Journal articles: 'Boundary triples'

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

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

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

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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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Hayashi, Toshinori, Alessandro A. Trani, and Yasushi Suto. "Dynamical Disruption Timescales and Chaotic Behavior of Hierarchical Triple Systems." Astrophysical Journal 939, no. 2 (November 1, 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 triples are much more stable and unstable, respectively, than coplanar prograde triples. Next, we estimate the disruption timescales of triples satisfying the stability condition up to 109 times the inner orbital period. The timescales follow the scaling predicted by Mushkin & Katz, especially at high e out where their random walk model is most valid. We obtain an improved empirical fit to the disruption timescales, which indicates that the coplanar retrograde triples are significantly more stable than the previous prediction. We furthermore find that the dependence on the mutual inclination can be explained by the energy transfer model based on a parabolic encounter approximation. We also show that the disruption timescales of triples are highly sensitive to tiny changes of the initial parameters, reflecting the genuine chaotic nature of the dynamics of those systems.

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Strelnikov, Dmytro. "Boundary triples for integral systems on finite intervals." Journal of Mathematical Sciences 231, no. 1 (April 18, 2018): 83–100. http://dx.doi.org/10.1007/s10958-018-3807-z.

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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 (June 28, 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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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 (December 31, 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 the following property: $$(\forall \varepsilon > 0) (L_{F} + \varepsilon 1)^{-1} \leq (\widetilde{L} + \varepsilon 1)^{-1} \leq (L_{K} + \varepsilon 1)^{-1}$$ in the set of all nonnegative selfadjoint subspace extensions $\widetilde{L}$ of $L_{0}.$ The boundary triple approach to the extension theory was initiated by F.S. Rofe-Beketov, M.L. and V.I. Gorbachuk, A.N. Kochubei, V.A. Mikhailets, V.O. Dercach, M.N. Malamud, Yu. M. Arlinskii and other mathematicians. In addition, it is showed that the construction of the mentioned extensions may be realized in a more simple way under the assumption that initial relation is a positively defined one.

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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 (February 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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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 (July 13, 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 subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.

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

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

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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 (May 16, 2024): 541–80. http://dx.doi.org/10.2140/paa.2024.6.541.

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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 (December 25, 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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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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Frymark, Dale. "Boundary triples and Weyl m-functions for powers of the Jacobi differential operator." Journal of Differential Equations 269, no. 10 (November 2020): 7931–74. http://dx.doi.org/10.1016/j.jde.2020.05.032.

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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 (May 19, 2020): 1278–327. http://dx.doi.org/10.1002/mana.201800300.

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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 (February 12, 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 a two-direction LSTM to filter and separate the information contained in a sentence and merges similar features through a splicing operation, thus solving the problem of the interaction imbalance between subtasks. In order to better extract the local feature information for each subtask, we designed a Named Entity Recognition Generation (NERG) module and a Relation Extraction Generation (REG) module by adopting the design idea of the decoder in Transformer and average pooling operations to better capture the entity boundary information in the sentence and the entity pair boundary information for each relation in the relational triple, respectively. Additionally, we propose a dynamic loss function that dynamically adjusts the learning weights of each subtask in each epoch according to the proportionality between each subtask, thus narrowing down the difference between the ideal and realistic results. We thoroughly evaluated our model on the SciERC dataset and the ACE2005 dataset. The experimental results demonstrate that our model achieves satisfactory results compared to the baseline model.

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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 (February 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 realizations are based on the notion of branched standard spine, and build on results previously obtained, Links are encoded by means of diagrams on branched spines, where the diagram is C 1 with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.

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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 (February 17, 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, we show that the constituent Atiyah–Hitchin and Taub–NUT geometries arise as boundary components of the five-dimensional geometry as the adiabatic parameter is taken to zero.

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Merenkov, Sergei. "Local rigidity for hyperbolic groups with Sierpiński carpet boundaries." Compositio Mathematica 150, no. 11 (August 27, 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 theorem applies to the fundamental groups of compact hyperbolic 3-manifolds with non-empty totally geodesic boundaries. One consequence of the main theorem is the following result. Assume that$G$is a torsion-free hyperbolic group whose boundary at infinity$\partial _{\infty }G$is a Sierpiński carpet that embeds quasisymmetrically into the standard 2-sphere. Then there exists a group$H$that contains$G$as a finite index subgroup and such that any quasisymmetric map$f$between open connected subsets of$\partial _{\infty }G$is the restriction of the induced boundary map of an element$h\in H$.

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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 (March 26, 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 susceptibility, i.e. the relative change in LWP scaled by the relative change in cloud droplet number concentration, in marine BLs triples in magnitude from −0.1 to −0.31 as the BL deepens from 300 to 1200 m and deeper. We further find deep BLs to be underrepresented in pollution tracks, process modelling, and in situ studies of aerosol–cloud interactions in marine stratocumulus. Susceptibility estimates based on these approaches are skewed towards shallow BLs of moderate LWP susceptibility. Therefore, extrapolating LWP susceptibility estimates from shallow BLs to the entire cloud climatology may underestimate the true LWP adjustment within subtropical stratocumulus and thus overestimate the effective aerosol radiative forcing in this region. Meanwhile, LWP susceptibility estimates in deep BLs remain poorly constrained. While susceptibility estimates in shallow BLs are found to be consistent with process modelling studies, they overestimate pollution track estimates.

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Gritsans, Armands, and Felix Sadyrbaev. "TWO-PARAMETER NONLINEAR OSCILLATIONS: THE NEUMANN PROBLEM." Mathematical Modelling and Analysis 16, no. 1 (April 8, 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, that solution surface associated with solutions with exactly i zeroes in the interval (a,b) is centro-affne equivalent to a solution surface of the Dirichlet problem (i), x(a) = 0 = x(b), (iii) corresponding to solutions with odd number of zeros 2j − 1 (i ≠ 2j)in the interval (a,b).

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Liu, Xing, Long Zhang, Qiusheng Zheng, Fupeng Wei, Kezheng Wang, Zheng Zhang, Ziwei Chen, Liyue Niu, and Jizong Liu. "Construction of an Event Knowledge Graph Based on a Dynamic Resource Scheduling Optimization Algorithm and Semantic Graph Convolutional Neural Networks." Electronics 13, no. 1 (December 19, 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 case of domestic universities, fewer studies have studied knowledge graph construction methods for traffic safety incidents. In event knowledge graph construction, the reasonable release and recycling of computational resources are inefficient, and existing entity–relationship joint extraction methods are unable to deal with ternary overlapping and entity boundary ambiguity problems in relationship extraction. In response to the above problems, this paper proposes a knowledge graph construction method for university on-campus traffic safety events with improved dynamic resource scheduling algorithms and multi-layer semantic graph convolutional neural networks. The experiment’s results show that the proposed dynamic computational resource scheduling method increases GPU and CPU use by 25% and 9%. On the public dataset, the proposed data extraction model’s F1 scores for event triples increase by 1.3% on the NYT dataset and by 0.4% on the WebNLG dataset. This method can help the relevant university personnel in dealing with unexpected traffic incidents and reduce the impact on public opinion.

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Washbrook, E., and K. R. Fox. "Alternate-strand DNA triple-helix formation using short acridine-linked oligonucleotides." Biochemical Journal 301, no. 2 (July 15, 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 arranged antiparallel to each other. We find that Acr-T5G5 binds to the target sequence G6T6.-A6C6, in the presence of magnesium at pH 7.0, generating clear DNAse I footprints. In this structure the central guanine is not recognized by the third strand and is accessible to modification by dimethyl sulphate. Under these conditions no footprint was observed with Acr-G5T5 and T6G6.C6A6, though this triplex was evident in the presence of manganese chloride. Manganese also facilitated the binding of Acr-T5G5 to a second site in the fragment containing the sequence T6G6.C6A6. This represents interaction with the sequence G4ATCT6, located at the boundary between the synthetic insert and the remainder of the fragment, and suggests that this bivalent metal ion may stabilize triplexes that contain one or two mismatches. Manganese did not affect the interaction of either oligonucleotide with G6T6.A6C6.

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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 (December 8, 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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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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Suba, János. "A trianoni hármashatárok kijelölése." Jelenkori Társadalmi és Gazdasági Folyamatok 4, no. 3-4 (January 1, 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 tergeminate frontier marks have been positioned, together with the presentation of the different types of the monuments. It is worth mentioning that no one of the original four Trianon tergeminate frontier marks are standing on their primary places today.

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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 (June 30, 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 necessary conditions for optimality and the sufficient conditions for optimality of the classical continuous constraints boundary optimal triple control vector problem are stated and proven.

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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 described and accounts for variation of both with lateral image position and wall distance. Geometrically constrained templates of 2d Gaussians are used to provide least square fitting of triple image intensities, thereby iteratively improving the initial centers and depth position of each particle. In addition to Gaussian weighting, the convolution of a Gaussian and a Lorentzian is studied, that latter of which is considered promising for modeling defocused particle images at large distances from the focus. Lagrangian particle tracks are reconstructed from 3d particle positions using state-of-the-art tracking procedures. Comparative profile-PIV measurements provide reference measurements including estimates of the wall shear stress. A comparison with PIV flow statistics is possible by bin-averaging the velocities of the particle tracks in the wall-normal direction. Mean wall shear rates obtained from MA-µPTV and using single-line cross-correlation on the PIV data are in good agreement and within the uncertainty of the flow parameters. Statistics from bin-averaged velocities of all tracked particles indicate consistency with profile-PIV and agree well with DNS data up to wall distances of 30 wall units.

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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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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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Gamsjäger, Ernst, Daniel Ogris, and Jiří Svoboda. "Kinetics of Grain Boundary Networks Controlled by Triple Junction and Grain Boundary Mobility." Metals 8, no. 12 (November 22, 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 numerical results coincide with the corrected analytical solution. This solution can be derived either by applying the principle of maximum dissipation, or by applying the force balance at the triple junction within the framework of linear irreversible thermodynamics. The change of the area of infinite and finite grains is investigated analytically and numerically. By comparing the results of both approaches, the influence of the initial topology of the structural elements on the kinetics of grain growth can be estimated. Furthermore, the kinetics of grain growth of different idealized grain boundary networks is investigated. It is shown that square shaped grains surrounded by hexagons and dodecagons result in a more realistic grain growth scenarios than squares surrounded by octagons. A deviation from idealized grain boundary arrangements is e.g., observed, due to different triple junction mobilities, and the initially n-sided regular grain deforms in a complex manner.

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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 (August 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 experiments by Dahmen and Thangaraj.6,25 In accordance with their experiments, we find in numerical simulations that any two neighboring triple junctions belong to different symmetry classes. We introduce a local equilibrium condition at triple junctions which can be interpreted as a crystalline version of Young's law. The local equilibrium condition at triple junctions is purely determined by the grain boundary energies. In particular no triple junction energies are necessary to explain which triple junctions are possible. All triple junctions observed in the experiments as well as in the simulations fulfil the crystalline version of Young's law. Our approach is also capable of describing grain boundary motion in general polycrystalline thin films.

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Gaberdiel, Matthias R., and Ingo Runkel. "The logarithmic triplet theory with boundary." Journal of Physics A: Mathematical and General 39, no. 47 (November 8, 2006): 14745–79. http://dx.doi.org/10.1088/0305-4470/39/47/016.

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Rollett, A. D., C. C. Yang, W. W. Mullins, B. L. Adams, C. T. Wu, C. L. Bauer, D. Kinderlehrer, et al. "Extraction of Grain Boundary Energies from Triple Junction Geometry." Microscopy and Microanalysis 5, S2 (August 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-plane images and successive sections characterizes triple junction tangents from which true dihedral angles are calculated. If there is local equilibrium at each triple junction, we may apply Herring's relation. By limiting grain boundary character to a (three parameter) specification of misorientation for the preliminary analysis, we can neglect the torque terms and apply the sine law to the three boundaries. This provides two independent relations per triple junction between grain boundary energies and dihedral angles. By discretizing the misorientation and employing multiscale statistical analysis on large data sets, (relative) grain boundary energy as a function of boundary character can be extracted from triple junction geometry. The results are discussed with respect to current understanding of grain boundary structure based on their crystallography. The results suggest that a three parameter characterization of grain boundaries (lattice disorientation) is not an adequate description of boundary character. A full analysis including torque terms and a five parameter boundary description is under development.

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Straumal, B. B., V. G. Sursaeva, and B. Baretzky. "Grain boundary ridges and triple lines." Scripta Materialia 62, no. 12 (June 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 (April 2001): 141–50. http://dx.doi.org/10.1016/s0921-5093(00)01366-6.

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Lorenz, Oliver, Alexander Kühne, Martin Rudolph, Wahyu Diyatmika, Andrea Prager, Jürgen W. Gerlach, Jan Griebel, et al. "Role of Reaction Intermediate Diffusion on the Performance of Platinum Electrodes in Solid Acid Fuel Cells." Catalysts 11, no. 9 (August 31, 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 240 nm. These electrodes are characterized by a triple-phase boundary length and a thickness-depending double-phase boundary area. We reveal that the double-phase boundary is the active catalytic interface for the HOR. For Pt layers ≤ 60 nm, the HOR rate is rate-limited by the processes at the gas/catalyst and/or the catalyst/electrolyte interface while the hydrogen surface diffusion step is fast. For thicker layers (>60 nm), the diffusion of reaction intermediates on the surface of Pt becomes the limiting process. For the ORR, the predominant reaction pathway is via the triple-phase boundary. The double-phase boundary contributes additionally with a diffusion length of a few nanometers. Based on our results, we propose that the molecular reaction mechanism at the electrode interfaces based upon the triple-phase boundary concept may need to be extended to an effective area near the triple-phase boundary length to include all catalytically relevant diffusion processes of the reaction intermediates.

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Liu, Dan Dan, Jochen Fiebig, Martin Peterlechner, Simon Trubel, Matthias Wegner, Yong Du, Zhan Peng Jin, Gerhard Wilde, and S. Divinsky. "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 structure with temperature was used to interpret this phenomenon.

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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 (March 30, 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 corresponding CCBTCV is stated and demonstrated. The continuity of the Lipschitz (LIP.) operator between the STVS of the WFo for the QNLPBVP and the corresponding CCBTCV is proved. The existence of a CCBOTCV is stated and demonstrated under suitable conditions.

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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 modified form of the Zener force and the Gibbs-Thomson relation can be derived to reveal the influence of the triple line energy on second phase particles and the change of the equilibrium concentration of vacancies in the vicinity of voids at a grain boundary. The impact of triple junctions on the sintering of nanopowders is discussed. The role of “grain boundary - free surface” triple lines in the adhesive contact formation between spherical nanoparticles is considered. It is shown that there is a critical value of the triple line energy above which the nanoparticles do not stick together. Based on this result, a new nanoparticle agglomeration mechanism is proposed, which accounts for the formation of large agglomerates of crystallographically aligned nanoparticles during the nanopowder processing.

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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 compared and discussed. 2. A new approach will be presented that makes it possible to correctly measure the grain boundary triple line tension. For this the topography at an equilibrated triple junction was measured by atomic force microscopy. Preliminary results of grain boundary triple line energy measurements are presented. 3. The problem is discussed whether it is possible to achieve an equilibrium grain size during grain growth in single phase alloys. Various approaches to the problem are considered. It is shown that the most realistic possibility to stabilize the grain size in a polycrystal is by impurities with negative grain boundary adsorption.

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Protasova, Svetlana, and Vera G. Sursaeva. "Some Features of the Triple Junction Motion in Aluminium." Materials Science Forum 467-470 (October 2004): 795–800. http://dx.doi.org/10.4028/www.scientific.net/msf.467-470.795.

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The migration of the systems of tilt grain boundaries with a triple junction (<100>, <110> and <111>) in high-purity aluminium are presented. The experimental results demonstrate that the motion of grain boundary systems with triple junctions in Al at low temperature can be controlled by slowly moving triple junctions. In the high temperature range the triple junctions less affected the motion of the systems and the activation enthalpy was smaller than that at low temperature. The experiments revealed a drastic difference between activation enthalpy of grain boundary and triple junction motion at different temperatures. The compensation effect (linear dependence of migration activation enthalpy on preexponential mobility factor) at the migration of the systems with triple junction was observed. The compensation temperature was revealed to be close to the temperature for the triple junction mobility.

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Ryzhov, Oleg S. "Triple-Deck Instability of Supersonic Boundary Layers." AIAA Journal 50, no. 8 (August 2012): 1733–41. http://dx.doi.org/10.2514/1.j051534.

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Koropecki, Andres, Patrice Le Calvez, and Fabio Armando Tal. "A triple boundary lemma for surface homeomorphisms." Proceedings of the American Mathematical Society 147, no. 2 (November 8, 2018): 681–86. http://dx.doi.org/10.1090/proc/14258.

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Straumal, B. B., O. Kogtenkova, and P. Zięba. "Wetting transition of grain-boundary triple junctions." Acta Materialia 56, no. 5 (March 2008): 925–33. http://dx.doi.org/10.1016/j.actamat.2007.10.043.

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Tsurekawa, Sadahiro, Shinya Nakamichi, and Tadao Watanabe. "Determination of Percolation Threshold for Random Boundary Network on the Basis of EBSD/OIM Observations." Materials Science Forum 539-543 (March 2007): 2371–76. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2371.

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Grain boundary engineering through the control of grain boundary character distribution (GBCD) has been extensively employed as a powerful tool for achieving enhanced properties and for development of high performance both structural and functional polycrystalline materials. Many efforts were made firstly to increase the frequency of low-energy CSL boundaries of polycrystalline materials in grain boundary engineering. However, the connectivity of grain boundaries can be an important microstructural parameter governing bulk properties of polycrystalline materials as well as the GBCD. In the present work, the connectivity of random grain boundaries was quantitatively evaluated using both the triple junction distribution and random boundary cluster length on the basis of SEM-EBSD/OIM observations, and then these evaluated parameters were linked to intergranular corrosion of SUS304 stainless steel. We have found that the length of the maximum random boundary cluster drastically decrease with increasing CSL boundaries in the fraction ranging 60 – 80% CSL boundaries, which leads to percolation threshold occurring at approximately 70±5% CSL boundary fraction (at 30±5% random boundary fraction). The experimentally observed percolation threshold is much higher than theoretically obtained one based on randomly assembled network (at 35% resistant bonds for a 2D hexagonal lattice). In addition, the fraction of resistant triple junctions is found to increase with increasing the the CSL boundary fraction. An increase in the frequency of resistant triple junctions can enhance intergranular corrosion resistance of polycrystalline austenitic stainless steel even if the GBCD is the same.

Journal articles on the topic 'Boundary triples'

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