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Published: 4 June 2021

Last updated: 1 February 2022

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1

Schief, W. K., and C. Rogers. "The Da Rios system under a geometric constraint: the Gilbarg problem." Journal of Geometry and Physics 54, no. 3 (July 2005): 286–300. http://dx.doi.org/10.1016/j.geomphys.2004.10.001.

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2

Fernández-Rincón, Sergio, and Julián López-Gómez. "The Singular Perturbation Problem for a Class of Generalized Logistic Equations Under Non-classical Mixed Boundary Conditions." Advanced Nonlinear Studies 19, no. 1 (February 1, 2019): 1–27. http://dx.doi.org/10.1515/ans-2018-2034.

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Abstract This paper studies a singular perturbation result for a class of generalized diffusive logistic equations, {d\mathcal{L}u=uh(u,x)} , under non-classical mixed boundary conditions, {\mathcal{B}u=0} on {\partial\Omega} . Most of the precursors of this result dealt with Dirichlet boundary conditions and self-adjoint second order elliptic operators. To overcome the new technical difficulties originated by the generality of the new setting, we have characterized the regularity of {\partial\Omega} through the regularity of the associated conormal projections and conormal distances. This seems to be a new result of a huge relevance on its own. It actually complements some classical findings of Serrin, [39], Gilbarg and Trudinger, [21], Krantz and Parks, [27], Foote, [18] and Li and Nirenberg [28] concerning the regularity of the inner distance function to the boundary.

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3

Volz, M. G., M. Brazil, C. J. Ras, K. J. Swanepoel, and D. A. Thomas. "The Gilbert arborescence problem." Networks 61, no. 3 (July 18, 2012): 238–47. http://dx.doi.org/10.1002/net.21475.

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4

McLoughlin, John Grant. "Solutions to Calendar." Mathematics Teacher 90, no. 4 (April 1997): 298–99. http://dx.doi.org/10.5951/mt.90.4.0298.

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Problems 1–19, 28, and 29 were submitted by Margaret J. Kenney and Stanley J. Bezuszka. S.J. of the Mathematics Institute, Boston College, Chestnut Hill. MA 02167-3809. Problems 20–22 appear in The Wohascum County Problem Book by George T. Gilbert. Mark I. Krusemeyer, and Loren C. Larson Washington, D. C.: Mathematics) Association of America, 1993). Problems 23–27 were prepared by Robert Gerver and hts mathematics-research students, Sharon Poczter, Parisa Golestaneh, Nancy Friedlander, A1exis Soterakis, Nicole Miritello, Laura Henning, and Dalita Balassanian of North Shore High School, Glen Head, NY 11545.

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5

Gnedin, Alexander V., and Denis I. Miretskiy. "Winning Rate in the Full-Information Best-Choice Problem." Journal of Applied Probability 44, no. 02 (June 2007): 560–65. http://dx.doi.org/10.1017/s002190020000317x.

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6

Gnedin, Alexander V., and Denis I. Miretskiy. "Winning Rate in the Full-Information Best-Choice Problem." Journal of Applied Probability 44, no. 02 (June 2007): 560–65. http://dx.doi.org/10.1017/s0021900200118030.

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7

Gnedin, Alexander V., and Denis I. Miretskiy. "Winning Rate in the Full-Information Best-Choice Problem." Journal of Applied Probability 44, no. 2 (June 2007): 560–65. http://dx.doi.org/10.1239/jap/1183667422.

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8

Bonafini, Mauro, and Édouard Oudet. "A convex approach to the Gilbert–Steiner problem." Interfaces and Free Boundaries 22, no. 2 (July 6, 2020): 131–55. http://dx.doi.org/10.4171/ifb/436.

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9

Samuels, Stephen M. "Why do these quite different best-choice problems have the same solutions?" Advances in Applied Probability 36, no. 02 (June 2004): 398–416. http://dx.doi.org/10.1017/s0001867800013537.

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The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of n i.i.d. standard uniform random variables. Porosiński, in 1987, replaced a fixed n by a random N, uniform on {1,2,…,n} and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosiński compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosiński-Petruccelli stopping rule, and the full-information ‘duration of holding the best’ problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosiński problem in disguise.

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10

Samuels, Stephen M. "Why do these quite different best-choice problems have the same solutions?" Advances in Applied Probability 36, no. 2 (June 2004): 398–416. http://dx.doi.org/10.1239/aap/1086957578.

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The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of n i.i.d. standard uniform random variables. Porosiński, in 1987, replaced a fixed n by a random N, uniform on {1,2,…,n} and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosiński compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosiński-Petruccelli stopping rule, and the full-information ‘duration of holding the best’ problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosiński problem in disguise.

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11

Huestis, S. P. "The Backus-Gilbert problem for sampled band-limited functions." Inverse Problems 8, no. 6 (December 1, 1992): 873–87. http://dx.doi.org/10.1088/0266-5611/8/6/006.

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12

Bílek, Jaroslav, and Ľubomír Lupták. "Československo 1945–1948: Případ hybridního režimu?" Středoevropské politické studie Central European Political Studies Review 16, no. 2–3 (August 1, 2014): 188–213. http://dx.doi.org/10.5817/cepsr.2014.23.188.

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This article presents an interpretative case study utilizing the concept of hybrid regimes as presented by Leah Gilbert and Payam Mohseni to analyse the political regime of Czechoslovakia between the years 1945–1948. Our aim is to demonstrate that rather than a mere transitional phase on the road from democracy to authoritarianism or an episode of final tremors of the pre-war (democratic) regime, the 1945–1945 regime represents a full-fledged hybrid, rooted in the specific conditions of the post-war period. One of the major problems in contemporary discussions about hybrid regimes is the blurred and somewhat unstable boundary between democratic and authoritarian regimes, especially when viewed only as a function of the electoral processes and mechanics. Gilbert and Mohseni’s classification of hybrid regimes attempts to overcome this problem by including two additional analytic dimensions, allowing to point at the dynamic development of the political regime in post-war Czechoslovakia and its rather lively movement on the scale between authoritarianism and democracy.

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13

Valente, Luisa. "Praedicaturi supponimus. Is Gilbert of Poitiers’ approach to the problem of linguistic reference a pragmatic one?" Vivarium 49, no. 1-3 (2011): 50–74. http://dx.doi.org/10.1163/156853411x590435.

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AbstractThe article investigates how the problem of (linguistic) reference is treated in Gilbert of Poitiers’ Commentaries on Boethius’ Opuscula sacra. In this text the terms supponere, suppositus,-a,-um, and suppositio mainly concern the act of a speaker (or of the author of a written text) that consists of referring—by choosing a name as subject term in a proposition—to one or more subsistent things as what the speech act (or the written text) is about. Supposition is for Gilbert an action performed by a speaker, not a property of terms, and his ‘contextual approach’ has a pragmatic touch: “we do not predicate in order to supposit as much as we supposit in order to predicate”. Language is considered by Gilbert as a system for communication between human beings, key notions are the ‘sense in the author’s mind’ (sensus mentis eius qui loquitur) and the ‘interpreter’s understanding’ (intelligentia lectoris). The phenomenon of ‘disciplinal’ discourse (“man is a species of individuals”) is treated by means of these hermeneutic notions and not by means of a special kind of supposition.

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14

Rogerson, Peter A. "Probabilities of choosing applicants of arbitrary rank in the secretary problem." Journal of Applied Probability 24, no. 2 (June 1987): 527–33. http://dx.doi.org/10.2307/3214276.

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Gilbert and Mosteller (1966) derive the probability of obtaining the best secretary when a fixed number of potential employees of varying quality are interviewed sequentially by an employer. This paper extends these results by deriving the probability of selecting an applicant of arbitrary rank under a variety of circumstances concerning the objective of employers and the amount of information employers have about applicant quality.

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15

Rogerson, Peter A. "Probabilities of choosing applicants of arbitrary rank in the secretary problem." Journal of Applied Probability 24, no. 02 (June 1987): 527–33. http://dx.doi.org/10.1017/s0021900200031168.

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Gilbert and Mosteller (1966) derive the probability of obtaining the best secretary when a fixed number of potential employees of varying quality are interviewed sequentially by an employer. This paper extends these results by deriving the probability of selecting an applicant of arbitrary rank under a variety of circumstances concerning the objective of employers and the amount of information employers have about applicant quality.

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16

Wilson, J. A., and J. A. MacBain. "A Resistance Problem (E. N. Gilbert and L. A. Shepp)." SIAM Review 27, no. 3 (September 1985): 449–52. http://dx.doi.org/10.1137/1027119.

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17

Bhargava, D. K. "A Resistance Problem (E. N. Gilbert and L. A. Shepp)." SIAM Review 35, no. 3 (September 1993): 492–93. http://dx.doi.org/10.1137/1035099.

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18

Cimpoesu, Dorin, Leonard Spinu, and Alexandru Stancu. "Transverse Susceptibility Method in Nanoparticulate Magnetic Media." Journal of Nanoscience and Nanotechnology 8, no. 6 (June 1, 2008): 2731–44. http://dx.doi.org/10.1166/jnn.2008.18304.

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Transverse susceptibility (TS) method is a reliable method for the determination of anisotropy in nanoparticulate media. To correctly evaluate the value of anisotropy in various modern nanostructured materials, a number of theoretical problems related to the method have to be well understood to avoid significant systematic errors. This paper presents the state of the art in the TS method which includes the expression for single domain particles with any type of anisotropy, the theoretical and micromagnetic, using Landau-Lifshitz-Gilbert (LLG) equation and stochastic LLG equation studies of the effects of ac field amplitude, inter-particle interactions, and magnetic relaxation. The problem of both real and imaginary parts of the TS signal is also discussed.

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19

Hon, Y. C., and T. Wei. "Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation." Inverse Problems 17, no. 2 (February 14, 2001): 261–71. http://dx.doi.org/10.1088/0266-5611/17/2/306.

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20

Tsutsumi, Masayoshi. "On the Cauchy problem for the noncompact Landau–Lifshitz–Gilbert equation." Journal of Mathematical Analysis and Applications 344, no. 1 (August 2008): 157–74. http://dx.doi.org/10.1016/j.jmaa.2008.02.020.

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21

Heredia, Juan Manuel. "Simondon y el problema de la analogía." Ideas y Valores 68, no. 171 (September 1, 2019): 209–30. http://dx.doi.org/10.15446/ideasyvalores.v68n171.65307.

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El artículo analiza y problematiza el “método analógico” puesto en juego por la filosofía de la individuación de Gilbert Simondon. Plantea las condiciones del problema y reconstruye el debate que ha propiciado entre los intérpretes; precisa el carácter isodinámico y genético de la práctica analógica simondoniana, así como su objeto específico; analiza el vínculo teórico que mantiene con el Dialogue sur l’analogie (1946) de Bruno de Solages, y concluye con una reflexión relativa a las tensiones que recorren al método analógico en tanto intermediario entre epistemología y metafísica.

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22

Weirich, Paul. "Coordination and Hyperrationality." ProtoSociology 35 (2018): 197–214. http://dx.doi.org/10.5840/protosociology20183511.

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Margaret Gilbert (1990) argues that although the rationality of the agents in a standard coordination problem does not suffice for their coordination, a social convention of coordination, understood as the agents’ joint acceptance of a principle requiring their coordination, does the job. Gilbert’s argument targets agents rational in the game-theoretic sense, which following Sobel (1994: Chap. 14), I call hyperrational agents. I agree that hyperrational agents may fail to coordinate in some cases despite the obvious benefits of coordination. However, I add that fully rational agents, who rationally exercise rationality’s permissions, may coordinate in these cases without jointly accepting a principle of coordination. I make this point using a model that adopts common simplifying assumptions about agents and their coordination problems.

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23

Kambites, Mark. "Anisimov's Theorem for inverse semigroups." International Journal of Algebra and Computation 25, no. 01n02 (February 2015): 41–49. http://dx.doi.org/10.1142/s0218196715400032.

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The idempotent problem of a finitely generated inverse semigroup is the formal language of all words over the generators representing idempotent elements. This paper proves that a finitely generated inverse semigroup with regular idempotent problem is necessarily finite. This answers a question of Gilbert and Noonan Heale, and establishes a generalization to inverse semigroups of Anisimov's Theorem for groups.

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24

Sezer, Ali Devin, and Ferruh Özbudak. "Approximation of bounds on mixed-level orthogonal arrays." Advances in Applied Probability 43, no. 02 (June 2011): 399–421. http://dx.doi.org/10.1017/s0001867800004912.

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Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

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25

Sezer, Ali Devin, and Ferruh Özbudak. "Approximation of bounds on mixed-level orthogonal arrays." Advances in Applied Probability 43, no. 2 (June 2011): 399–421. http://dx.doi.org/10.1239/aap/1308662485.

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Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays. The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms. The first is a recursive algorithm that computes the bounds exactly, the second is based on an asymptotic analysis, and the third is a simulation algorithm. They are all based on the representation of the combinatorial expressions that appear in the bounds as expectations involving a symmetric random walk. The Markov property of the underlying random walk gives the recursive formula to compute the expectations. A large deviation (LD) analysis of the expectations provides the asymptotic algorithm. The asymptotically optimal importance sampling (IS) of the same expectation provides the simulation algorithm. Both the LD analysis and the construction of the IS algorithm use a representation of these problems as a sequence of stochastic optimal control problems converging to a limit calculus of a variations problem. The construction of the IS algorithm uses a recently discovered method of using subsolutions to the Hamilton-Jacobi-Bellman equations associated with the limit problem.

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26

Pujol, Jose M. "The Backus-Gilbert method and their minimum-norm solution." GEOPHYSICS 78, no. 3 (May 1, 2013): W9—W30. http://dx.doi.org/10.1190/geo2012-0264.1.

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This paper has two objectives. One is to review the Backus-Gilbert (BG) method. Backus and Gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods. If [Formula: see text] is an earth property of interest, the BG method provides average values of [Formula: see text] over some radial intervals. If an interval [Formula: see text] is relatively short and centered near a particular radius [Formula: see text], the BG average will be a local average of [Formula: see text] near [Formula: see text] with a resolving length of [Formula: see text]. Backus and Gilbert also introduce the concept of trade-off between resolution and error, which is essential in inverse theory regardless of the inversion method. In spite of its importance, inverse theory texts neither describe the BG method in full nor show how to apply it in all its generality. Because the three papers that introduce the BG method are mathematically difficult, this paper provides background material and a detailed derivation of the method, as well as two completely worked-out synthetic 1D examples. In addition, the application of the method to disciplines other than solid-earth geophysics is discussed. The second objective is to derive the minimum-norm solution for the continuous case, also introduced by Backus and Gilbert. Their derivation is little known, and it is completely different from a better known, simpler derivation that has some logical difficulties. The minimum-norm solution lacks a constraint that the BG averages have, which may lead to results affected by significant error. To address this problem, a constrained minimum-norm solution is derived here. The two examples for the BG method were used to compute minimum-norm solutions. Interestingly, these examples show that the BG averages can be closer to the true values than the corresponding minimum-norm solutions, although these results should not be considered general.

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27

Kim, Jaegwon. "The Mind–Body Problem after Fifty Years." Royal Institute of Philosophy Supplement 43 (March 1998): 3–21. http://dx.doi.org/10.1017/s1358246100004276.

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It was about half a century ago that the mind–body problem, which like much else in serious metaphysics had been moribund for several decades, was resurrected as a mainstream philosophical problem. The first impetus came from Gilbert Ryle'sThe Concept of Mind, published in 1948, and Wittgenstein's well-known, if not well-understood, reflections on the nature of mentality and mental language, especially in hisPhilosophical Investigationswhich appeared in 1953. The primary concerns of Ryle and Wittgenstein, however, focused on the logic of mental discourse rather than the metaphysical issue of how our mentality is related to our bodily nature. In fact, Ryle and Wittgenstein would have regarded, each for different reasons, the metaphysical problem of the mind-body relation as arising out of deplorable linguistic confusions and not amenable to intelligible discussion. There was C. D. Broad's earlier and much neglected classic,The Mind and Its Place in Nature, which appeared in 1925, but this work, although robustly metaphysical, failed to connect with, and shape, the mind–body debate in the second half of this century.

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28

Snieder, R. "An extension of Backus-Gilbert theory to nonlinear inverse problems." Inverse Problems 7, no. 3 (June 1, 1991): 409–33. http://dx.doi.org/10.1088/0266-5611/7/3/008.

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29

Greig, Martin. "Gilbert Burnet and the Problem of Nonconformity in Restoration Scotland and England." Canadian Journal of History 32, no. 1 (April 1997): 1–24. http://dx.doi.org/10.3138/cjh.32.1.1.

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30

Clemence, Dominic P. "Subordinacy Analysis and Absolutely Continuous Spectra for Sturm-Liouville Equations with Two Singular Endpoints." Canadian Mathematical Bulletin 41, no. 1 (March 1, 1998): 23–27. http://dx.doi.org/10.4153/cmb-1998-005-6.

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AbstractThe Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.

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31

Valente, Luisa. "Supposition Theory and Porretan Theology: Summa Zwettlensis and Dialogus Ratii et Everardi." Vivarium 51, no. 1-4 (2013): 119–44. http://dx.doi.org/10.1163/15685349-12341244.

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Abstract The article investigates how the problem of (linguistic) reference is treated in the theology of two pupils of Gilbert of Poitiers by means of suppo* terms (supponere; suppositus,-a,-um; suppositio). Supposition is for Gilbert an action performed by a speaker, not a property of terms, and he considers language as a system for communication between human beings: key notions are the ‘sense in the author’s mind’ and the ‘interpreter’s understanding’. In contrast, the two Porretans tend to objectify language as a formal system of terms. Suppositio becomes in the Summa Zwettlensis the name itself as subject term in a proposition, and is divided into many kinds; formal rules are described which govern the influence of the predicate on the subject term’s denotation. In Everard of Ypres’ Dialogus Ratii et Everardi, supponere is a function (officium) of the name, and ‘human is a species of individuals’ is, as in some logical treatises and differently from Gilbert, a case of rhetorical transfer.

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32

Daechsel, Stefano. "Simondon’s Technical Culture and a Politics of Problems." Sensorium Journal 3 (March 26, 2021): 5–17. http://dx.doi.org/10.3384/sens.2002-3030.2021.3.5-17.

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There is a timeliness to Gilbert Simondon’s call in On the Mode of Existence of Technical Objects (1958) for a technical culture that fosters a ”genuine awareness of technical realities.” Writing in the context of mid-20th century France, Simondon worried about a lack of technological understanding and envisaged a technical culture in which technological education would be considered as essential as literacy to meaningful participation in society. Sixty years on, the need for widespread technological awareness is greater than ever. The aim of this article is to clarify and support this claim by examining it through the lens of a politics of problems that can be found in Deleuze’s Difference and Repetition (1968).

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33

Jenson, Robert W. "Dante’s Vision." Studies in Christian Ethics 30, no. 2 (January 6, 2017): 167–69. http://dx.doi.org/10.1177/0953946816684442.

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If we desire God with everything in us, how can we also love our created neighbor? Gilbert Meilaender displays Dante’s Paradiso as a resolution of this ancient problem. Jenson admires the beauty of Dante-according-according-to-Meilaender, but proposes that it must be tweaked a little to be fully satisfactory.

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34

Heredia, Juan Manuel. "Elementos para pensar el problema de la tecnocracia en Gilbert Simondon." Isegoría, no. 63 (December 30, 2020): 507. http://dx.doi.org/10.3989/isegoria.2020.063.12.

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Tras plantear el problema de la tecnocracia a partir del debate entre Marcuse y Habermas, el artículo sitúa la perspectiva de Simondon frente a la cuestión y, tematizando las relaciones entre sociedad, cultura y desarrollo tecnológico, analiza una serie de elementos éticos y políticos implicados en su filosofía. En este sentido, el texto aborda las críticas simondonianas a la utopía tecnocrática, introduce su conceptualización de la técnica, y examina sobre dicha base los tres conceptos que aporta para repensar la práctica política (pensamientos político-sociales, acto de gobierno, juicio político).

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35

Holt, Geoffrey. "Gilbert Talbot and the Talbot Case." Recusant History 24, no. 2 (October 1998): 166–70. http://dx.doi.org/10.1017/s0034193200002454.

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In the 1740s the English Jesuit house at Liège where students of philosophy and theology were prepared for the priesthood was in financial difficulties. One of the main supports of the college was an annual pension from Bavaria but in the 1740s Bavaria was involved in war and the pension was frequently not paid. The number in the community had to be reduced, many students being charitably welcomed in other Jesuit houses in Europe. It was at this time when the finances of the English province were strained that two plans came up for consideration. One was to extend the apostolate of the Maryland English Jesuit mission in Pennsylvania; the other was to open at Boulogne a preparatory school for St. Omers College. The problem was how to obtain the necessary funds.

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36

Hadda, Mohammed, and Mouhcine Tilioua. "Thin Film Limits in Magnetoelastic Interactions." Mathematical Problems in Engineering 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/165962.

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This paper deals with classical dimensional reductions 3D-2D and 3D-1D in magnetoelastic interactions. We adopt a model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem both for flat and slender media by using the so-called energy method.

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37

Kennedy, Angela. "Compassion-Focused EMDR." Journal of EMDR Practice and Research 8, no. 3 (2014): 135–46. http://dx.doi.org/10.1891/1933-3196.8.3.135.

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Compassion-focused therapy was developed to enhance physiological systems related to well-being, safeness, and connectedness in people where shame and self-criticism inhibited progress in therapy (Gilbert, 2000; Gilbert & Irons, 2005). This system links attachment experiences with emotion regulation capacities, with integrative capacities of the mind and also with the interplay between different motivational systems, which are played out in multiple self-states (Cortina & Liotti, 2010; Cozolino, 2010; Gilbert, 2009; Liotti & Gilbert, 2011). Hence, a compassionate focus could potentially prove valuable in eye movement desensitization and reprocessing (EMDR), particularly where shame or attachment trauma is involved or for those traumas that have impacted on the structure of the self, for example, dissociation. A structured compassion-focused EMDR (CF-EMDR) seems likely to be particularly useful for therapists wishing to pay positive attention to strengths and well-being. The primary task of the CF-EMDR therapist would therefore be to facilitate a warm and wise relationship to the problems that brought the person to EMDR. This article outlines the potential benefit of a compassionate focus in the processing phases of EMDR to address self-critical blocks, giving clinical examples in tables to illustrate the process and language.

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38

Staller, Jerome M., Brian P. Sullivan, and Edward A. Friedman. "Special Problems With Value-Of-Life Estimates: A Reply To Dr. Gilbert." Journal of Forensic Economics 12, no. 1 (December 1, 1999): 65–66. http://dx.doi.org/10.5085/0898-5510-12.1.65.

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ANTONOPOULOS, D., N. V. KANG, and R. DEBONO. "Our Experience with the Use of the Dorsal Ulnar Artery Flap in Hand and Wrist Tissue Cover." Journal of Hand Surgery 22, no. 6 (December 1997): 739–44. http://dx.doi.org/10.1016/s0266-7681(97)80437-8.

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We describe a series of six cases exploring the limits of reliability of the dorsal ulnar artery fasciocutaneous flap as described by Becker and Gilbert (1988a; b). Although the territory supplied by the dorsal ulnar artery is 10 cm to 20 cm long by 5 cm to 9 cm wide, Becker and Gilbert suggested that flaps should be confined to smaller dimensions. We have found that larger flaps (15 to 20 cm long and 5 to 8 cm wide) are feasible, extending the use of the flap to the radial side of the wrist and hand. However, problems were encountered with venous drainage and these larger flaps should be used with caution.

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Lin, Junyu, and Shijin Ding. "Smooth solution to the one-dimensional inhomogeneous non-automorphic Landau–Lifshitz equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2072 (March 21, 2006): 2397–413. http://dx.doi.org/10.1098/rspa.2006.1689.

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Using the differential–difference method and viscosity vanishing approach, we obtain the existence and uniqueness of the global smooth solution to the periodic initial-value problem of the inhomogeneous, non-automorphic Landau–Lifshitz equation without Gilbert damping terms in one dimension. To establish the uniform estimates, we use some identities resulting from the fact and the fact that the vectors form an orthogonal base of the space .

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Driska, Andrew P., and Daniel R. Gould. "Evaluating a Problem-Based Group Learning Strategy for Online, Graduate-Level Coach Education." Kinesiology Review 3, no. 4 (November 2014): 227–34. http://dx.doi.org/10.1123/kr.2014-0061.

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Research has shown that coaches learn through reflective practice (Trudel & Gilbert, 2006), that communities of practice can assist the reflective process (Culver & Trudel, 2008), and that problem-based learning can increase critical thought by coaches (Jones & Turner, 2006). To help coaches develop reflective practice skills in an online course, the authors designed and implemented a novel assignment combining the principles of a community of practice with problem-based learning. Small groups of students were presented with a problem scenario and then met synchronously online using a low bandwidth group chat application (EtherPad) to diagnose the problem, strategize, and outline a solution. Students were able to conduct group meetings with only minor technical diffculties, and their written work demonstrated that a moderate level of refection had occurred. Future assignment redesigns should allow more opportunities for student-instructor interaction to facilitate greater development of student reflective practice skills.

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de HOOG, FRANK R., and ROBERT S. ANDERSSEN. "ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE PROBLEMS IN LIOUVILLE NORMAL FORM." Mathematical Models and Methods in Applied Sciences 11, no. 01 (February 2001): 43–56. http://dx.doi.org/10.1142/s0218202501000738.

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In the analysis of both continuous and discrete eigenvalue problems, asymptotic formulas play a central and crucial role. For example, they have been fundamental in the derivation of results about the inversion of the free oscillation problem of the Earth and related inverse eigenvalue problems, the computation of uniformly valid eigenvalues approximations, the proof of results about the behavior of the eigenvalues of Sturm–Liouville problems with discontinuous coefficients, and the construction of a counterexample to the Backus–Gilbert conjecture. Useful formulas are available for continuous eigenvalue problems with general boundary conditions as well as for discrete eigenvalue problems with Dirichlet boundary condition. The purpose of this paper is the construction of asymptotic formulas for discrete eigenvalue problems with general boundary conditions. The motivation is the computation of uniformly valid eigenvalue approximations. It is now widely accepted that the algebraic correction procedure, first proposed by Paine et al.,13 is one of the simplest methods for computing uniformly valid approximations to a sequence of eigenvalues of a continuous eigenvalue problem in Liouville normal form.8 This relates to the fact that, for Liouville normal forms with Dirichlet boundary conditions, it is not too difficult to prove that such procedures yield, under quite weak regularity conditions, uniformly valid O(h2) approximations. For Liouville normal forms with general boundary conditions, the corresponding error analysis is technically more challenging. Now it is necessary to have, for such Liouville normal forms, higher order accurate asymptotic formulas for the eigenvalues and eigenfunctions of their continuous and discrete counterparts. Assuming that such asymptotic formulas are available, it has been shown1 how uniformly valid O(h2) results could be established for the application of the algebraic correction procedure to Liouville normal forms with general boundary conditions. Algorithmically, this methodology represents an efficient procedure for determining uniformly valid approximations to sequences of eigenvalues, even though it is more complex than for Liouville normal forms with Dirichlet boundary conditions. As well as giving a brief review of the subject for general (Robin) boundary conditions, this paper sketches proofs for the asymptotic formulas, for Robin boundary conditions, which are required in order to construct the mentioned O(h2) results.

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Fine, Benjamin, Gerhard Rosenberger, and Michael Stille. "The isomorphism problem for a class of para-free groups." Proceedings of the Edinburgh Mathematical Society 40, no. 3 (October 1997): 541–49. http://dx.doi.org/10.1017/s0013091500024007.

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In 1962 Gilbert Baumslag introduced the class of groups Gi, j for natural numbers i, j, defined by the presentations Gi, j = < a, b, t; a−1 = [bi, a] [bj, t] >. This class is of special interest since the groups are para-free, that is they share many properties with the free group F of rank 2.Magnus and Chandler in their History of Combinatorial Group Theory mention the class Gi, j to demonstrate the difficulty of the isomorphism problem for torsion-free one-relator groups. They remark that as of 1980 there was no proof showing that any of the groups Gi, j are non-isomorphic. S. Liriano in 1993 using representations of Gi, j into PSL(2, pk), k ∈ ℕ, showed that G1,1 and G30,30 are non-isomorphic. In this paper we extend these results to prove that the isomorphism problem for Gi, 1, i ∈ ℕ is solvable, that is it can be decided algorithmically in finitely many steps whether or not an arbitrary one-relator group is isomorphic to Gi, 1. Further we show that Gi, 1 ≇ G1, 1 for all i > 1 and if i, k are primes then Gi, 1 ≅ Gk, 1 if and only if i = k.

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Summers, Kirk. "“Prudentius Psychomachia 317”." Vigiliae Christianae 66, no. 4 (2012): 426–29. http://dx.doi.org/10.1163/157007212x635830.

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Abstract The Latin text at Prudentius, Psychomachia 317 presents some syntactical difficulties, mostly stemming from the unexpected word quia. The manuscripts and glossa vetus offer little help on the matter. Gilbert Wakefield offered a convincing solution to the problem in a note that was buried in an edition of Lucretius that he edited in 1797. No subsequent editor of Prudentius has noticed his emendation, which should be revived and included in future editions.

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Leahy, Robert L. "The Therapeutic Relationship in Cognitive-Behavioral Therapy." Behavioural and Cognitive Psychotherapy 36, no. 6 (November 2008): 769–77. http://dx.doi.org/10.1017/s1352465808004852.

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AbstractCognitive behavioral therapy has often been criticized for ignoring the role of the therapeutic relationship. In this article, I outline several dimensions for case formulation and intervention that suggest that the cognitive-behavioral approach can be a powerful theoretical model for understanding the causes of and the strategies for overcoming impasses in therapy. I review how the clinician and patient can collaborate in understanding the importance of case conceptualization, validation, emotional philosophies, victim resistance, schematic resistance, schematic mismatch, sunk-cost commitment, and self-handicapping. The relevance of these factors for both patient and therapist are discussed. During the last decade there has been increased interest in the nature of the therapeutic relationship in cognitive behavioral therapy (Gilbert, 1992; Safran, 1998; Safran and Muran, 2000; Greenberg, 2002; Leahy, 2001; Gilbert and Irons, 2005; Leahy, 2005; Bennett-Levy and Thwaites, 2007; Gilbert and Leahy, 2007). Cognitive behavioral therapists have proposed that the therapeutic relationship reflects interpersonal schemas, earlier attachment problems, emotional processing, failures in validation and compassion, and a variety of processes underlying non-compliance or resistance. Resolving “ruptures” in the therapeutic relationship provides an often essential opportunity for using the relationship as a means to modify cognitive and emotional problems (Safran, Muran, Samstag and Stevens, 2002; Katzow and Safran 2007). In light of the emphasis on “empirically supported treatments” (such as CBT) there is the risk that the alliance in therapy may be foreshadowed by the techniques and protocols used in CBT, perhaps giving credibility to Mahoney's (1991) earlier claim that therapy can become “technolatry”.

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Gutiérrez, Susana, and André de Laire. "The Cauchy problem for the Landau–Lifshitz–Gilbert equation in BMO and self-similar solutions." Nonlinearity 32, no. 7 (June 18, 2019): 2522–63. http://dx.doi.org/10.1088/1361-6544/ab1296.

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Melcher, Christof. "Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions." Indiana University Mathematics Journal 61, no. 3 (2012): 1175–200. http://dx.doi.org/10.1512/iumj.2012.61.4717.

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BLAKELY, CHRISTOPHER D. "A NEW BACKUS–GILBERT MESHLESS APPROXIMATION METHOD FOR INITIAL-BOUNDARY VALUE PARTIAL DIFFERENTIAL EQUATIONS." International Journal of Computational Methods 03, no. 03 (September 2006): 337–53. http://dx.doi.org/10.1142/s0219876206000783.

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A Backus–Gilbert approximation method is introduced in this paper as a tool for numerically solving initial-boundary value problems. The formulation of the method with its connection to the standard moving least-squares formulation will be given along with some numerical examples including a numerical solution to the viscous nonlinear Burgers equation in two-dimensions. In addition, we highlight some of the main advantages of the method over previous numerical methods based on meshless collocation approximation in order to validate its robust approximating power and easy handling of initial-boundary value problems.

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Pilkington, M., and J. P. Todoeschuck. "Naturally smooth inversions with a priori information from well logs." GEOPHYSICS 56, no. 11 (November 1991): 1811–18. http://dx.doi.org/10.1190/1.1442993.

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Regularization is usually necessary to guarantee a solution to a given inverse problem. When constructing a model that gives an adequate fit to the data, some suitable method of regularization which provides numerical stability can be used. When investigating the resolution and variance of the computed model parameters, the character of regularization should be specified by the a priori information available. This avoids arbitrary variation of the damping to suit the interpreter. For geophysical inverse problems we determine the appropriate level of regularization (in the form of parameter covariances) from power spectral analysis of well‐log measurements. For resistivity data, well logs indicate that the spatial variation with depth can be described adequately by a scaling noise model, that is, one in which the power spectral density is proportional to some power (α) of the frequency. We show that α, the scaling exponent, controls the smoothness of the final model. For α < 0, the model becomes smoother as α becomes more negative. As a specific example, this approach is applied to the magnetotelluric inverse problem. A synthetic example illustrates the smoothing effect of α on inversion. Comparison between the scaling noise approach and a previous Backus‐Gilbert type inversion on some field data shows that using the appropriate value of α (−1.8 for this example) results in a model which is structurally simple and contains only those features well resolved by the data.

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Schmidgen, Henning. "Thinking technological and biological beings: Gilbert Simondon's philosophy of machines." Revista do Departamento de Psicologia. UFF 17, no. 2 (December 2005): 11–18. http://dx.doi.org/10.1590/s0104-80232005000200002.

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The article proposes an investigation of the contributions of G. Simondon in the studies of Science and Technology. Leaving the contributions of cybernetics behind, Simondon investigates the processes of individuation, development and evolution of technology. According to his philosophy of machines, technical objects are contextualized both synchronically and diachronically. In contrast with other theoretical approaches of this problem, we emphasize that the interest of this author lies in the energetic determinism that is manifested in and outside technical objects. At last, we point out the contributions of this theoretical approach to contemporary studies on the history of scientific experiments.

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