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1
Schlitt, G. "The Lindelöf Tychonoff Theorem and choice principles." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (July 1991): 57–65. http://dx.doi.org/10.1017/s0305004100070110.
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AbstractIt is an important result in frame theory that the coproduct of a family of regular Lindelöf frames is Lindelöf [3]. We show that this ‘Lindelöf Tychonoff Theorem’ or ‘LTT’ is independent of ZF and indeed lies close in logical strength to the Axiom of Countable Choice, quite unlike the case with the usual (frame) Tychonoff Theorem. Along the way we construct the regular Lindelöf coreflection and obtain a simple proof of the LTT as a corollary.
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Soulé, Christophe. "Erratum: Linear Projections and Successive Minima." Nagoya Mathematical Journal 216 (2014): 111–15. http://dx.doi.org/10.1017/s0027763000022455.
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The proof of Proposition 1 and Theorem 2 in [3] is incorrect. Indeed, Sections 2.5 and 2.7 in [3] contain a vicious circle: the definition of the filtrationVi, 1 ≤i≤n, in Section 2.5 of that article depends on the choice of the integersni, when the definition of the integersniin Section 2.7 depends on the choice of the filtration(Vi). Thus, only Theorem 1 and Corollary 1 in [3] are proved. In the following we will prove another result instead of [3, Proposition 1].
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Friedman, Sy-David, Victoria Gitman, and Vladimir Kanovei. "A model of second-order arithmetic satisfying AC but not DC." Journal of Mathematical Logic 19, no. 01 (June 2019): 1850013. http://dx.doi.org/10.1142/s0219061318500137.
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We show that there is a [Formula: see text]-model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a [Formula: see text]-assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of [Formula: see text]. This work is a rediscovery by the first two authors of a result obtained by the third author in [V. G. Kanovei, On descriptive forms of the countable axiom of choice, Investigations on nonclassical logics and set theory, Work Collect., Moscow, 3-136 (1979)].
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Soulé, Christophe. "Erratum: Linear Projections and Successive Minima." Nagoya Mathematical Journal 216 (2014): 111–15. http://dx.doi.org/10.1215/00277630-2847567.
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The proof of Proposition 1 and Theorem 2 in [3] is incorrect. Indeed, Sections 2.5 and 2.7 in [3] contain a vicious circle: the definition of the filtration Vi, 1 ≤ i ≤ n, in Section 2.5 of that article depends on the choice of the integers ni, when the definition of the integers ni in Section 2.7 depends on the choice of the filtration (Vi). Thus, only Theorem 1 and Corollary 1 in [3] are proved. In the following we will prove another result instead of [3, Proposition 1].
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WILKIN, GRAEME. "HOMOTOPY GROUPS OF MODULI SPACES OF STABLE QUIVER REPRESENTATIONS." International Journal of Mathematics 21, no. 09 (September 2010): 1219–38. http://dx.doi.org/10.1142/s0129167x1000646x.
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The purpose of this paper is to describe a method for computing homotopy groups of the space of α-stable representations of a quiver with fixed dimension vector and stability parameter α. The main result is that the homotopy groups of this space are trivial up to a certain dimension, which depends on the quiver, the choice of dimension vector, and the choice of parameter. As a corollary we also compute low dimensional homotopy groups of the moduli space of α-stable representations of the quiver with fixed dimension vector, and apply the theory to the space of non-degenerate polygons in three-dimensional Euclidean space.
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Belli, P., A. Incicchitti, and F. Cappella. "Inorganic scintillators in direct dark matter investigation." International Journal of Modern Physics A 29, no. 19 (July 30, 2014): 1443011. http://dx.doi.org/10.1142/s0217751x14430118.
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The discoveries, the developments and the studies that have been performed in the research of new materials and purification techniques, nowadays allow us a wide choice among inorganic scintillators for a variety of uses. In this paper the application of the inorganic crystal scintillators to direct dark matter investigation will be considered in more detail. The present framework of the detectors used at low energy for direct dark matter investigation also offers useful hints for further corollary developments.
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Powell, Thomas. "Parametrized bar recursion: a unifying framework for realizability interpretations of classical dependent choice." Journal of Logic and Computation 29, no. 4 (June 6, 2019): 519–54. http://dx.doi.org/10.1093/logcom/exv056.
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Abstract During the last 20 years or so, a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with some form of bar recursion, which realizes the negative translation of either countable or countable dependent choice. In this work, we present the many variants of bar recursion used in this context as instantiations of a parametrized form of backward recursion, and give a uniform proof that under certain conditions this recursor realizes a corresponding family of parametrized dependent choice principles. From this proof, the soundness of most of the existing bar recursive realizability interpretations of choice, including those based on the Berardi–Bezem–Coquand functional, modified realizability and the more recent products of selection functions of Escardó and Oliva, follows as a simple corollary. We achieve not only a uniform framework in which familiar realizability interpretations of choice can be compared, but show that these represent just simple instances of a large family of potential interpretations of dependent choice principles.
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PASCU, MIHAI N., and NICOLAE R. PASCU. "NEIGHBOURHOODS OF UNIVALENT FUNCTIONS." Bulletin of the Australian Mathematical Society 83, no. 2 (September 14, 2010): 210–19. http://dx.doi.org/10.1017/s0004972710000468.
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AbstractThe main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also present an application of the main result in terms of Taylor series, and we show that the hypothesis of our main result is sharp.
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Bruns, Winfried, and Jürgen Herzog. "On multigraded resolutions." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 2 (September 1995): 245–57. http://dx.doi.org/10.1017/s030500410007362x.
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This paper was initiated by a question of Eisenbud who asked whether the entries of the matrices in a minimal free resolution of a monomial ideal (which, after a suitable choice of bases, are monomials) divide the least common multiple of the generators of the ideal. We will see that this is indeed the case, and prove it by lifting the multigraded resolution of an ideal, or more generally of a multigraded module, keeping track of how the shifts ‘deform’' in such a lifting; see Theorem 2·1 and Corollary 2·2.
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Benson-Allott, Caetlin. "The Ennui of the Scroll." Film Quarterly 75, no. 2 (2021): 84–88. http://dx.doi.org/10.1525/fq.2021.75.2.84.
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Inspired by her difficulty selecting a film as the subject for her column, Film Quarterly regular Caetlin Benson-Allott explores the concept of the “paradox of choice” in relation to contemporary film culture. A common feature of late-stage capitalism with its characteristic consumer abundance, the paradox of choice afflicts people with too many options, decreasing their happiness and increasing anxiety. In her column, Benson-Allott explores the paradox of choice as a condition of the current streaming era, while also historicizing television culture’s ideology of plenty. She traces this notion of superabundance, which undergirds digital cable and streaming culture today, back to the 1950s when print media such as TV Guide pioneered a print-heavy layout that stupefied the eye into an impression of excess. Arguing that browsing print program guides and its more recent corollary, channel surfing, are numbing experiences that discourage risk-taking, Benson-Allott ultimately finds relief from the ennui of the scroll in the pleasures—both expected and unexpected—of the genre film.
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Kraus, Johannes, Panayot Vassilevski, and Ludmil Zikatanov. "Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods." Computational Methods in Applied Mathematics 12, no. 4 (2012): 448–68. http://dx.doi.org/10.2478/cmam-2012-0026.
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AbstractWe derive defect correction scheme for constructing the sequence of polynomials of best approximation in the uniform norm to 1/x on a finite interval with positive endpoints. As an application, we consider two-level methods for scalar elliptic partial differential equation (PDE), where the relaxation on the fine grid uses the aforementioned polynomial of best approximation. Based on a new smoothing property of this polynomial smoother that we prove, combined with a proper choice of the coarse space, we obtain as a corollary, that the convergence rate of the resulting two-level method is uniform with respect to the mesh parameters, coarsening ratio and PDE coefficient variation.
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Miller, Ranee A., and William B. Smith. "PSIII-28 Kibbles ‘n Conjecture: A corollary analysis of ingredient composition, price, and nutritive value of commercial dog food." Journal of Animal Science 97, Supplement_3 (December 2019): 275–76. http://dx.doi.org/10.1093/jas/skz258.560.
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Abstract Quality nutrition for canine species contributes to a large global economic and health care field. Choices abound in terms of the availability of food in any given retail outlet. Likewise, there is copious conjecture surrounding the supposed benefits of certain brands or types over others, especially in the choice of conventional versus grain-free food types. A comparison of nutritive value of feeds relative to ingredient formulation and consumer cost would provide useful insight to the consumer when making selections for canine companion animals. This study sought to ascertain the correlations among ingredient position, nutritive value, and cost of commercially-available dog food. Over the course of February and March of 2019, commercially-available dog food was evaluated at local retail outlets in Stephenville, TX. For each observation, records were made of brand name, formulation, ingredient list, guaranteed nutritive analysis, and cost. Pearson’s correlation coefficients were calculated using PROC CORR, and effect of conventional versus grain-free claims on cost and nutritive value were analyzed using PROC MIXED of SAS v. 9.4. Order in which meat, meat meal, or corn occurred in the ingredient list was not statistically correlated to cost per kg (P ≥ 0.33) or concentrations of crude protein (P ≥ 0.35), crude fat (P ≥ 0.13), or crude fiber (P ≥ 0.35). Grain-free formulations cost significantly more than conventional formulations ($2.70 vs. $4.60/kg; P < 0.01). However, there was no effect of formulation on concentrations of crude protein (P = 0.07), crude fat (P = 0.37), or crude fiber (P = 0.44). Results are interpreted to mean that, despite claims to the contrary, order of ingredients in a formulation have no observable effect on the nutritive value, but large effects on cost, of commercially-available dog food.
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Dewitt, Barry, and George W. Torrance. "Incorporating Mortality in Health Utility Measures." Medical Decision Making 40, no. 7 (September 30, 2020): 862–72. http://dx.doi.org/10.1177/0272989x20951778.
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The creation of multiattribute health utility systems requires design choices that have profound effects on the utility model, many of which have been documented and studied in the literature. Here we describe one design choice that has, to the best of our knowledge, been unrecognized and therefore ignored. It can emerge in any multiattribute decision analysis in which one or more essential outcomes cannot be described in terms of the multiattribute space. In health applications, the state of being dead is such an outcome. When the remaining health is conceptualized as a multidimensional space, determining the utility of the state of being dead requires using the interval-scale properties of cardinal utility, combined with elicited utilities for the state of being dead and the all-worst state, to produce a utility function in which the state of being dead has a utility of 0 and full health has a utility of 1 (i.e., the quality-adjusted life-year scale). Although previously unrecognized, there are two approaches to accomplish that step, and they produce different results in almost all cases. As a corollary, the choice of approach determines the proportion of states rated as worse than dead by the system. For example, in the Health Utility Index 3 (HUI3), the method used classifies 78% of the 972,000 unique health states in the classification system as worse than dead, and that proportion increases to 85% when the HUI3 is recalculated using the alternative approach. Studies of populations with significant morbidity are the most likely to be sensitive to the design choice. Those who design utility measures should be aware that they are using a researcher degree of freedom when they decide how to scale the state of being dead.
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Apter, Arthur W., and Grigor Sargsyan. "Jonsson-like partition relations and j: V → V." Journal of Symbolic Logic 69, no. 4 (December 2004): 1267–81. http://dx.doi.org/10.2178/jsl/1102022223.
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Abstract.Working in the theory ”ZF + There is a nontrivial elementary embedding j : V → V“, we show that a final segment of cardinals satisfies certain square bracket finite and infinite exponent partition relations. As a corollary to this, we show that this final segment is composed of Jonsson cardinals. We then show how to force and bring this situation down to small alephs. A prototypical result is the construction of a model for ZF in which every cardinal μ ≥ ℵ2 satisfies the square bracket infinite exponent partition relation . We conclude with a discussion of some consistency questions concerning different versions of the axiom asserting the existence of a nontrivial elementary embedding j: V → V. By virtue of Kunen's celebrated inconsistency result, we use only a restricted amount of the Axiom of Choice.
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Cichosz, Anna, and Maciej Grabski. "The position of the genitive in Old English prose: Intertextual differences and the role of Latin." Folia Linguistica 54, s41-s1 (December 1, 2020): 1–35. http://dx.doi.org/10.1515/flih-2020-0001.
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Abstract The present article is a systematic, large-scale corpus study of the varying position of the Old English adnominal genitive. Particular focus is put on intertextual variation and the potential influence of Latin, which is analysed alongside such intra-linguistic factors as syntactic weight and the animacy of the referent. The model of logistic regression adopted helps address a key issue in studies on genitive placement, namely, if and how multiple variables exert combined impact on the choice of the variant. The paper highlights the importance of a bottom-to-top approach in studies of older English syntax, as global tendencies turn out to be the corollary of significantly different contributions on the level of individual texts, whose translation status (original composition or translation) is also of importance to the variation studied.
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Saboonchi, Fatemeh, and Asgar Mahmoudi. "Effect of Elementary EFL Learners’ Negotiation on Their Classroom Participation and Grammatical Achievement." Journal of Language Teaching and Research 8, no. 2 (March 1, 2017): 411. http://dx.doi.org/10.17507/jltr.0802.26.
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The principal concern of the present study was to explore the effects of two types of negotiation (group work and pair work) on the degree of elementary EFL students’ participation and its corollary impact on their grammatical achievement. Both classes in the study received grammar instruction for twenty sessions. The learners took two grammar tests before and after the treatment in the multiple-choice format. The results showed that negotiation in pairs leads to less participation but better grammatical achievement. In other words, while students in the group work negotiated more, their grammatical achievement was significantly less than the students in the pair work who participated less. It could be concluded, therefore, that while group work leads to more participation, higher grammatical knowledge is possible to be obtained by less participative students.
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Michelini, Rinaldo C., and Roberto P. Razzoli. "The Mankind Growth Consistency." Information Resources Management Journal 25, no. 2 (April 2012): 69–84. http://dx.doi.org/10.4018/irmj.2012040105.
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The international stability is viewed as corollary of the sustainable growth. This has only technology-driven solution, at global village extension, with required appropriateness and shared acceptation. The survey, on such guess, looks at the robot age potential, as supplementary aid in the balanced world deployment that adds to the socio-economic and politico-legal frames. The analysis moves from the globalisation issues, at the known (economic) global and (ecologic) no-global pictures, to outline the traits of the post-global robot age, consistent with the sustainable growth, international stability, and grounded on the force of the law. Stability based on the law of the force was the past option, even allowing steady truces. In this analysis, globalisation makes this choice unfit, having doubtful economic and social sustainability and not achieving ecologic sustainability consistently and for the long term.
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Ter-Kazarian, Gagik. "Modified Theories of Gravitation behind the Spacetime Deformation." Physics Research International 2015 (March 2, 2015): 1–19. http://dx.doi.org/10.1155/2015/152846.
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In the framework of proposed theory of spacetime deformation/distortion, we have a way to deform the spacetime through a nontrivial choice of the distortion-complex, displaying different connections, which may reveal different post-Riemannian spacetime structures as corollary. We extend this theory to address, in particular, the gauge model of the most general metric-affine gravity carrying both nontrivial torsion and nonmetricity. This model is constructed in the framework of the first order Lagrangian expressed in terms of the gauge potentials and their first derivatives. The equations of the standard theory, which have no propagating modes for torsion, can be equivalently replaced in modified framework by the modified equations, which in the limit of reducing the affine group leads to the modified Einstein-Cartan theory with dynamical torsion and beyond. In testing the modified framework for various particular cases, we use the Lagrange multipliers for extinguishing nonmetricity and torsion.
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Flew, Antony. "Retrospect and Prospect, Retribution and Deterrence." Israel Law Review 25, no. 3-4 (1991): 376–87. http://dx.doi.org/10.1017/s0021223700010487.
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(1) During my lifetime most of the discussion of punishment in British philosophical journals has started from an article first published in 1939. Thirty years later this was reprinted, along with a selection of eleven of the most substantial subsequent contributions, to form a volume which has since served to introduce further student generations to The Philosophy of Punishment. In that seminal paper the late John Mabbott — whom it was later my good fortune to have as one of my tutors — proposed “to defend a retributive theory of punishment, and to reject absolutely all utilitarian considerations from its justification”.His initial claim perhaps sounded bolder, or rasher, than it was. For Mabbott in his second paragraph explained: “The question I am asking is this. Under what circumstances is the punishment of some particular person justified, and why?” After giving and defending his retributive answer to this question Mabbott turned to the “distinction between abolishing injustice in punishment and abolishing punishment altogether”. While still insisting that “punishment is a corollary of law breaking …” he went on to allow that “considerations of utility come in on two quite different issues. Should there be laws, and what laws should there be? … The choice which is the essential prius of punishment is the choice that there should be laws”.
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DA LUZ, ADRIANA, and EZEQUIEL MADERNA. "On the free time minimizers of the NewtonianN-body problem." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 2 (November 26, 2013): 209–27. http://dx.doi.org/10.1017/s0305004113000650.
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AbstractIn this paper we study the existence and the dynamics of a very special class of motions, which satisfy a strong global minimization property. More precisely, we call a free time minimizer a curve which satisfies the least action principle between any pair of its points without the constraint of time for the variations. An example of a free time minimizer defined on an unbounded interval is a parabolic homothetic motion by a minimal central configuration. The existence of a large amount of free time minimizers can be deduced from the weak KAM theorem. In particular, for any choice ofx0, there should be at least one free time minimizerx(t)defined for allt≥ 0 and satisfyingx(0)=x0. We prove that such motions are completely parabolic. Using Marchal's theorem we deduce as a corollary that there are no entire free time minimizers, i.e. defined on$\mathbb{R}$. This means that the Mañé set of the NewtonianN-body problem is empty.
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Chen, Mingchun, Zhiying Liu, and Chaoliang Ma. "Early bird or versioning." Asia Pacific Journal of Marketing and Logistics 32, no. 3 (July 18, 2019): 769–92. http://dx.doi.org/10.1108/apjml-12-2018-0529.
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Purpose Crowdfunding, especially reward-based crowdfunding, has quickly evolved into a commonly used vehicle for innovating entrepreneurs to develop their products. Many crowdfunding platforms allow creators maximum flexibility in terms of the prices and rewards offered in a project to gain sufficient capital. However, creators need to understand how to design project rewards and how to select a pricing strategy, in addition to whether the creator should spend resources on designing multiple rewards of varying quality. The purpose of this paper is to address these issues by answering whether and why there are significant differences in the application of early-bird and versioning pricing strategies in crowdfunding. Design/methodology/approach This paper develops a two-stage dynamic game model with incomplete information, proposes a corollary calculated by analyzing a perfect Bayesian equilibrium, and then tests Corollary 1 by empirical analysis. Findings Contrary to the findings of other studies, the results show that an early-bird pricing strategy is likely better than a versioning pricing strategy for earning greater revenue in a crowdfunding context, on average. This finding means that creators do not have to spend as much in designing rewards of various qualities; rather, they should only provide multiple price options for high-quality rewards. However, if the heterogeneity of target backers’ valuations and the quality difference between two types of products are adequately high, a versioning pricing strategy may be a good choice for creators. Practical implications This paper provides a reference for creators regarding the selection of pricing strategies and the design of reward quality when launching crowdfunding projects. Originality/value This paper explains an interesting and practical issue in the design of reward quality and the selection of a pricing strategy after fully considering the role of the crowdfunding all-or-nothing mechanism and special backer behavior.
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Šuster, Danilo. "Arguing about Free Will." Croatian journal of philosophy 21, no. 63 (December 27, 2021): 375–403. http://dx.doi.org/10.52685/cjp.21.63.2.
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I explore some issues in the logics and dialectics of practical modalities connected with the Consequence Argument (CA) considered as the best argument for the incompatibility of free will and determinism. According to Lewis (1981) in one of the possible senses of (in)ability, the argument is not valid; however, understood in the other of its possible senses, the argument is not sound. This verdict is based on the assessment of the modal version of the argument, where the crucial notion is power necessity (“no choice” operator), while Lewis analyses the version where the central notion is the locution “cannot render false.”Lewis accepts closure of the relevant (in)ability operator under entailment but not closure under implication. His strategy has a seemingly strange corollary: a free predetermined agent is able (in a strong, causal sense) to falsity the conjunction of history and law. I compare a Moorean position with respect to radical skepticism and knowledge closure with ability closure and propose to explain Lewis’s strategy in the framework of his Moorean stance.
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Humphries, Jane. "The Gender Gap in Wages." Social Science History 33, no. 4 (2009): 481–88. http://dx.doi.org/10.1017/s0145553200011111.
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Explanations of the gender pay gap and related labor market segregation remain fiercely debated. On the one side are those economic historians who take a primarily neoclassical view, in which competition among workers and employers eliminates wage differences that do not reflect productivity and occupational segregation that is not the outcome of choice. Persistent discrimination must reflect anticompetitive institutions, for instance, trade unions. A corollary of the neoclassical perspective is that markets are liberating, freeing agents, including women, from cultural stereotypes and ensuring that they get paid what they are worth, although of course this need not imply wage equality if there are gender differences in productivity. On the other side are those cultural historians who interpret wage differences as reflecting custom and, as far as women are concerned, the cultural deprecation of women's work, while occupational segregation represents gender stereotypes of fit work for women. In this view, socially and culturally constructed gender identities can influence market outcomes, producing discrimination in wages and work that persists even in the face of competitive forces.
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Skylark, William J., and Sidharth Prabhu-Naik. "A new test of the risk-reward heuristic." Judgment and Decision Making 13, no. 1 (January 2018): 73–78. http://dx.doi.org/10.1017/s1930297500008834.
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AbstractRisk and reward are negatively correlated in a wide variety of environments, and in many cases this trade off approximates a fair bet. Pleskac and Hertwig (2014) recently proposed that people have internalized this relationship and use it as the basis for probability estimation and subsequent choice under conditions of uncertainty. Specifically, they showed that risky options with high-value outcomes are inferred to have lower probability than options offering a less valuable reward. We report two experiments that test a simple corollary of this idea. In both studies, participants estimated the magnitude of prizes offered by lotteries with known win-probabilities. The relationship between estimates and probabilities followed the power relationship predicted by the risk-reward heuristic, albeit with a tendency to overestimate outcome magnitude. In addition, people’s estimates predicted their willingness to take the gamble. Our results provide further evidence that people have internalized the ecological relationship between risk and reward in financial lotteries, and we suggest that this relationship exerts a wide-ranging influence on decision-making.
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Ganuza, Carina V. "INDIFFERENCE, CONTAMINATION AND CONTINUITY IN THE EXERCISE OF POWER: RATIONAL CHOICE AND NEOINSTITUTIONALISM IN THE CORDON INDUSTRIAL (SANTA FE, ARGENTINA)." Politology bulletin, no. 86 (2021): 225–36. http://dx.doi.org/10.17721/2415-881x.2021.86.225-236.
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This article is a brief approximation to the knowledge of a singular reality characterised by the pollution caused by different companies located in an area of 589 km2 known as Cordón Industrial Gran Rosario (province of Santa Fe, Argentina). It combines the almost uninterrupted permanence of different local authorities and confirmed measurements of air pollutants in two of the main cities, Puerto General San Martin and San Lorenzo, as well as multiple complaints in judicial instances for irregularities by various companies from other localities that make up the Cordon, whose main relevance lies in its outlet to the Paraná River, a source of maritime transport. Therefore, this phenomenon is analysed from two theoretical contributions of Political Science: the Theory of Rational Choice, which supports the interest of people as their preferences when making decisions, as well as the search for rents as possible priorities; and on the other hand, Neo-institutionalism, institutions as pillars of politics, which refers to the state, legislature, legal forms, rules or procedures adopted by political relations. Finally, the corollary of this analysis is marked by the apparent contradiction between citizens’ decisions to elect authorities who exercise power for more than two constitutional periods, who in turn become instruments for the continued survival of polluting companies that threaten the individual and societal health of all the cities of the Industrial Cordon studied, and ultimately, the consequent ineffectiveness of the institutions that form part of the government organisations as a control body.
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Bozeman, Theodore Dwight. "John Clarke and the Complications of Liberty." Church History 75, no. 1 (March 2006): 69–93. http://dx.doi.org/10.1017/s0009640700088338.
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In the historiography of English and American Baptist movements there is no more familiar convention than this: Baptists early and late championed freedom of the religious conscience, rejected the use of force in spiritual affairs, and, either expressly or by implication, accepted the corollary of religious pluralism. With few exceptions, modern scholars have either assumed or implied by the logic of their arguments that the historic Baptist commitment to religious liberty was not only strong but categoric. By implication also, it did not evolve but arose full blown in the initial Anglo-American Baptist insurgency itself in the seventeenth century. To take one example: in a chapter-length treatment of the “struggle for religious liberty,” a currently authoritative history of American Baptists affirms that colonial Baptists “led other dissenters in championing the cause of religious liberty” and the separation of church and state. Then as later, the advocacy of freedom “for persons of all faiths—or no faith” was their “genius.“ Genius—here is the key claim. Liberty of religious choice and practice is joined to conversion or adult baptism as a principle of the faith both original and definitive. Baptist intoleration in any form becomes a virtual oxymoron.
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Radul, Alexey, Adam Paszke, Roy Frostig, Matthew J. Johnson, and Dougal Maclaurin. "You Only Linearize Once: Tangents Transpose to Gradients." Proceedings of the ACM on Programming Languages 7, POPL (January 9, 2023): 1246–74. http://dx.doi.org/10.1145/3571236.
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Automatic differentiation (AD) is conventionally understood as a family of distinct algorithms, rooted in two “modes”—forward and reverse—which are typically presented (and implemented) separately. Can there be only one? Following up on the AD systems developed in the JAX and Dex projects, we formalize a decomposition of reverse-mode AD into (i) forward-mode AD followed by (ii) unzipping the linear and non-linear parts and then (iii) transposition of the linear part. To that end, we define a (substructurally) linear type system that can prove a class of functions are (algebraically) linear. Our main results are that forward-mode AD produces such linear functions, and that we can unzip and transpose any such linear function, conserving cost, size, and linearity. Composing these three transformations recovers reverse-mode AD. This decomposition also sheds light on checkpointing, which emerges naturally from a free choice in unzipping let expressions. As a corollary, checkpointing techniques are applicable to general-purpose partial evaluation, not just AD. We hope that our formalization will lead to a deeper understanding of automatic differentiation and that it will simplify implementations, by separating the concerns of differentiation proper from the concerns of gaining efficiency (namely, separating the derivative computation from the act of running it backward).
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Faroldi, Federico L. G. "Deontic modals and hyperintensionality." Logic Journal of the IGPL 27, no. 4 (May 28, 2019): 387–410. http://dx.doi.org/10.1093/jigpal/jzz011.
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Abstract In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis (that deontic modals are not hyperintensional) leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power (e.g. Ross’s paradox, the Gentle Murderer, The Good Samaritan, Free Choice Permission and the Miners’ Paradox disappear). I then propose a philosophical analysis of this thesis and outline some consequences. In Section 1 I introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics.
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van Atten, Mark, and Dirk van Dalen. "Arguments for the Continuity Principle." Bulletin of Symbolic Logic 8, no. 3 (September 2002): 329–47. http://dx.doi.org/10.2178/bsl/1182353892.
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There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers, occurs for the first time in print in [4]. It is formulated and immediately applied to show that the set of numerical choice sequences is not enumerable. In fact, the idea of the continuity property can be dated fairly precisely, it is to be found in the margin of Brouwer's notes for his course on Pointset Theory of 1915/16. The course was repeated in 1916/17 and he must have inserted his first formulation of the continuity principle in the fall of 1916 as new material right at the beginning of the course.In modern language, the principle readswhere α and β range over choice sequences of natural numbers, m and x over natural numbers, and stands for ⟨α(0), α(1), …, α(m − 1)⟩, the initial segment of α of length m.An immediate consequence of WC-N is that all full functions are continuous, and, as a corollary, that the continuum is unsplittable [28]. Note that WC-N is incompatible with Church's thesis, [22], section 4.6.After Brouwer asserted WC-N, Troelstra was the first to ask in print for a conceptual motivation, but he remained an exception; most authors followed Brouwer by simply asserting it, cf. [18].Let us note first that in one particular case the principle is obvious indeed, namely in the case of the lawless sequences. The notion of lawless sequence surfaced fairly late in the history of intuitionism. Kreisel introduced it in [17] for metamathematical purposes. There is a letter from Brouwer to Heyting in which the phenomenon also occurs [7]. This is an important and interesting fact since it is (probably) the only time that Brouwer made use of a possibility expressly stipulated in, e.g., [5], see below.
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Barikova, Anna, and Yan Bernaziuk. "Discretion in Applying Provisions of Law: Linguistic Prospects For AI and Machine Learning." ECS Transactions 107, no. 1 (April 24, 2022): 18545–58. http://dx.doi.org/10.1149/10701.18545ecst.
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The note presents the will of actions in using the provisions of the law as an assessment when making an opinion, or as a choice of a more favorable and correct conclusion from the number of varieties allowed by law. This legal appearance was presented in the guise of a targeted cause-and-effect graph, in which all actions are associated with a friend with another, are considered the reasons or consequences of a friend of a friend. Any of its vertex points is an event, an edge is an association, the orientation of the edges is from the corollary to the base. The features of the euro legislation on AI are considered. The essence of the artificial origin of the mind has been studied for making conclusions at personal discretion. The reprimand was made on the model of AI and machine learning, which have every chance to be: multifunctional, dynamic, expressed in the definitions of mathematical functions, risk models, credit optimization; static, expressed in relationships between data objects (chart of accounts, affairs between subjects). The Abstraction and Reasoning Corpus dataset has been demonstrated as a benchmark for robust AI. Methods of controlled machine learning have been discovered, encompassing authorized learning ("student's task"), inductive programming ("life experience"), predictive power ("scientist's task"), study campaign ("teacher's task"). The classification of arguments, methodologies and layouts has been determined for a discretionary judgment process with a pertinent case of the Euro Court of Human Rights.
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Hulstijn, Jan H., and Elaine Marchena. "Avoidance." Studies in Second Language Acquisition 11, no. 3 (September 1989): 241–55. http://dx.doi.org/10.1017/s0272263100008123.
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This article follows up on a study by Dagut and Laufer (1985), who found that Hebrew learners of English avoid phrasal verbs, such as ‘let down’, while preferring one-word verbs, such as ‘;disappoint’, since phrasal verbs do not exist in Hebrew. A corollary derived from Dagut and Laufer's study is that Dutch learners of English would tend not to avoid English phrasal verbs, since phrasal verbs also exist in Dutch. It was hypothesized, however, that Dutch learners of English as a second language (ESL) would avoid phrasal verbs, too, not for structural, but for semantic reasons. Three tests (multiple choice, memorization, and translation) were administered to intermediate and advanced Dutch learners of English. Each test contained 15 sentences, eliciting preference for either a phrasal verb or an equivalent one-word verb. The results show that, as expected, Dutch learners of English do not avoid phrasal verbs categorically. However, they seem to avoid those idiomatic phrasal verbs that they perceive as too Dutch-like (lack of contrast between the first and second language). Furthermore, they exhibit a tendency to adopt a play-it-safe strategy, preferring one-word verbs with general, multi-purpose meanings over phrasal verbs with specific, sometimes idiomatic, meanings. It is argued that this semantic play-it-safe strategy may have also played a causal role in the avoidance behavior of the Hebrew ESL learners observed by Dagut and Laufer.
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Mohammed H. Al-Ahdal, Arif Ahmed, and Salmeen Abdulrahman Abdullah Al-Awaid. "ENGLISH AS THE LINGUA FRANCA OF DEVELOPMENT: FINDING COMMON CORRELATES IN SAUDI ARABIA." Malaysian Journal of Languages and Linguistics (MJLL) 7, no. 1 (June 1, 2018): 1–7. http://dx.doi.org/10.24200/mjll.vol7iss1pp1-7.
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Technological dependence, interconnectivity of nations, interlinked economies, and interdependent politics across countries in the global village have given a new definition to communication. With one sure though slow thrust, peoples across borders are moving towards what can be seen as one unifying characteristic for the human race: One language to communicate, and the natural choice is English. True, it is Mandarin and not English that is spoken by the largest number of people, but true also is the fact that this is more a matter of natural circumstance than choice. The second most popular language is Spanish but then, it is the English and not Spanish speaking people who are in a position to influence economies, develop trade and move the commerce. In other words, proficiency in English can be directly linked to socio-economic prosperity. In the KSA too, as in the other members of the so-called Developing Bloc of nations, there is a growing consciousness to the fact that to realise the dream of Vision 2030 and to establish a petro-money free economy, the country has to abandon its insular character and adopt a more open-door attitude. One significant factor in the success of this approach will, of course, be the ability of the people to communicate with the world. Hence the need of the hour: Proficiency in English. Globally, researchers have postulated on the effects of English learning on the ‘development’ of limited groups and even individuals. As a corollary to this observation, the role of effective communication and negotiation cannot be overstated in any circumstance that involves people. In fact, ability to ‘communicate in English’ appears to be the catch phrase in academic, political, economic, and even social situations. However, such endeavours are notably missing in the Saudi Arabian context, given the older policies of keeping ‘outside’ influence at a minimal to preserve the purity of the local culture. The current study presents a catalogue and review of the previous studies linking socio-economic development to English with the aim to establish why and how the country stands to benefit in the long run by empowering the general public with English language.
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Blanca, Antonio, and Reza Gheissari. "Random-Cluster Dynamics on Random Regular Graphs in Tree Uniqueness." Communications in Mathematical Physics 386, no. 2 (April 17, 2021): 1243–87. http://dx.doi.org/10.1007/s00220-021-04093-z.
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AbstractWe establish rapid mixing of the random-cluster Glauber dynamics on random $$\varDelta $$ Δ -regular graphs for all $$q\ge 1$$ q ≥ 1 and $$p<p_u(q,\varDelta )$$ p < p u ( q , Δ ) , where the threshold $$p_u(q,\varDelta )$$ p u ( q , Δ ) corresponds to a uniqueness/non-uniqueness phase transition for the random-cluster model on the (infinite) $$\varDelta $$ Δ -regular tree. It is expected that this threshold is sharp, and for $$q>2$$ q > 2 the Glauber dynamics on random $$\varDelta $$ Δ -regular graphs undergoes an exponential slowdown at $$p_u(q,\varDelta )$$ p u ( q , Δ ) . More precisely, we show that for every $$q\ge 1$$ q ≥ 1 , $$\varDelta \ge 3$$ Δ ≥ 3 , and $$p<p_u(q,\varDelta )$$ p < p u ( q , Δ ) , with probability $$1-o(1)$$ 1 - o ( 1 ) over the choice of a random $$\varDelta $$ Δ -regular graph on n vertices, the Glauber dynamics for the random-cluster model has $$\varTheta (n \log n)$$ Θ ( n log n ) mixing time. As a corollary, we deduce fast mixing of the Swendsen–Wang dynamics for the Potts model on random $$\varDelta $$ Δ -regular graphs for every $$q\ge 2$$ q ≥ 2 , in the tree uniqueness region. Our proof relies on a sharp bound on the “shattering time”, i.e., the number of steps required to break up any configuration into $$O(\log n)$$ O ( log n ) sized clusters. This is established by analyzing a delicate and novel iterative scheme to simultaneously reveal the underlying random graph with clusters of the Glauber dynamics configuration on it, at a given time.
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Lori, Nicolas F., Jos Neves, Alex H. Blin, and Victor Alves. "Some considerations on quantum computing at sub-atomic scales and its impact in the future of Moore's law." Quantum Information and Computation 20, no. 1&2 (February 2020): 1–13. http://dx.doi.org/10.26421/qic20.1-2-1.
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The contemporary development of Quantum Computers has opened new possibilities for computation improvements, but the limits of Moore's law validity are starting to show. We analyze here the possibility that miniaturization will continue to be the source of Moore's law validity in the near future, and our conclusion is that miniaturization is no longer a reliable answer for the future development of computer science, but instead we suggest that lateralization is the correct approach. By lateralization, we mean the use of biology as the correct format for the implementation of ubiquitous computerized systems, a format that might in many circumstances eschew miniaturization as an overly expensive useless advantage whereas in other cases miniaturization might play a key role. Thus, the future of computer science is not towards a miniaturization that goes from the atom-scale (its present application scale) towards the nucleus-scale, but rather in developing more integrated circuits at the micrometer to nanometer scale, so as to better mimic and interact with biological systems. We analyze some "almost sci-fi" approaches to the development of better computer systems near the Bekenstein bound limit, and unsurprisingly they fail to have any realistic feasibility. Then, we use the difference between the classical vs. quantum version of the Hammerstein-Clifford theorem to explain why biological systems eschewed quantum computation to represent the world but have chosen classical computation instead. Finally, we analyze examples of recent work which indicate future possibilities of integration between computers and biological systems. As a corollary of that choice by the biological systems, we propose that the predicted lateralization-driven evolution in computer science will not be based in quantum computers, but rather in classical computers.
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SHI, XIANGHUI. "AXIOM I0 AND HIGHER DEGREE THEORY." Journal of Symbolic Logic 80, no. 3 (July 22, 2015): 970–1021. http://dx.doi.org/10.1017/jsl.2015.15.
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AbstractIn this paper, we analyze structures of Zermelo degrees via a list of four degree theoretic questions (see §2) in various fine structure extender models, or under large cardinal assumptions. In particular we give a detailed analysis of the structures of Zermelo degrees in the Mitchell model for ω many measurable cardinals. It turns out that there is a profound correlation between the complexity of the degree structures at countable cofinality singular cardinals and the large cardinal strength of the relevant cardinals. The analysis applies to general degree notions, Zermelo degree is merely the author’s choice for illustrating the idea.I0(λ) is the assertion that there is an elementary embedding j : L(Vλ+1) → L(Vλ+1) with critical point < λ. We show that under I0(λ), the structure of Zermelo degrees at λ is very complicated: it has incomparable degrees, is not dense, satisfies Posner–Robinson theorem etc. In addition, we show that I0 together with a mild condition on the critical point of the embedding implies that the degree determinacy for Zermelo degrees at λ is false in L(Vλ+1). The key tool in this paper is a generic absoluteness theorem in the theory of I0, from which we obtain an analogue of Perfect Set Theorem for “projective” subsets of Vλ+1, and the Posner–Robinson follows as a corollary. Perfect Set Theorem and Posner–Robinson provide evidences supporting the analogy between $$AD$$ over L(ℝ) and I0 over L(Vλ+1), while the failure of degree determinacy is one for disanalogy. Furthermore, we conjecture that the failure of degree determinacy for Zermelo degrees at any uncountable cardinal is a theorem of $$ZFC$$.
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Rodrik, Dani. "When Ideas Trump Interests: Preferences, Worldviews, and Policy Innovations." Journal of Economic Perspectives 28, no. 1 (February 1, 2014): 189–208. http://dx.doi.org/10.1257/jep.28.1.189.
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Ideas are strangely absent from modern models of political economy. In most prevailing theories of policy choice, the dominant role is instead played by “vested interests”—elites, lobbies, and rent-seeking groups which get their way at the expense of the general public. Any model of political economy in which organized interests do not figure prominently is likely to remain vacuous and incomplete. But it does not follow from this that interests are the ultimate determinant of political outcomes. Here I will challenge the notion that there is a well-defined mapping from “interests” to outcomes. This mapping depends on many unstated assumptions about the ideas that political agents have about: 1) what they are maximizing, 2) how the world works, and 3) the set of tools they have at their disposal to further their interests. Importantly, these ideas are subject to both manipulation and innovation, making them part of the political game. There is, in fact, a direct parallel, as I will show, between inventive activity in technology, which economists now routinely make endogenous in their models, and investment in persuasion and policy innovation in the political arena. I focus specifically on models professing to explain economic inefficiency and argue that outcomes in such models are determined as much by the ideas that elites are presumed to have on feasible strategies as by vested interests themselves. A corollary is that new ideas about policy—or policy entrepreneurship—can exert an independent effect on equilibrium outcomes even in the absence of changes in the configuration of political power. I conclude by discussing the sources of new ideas.
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Chung, Hee-Joong, Dohyeong Kim, Minhyong Kim, George Pappas, Jeehoon Park, and Hwajong Yoo. "Erratum: “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”." International Mathematics Research Notices 2019, no. 18 (May 31, 2019): 5854–57. http://dx.doi.org/10.1093/imrn/rnz097.
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Abstract We wish to point out errors in the paper “Abelian Arithmetic Chern–Simons Theory and Arithmetic Linking Numbers”, International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–29. The main error concerns the symmetry of the “ramified case” of the height pairing, which relies on the vanishing of the Bockstein map in Proposition 3.5. The surjectivity claimed in the 1st line of the proof of Proposition 3.5 is incorrect. The specific results that are affected are Proposition 3.5; Lemmas 3.6, 3.7, 3.8, and 3.9; and Corollary 3.11. The definition of the $(S,n)$-height pairing following Lemma 3.9 is also invalid, since the symmetry of the pairing was required for it to be well defined. The results of Section 3 before Proposition 3.5 as well as those of the other Sections are unaffected. Proposition 3.10 is correct, but the proof is unclear and has some sign errors. So we include here a correction. As in the paper, let $I$ be an ideal such that $I^n$ is principal in ${\mathcal{O}}_{F,S}$. Write $I^n=(f^{-1})$. Then the Kummer cocycles $k_n(f)$ will be in $Z^1(U, {{\mathbb{Z}}/{n}{\mathbb{Z}}})$. For any $a\in F$, denote by $a_S$ its image in $\prod _{v\in S} F_v$. Thus, we get an element $$\begin{equation*}[f]_{S,n}:=[(k_n(f), k_{n^2}(f_S), 0)] \in Z^1(U, {{{\mathbb{Z}}}/{n}{{\mathbb{Z}}}} \times_S{\mathbb{Z}}/n^2{\mathbb{Z}}),\end{equation*}$$which is well defined in cohomology independently of the choice of roots used to define the Kummer cocycles. (We have also trivialized both $\mu _{n^2}$ and $\mu _n$.)
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Bellamy, Gwyn, and Alastair Craw. "Birational geometry of symplectic quotient singularities." Inventiones mathematicae 222, no. 2 (April 30, 2020): 399–468. http://dx.doi.org/10.1007/s00222-020-00972-9.
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Abstract For a finite subgroup $$\Gamma \subset \mathrm {SL}(2,\mathbb {C})$$ Γ ⊂ SL ( 2 , C ) and for $$n\ge 1$$ n ≥ 1 , we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of n points on the minimal resolution S of the Kleinian singularity $$\mathbb {C}^2/\Gamma $$ C 2 / Γ . It is well known that $$X:={{\,\mathrm{{\mathrm {Hilb}}}\,}}^{[n]}(S)$$ X : = Hilb [ n ] ( S ) is a projective, crepant resolution of the symplectic singularity $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , where $$\Gamma _n=\Gamma \wr \mathfrak {S}_n$$ Γ n = Γ ≀ S n is the wreath product. We prove that every projective, crepant resolution of $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n can be realised as the fine moduli space of $$\theta $$ θ -stable $$\Pi $$ Π -modules for a fixed dimension vector, where $$\Pi $$ Π is the framed preprojective algebra of $$\Gamma $$ Γ and $$\theta $$ θ is a choice of generic stability condition. Our approach uses the linearisation map from GIT to relate wall crossing in the space of $$\theta $$ θ -stability conditions to birational transformations of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n . As a corollary, we describe completely the ample and movable cones of X over $$\mathbb {C}^{2n}/\Gamma _n$$ C 2 n / Γ n , and show that the Mori chamber decomposition of the movable cone is determined by an extended Catalan hyperplane arrangement of the ADE root system associated to $$\Gamma $$ Γ by the McKay correspondence. In the appendix, we show that morphisms of quiver varieties induced by variation of GIT quotient are semismall, generalising a result of Nakajima in the case where the quiver variety is smooth.
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Milosevic, Predrag. "The concept and principles of sustainable architectural design for national parks in Serbia." Spatium, no. 11 (2004): 91–105. http://dx.doi.org/10.2298/spat0411091m.
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The paper elaborates the concept of sustainable architectural design that has come to the forefront in the last 20 years, and in the light of the National Park. This concept recognizes that human civilization is an integral part of the natural world and that nature must be preserved and perpetuated if the human community itself is to survive. Sustainable design articulates this idea through developments that exemplify the principles of conservation and encourage the application of those principles in our daily lives. A corollary concept, and one that supports sustainable design, is that of bio-regionalism - the idea that all life is established and maintained on a functional community basis and that all of these distinctive communities (bio-regions) have mutually supporting life systems that are generally self-sustaining. The concept of sustainable design holds that future technologies must function primarily within bioregional patterns and scales. They must maintain biological diversity and environmental integrity contribute to the health of air, water, and soils, incorporate design and construction that reflect bio-regional conditions, and reduce the impacts of human use. Sustainable design, sustainable development, design with nature environmentally sensitive design, holistic resource management - regardless of what it's called, "sustainability," the capability of natural and cultural systems being continued over time, is the key. Sustainable design must use an alternative approach to traditional design and the new design approach must recognize the impacts of every design choice on the natural and cultural resources of the local, regional, and global environments. Sustainable park and recreation development will succeed to the degree that it anticipates and manages human experiences. Interpretation provides the best single tool for shaping experiences and sharing values. By providing an awareness of the environment, values are taught that are necessary for the protection of the environment. Sustainable design will seek to affect not only immediate behaviors but also the long-term beliefs and attitudes of the visitors.
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Maw, David. ""Trespasser mesure": Meter in Machaut's Polyphonic Songs." Journal of Musicology 21, no. 1 (January 1, 2004): 46–126. http://dx.doi.org/10.1525/jm.2004.21.1.46.
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Comments by Jacques de Lige suggest that Ars nova notation operated metrically at more than one rhythmic level. This is borne out by Machaut's compositions, the lais in particular. Inconsistencies within and between the two complete editions of Machaut's works in the reductions of note-values used for transcription indicate that the matter has not been fully resolved; uncertainty concerning metrical level in the polyphonic songs is evident in the different barrings of modus-level rhythmic organization. The system of 12 "modes" (mensural types) in the Compendium de discantu mensurabili by Petrus frater dictus Palma Ociosa reveals that meters centering on both "modus" and "tempus" levels were equally part of polyphonic practice in the mid 1330s. Editors have been wary of recognizing the modus level in Machaut's polyphonic songs because of the frequent irregularities in metrical grouping at this level; yet variation in modus is acknowledged by the Ars nova treatises. A full re-evaluation of the presence of modus in Machaut's songs is warranted. Coordinated analysis of rhythmic "layers" (figural grouping, agogic accent, simultaneous attack, and syllabic rhythm) in two ballades (B35 and B25) justifies the irregular modus recognized by both editions and points to an important distinction between mensuration (pertaining to the notation) and meter (pertaining to the rhythmic organization). Figural disposition, varied recurrence of material, and syllabic rhythm provide other criteria for recognizing variable metrical form. A full-scale analysis on these terms reveals the extent and nature of Machaut's use of modus. His technique of metrical variation conforms to four types (phrasal "distension" and "contraction"; cadential "contraction" and "extension"), and ties in with a 14th-century aesthetic viewpoint that attached great significance to "variety." Machaut himself recognized it as a musical corollary of the amorous condition in lyric song ("trespasser mesure," Motet 7). Reassessment of the modus level has consequences for the editorial approach to notae finales, sectional rests, and also for the choice of tempo in performance.
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Scheepers, Marion. "Concerning n-tactics in the countable-finite game." Journal of Symbolic Logic 56, no. 3 (September 1991): 786–94. http://dx.doi.org/10.2178/jsl/1183743727.
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In the paper [S1] I introduced a game, denoted by MG(J) (where J is a free ideal on some infinite set S) and called “the meager nowhere dense game for J”. The special case when J is the collection of finite subsets of the set S is called the countable-finite game on S. It proceeds as follows.First player ONE picks a countable set C1, then player TWO picks a finite set F1. Then in the second inning ONE picks a countable set C2 with C1 ⊂ C2 (unless explicitly indicated otherwise, “⊂” means “is a proper subset of”) and TWO responds with a finite set F2, and so on. The players construct a sequence (C1,F1,C2,F2,…,Ck,Fk,…) where for each positive integer k(i) Ck denotes ONE's countable set picked during the kth inning,(ii) Fk denotes TWO's finite set picked during the kth inning, and(iii) Ck ⊂ Ck + 1.Such a sequence is a play of the countable-finite game on S, and TWO wins this play if is contained in . The notion of a winning perfect information strategy is defined as usual (see, for example, [S1]). Zermelo-Fraenkel set theory together with the axiom of choice (denoted by ZFC; for a statement of the axioms see pp. xv–xvi of [K]) is a strong enough theory to build a winning perfect information strategy for player TWO in this game.Does TWO have a winning strategy requiring less than perfect information? Fix a positive integer k. A strategy of TWO which requires knowledge of only at the most the k most recent moves of ONE is said to be a k-tactic. For the countable-finite game on an infinite set S the following facts about the existence of winning k-tactics for TWO are proved in [S1]:1) TWO does not have a winning 1-tactic (Theorem 1 of [S1]).2) If the cardinality of S is less than ℵ2 then TWO has a winning 2-tactic (Corollary 4 of [S1]).3) If TWO has a winning k-tactic in the countable-finite game on an infinite set S, then TWO has a winning 3-tactic (Proposition 15 of [SI]).
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Stalcup, M., and S. Verguet. "Mothers and Children: Designing research toward integrated care for both." Health, Culture and Society 3, no. 1 (August 14, 2012): 159–71. http://dx.doi.org/10.5195/hcs.2012.91.
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In this paper we examine pragmatic corollaries to the design and implementation of Millennium Development Goals (MDG) 4 and 5. The first corollary we analyze is how the timeframe imposed on the MDGs affects choices about how to implement health care interventions to meet those goals, which we look at specifically in terms of the trade-off between strengthening a health care system or increasing mass campaigns. The second corollary is that, in the allocation of resources, those choices must often be made between providing health care interventions for certain members of the population as opposed to others. We analyze aspects of these unintentional effects of the MDGs, and then offer a model for designing research on the provision of maternal and child health that does aim to take them into account.
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BEESON, MICHAEL. "CONSTRUCTIVE GEOMETRY AND THE PARALLEL POSTULATE." Bulletin of Symbolic Logic 22, no. 1 (March 2016): 1–104. http://dx.doi.org/10.1017/bsl.2015.41.
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AbstractEuclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. This involves finding “uniform” constructions where normally a case distinction is used. For example, in finding a perpendicular to line L through point p, one usually uses two different constructions, “erecting” a perpendicular when p is on L, and “dropping” a perpendicular when p is not on L, but in constructive geometry, it must be done without a case distinction. Classically, the models of Euclidean (straightedge-and-compass) geometry are planes over Euclidean fields. We prove a similar theorem for constructive Euclidean geometry, by showing how to define addition and multiplication without a case distinction about the sign of the arguments. With intuitionistic logic, there are two possible definitions of Euclidean fields, which turn out to correspond to different versions of the parallel postulate.We consider three versions of Euclid’s parallel postulate. The two most important are Euclid’s own formulation in his Postulate 5, which says that under certain conditions two lines meet, and Playfair’s axiom (dating from 1795), which says there cannot be two distinct parallels to line L through the same point p. These differ in that Euclid 5 makes an existence assertion, while Playfair’s axiom does not. The third variant, which we call the strong parallel postulate, isolates the existence assertion from the geometry: it amounts to Playfair’s axiom plus the principle that two distinct lines that are not parallel do intersect. The first main result of this paper is that Euclid 5 suffices to define coordinates, addition, multiplication, and square roots geometrically.We completely settle the questions about implications between the three versions of the parallel postulate. The strong parallel postulate easily implies Euclid 5, and Euclid 5 also implies the strong parallel postulate, as a corollary of coordinatization and definability of arithmetic. We show that Playfair does not imply Euclid 5, and we also give some other independence results. Our independence proofs are given without discussing the exact choice of the other axioms of geometry; all we need is that one can interpret the geometric axioms in Euclidean field theory. The independence proofs use Kripke models of Euclidean field theories based on carefully constructed rings of real-valued functions. “Field elements” in these models are real-valued functions.
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Kaczorowski, Rainee L., Alison R. Seliger, Anne C. Gaskett, Sarah K. Wigsten, and Robert A. Raguso. "Corolla shape vs. size in flower choice by a nocturnal hawkmoth pollinator." Functional Ecology 26, no. 3 (April 17, 2012): 577–87. http://dx.doi.org/10.1111/j.1365-2435.2012.01982.x.
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Manor, Gal. "Victorian Mages: Robert Browning’s “Pietro of Abano” as a Critical Corollary to Alfred Tennyson’s Merlin." Anglia 137, no. 3 (September 13, 2019): 395–410. http://dx.doi.org/10.1515/ang-2019-0036.
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Abstract Against the backdrop of Victorian celebrity culture, Robert Browning and Alfred Tennyson conjure the literary trope of the magician in order to convey their poetic choices and to examine the relationship between the poet and his audience. Whereas Browning’s magician, “Pietro of Abano” of Dramatic Idyls (1880), is subversive, odd and persecuted, the Poet Laureate’s Merlin of the Idylls of the King (1859–1875) is acknowledged and well admired. This essay will explore Browning’s Pietro as a critical response to Tennyson’s Merlin, reflecting the complex personal relationship between the two poets, their stylistic differences and their dissimilar reception by their contemporaries.
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Shlyk, Vladimir. "Criteria of Removable Sets for Harmonic Functions in the Sobolev Spaces L1p,w." Mathematical Physics and Computer Simulation, no. 2 (June 2019): 51–64. http://dx.doi.org/10.15688/mpcm.jvolsu.2019.2.4.
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Ahlfors and Beurling [16] proved that set 𝐸 is removable for class 𝐴𝐷2 of analytic functions with the finite Dirichlet integral if and only if 𝐸 does not change extremal distances. Their proof uses the conformal invariance of class 𝐴𝐷2, so it does not immediately generalize to 𝑝 ̸= 2 and to the relevant classes of harmonic functions in the space. In 1974 Hedberg [19] proposed new approaches to the problem of describing removable singularities in the function theory. In particular he gave the exact functional capacitive conditions for a set to be removable for class 𝐻𝐷𝑝(𝐺). Here 𝐻𝐷𝑝(𝐺) is the class of real-valued harmonic functions 𝑢 in a bounded open set 𝐺 ⊂ 𝑅𝑛, 𝑛 ≥ 2, and such that ∫︁ 𝐺 |∇𝑢|𝑝 𝑑𝑥 < ∞, 𝑝 > 1. In this paper we extend Hedberg’s results on class 𝐻𝐷𝑝,𝑤(𝐺) of harmonic functions 𝑢 in 𝐺 and such that ∫︁ 𝐺 |∇𝑢|𝑝 𝑤𝑑𝑥 < ∞. Here a locally integrable function 𝑤 : 𝑅𝑛 → (0,+∞) satisfies the Muckenhoupt condition [20] sup 1 |𝑄| ∫︁ 𝑄 𝑤𝑑𝑥 ⎛ ⎝ 1 |𝑄| ∫︁ 𝑄 𝑤1−𝑞𝑑𝑥 ⎞ ⎠ 𝑝−1 < ∞, where the supremum is taking over all coordinate cubes 𝑄 ⊂ 𝑅𝑛, 𝑞 ∈ (1,+∞) and 1 𝑝 + 1 𝑞 = 1; by ℒ𝑛(𝑄) = |𝑄| we denote the 𝑛-dimensional Lebesgue measure of 𝑄. We denote by 𝐿1 𝑞 , ˜ 𝑤(𝐺) the Sobolev space of locally integrable functions 𝐹 on 𝐺, whose generalized gradient in 𝐺 are such that ‖𝑓‖𝐿1 𝑞 , ˜ 𝑤(𝐺) = ⎛ ⎝ ∫︁ 𝐺 |∇𝑓|𝑞 ˜ 𝑤𝑑𝑥 ⎞ ⎠ 1 𝑞 < ∞, where ˜ 𝑤 = 𝑤1−𝑞. The closure of 𝐶∞ 0 (𝐺) in ‖ · ‖𝐿1 𝑞 , ˜ 𝑤(𝐺) is denoted by ∘L 1 𝑞, ˜ 𝑤(𝐺). For compact set 𝐾 ⊂ 𝐺 (𝑞, ˜ 𝑤)-capacity regarding 𝐺 is defined by 𝐶𝑞, ˜ 𝑤(𝐾) = inf 𝑣 ∫︁ 𝐺 |∇𝑣|𝑞 ˜ 𝑤𝑑𝑥, where the infimum is taken over all 𝑣 ∈ 𝐶∞ 0 (𝐺) such that 𝑣 = 1 in some neighbourhood of 𝐾. Note that 𝐶𝑞, ˜ 𝑤(𝐾) = 0 is independent from the choice of bounded set 𝐺 ⊂ 𝑅𝑛. We set 𝐶𝑞, ˜ 𝑤(𝐹) = 0 for arbitrary 𝐹 ⊂ 𝑅𝑛 if for every compact 𝐾 ⊂ 𝐹 there exists a bounded open set 𝐺 such that 𝐶𝑞, ˜ 𝑤(𝐾) = 0 regarding 𝐺. To conclude, we formulate the main results. Theorem 1. Compact 𝐸 ⊂ 𝐺 is removable for 𝐻𝐷𝑝,𝑤(𝐺) if and only if 𝐶∞ 0 (𝐺 ∖ 𝐸) is dense in ∘L 1 𝑞, ˜ 𝑤(𝐺). Theorem 2. Compact 𝐸 ⊂ 𝐺 is removable for 𝐻𝐷𝑝,𝑤(𝐺) if and only if 𝐶𝑞, ˜ 𝑤(𝐸) = 0. Corollary. The property of being removable for 𝐻𝐷𝑝,𝑤(𝐺) is local, i.e. compact 𝐸 ⊂ 𝐺 is removable if and only if every 𝑥 ∈ 𝐸 has a compact neighbourhood, whose intersection with 𝐺 is removable. Theorem 3. If 𝐺 is an open set in 𝑅𝑛 and 𝐶𝑞, ˜ 𝑤(𝑅𝑛 ∖𝐺) = 0. Then 𝐶∞ 0 (𝐺) is dense in ∘L 1 𝑞, ˜ 𝑤(𝑅𝑛).
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Zirkel, Perry A. "An Update of Judicial Rulings Specific to FBAs or BIPs Under the IDEA and Corollary State Laws." Journal of Special Education 51, no. 1 (February 15, 2017): 50–56. http://dx.doi.org/10.1177/0022466917693386.
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Exemplifying the insufficient treatment of legal issues in refereed journals in special education and related fields, the limited legal coverage of functional behavioral assessments (FBAs) and behavior intervention plans (BIPs) tends to view the applicable case law through normative lenses. This skewed view characterizes the case law as requiring FBAs and BIPs rather broadly in terms of entitlement and rather rigorously in terms of appropriateness. In stark contrast, this systematic analysis of 91 recent judicial rulings concerning FBAs and BIPs reveals that, aligned with the trajectory of previous court decisions, the outcomes favor the defendant districts on almost a 7:1 ratio and that the pronounced prodistrict trend applies to entitlement as well as appropriateness. Special education professionals need careful differentiation of legal requirements from professional norms to make informed choices about FBAs and BIPs that balance the individual interests and the competing priorities within limited resources of school districts.
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KIDYOO, MANIT. "A new species of Ceropegia (Asclepiadoideae, Apocynaceae) from eastern Thailand." Phytotaxa 385, no. 1 (December 20, 2018): 31. http://dx.doi.org/10.11646/phytotaxa.385.1.4.
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Ceropegia boonjarasii Kidyoo, a new species from eastern Thailand is here described, illustrated and compared morphologically and ecologically to C. sootepensis Craib and C. laotica Rodda & Meve, its putative close relatives. These three species display clear differences in habitat choice, hairiness of leaf surface and corolla lobes, and in the shape of interstaminal corona segments.
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Lehrer, Mark, and Stefan Schmid. "Strategic discipline: inconspicuous lessons from Germanic Mittelstand firms." Journal of Business Strategy 41, no. 4 (June 19, 2019): 3–9. http://dx.doi.org/10.1108/jbs-03-2019-0058.
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Purpose The purpose of this paper is to develop the hitherto unexplored concept of strategic discipline. Design/methodology/approach Three fairly iconic firms of the Germanic Mittelstand (ALDI, Stihl and Hipp) are examined. The meaning and relevance of strategic discipline is derived. Findings Intuitively, strategic discipline may seem like the antipode to the much-discussed concept of pivoting. In fact, strategic discipline is shown to be the natural corollary of strategic pivoting as a successive phase in a company’s development. Research limitations/implications In fast-moving or fast-changing environments, strategic discipline may be inappropriate. Furthermore, the exercise of strategic discipline can restrain growth. Once firms have attained a certain size and saturation of the market, the desire for further growth may entail a willingness to loosen the hold of strategic discipline. Practical implications Strategic discipline can enable firms to avoid falling into common strategic pitfalls. From this paper, the authors distill three basic dimensions of strategic discipline: cultivating simplicity, resisting short-term temptations and focusing on implementability. Originality/value The success of firms depends as much on the strategic choices they make as upon the strategic choices they decide not to make. Most prior research has focused on the visible strategy choices companies have made a lot more than on the practically invisible history of strategic choices that firms have not made. This contribution does the opposite, filling an evident gap.
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Pagariya, R. F. "GREEN CHEMISTRY: ROSELLE’S COROLLA EXTRACT AS A SUBSTITUTE FOR HAZARDOUS INTERNAL INDICATORS IN VOLUMETRIC ANALYSIS." International Journal of Research -GRANTHAALAYAH 7, no. 9 (September 30, 2019): 118–22. http://dx.doi.org/10.29121/granthaalayah.v7.i9.2019.567.
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Indicators used in acid-base titration show well marked changes of colour in certain intervals of pH. Most of these indicators are organic dyes and are of synthetic origin. Today synthetic indicators are the choice of neutralization titrations. But due to environmental pollution, availability and cost, the search for natural compounds as an acid-base indicator was started. The present work highlights the use of the ethanolic extract of the corolla of Roselle (Hibiscus sabdariffa) as a pH indicator in strong acid-strong base, strong acid weak base, weak acid strong base and weak acid-weak base titrations. This natural indicator is easy to extract as well as easily available. The results showed that the Roselle’s corolla indicator gave red color in acidic solution, while green in basic solution. The comparison indicators used in this research were phenolphthalein, methyl red and phenol red. Hopeful results were obtained when it was compared against standard synthetic indicators. The equivalence points obtained match with the equivalence points obtained by standard indicators. Therefore this natural indicator is found to be useful, economical, simple, precise and eco-friendly for acid base titration.