stationary covariance functions are compared in 2D LSC to the empirical example of gravity anomaly interpolation. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation. Both non-stationarity of mean and covariance are considered in planar geoid determination by LSC to test how differently non-stationarity of mean and covariance affects the LSC result compared with GPS-levelling points in this area. Non-stationarity of the mean was not very considerable in this case, but non-stationary covariances were very effective when optimising the gravimetric quasigeoid to agree with the geometric quasigeoid.
In addition, the importance of the choice of the parameters of the non-stationary covariance functions within a Bayesian framework and the improvement of the new method for different functionals on the globe are pointed out.
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Thomas, Armin W. Verfasser], Hauke R. [Akademischer Betreuer] Heekeren, Klaus-Robert [Gutachter] [Akademischer Betreuer] [Müller, Hauke R. [Gutachter] Heekeren, and Russell A. [Gutachter] Poldrack. "Machine learning methods for modeling gaze allocation in simple choice behavior and functional neuroimaging data on the level of the individual / Armin W. Thomas ; Gutachter: Klaus-Robert Müller, Hauke R. Heekeren, Russell A. Poldrack ; Klaus-Robert Müller, Hauke R. Heekeren." Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1223981657/34.

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Thomas, Armin W. [Verfasser], Hauke R. Akademischer Betreuer] Heekeren, Klaus-Robert [Gutachter] [Akademischer Betreuer] [Müller, Hauke R. [Gutachter] Heekeren, and Russell A. [Gutachter] Poldrack. "Machine learning methods for modeling gaze allocation in simple choice behavior and functional neuroimaging data on the level of the individual / Armin W. Thomas ; Gutachter: Klaus-Robert Müller, Hauke R. Heekeren, Russell A. Poldrack ; Klaus-Robert Müller, Hauke R. Heekeren." Berlin : Technische Universität Berlin, 2020. http://nbn-resolving.de/urn:nbn:de:101:1-2020122301024292024902.

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Books on the topic "R-functions method"

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Hodges, John R. Cognitive Assessment for Clinicians. Oxford University Press, 2013. http://dx.doi.org/10.1093/med/9780192629760.001.0001.

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This resource aims to incorporate the enormous advances over the last decade in our understanding of cognitive function into clinical practice, particularly the aspects of memory, language and attention. These advances in theory provide a practical approach to cognitive valuation at the bedside, based on methods developed at the Cambridge clinic over the past 15 years. Designed primarily for neurologists, psychiatrists and geriatricians in training who require a practical guide to assessing higher mental function, the resource will also be of interest to clinical psychologists. In this second edition, John Hodges has substantially re-organised and expanded on the original edition. It includes a new chapter devoted to the Revised Version of the Addenbrooke's Cognitive Examination (ACE-R), with a description of its uses and limitations along with normative data. Given the importance of the early detection of dementia, a chapter is dedicated to this topic that draws on advances over the past decade. Several new illustrative case histories have also been added and all of the case descriptions have been orientated around the use of the ACE-R in clinical practice.
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Láruson, Áki Jarl, and Floyd Allan Reed. Population Genetics with R. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198829539.001.0001.

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Population genetics is an inherently quantitative discipline. Because the focus of population genetics studies is usually on abstract concepts like the frequencies of genetic variants over time, it can at first glance be difficult to conceptualize and appropriately visualize. As more and more quantitative models and methods have become established in the discipline, it has become necessary for people just entering the field to quickly develop a good understanding of the many layers of complex approaches, so as to correctly interpret even basic results. An unfortunate side effect of the widespread implementation of ready-to-use quantitative software packages is that some facets of analysis can become rote, which at best might lead to implementation without the full understanding of the user and at worst, inappropriate application leading to misguided conclusions. In this book a “learning by doing” approach is employed to encourage readers to begin developing an intuitive understanding of population genetics concepts. The analytical software R, which has increasingly been the program of choice for early exposure to basic statistical programming, is freely available online, has cross-platform compatibility (Windows, Mac, and Linux all support distributions of R), and offers the potential for hands-on implementation by the students, in addition to using pre-packaged functions.
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Book chapters on the topic "R-functions method"

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Detka, Marcin, and Czesław Cichoń. "Application of R-Functions Method and Parallel Computations to the Solution of 2D Elliptic Boundary Value Problems." In Computational Science – ICCS 2008, 1022–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-69384-0_107.

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Quicke, Donald, Buntika A. Butcher, and Rachel Kruft Welton. "Principal components analysis." In Practical R for biologists: an introduction, 194–99. Wallingford: CABI, 2021. http://dx.doi.org/10.1079/9781789245349.0194.

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Abstract This chapter focuses on how to conduct a principal components analysis. To conduct principal components analysis, R has two similar built-in functions prcomp and princomp in the default stats package. Other implementations can be found in various downloadable packages, e.g. the function PCA from the package FactoMineR, the function dudi.pca from the package ade4 and the function acp from the package amap. The functions prcomp and princomp employ different calculation methods but in practice the results they return will be almost identical.
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Quicke, Donald, Buntika A. Butcher, and Rachel Kruft Welton. "Principal components analysis." In Practical R for biologists: an introduction, 194–99. Wallingford: CABI, 2021. http://dx.doi.org/10.1079/9781789245349.0017.

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Abstract This chapter focuses on how to conduct a principal components analysis. To conduct principal components analysis, R has two similar built-in functions prcomp and princomp in the default stats package. Other implementations can be found in various downloadable packages, e.g. the function PCA from the package FactoMineR, the function dudi.pca from the package ade4 and the function acp from the package amap. The functions prcomp and princomp employ different calculation methods but in practice the results they return will be almost identical.
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Swenson, Nathan G. "Comparative Methods and Phylogenetic Signal." In Functional and Phylogenetic Ecology in R, 147–71. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9542-0_7.

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Poterasu, V. F., and N. Mihalache. "Brittle Fracture Materials by BEM and R-Functions." In Boundary Element Methods, 298–307. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-06153-4_33.

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Hair, Joseph F., G. Tomas M. Hult, Christian M. Ringle, Marko Sarstedt, Nicholas P. Danks, and Soumya Ray. "Overview of R and RStudio." In Classroom Companion: Business, 31–47. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80519-7_2.

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AbstractComputational statistics is now an increasingly popular method of analysis for researchers that combines a vast array of algorithms, statistical methods, and the power of functional coding. The R programming language, in particular, has benefitted from this development alongside of traditional graphical user interface (GUI) software. Today, it has become the language of choice for empirical researchers. In this chapter, we introduce the R programming language as well as its popular development environment in the form of RStudio. We walk the reader through downloading both the R language and the RStudio integrated development environment (IDE). Then, we discuss the software layout and demonstrate how to interact with the software. Finally, we address creating and managing R projects and scripts, gaining access to documentation and help via various sources. This chapter is not intended as a tutorial on the writing of code in the R programming language. We do, however, provide useful open-source resources for learning R, which can be accessed from the R console RStudio environment.
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Anarova, Sh A., and Z. E. Ibrohimova. "Methods of Constructing Equations for Objects of Fractal Geometry and R-Function Method." In Intelligent Human Computer Interaction, 425–36. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-98404-5_40.

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Cecot, W., and J. Orkisz. "On Coupling of the Boundary Element and R-Function Methods." In Mathematical and Computational Aspects, 435–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-21908-9_28.

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Moffett, Peter. "Fragment Complementation and Co-immunoprecipitation Assays for Understanding R Protein Structure and Function." In Methods in Molecular Biology, 9–20. Totowa, NJ: Humana Press, 2011. http://dx.doi.org/10.1007/978-1-61737-998-7_2.

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Kleine, Liliana López, Rosa Montaño, and Francisco Torres-Avilés. "Classification and Clustering on Microarray Data for Gene Functional Prediction Using R." In Methods in Molecular Biology, 41–54. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/7651_2015_240.

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Conference papers on the topic "R-functions method"

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Basarab, M. A., and O. V. Kravchenko. "Solving magnetohydrodynamic free convection problems in complex-shaped cavities by the R-functions method." In 2017 Progress in Electromagnetics Research Symposium - Fall (PIERS - FALL). IEEE, 2017. http://dx.doi.org/10.1109/piers-fall.2017.8293167.

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Basarab, M. A., N. S. Konnova, D. A. Basarab, and O. V. Kravchenko. "Numerical Simulation of Magnetohydrodynamic Blood Flow through Stenosed Arteries Using the R-functions Method." In 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring). IEEE, 2019. http://dx.doi.org/10.1109/piers-spring46901.2019.9017841.

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Basarab, M. "Neural Network Approach for Solving Boundary Value Problems of Electrodynamics by the R-Functions Method." In 2007 International Kharkiv Symposium Physics and Engrg. of Millimeter and Sub-Millimeter Waves (MSMW). IEEE, 2007. http://dx.doi.org/10.1109/msmw.2007.4294865.

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Lopez, P., and Y. Bayazitoglu. "A Note on Modeling of Nano-Scale Thermal Flow via the Lattice Boltzmann Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89923.

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Lattice Boltzmann (LB) method models have been demonstrated to provide an accurate representation of the flow characteristics in rarefied flows. Conditions in such flows are characterized by the Knudsen number (Kn), defined as the ratio between the gas molecular Mean Free Path ( MFP, λ) and the device characteristic length (L). As the Knudsen number increases, the behavior of the flow near the walls is increasingly dominated by interactions between the gas molecules and the solid surface. Due to this, linear constitutive relations for shear stress and heat flux, which are assumed in the Navier-Stokes-Fourier (NSF) system of equations, are not valid within the Knudsen Layer (KL). Fig. 1 illustrates the characteristics of the velocity field within the Knudsen layer in a shear-driven flow. It is easily observed that although the NSF equations with slip flow boundary conditions (represented by dashed line) can predict the velocity profile in the bulk flow region, they fail to capture the flow characteristics inside the Knudsen layer. Slip flow boundary conditions have also been derived using the integral transform technique [1]. Various methods have been explored to extend the applicability of LB models to higher Knudsen number flows, including using higher order velocity sets, and using wall-distance functions to capture the effect of the walls on the mean free path by incorporating such functions on the determination of the local relaxation parameters. In this study, a high order velocity model which contains a two-dimensional, thirteen velocity direction set (e.g., D2Q13), as shown in Fig. 2, is used as the basis of the current LB model. The LB model consists of two independent distribution functions to simulate the density and temperature fields, while the Diffuse Scattering Boundary Condition (DSBC) method is used to simulate the fluid interaction with the walls. To further improve the characterization of transition flow conditions expected in nano-scale heat transfer, we explored the implementation of two wall-distance functions, derived recently based on an integrated form of a probability distribution function, to the high-order LB model. These functions are used to determine the effective mean free path values throughout the height of the micro/nano-channel, and the resulting effect is first normalized and then used to determine local relaxation times for both momentum and energy using a relationship based on the local Knudsen number. The two wall-distance functions are based on integral forms of 1) the classical probability distribution function, ψ(r) = λ0−1e−r/λ0, derived by Arlemark et al [2], in which λ0represents the reference gas mean free path, and 2) a Power-Law probability distribution function, derived by Dongari et al [3]. Thus, the probability that a molecule travels a distance between r and r+dr between two successive collisions is equal to ψ(r)dr. The general form of the integral of the two functions used can be described by ψ(r) = C − f(r), where f(r) represents the base function (exponential or Power Law), and C is set to 1 so that the probability that a molecule will travel a distance r+dr without a collision ranges from zero to 1. The performance of the present LB model coupled with the implementation of the two wall-distance functions is tested using two classical flow cases. The first case considered is that of isothermal, shear-driven Couette flow between two parallel, horizontal plates separated by a distance H, moving in opposite directions at a speed of U0. Fig. 3 shows the normalized velocity profiles across the micro-channel height for various Knudsen numbers in the transition flow regime based on our LB models as compared to data based on the Linearized Boltzmann equation [4]. The results show that our two LB models provide results that are in excellent agreement with the reference data up to the high end of the transition flow regime, with Knudsen numbers greater than 1. The second case is rarefied Fourier flow within horizontal, parallel plates, with the plates being stationary and set to a constant temperature (TTop > TBottom), and the Prandtl number is set to 0.67 to match the reference data based on the Direct Simulation Monte Carlo (DSMC) method [5]. Fig. 4 shows the normalized temperature profiles across the microchannel height for various Knudsen numbers in the slip/transition How regime. For the entire Knudsen number range studied, our two LB models provide temperature profiles that are in excellent agreement with the non-linear profile seen in the reference data. The results obtained show that the effective MFP relationship based on the exponential function improves the results obtained with the high order LB model for both shear-driven and Fourier flows up to Kn∼1. The results also show that the effective MFP relationship based on the Power Law distribution function greatly enhances the results obtained with the high order LB model for the two cases addressed, up to Kn∼3. In conclusion, the resulting LB models represent an effective tool in modeling non-equilibrium gas flows expected within micro/nano-scale devices.
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Basarab, M., and M. Ivoilov. "Application of Genetic Algorithms for Solving Problems of VLSI Blocks Optimum Placement by the R-Functions Method." In 2007 International Kharkiv Symposium Physics and Engrg. of Millimeter and Sub-Millimeter Waves (MSMW). IEEE, 2007. http://dx.doi.org/10.1109/msmw.2007.4294880.

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DasNeogi, Protyusha, Elizabeth Cudney, Akim Adekpedjou, and Rodney Kestle. "Comparing the Predictive Ability of T-Method and Cobb-Douglas Production Function for Warranty Data." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12668.

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Predictive models are used in an attempt to anticipate future transitions, mitigate losses, and maximize economic gains. In today’s market, companies look for high reliability and quality of products due to great market competition. Hence warranty data is of considerable interest to companies. Warranty shows the ability of a system or component to perform its functions within a given customer usage. Many statistical and data mining methods are available to predict the warranty data. This study focuses on analyzing the predictive efficiency of the T-method and Cobb-Douglas production function on warranty data by comparing their prediction capability. The T-method, developed by Genichi Taguchi, is founded upon the fundamentals of the Taguchi System of Quality Engineering which is used to calculate an overall prediction based on signal-to-noise ratio. Using this method, the required parameters are calculated to obtain an overall estimate of the true value of the output for each signal member. The Cobb-Douglas production function is then applied on the same dataset. In economics, the Cobb-Douglas functional form of production function is widely used to represent the relationship of the output to inputs. The strength of the relationship is then assessed using the R-squared and adjusted R-squared values.
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Tolok, Alexey, and Pavel Petukhov. "Development of a Gradient Descent Algorithm for Pathway Routing Based on Functional-Voxel Modeling." In 31th International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/graphicon-2021-3027-689-696.

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This paper considers a pathfinding algorithm using the gradient method for functional-voxel modeling problems. The basic principles of constructing gradient lines based on the functional voxel model are investigated. The tool to describe the scene with obstacles is the mathematical apparatus of R-functions. To solve the problem of pathfinding in a weakly deterministic environment, we propose an algorithm that is based on the use of: gradient method analyzing the color palette of images of local features of the function; mathematical apparatus of R- functions describing the topography of the solution surface at the current moment in time. An algorithm of target control that solves the problem of getting out of possible "trapped objects" is considered. For this, the principle of changing the position of the target was developed to control the gradient direction.
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Lorenzo, Carl F., Rachid Malti, and Tom T. Hartley. "The Solution of Linear Fractional Differential Equations Using the Fractional Meta-Trigonometric Functions." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47395.

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A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.
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Kravchenko, Victor F., Aleksey V. Yurin, Börje Nilsson, Louis Fishman, Anders Karlsson, and Sven Nordebo. "The Selection of Basis Functions Systems for Determination of Cutoff Frequency of Waveguides and Resonators of Complex Shape with the Help of R-functions Method." In MATHEMATICAL MODELING OF WAVE PHENOMENA: 3rd Conference on Mathematical Modeling of Wave Phenomena, 20th Nordic Conference on Radio Science and Communications. AIP, 2009. http://dx.doi.org/10.1063/1.3117095.

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Bodnar, Yurii, Mykola Syniekop, and Adam Podhorecki. "Consideration of heat transfer speed while measuring two-dimensional thermal stresses by means of the method of R-functions." In SCIENTIFIC SESSION ON APPLIED MECHANICS X: Proceedings of the 10th International Conference on Applied Mechanics. Author(s), 2019. http://dx.doi.org/10.1063/1.5091868.

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Reports on the topic "R-functions method"

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Lichter, Amnon, Gopi K. Podila, and Maria R. Davis. Identification of Genetic Determinants that Facilitate Development of B. cinerea at Low Temperature and its Postharvest Pathogenicity. United States Department of Agriculture, March 2011. http://dx.doi.org/10.32747/2011.7592641.bard.

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Botrytis cinerea is the postharvest pathogen of many agricultural produce with table grapes, strawberries and tomatoes as major targets. The high efficiency with which B. cinerea causes disease on these produce during storage is attributed in part due to its exceptional ability to develop at very low temperature. Our major goal was to understand the genetic determinants which enable it to develop at low temperature. The specific research objectives were: 1. Identify expression pattern of genes in a coldenriched cDNA library. 2. Identify B. cinerea orthologs of cold-induced genes 3. Profile protein expression and secretion at low temperature on strawberry and grape supplemented media. 4. Test novel methods for the functional analysis of coldresponsive genes. Objective 1 was modified during the research because a microarray platform became available and it allowed us to probe the whole set of candidate genes according to the sequence of 2 strains of the fungus, BO5.10 and T4. The results of this experiment allowed us to validate some of our earlier observations which referred to genes which were the product of a SSH suppression-subtraction library. Before the microarray became available during 2008 we also analyzed the expression of 15 orthologs of cold-induced genes and some of these results were also validated by the microarray experiment. One of our goals was also to perform functional analysis of cold-induced genes. This goal was hampered for 3 years because current methodology for transformation with ‘protoplasts’ failed to deliver knockouts of bacteriordopsin-like (bR) gene which was our primary target for functional analysis. Consequently, we developed 2 alternative transformation platforms, one which involves an air-gun based technique and another which involves DNA injection into sclerotia. Both techniques show great promise and have been validated using different constructs. This contribution is likely to serve the scientific community in the near future. Using these technologies we generated gene knockout constructs of 2 genes and have tested there effect on survival of the fungus at low temperature. With reference to the bR genes our results show that it has a significant effect on mycelial growth of the B. cinerea and the mutants have retarded development at extreme conditions of ionic stress, osmotic stress and low temperature. Another gene of unknown function, HP1 is still under analysis. An ortholog of the yeast cold-induced gene, CCH1 which encodes a calcium tunnel and was shown to be cold-induced in B. cinerea was recently cloned and used to complement yeast mutants and rescue them from cold-sensitivity. One of the significant findings of the microarray study involves a T2 ribonuclease which was validated to be cold-induced by qPCR analysis. This and other genes will serve for future studies. In the frame of the study we also screened a population of 631 natural B. cinerea isolates for development at low temperature and have identified several strains with much higher and lower capacity to develop at low temperature. These strains are likely to be used in the future as candidates for further functional analysis. The major conclusions from the above research point to specific targets of cold-induced genes which are likely to play a role in cold tolerance. One of the most significant observations from the microarray study is that low temperature does not induce ‘general stress response in B. cinerea, which is in agreement to its exceptional capacity to develop at low temperature. Due to the tragic murder of the Co-PI Maria R. Davis and GopiPodila on Feb. 2010 it is impossible to deliver their contribution to the research. The information of the PI is that they failed to deliver objective 4 and none of the information which relates to objective 3 has been delivered to the PI before the murder or in a visit to U. Alabama during June, 2010. Therefore, this report is based solely on the IS data.
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Whitham, Steven A., Amit Gal-On, and Victor Gaba. Post-transcriptional Regulation of Host Genes Involved with Symptom Expression in Potyviral Infections. United States Department of Agriculture, June 2012. http://dx.doi.org/10.32747/2012.7593391.bard.

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Understanding how RNA viruses cause disease symptoms in their hosts is expected to provide information that can be exploited to enhance modern agriculture. The helper component-proteinase (HC-Pro) protein of potyviruses has been implicated in symptom development. Previously, we demonstrated that symptom expression is associated with binding of duplex small-interfering-RNA (duplex-siRNA) to a highly conserved FRNK amino acid motif in the HC-Pro of Zucchini yellow mosaic virus (ZYMV). This binding activity also alters host microRNA (miRNA) profiles. In Turnip mosaic virus (TuMV), which infects the model plant Arabidopsis, mutation of the FRNK motif to FINK was lethal providing further indication of the importance of this motif to HC-Pro function. In this continuation project, our goal was to further investigate how ZYMV and TuMV cause the mis-expression of genes in cucurbits and Arabidopsis, respectively, and to correlate altered gene expression with disease symptoms. Objective 1 was to examine the roles of aromatic and positively charged residues F164RNH and K215RLF adjacent to FR180NK in small RNA binding. Objective 2 was to determine the target genes of the miRNAs which change during HC-Pro expression in infected tissues and transgenic cucumber. Objective 3 was to characterize RNA silencing mechanisms underlying differential expression of host genes. Objective 4 was to analyze the function of miRNA target genes and differentially expressed genes in potyvirus-infected tissues. We found that the charged K/R amino acid residues in the FKNH and KRLF motifs are essential for virus viability. Replacement of K to I in FKNH disrupted duplex-siRNA binding and virus infectivity, while in KRLF mutants duplex-siRNA binding was maintained and virus infectivity was limited: symptomless following a recovery phenomenon. These findings expanded the duplex-siRNA binding activity of HC-Pro to include the adjacent FRNK and FRNH sites. ZYMV causes many squash miRNAs to hyper-accumulate such as miR166, miR390, mir168, and many others. Screening of mir target genes showed that only INCURVATA-4 and PHAVOLUTA were significantly upregulated following ZYMVFRNK infection. Supporting this finding, we found similar developmental symptoms in transgenic Arabidopsis overexpressing P1-HC-Pro of a range of potyviruses to those observed in miR166 mutants. We characterized increased transcription of AGO1 in response to infection with both ZYMV strains. Differences in viral siRNA profiles and accumulation between mild and severe virus infections were characterized by Illumina sequencing, probably due to the differences in HC-Pro binding activity. We determined that the TuMV FINK mutant could accumulate and cause symptoms in dcl2 dcl4 or dcl2 dcl3 dcl4 mutants similar to TuMV FRNK in wild type Arabidopsis plants. These dcl mutant plants are defective in antiviral defenses, and the results show that factors other than HC-ProFRNK motif can induce symptoms in virus-infected plants. As a result of this work, we have a better understanding of the FRNK and FKNH amino acid motifs of HC-Pro and their contributions to the duplex-siRNA binding functions. We have identified plant genes that potentially contribute to infectivity and symptoms of virus infected plants when they are mis-expressed during potyviral infections. The results establish that there are multiple underlying molecular mechanisms that lead viral pathogenicity, some dependent on HC-Pro. The potential benefits include the development of novel strategies for controlling diseases caused by viruses, methods to ensure stable expression of transgenes in genetically improved crops, and improved potyvirus vectors for expression of proteins or peptides in plants.
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Phillips, Donald, and Yoram Kapulnik. Using Flavonoids to Control in vitro Development of Vesicular Arbuscular Mycorrhizal Fungi. United States Department of Agriculture, January 1995. http://dx.doi.org/10.32747/1995.7613012.bard.

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Vesicular-arbuscular mycorrhizal (VAM) fungi and other beneficial rhizosphere microorganisms, such as Rhizobium bacteria, must locate and infect a host plant before either symbiont profits. Although benefits of the VAM association for increased phosphorous uptake have been widely documented, attempts to improve the fungus and to produce agronomically useful amounts of inoculum have failed due to a lack of in vitro production methods. This project was designed to extend our prior observation that the alfalfa flavonoid quercetin promoted spore germination and hyphal growth of VAM fungi in the absence of a host plant. On the Israeli side of the project, a detailed examination of changes in flavonoids and flavonoid-biosynthetic enzymes during the early stages of VAM development in alfalfa found that VAM fungi elicited and then suppressed transcription of a plant gene coding for chalcone isomerase, which normally is associated with pathogenic infections. US workers collaborated in the identification of flavonoid compounds that appeared during VAM development. On the US side, an in vitro system for testing the effects of plant compounds on fungal spore germination and hyphal growth was developed for use, and intensive analyses of natural products released from alfalfa seedlings grown in the presence and absence of microorganisms were conducted. Two betaines, trigonelline and stachydrine, were identified as being released from alfalfa seeds in much higher concentrations than flavonoids, and these compounds functioned as transcriptional signals to another alfalfa microsymbiont, Rhizobium meliloti. However, these betaines had no effect on VAM spore germination or hyphal growth i vitro. Experiments showed that symbiotic bacteria elicited exudation of the isoflavonoids medicarpin and coumestrol from legume roots, but neither compound promoted growth or germination of VAM fungi in vitro. Attempts to look directly in alfalfa rhizosphere soil for microbiologically active plant products measured a gradient of nod-gene-inducing activity in R. meliloti, but no novel compounds were identified for testing in the VAM fungal system in vitro. Israeli field experiments on agricultural applications of VAM were very successful and developed methods for using VAM to overcome stunting in peanuts and garlic grown in Israel. In addition, deleterious effects of soil solarization on growth of onion, carrot and wheat were linked to effects on VAM fungi. A collaborative combination of basic and applied approaches toward enhancing the agronomic benefits of VAM asociations produced new knowledge on symbiotic biology and successful methods for using VAM inocula under field conditions
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Hodges, Thomas K., and David Gidoni. Regulated Expression of Yeast FLP Recombinase in Plant Cells. United States Department of Agriculture, September 2000. http://dx.doi.org/10.32747/2000.7574341.bard.

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Research activities in both our laboratories were directed toward development of control of the FLP/frt recombination system for plants. As described in the text of the research proposal, the US lab has been engaged in developing regulatory strategies such as tissue-specific promoters and the steroid-inducible activation of the FLP enzyme while the main research activities in Israel have been directed toward the development and testing of a copper-regulated expression of flp recombinase in tobacco (this is an example of a promoter activation by metal ions). The Israeli lab hat additionally completed experiments of previous studies regarding factors affecting the efficiency of recombinase activity using both a gain-of-function assay (excisional-activation of a gusA marker) and loss of function assay (excision of a rolC marker) in tobacco. Site-specific recombinase systems, in particular the FLP/frt and R/RS systems of yeast and the Cre/lox system of bacteriophage P1, have become an essential component of targeted genetic transformation procedures both in animal and plant organisms. To provide more flexibility in transgene excisions by the recombinase systems as well as gene targeting, and to widen possible applications, the development of controlled or regulated recombination systems is highly desirable and was therefore the subject of this research proposal. There are a few possible mechanisms to regulate expression of a recombinase system. They include: 1) control of the recombination system by having the target sites (e.g. frt) in one plant and the flp recombinase gene in another, and bringing the two together by cross fertilization. 2) regulation of promoter activities by external stimuli such as temperature, chemicals, metal ions, etc. 3) regulation of promoter activities by internal signals, i.e. cell- or tissue-specific, or developmental regulation. 4) regulation of enzyme activity by providing cofactors essential for biochemical reactions to take place such as steroid molecules in conjunction with a steroid ligand-binding protein (domains). During the course of this research our major emphasis have been focused toward studying the feasibility of hybrid seed production in Arabidopsis, using FLP/frt. Male-sterility was induced using the antisence of a pollen- and tapetum-specific gene, bcp1, isolated from Arabidopsis. The sterility inducing gene was flanked by frt sites. Upon cross pollination of flowers of male-sterile plants with pollen from FLP-containing plants, viable seeds were produced, and the progeny hybrid plants developed normally. The major achievement from this work is the first demonstration of using a site-specific recombinase to restore fertility in male-sterile plants (see attached paper, Luo et al., Plant J 2000; 23:423-430). The implication from this finding is that site-specific recombination systems can be applied in crop plants as a useful alternative method for hybrid seed production.
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Sessa, Guido, and Gregory Martin. MAP kinase cascades activated by SlMAPKKKε and their involvement in tomato resistance to bacterial pathogens. United States Department of Agriculture, January 2012. http://dx.doi.org/10.32747/2012.7699834.bard.

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The research problem: Pseudomonas syringae pv. tomato (Pst) and Xanthomonas campestrispv. vesicatoria (Xcv) are the causal agents of tomato bacterial speck and spot diseases, respectively. These pathogens colonize the aerial parts of the plant and cause economically important losses to tomato yield worldwide. Control of speck and spot diseases by cultural practices or chemicals is not effective and genetic sources of resistance are very limited. In previous research supported by BARD, by gene expression profiling we identified signaling components involved in resistance to Xcvstrains. Follow up experiments revealed that a tomato gene encoding a MAP kinase kinase kinase (MAPKKKe) is required for resistance to Xcvand Pststrains. Goals: Central goal of this research was to investigate the molecular mechanisms by which MAPKKKεand associated MAP kinase cascades regulate host resistance. Specific objectives were to: 1. Determine whether MAPKKKεplays a broad role in defense signaling in plants; 2. Identify components of MAP kinase cascades acting downstream of MAPKKKε; 3. Determine the role of phosphorylation-related events in the function of MAPKKKε; 4. Isolate proteins directly activated by MAPKKKε-associatedMAPK modules. Our main achievements during this research program are in the following major areas: 1. Characterization of MAPKKKεas a positive regulator of cell death and dissection of downstream MAP kinase cascades (Melech-Bonfil et al., 2010; Melech-Bonfil and Sessa, 2011). The MAPKKKεgene was found to be required for tomato resistance to Xcvand Pstbacterial strains and for hypersensitive response cell death triggered by different R gene/effector gene pairs. In addition, overexpression analysis demonstrated that MAPKKKεis a positive regulator of cell death, whose activity depends on an intact kinase catalytic domain. Epistatic experiments delineated a signaling cascade downstream of MAPKKKεand identified SIPKK as a negative regulator of MAPKKKε-mediated cell death. Finally, genes encoding MAP kinase components downstream of MAPKKKεwere shown to contribute to tomato resistance to Xcv. 2. Identification of tomato proteins that interact with MAPKKKεand play a role in plant immunity (Oh et al., 2011). We identified proteins that interact with MAPKKKε. Among them, the 14-3-3 protein TFT7 was required for cell death mediated by several R proteins. In addition, TFT7 interacted with the MAPKK SlMKK2 and formed homodimersin vivo. Thus, TFT7 is proposed to recruit SlMKK2 and MAPKKK client proteins for efficient signal transfer. 3. Development of a chemical genetic approach to identify substrates of MAPKKKε-activated MAP kinase cascades (Salomon et al., 2009, 2011). This approach is based on engineering the kinase of interest to accept unnatural ATP analogs. For its implementation to identify substrates of MAPKKKε-activated MAP kinase modules, we sensitized the tomato MAP kinase SlMPK3 to ATP analogs and verified its ability to use them as phosphodonors. By using the sensitized SlMPK3 and radiolabeled N6(benzyl)ATP it should be possible to tag direct substrates of this kinase. 4. Development of methods to study immunity triggered by pathogen-associated molecular patterns (PAMPs) in tomato and N. benthamiana plants (Kim et al., 2009; Nguyen et al. 2010). We developed protocols for measuring various PTI-associatedphenotypes, including bacterial populations after pretreatment of leaves with PAMPs, induction of reporter genes, callose deposition at the cell wall, activation of MAP kinases, and a luciferase-based reporter system for use in protoplasts. Scientific and agricultural significance: Our research activities discovered and characterized a signal transduction pathway mediating plant immunity to bacterial pathogens. Increased understanding of molecular mechanisms of immunity will allow them to be manipulated by both molecular breeding and genetic engineering to produce plants with enhanced natural defense against disease. In addition, we successfully developed new biochemical and molecular methods that can be implemented in the study of plant immunity and other aspects of plant biology.
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