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Journal articles on the topic 'Boundary triples'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Behrndt, Jussi, and Till Micheler. "Boundary triples and quasi boundary triples for elliptic operators." PAMM 11, no. 1 (2011): 883–84. http://dx.doi.org/10.1002/pamm.201110428.

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2

Strelnikov, D. I. "Boundary triples for integral systems." Reports of the National Academy of Sciences of Ukraine, no. 7 (July 24, 2018): 3–9. http://dx.doi.org/10.15407/dopovidi2018.07.003.

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3

Post, O. "First-order operators and boundary triples." Russian Journal of Mathematical Physics 14, no. 4 (2007): 482–92. http://dx.doi.org/10.1134/s1061920807040139.

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4

Iochum, B., and C. Levy. "Spectral triples and manifolds with boundary." Journal of Functional Analysis 260, no. 1 (2011): 117–34. http://dx.doi.org/10.1016/j.jfa.2010.09.006.

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5

Brown, B. M., M. Marletta, S. Naboko, and I. Wood. "Inverse problems for boundary triples with applications." Studia Mathematica 237, no. 3 (2017): 241–75. http://dx.doi.org/10.4064/sm8613-11-2016.

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6

Hayashi, Toshinori, Alessandro A. Trani, and Yasushi Suto. "Dynamical Disruption Timescales and Chaotic Behavior of Hierarchical Triple Systems." Astrophysical Journal 939, no. 2 (2022): 81. http://dx.doi.org/10.3847/1538-4357/ac8f48.

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Abstract We examine the stability of hierarchical triple systems using direct N-body simulations without adopting a secular perturbation assumption. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with particular attention to the mutual inclination between the inner and outer orbits. First, we improve the fit to the dynamical stability criterion by Mardling & Aarseth widely adopted in the previous literature. Especially, we find that that the stability boundary is very sensitive to the mutual inclination; coplanar retrograde triples and orthogonal

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7

Strelnikov, Dmytro. "Boundary triples for integral systems on finite intervals." Journal of Mathematical Sciences 231, no. 1 (2018): 83–100. http://dx.doi.org/10.1007/s10958-018-3807-z.

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8

Behrndt, Jussi, Matthias Langer, Vladimir Lotoreichik, and Jonathan Rohleder. "Quasi boundary triples and semi-bounded self-adjoint extensions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 5 (2017): 895–916. http://dx.doi.org/10.1017/s0308210516000421.

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In this note semi-bounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on the parameters in the boundary space to induce self-adjoint realizations, and to relate the decay of the Weyl function to estimates on the lower bound of the spectrum. The abstract results are illustrated with uniformly elliptic second-order partial differential equations on domains with non-compact boundaries.

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9

BRÜNING, JOCHEN, VLADIMIR GEYLER, and KONSTANTIN PANKRASHKIN. "SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS." Reviews in Mathematical Physics 20, no. 01 (2008): 1–70. http://dx.doi.org/10.1142/s0129055x08003249.

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We give a self-contained presentation of the theory of self-adjoint extensions using the technique of boundary triples. A description of the spectra of self-adjoint extensions in terms of the corresponding Krein maps (Weyl functions) is given. Applications include quantum graphs, point interactions, hybrid spaces and singular perturbations.

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10

Storozh, O. G. "On an approach to the construction of the Friedrichs and Neumann-Krein extensions of nonnegative linear relations." Carpathian Mathematical Publications 10, no. 2 (2018): 387–94. http://dx.doi.org/10.15330/cmp.10.2.387-394.

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Let $L_{0}$ be a closed linear nonnegative (probably, positively defined) relation ("multivalued operator") in a complex Hilbert space $H$. In terms of the so called boundary value spaces (boundary triples) and corresponding Weyl functions and Kochubei-Strauss characteristic ones, the Friedrichs (hard) and Neumann-Krein (soft) extensions of $L_{0}$ are constructed. It should be noted that every nonnegative linear relation $L_{0}$ in a Hilbert space $H$ has two extremal nonnegative selfadjoint extensions: the Friedrichs extension $L_{F}$ and the Neumann-Krein extension $L_{K},$ satisfying

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11

Naboko, S., and I. Wood. "The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem." Annales Henri Poincaré 21, no. 10 (2020): 3141–56. http://dx.doi.org/10.1007/s00023-020-00935-z.

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Abstract We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspa

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12

Battisti, Ubertino, and Joerg Seiler. "Boundary value problems with Atiyah–Patodi–Singer type conditions and spectral triples." Journal of Noncommutative Geometry 11, no. 3 (2017): 887–917. http://dx.doi.org/10.4171/jncg/11-3-4.

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13

Clerc, Jean-Louis, and Karl-Hermann Neeb. "Orbits of triples in the Shilov boundary of a bounded symmetric domain." Transformation Groups 11, no. 3 (2006): 387–426. http://dx.doi.org/10.1007/s00031-005-1117-2.

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14

Cassano, Biagio, and Fabio Pizzichillo. "Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations." Journal of Mathematical Physics 60, no. 4 (2019): 041502. http://dx.doi.org/10.1063/1.5063986.

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15

Monard, François, and Yuzhou (Joey) Zou. "Boundary triples for a family of degenerate elliptic operators of Keldysh type." Pure and Applied Analysis 6, no. 2 (2024): 541–80. http://dx.doi.org/10.2140/paa.2024.6.541.

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16

Ershova, Yu Yu, I. I. Karpenko, and A. V. Kiselev. "On inverse topology problem for Laplace operators on graphs." Carpathian Mathematical Publications 6, no. 2 (2014): 230–36. http://dx.doi.org/10.15330/cmp.6.2.230-236.

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Laplacian operators on finite compact metric graphs are considered under the assumption that matching conditions at graph vertices are of $\delta$ type. Under one additional assumption, the inverse topology problem is treated. Using the apparatus of boundary triples, we generalize and extend existing results on necessary conditions of isospectrality of two Laplacians defined on different graphs. A result is also given covering the case of Schrodinger operators.

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17

Clerc, Jean-Louis. "An invariant for triples in the Shilov boundary of a bounded symmetric domain." Communications in Analysis and Geometry 15, no. 1 (2007): 147–74. http://dx.doi.org/10.4310/cag.2007.v15.n1.a5.

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18

Frymark, Dale. "Boundary triples and Weyl m-functions for powers of the Jacobi differential operator." Journal of Differential Equations 269, no. 10 (2020): 7931–74. http://dx.doi.org/10.1016/j.jde.2020.05.032.

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19

Derkach, Volodymyr, Seppo Hassi, and Mark Malamud. "Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions." Mathematische Nachrichten 293, no. 7 (2020): 1278–327. http://dx.doi.org/10.1002/mana.201800300.

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20

Sunitha, C., Jaya A, and Ganesh Amal. "Automatic summarization of Malayalam documents using clause identification method." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 6 (2019): 4929–38. https://doi.org/10.11591/ijece.v9i6.pp4929-4938.

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Text summarization is an active research area in the field of natural language processing. Huge amount of information in the internet necessitates the development of automatic summarization systems. There are two types of summarization techniques: Extractive and Abstractive. Extractive summarization selects important sentences from the text and produces summary as it is present in the original document. Abstractive summarization systems will provide a summary of the input text as is generated by human beings. Abstractive summary requires semantic analysis of text. Limited works have been carri

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21

Dai, Qicai, Wenzhong Yang, Fuyuan Wei, Liang He, and Yuanyuan Liao. "FSN: Joint Entity and Relation Extraction Based on Filter Separator Network." Entropy 26, no. 2 (2024): 162. http://dx.doi.org/10.3390/e26020162.

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Joint entity and relation extraction methods have attracted an increasing amount of attention recently due to their capacity to extract relational triples from intricate texts. However, most of the existing methods ignore the association and difference between the Named Entity Recognition (NER) subtask features and the Relation Extraction (RE) subtask features, which leads to an imbalance in the interaction between these two subtasks. To solve the above problems, we propose a new joint entity and relation extraction method, FSN. It contains a Filter Separator Network (FSN) module that employs

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22

Zhang, Pengfei, Huang Peng, Yang Fang, et al. "Universal Knowledge Graph Embedding Framework Based on High-Quality Negative Sampling and Weighting." Mathematics 12, no. 22 (2024): 3489. http://dx.doi.org/10.3390/math12223489.

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The traditional model training approach based on negative sampling randomly samples a portion of negative samples for training, which can easily overlook important negative samples and adversely affect the training of knowledge graph embedding models. Some researchers have explored non-sampling model training frameworks that use all unobserved triples as negative samples to improve model training performance. However, both training methods inevitably introduce false negative samples and easy-to-separate negative samples that are far from the model’s decision boundary, and they do not consider

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23

Schroers, B. J., and M. A. Singer. "Dk Gravitational Instantons as Superpositions of Atiyah–Hitchin and Taub–NUT Geometries." Quarterly Journal of Mathematics 72, no. 1-2 (2021): 277–337. http://dx.doi.org/10.1093/qmath/haab002.

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Abstract We obtain Dk ALF gravitational instantons by a gluing construction which captures, in a precise and explicit fashion, their interpretation as nonlinear superpositions of the moduli space of centred SU(2) monopoles, equipped with the Atiyah–Hitchin metric, and k copies of the Taub–NUT manifold. The construction proceeds from a finite set of points in euclidean space, reflection symmetric about the origin, and depends on an adiabatic parameter which is incorporated into the geometry as a fifth dimension. Using a formulation in terms of hyperKähler triples on manifolds with boundaries, w

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24

BENEDETTI, RICCARDO, and CARLO PETRONIO. "COMBED 3-MANIFOLDS WITH CONCAVE BOUNDARY, FRAMED LINKS, AND PSEUDO-LEGENDRIAN LINKS." Journal of Knot Theory and Its Ramifications 10, no. 01 (2001): 1–35. http://dx.doi.org/10.1142/s0218216501000706.

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We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M, v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly ∂M≠∅, and v may be tangent to ∂M, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M, v, L), with (M, v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transverality-preserving simultaneous homotopy of v and isotopy of L). All rea

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25

Merenkov, Sergei. "Local rigidity for hyperbolic groups with Sierpiński carpet boundaries." Compositio Mathematica 150, no. 11 (2014): 1928–38. http://dx.doi.org/10.1112/s0010437x14007490.

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AbstractLet$G$and$\tilde{G}$be Kleinian groups whose limit sets$S$and$\tilde{S}$, respectively, are homeomorphic to the standard Sierpiński carpet, and such that every complementary component of each of$S$and$\tilde{S}$is a round disc. We assume that the groups$G$and$\tilde{G}$act cocompactly on triples on their respective limit sets. The main theorem of the paper states that any quasiregular map (in a suitably defined sense) from an open connected subset of$S$to$\tilde{S}$is the restriction of a Möbius transformation that takes$S$onto$\tilde{S}$, in particular it has no branching. This theore

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26

Noskov, Alexey, and Yerach Doytsher. "Triangulation and Segmentation-based Approach for Improving the Accuracy of Polygon Data." International Journal on Advances in Software 9, no. 1&2 (2016): 24–36. https://doi.org/10.5281/zenodo.1314451.

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Often, same polygon objects are presented in Geoinformational Systems by distinct geometries with random positional discrepancies. It makes difficult to detect correspondences between data layers containing same object or parts of objects. The suggested method allows the user to improve the accuracy of one polygon layer by another more accurate polygon dataset by defining correspondences between polygons and parts of polygon boundaries. Two main techniques are applied: triangulation and segmentation. The triangulation is used to define correspondences between whole polygons by comparing triple

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27

Gritsans, Armands, and Felix Sadyrbaev. "TWO-PARAMETER NONLINEAR OSCILLATIONS: THE NEUMANN PROBLEM." Mathematical Modelling and Analysis 16, no. 1 (2011): 23–38. http://dx.doi.org/10.3846/13926292.2011.559449.

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Boundary value problems of the form are considered, where In our considerations functions f and g are generally nonlinear. We give a description of a solution set of the problem (i), (ii). It consist of all triples () such that (λ,μ,x(t)) nontrivially ′solves the problem(i),(ii) and |x (z)| = α at zero points z of the function x(t) (iii). We show that this solution set is a union of solution surfaces which are centro-affine equivalent. Each solution surface is associated with nontrivial solutions with definite nodal type. Properties of solution surfaces are studied. It is shown, in particular,

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28

Possner, Anna, Ryan Eastman, Frida Bender, and Franziska Glassmeier. "Deconvolution of boundary layer depth and aerosol constraints on cloud water path in subtropical stratocumulus decks." Atmospheric Chemistry and Physics 20, no. 6 (2020): 3609–21. http://dx.doi.org/10.5194/acp-20-3609-2020.

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Abstract. The liquid water path (LWP) adjustment due to aerosol–cloud interactions in marine stratocumulus remains a considerable source of uncertainty for climate sensitivity estimates. An unequivocal attribution of LWP adjustments to changes in aerosol concentration from climatology remains difficult due to the considerable covariance between meteorological conditions alongside changes in aerosol concentrations. We utilise the susceptibility framework to quantify the potential change in LWP adjustment with boundary layer (BL) depth in subtropical marine stratocumulus. We show that the LWP su

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29

Chuiko, S. M., O. V. Chuiko, and O. V. O.V. Nesmelova. "Solving a nonlinear matrix equation by Newton's method." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 38 (December 18, 2024): 119–31. https://doi.org/10.37069/1683-4720-2024-38-11.

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The study of nonlinear boundary value problems, generally speaking, is not solved with respect to the derivative for ordinary differential equations. This area of research is a traditional focus of the Kyiv school of nonlinear oscillations, initiated in the 1930s by M.M. Krylov and M.M. Bogolyubov. Their work was continued by S. Campbell, V.F. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, and O.A. Boychuk, who focused on differential-algebraic boundary value problems. The linearization of nonlinear systems of differential equations that are not solved with respect to the derivative leads to l

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30

Liu, Xing, Long Zhang, Qiusheng Zheng, et al. "Construction of an Event Knowledge Graph Based on a Dynamic Resource Scheduling Optimization Algorithm and Semantic Graph Convolutional Neural Networks." Electronics 13, no. 1 (2023): 11. http://dx.doi.org/10.3390/electronics13010011.

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Presently, road and traffic control construction on most university campuses cannot keep up with the growth of the universities. Campus roads are not very wide, crossings do not have lights, and there are no full-time traffic management personnel. Teachers and students are prone to forming a peak flow of people when going to and from classes. This has led to a constant stream of traffic accidents. It is critical to conduct a comprehensive analysis of this issue by utilizing voluminous data pertaining to school traffic incidents in order to safeguard the lives of faculty and students. In the ca

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31

Washbrook, E., and K. R. Fox. "Alternate-strand DNA triple-helix formation using short acridine-linked oligonucleotides." Biochemical Journal 301, no. 2 (1994): 569–75. http://dx.doi.org/10.1042/bj3010569.

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We have used DNAse I footprinting to examine the formation of intermolecular DNA triple helices at sequences containing adjacent blocks of purines and pyrimidines. The target sites G6T6.A6C6 and T6G6.C6A6 were cloned into longer DNA fragments and used as substrates for DNAse I footprinting, which examined the binding of the acridine (Acr)-linked oligonucleotides Acr-T5G5 and Acr-G5T5 respectively. These third strands were designed to incorporate both G.GC triplets, with antiparallel Gn strands held together by reverse Hoogsteen base pairs, and T.AT triplets, with the two T-containing strands a

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32

Antunes, Pedro R. S., and Pedro Freitas. "On the inverse spectral problem for Euclidean triangles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2130 (2010): 1546–62. http://dx.doi.org/10.1098/rspa.2010.0540.

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We consider the inverse spectral problem for the Laplace operator on triangles with Dirichlet boundary conditions, providing numerical evidence to the effect that the eigenvalue triplet ( λ 1 , λ 2 , λ 3 ) is sufficient to determine a triangle uniquely. On the other hand, we show that other combinations such as ( λ 1 , λ 2 , λ 4 ) will not be enough, and that there will exist at least two triangles with the same values on these triplets.

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33

O’Hayre, Ryan, David M. Barnett, and Fritz B. Prinz. "The Triple Phase Boundary." Journal of The Electrochemical Society 152, no. 2 (2005): A439. http://dx.doi.org/10.1149/1.1851054.

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34

Suba, János. "A trianoni hármashatárok kijelölése." Jelenkori Társadalmi és Gazdasági Folyamatok 4, no. 3-4 (2009): 276–81. http://dx.doi.org/10.14232/jtgf.2009.3-4.276-281.

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A "triple" or "tergeminate" frontier is the meeting point of the frontiers of three neighbouring countries. The boundary stone which marks it, named "triplex confinum", is generally a monumental, obelisk-like work of art. Along the frontiers of Hungary, estab-lished by the Trianon Peace Treaty and traced out on the terrain, there were four such triplex confinia. Their establishing and indication was done as a result of long negotiations and without the knowledge of the Hungarian party sometimes. The study treats the political efforts in this concern and explains how the location of the tergemi

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35

Rashid, Yasameen H., Jamil A. Ali Al-Hawasy, and Ion Chryssoverghi. "Classical Continuous Constraint Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System." Al-Mustansiriyah Journal of Science 34, no. 2 (2023): 95–102. http://dx.doi.org/10.23851/mjs.v34i2.1272.

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In this paper, our purpose is to study the classical continuous constraints boundary optimal triple control vector problem dominating nonlinear triple parabolic boundary value problem. The existence theorem for a classical continuous triple optimal control vector CCCBOTCV is stated and proved under suitable assumptions. The mathematical formulation of the adjoint triple boundary value problem associated with the nonlinear triple parabolic boundary value problem is discovered. The Fréchet derivative of the Hamiltonian is derived. Under proper assumptions, both theorems are granted; the necessar

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36

Ivanov, V. A., Dmitri A. Molodov, Lasar S. Shvindlerman, and Günter Gottstein. "On the Effect of “Surface Triple Junction” on Grain Boundary Motion." Materials Science Forum 467-470 (October 2004): 757–62. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.757.

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The motion of a curved grain boundary with a “surface triple junction” (“free surface – boundary - free surface”) in aluminum bicrystals is studied. The effect of the “surface triple junction” on grain boundary motion is discussed in the terms of the equilibrium of boundary and junction velocity. Boundary motion in samples with different boundary curvature revealed a strict proportionality of boundary velocity and driving force. This result corroborates the fact that in the entire investigated temperature range the “surface” triple junction does not affect the boundary motion.

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37

Klinner, J., and C. Willert. "Feasibility Of Multi-Aperture µPTV For Wall Shear Stress Measurements." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 20 (July 11, 2022): 1–26. http://dx.doi.org/10.55037/lxlaser.20th.167.

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We present a feasibility study on 3d 3c micro PTV for boundary layer flows using a single high-speed camera with a microscope lens. Multi-aperture µPTV (MA-µPTV) relies on the “defocusing” concept (Willert & Gharib, 1992) and determines the wall distance of a particle from the size of projected particle image triplets generated by placing an triplet aperture on the entrance pupil of a microscope objective. Illumination with a high-speed pulsed laser is introduced through the same window used for imaging. The calibration of the orientation and size of the particle image triplets is describe

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38

Zhao, Bing Bing, Lasar S. Shvindlerman, and Günter Gottstein. "Grain Boundary Triple Line Tension in Copper." Materials Science Forum 715-716 (April 2012): 843–48. http://dx.doi.org/10.4028/www.scientific.net/msf.715-716.843.

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The current study introduces a thermodynamically correct approach which allows a direct precise measurement of the grain boundary triple line tension. The experimental technique utilizes the measurement of the surface topography of a crystal in the vicinity of a triple junction and grain boundary groove on thin wires by atomic force microscopy. The grain boundary triple line tension of a random triple line was measured to be in the order of 10-9J/m.

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39

Gamsjäger, Ernst, Daniel Ogris, and Jiří Svoboda. "Kinetics of Grain Boundary Networks Controlled by Triple Junction and Grain Boundary Mobility." Metals 8, no. 12 (2018): 977. http://dx.doi.org/10.3390/met8120977.

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The kinetics of a triple junction of grain boundaries with distinct specific energies and mobilities and a finite mobility of the triple junction is investigated. The microstructure is approximated by different 2D settings consisting of typical structural elements. First, the migration of the triple point together with the adjacent grain boundaries, is simulated, assuming that the grains are infinitely large. Secondly, growth or shrinkage of finite n-sided grains is simulated by altering the boundary conditions and the results are compared to the already published analytical solution. The nume

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40

GARCKE, HARALD, and BRITTA NESTLER. "A MATHEMATICAL MODEL FOR GRAIN GROWTH IN THIN METALLIC FILMS." Mathematical Models and Methods in Applied Sciences 10, no. 06 (2000): 895–921. http://dx.doi.org/10.1142/s021820250000046x.

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We use geometrical arguments based on grain boundary symmetries to introduce crystalline interfacial energies for interfaces in polycrystalline thin films with a cubic lattice. These crystalline energies are incorporated into a multi-phase field model. Our aim is to apply the multi-phase field method to describe the evolution of faceted grain boundary triple junctions in epitaxially growing microstructures. In particular, we are interested in symmetry properties of triple junctions in tricrystalline thin films. Symmetries of triple junctions in tricrystalline films have been studied in experim

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41

Rollett, A. D., C. C. Yang, W. W. Mullins, et al. "Extraction of Grain Boundary Energies from Triple Junction Geometry." Microscopy and Microanalysis 5, S2 (1999): 230–31. http://dx.doi.org/10.1017/s1431927600014471.

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Measurement of the geometry of triple junctions between grain boundaries in polycrystalline materials is used to generate large sets of dihedral angles from which maps of the grain boundary energy are extracted. A preliminary analysis has been performed for samples of magnesia and aluminum based on a three-parameter description of grain boundaries. An extended form of orientation imaging microscopy (OIM) was used to measure both triple junction geometry via image analysis in the SEM and local grain orientation via electron back scatter diffraction. Serial sectioning with registry of both in-pl

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42

Gaberdiel, Matthias R., and Ingo Runkel. "The logarithmic triplet theory with boundary." Journal of Physics A: Mathematical and General 39, no. 47 (2006): 14745–79. http://dx.doi.org/10.1088/0305-4470/39/47/016.

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43

Lorenz, Oliver, Alexander Kühne, Martin Rudolph, et al. "Role of Reaction Intermediate Diffusion on the Performance of Platinum Electrodes in Solid Acid Fuel Cells." Catalysts 11, no. 9 (2021): 1065. http://dx.doi.org/10.3390/catal11091065.

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Understanding the reaction pathways for the hydrogen oxidation reaction (HOR) and the oxygen reduction reaction (ORR) is the key to design electrodes for solid acid fuel cells (SAFCs). In general, electrochemical reactions of a fuel cell are considered to occur at the triple-phase boundary where an electrocatalyst, electrolyte and gas phase are in contact. In this concept, diffusion processes of reaction intermediates from the catalyst to the electrolyte remain unconsidered. Here, we unravel the reaction pathways for open-structured Pt electrodes with various electrode thicknesses from 15 to 2

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44

Liu, Dan Dan, Jochen Fiebig, Martin Peterlechner, et al. "Ti and Ni Grain Boundary Diffusion in B2 NiTi Compound." Defect and Diffusion Forum 363 (May 2015): 137–41. http://dx.doi.org/10.4028/www.scientific.net/ddf.363.137.

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The radiotracer technique was used to measure the grain boundary diffusion of44Ti and63Ni in slightly Ni-rich polycrystalline NiTi compound in the temperature range of 673 - 923 K. The temperature dependence of the grain boundary triple productP(P=sδDgb,sis the segregation coefficient,δis the grain boundary width, andDgbis the grain boundary diffusion coefficient) for Ti and Ni was determined. The triple products of both Ti and Ni grain boundary diffusion in NiTi reveal a unique behavior with significant deviations from an Arrhenius-type dependence. Probable evolution of the grain boundary str

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45

Straumal, B. B., V. G. Sursaeva, and B. Baretzky. "Grain boundary ridges and triple lines." Scripta Materialia 62, no. 12 (2010): 924–27. http://dx.doi.org/10.1016/j.scriptamat.2010.02.018.

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Shvindlerman, L. S., and G. Gottstein. "Grain boundary and triple junction migration." Materials Science and Engineering: A 302, no. 1 (2001): 141–50. http://dx.doi.org/10.1016/s0921-5093(00)01366-6.

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Ibnelazyz, Lahcen. "Tripled system of fractional Langevin equations with tripled multipoint boundary conditions." Filomat 38, no. 32 (2024): 11401–32. https://doi.org/10.2298/fil2432401i.

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This research focuses on examining the tripled system of nonlinear fractional Langevin equations with coupled multipoint boundary conditions. By utilizing the Banach contraction mapping, one can obtain the result of existence and uniqueness. The existence of a solution is validated through the use of Krasnoselskii?s fixed point theorem. Furthermore, The Ulam-Hyers stability of the mentioned system is studied. In the end, we present two examples to validate the effectiveness of our analysis.

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Al-hawasy, Jamil Amir Ali, and Yasameen H. Rashid. "Classical Continuous Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System." Al-Mustansiriyah Journal of Science 34, no. 1 (2023): 77–86. http://dx.doi.org/10.23851/mjs.v34i1.1241.

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In this paper, our purpose is to study the classical continuous boundary optimal triple control vector problem (CCBOTCVP) dominating by nonlinear triple parabolic boundary value problem (NLTPBVP). Under suitable assumptions and with given classical continuous boundary triple control vector (CCBTCV), the existence theorem for a unique state triple vector solution (STVS) of the weak form W.F for the NLTPBVP is stated and demonstrated via the Method of Galerkin (MGa), and the first compactness theorem. Furthermore, the continuity operator between the STVS of the WFO for the NLTPBVP and the corres

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Shvindlerman, Lasar S., and Günter Gottstein. "Novel Approaches to the Thermodynamis of Grain Boundaries and Grain Boundary Junctions." Materials Science Forum 558-559 (October 2007): 675–82. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.675.

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Three recent investigations in the field of thermodynamics of grain boundaries and grain boundary junctions are presented. 1. The grain boundary excess free volume (BFV) along with the surface tension belongs to the major thermodynamic properties of grain boundaries. A special technique, recently developed, makes it possible to measure the BFV for practically any grain boundary and provides a way of estimating the grain boundary excess free volume for grain boundaries of different classes with rather high accuracy. The experimental values of the BFV measured for different grain boundaries are

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Gottstein, Günter, and Lazar S. Shvindlerman. "Thermodynamics and Kinetics of 1D Structural Elements and Stability of Nanocrystalline Materials." Diffusion Foundations 5 (July 2015): 173–95. http://dx.doi.org/10.4028/www.scientific.net/df.5.173.

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Grain boundary triple junctions are the structural elements of a polycrystal. Recently it was recognized that they can strongly impact the microstructural evolution, and therefore there engender new opportunities to control and to design the grain microstructure of fine-grained and nanocrystalline materials due to their effect on recovery, recrystallization and grain growth. The measurement of triple junction energy and mobility is thus of great importance. The line energy of a triple junction constructs an additional driving force of grain growth. Taking the triple line energy into account, a

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