Search results for 'Generalized spaces' (try it on Scholar)

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  1. Fabio Cardone, Alessio Marrani & Roberto Mignani (2004). Killing Symmetries of Generalized Minkowski Spaces. I. Algebraic-Infinitesimal Structure of Spacetime Rotation Groups. Foundations of Physics 34 (4):617-641.score: 168.0
  2. Fabio Cardone, Alessio Marrani & Roberto Mignani (2004). Killing Symmetries of Generalized Minkowski Spaces. Part 2: Finite Structure of Space–Time Rotation Groups in Four Dimensions. Foundations of Physics 34 (8):1155-1201.score: 168.0
  3. Jan Paseka & Zdenka Riečanová (2011). Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras. Foundations of Physics 41 (10):1634-1647.score: 168.0
    We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.
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  4. Fabio Cardone, Alessio Marrani & Roberto Mignani (2004). Killing Symmetries of Generalized Minkowski Spaces, 3: Spacetime Translations in Four Dimensions. Foundations of Physics 34 (9):1407-1429.score: 144.0
  5. Robin H. Lock (1990). The Tensor Product of Generalized Sample Spaces Which Admit a Unital Set of Dispersion-Free Weights. Foundations of Physics 20 (5):477-498.score: 144.0
    Techniques for constructing the tensor product of two generalized sample spaces which admit unital sets of dispersion-free weights are discussed. A duality theory is developed, based on the 1-cuts of the dispersion-free weights, and used to produce a candidate for the tensor product. This construction is verified for Dacification manuals, a conjecture is given for other reflexive cases, and some adjustments for nonreflexive cases are considered. An alternate approach, using graphs of interpretation morphisms on the duals, is also (...)
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  6. Matthias P. Kläy & David J. Foulis (1990). Maximum Likelihood Estimation on Generalized Sample Spaces: An Alternative Resolution of Simpson's Paradox. [REVIEW] Foundations of Physics 20 (7):777-799.score: 144.0
    We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum likelihood estimator for a (...)
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  7. Jan Kraszewski (2001). Properties of Ideals on the Generalized Cantor Spaces. Journal of Symbolic Logic 66 (3):1303-1320.score: 136.0
    We define a class of productive σ-ideals of subsets of the Cantor space 2 ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal I we produce a σ-ideal I κ , of subsets of the generalized Cantor space 2 κ . In particular, starting from meagre sets and null sets in 2 ω we obtain meagre sets and null sets in 2 κ , respectively. Then we investigate (...)
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  8. C. Marcio do Amaral (1969). Flat-Space Metric in the Quaternion Formulation of General Relativity. Rio De Janeiro, Centro Brasileiro De Pesquisas Físicas.score: 100.0
     
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  9. Carlos Castro (2014). On Clifford Space Relativity, Black Hole Entropy, Rainbow Metrics, Generalized Dispersion and Uncertainty Relations. Foundations of Physics 44 (9):990-1008.score: 84.0
    An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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  10. Yuri Balashov (2000). Persistence and Space-Time. The Monist 83 (3):321-340.score: 78.0
    Although considerations based on contemporary space-time theories, such as special and general relativity, seem highly relevant to the debate about persistence, their significance has not been duly appreciated. My goal in this paper is twofold: (1) to reformulate the rival positions in the debate (i.e., endurantism [three-dimensionalism] and perdurantism [four-dimensionalism, the doctrine of temporal parts]) in the framework of special relativistic space-time; and (2) to argue that, when so reformulated, perdurantism exhibits explanatory advantages over endurantism. The argument builds on the (...)
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  11. Stephen OʹBrien (1952). Jump Conditions at Discontinuities in General Relativity. Dublin, Dublin Institute for Advanced Studies.score: 70.0
     
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  12. Hyōichirō Takeno (1966). The Theory of Spherically Symmetric Space-Times. Takehara, Japan, Research Institute for Theoretical Physics, Hiroshima University.score: 70.0
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  13. Sy-David Friedman & Tapani Hyttinen (2012). On Borel Equivalence Relations in Generalized Baire Space. Archive for Mathematical Logic 51 (3-4):299-304.score: 68.0
    We construct two Borel equivalence relations on the generalized Baire space κ κ , κ <κ = κ > ω, with the property that neither of them is Borel reducible to the other. A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy fails.
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  14. Carlos Castro (2012). Born's Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant. Foundations of Physics 42 (8):1031-1055.score: 66.0
    The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction (...)
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  15. Yuri Balashov (2010). Persistence and Spacetime. Oxford University Press.score: 62.0
    Background and assumptions. Persistence and philosophy of time ; Atomism and composition ; Scope ; Some matters of methodology -- Persistence, location, and multilocation in spacetime. Endurance, perdurance, exdurance : some pictures ; More pictures ; Temporal modification and the "problem of temporary intrinsics" ; Persistence, location and multilocation in generic spacetime ; An alternative classification -- Classical and relativistic spacetime. Newtonian spacetime ; Neo-Newtonian (Galilean) spacetime ; Reference frames and coordinate systems ; Galilean transformations in spacetime ; Special relativistic (...)
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  16. Jakub Szymanik (2009). Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. Dissertation, University of Amsterdamscore: 62.0
    In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial (...)
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  17. Luca Lusanna & Massimo Pauri, Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity.score: 60.0
    The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold M^4 in terms of the "autonomous degrees of freedom" of the vacuum gravitational field (Dirac observables), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to gauge variables) of (...)
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  18. Herbert Friedman (1963). Wavelength Generalization as a Function of Spacing of Test Stimuli. Journal of Experimental Psychology 65 (4):334.score: 60.0
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  19. Thomas Müller (forthcoming). A Generalized Manifold Topology for Branching Space-Times. Philosophical Explorations 80 (5):1089-1100.score: 60.0
    The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...)
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  20. Matthew W. Parker (2003). Three Concepts of Decidability for General Subsets of Uncountable Spaces. Theoretical Computer Science 351 (1):2-13.score: 60.0
    There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...)
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  21. M. C. B. Fernandes & J. D. M. Vianna (1999). On the Generalized Phase Space Approach to Duffin-Kemmer-Petiau Particles. Foundations of Physics 29 (2):201-219.score: 58.0
    We present a general derivation of the Duffin-Kemmer-Petiau (D.K.P) equation on the relativistic phase space proposed by Bohm and Hiley. We consider geometric algebras and the idea of algebraic spinors due to Riesz and Cartan. The generators βμ (p) of the D.K.P algebras are constructed in the standard fashion used to construct Clifford algebras out of bilinear forms. Free D.K.P particles and D.K.P particles in a prescribed external electromagnetic field are analized and general Liouville type equations for these cases are (...)
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  22. Göran Sonesson (2014). New Rules for the Spaces of Urbanity. International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 27 (1):7-26.score: 58.0
    The best way to conceive semiotical spaces that are not identical to single buildings, such as a cityscape, is to define the place in terms of the activities occurring there. This conception originated in the proxemics of E. T. Hall and was later generalized in the spatial semiotics of Manar Hammad. It can be given a more secure grounding in terms of time geography, which is involved with trajectories in space and time. We add to this a qualitative (...)
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  23. Roger N. Shepard (1958). Stimulus and Response Generalization: Tests of a Model Relating Generalization to Distance in Psychological Space. Journal of Experimental Psychology 55 (6):509.score: 56.0
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  24. Eduard Prugovečki (1979). Stochastic Phase Spaces and Master Liouville Spaces in Statistical Mechanics. Foundations of Physics 9 (7-8):575-587.score: 54.0
    The concept of probability space is generalized to that of stochastic probability space. This enables the introduction of representations of quantum mechanics on stochastic phase spaces. The resulting formulation of quantum statistical mechanics in terms of Γ-distribution functions bears a remarkable resemblance to its classical counterpart. Furthermore, both classical and quantum statistical mechanics can be formulated in one and the same master Liouville space overL 2(Γ). A joint derivation of a classical and quantum Boltzman equation provides an illustration (...)
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  25. Stanley Gudder (1973). Generalized Measure Theory. Foundations of Physics 3 (3):399-411.score: 54.0
    It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics (...)
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  26. Carlos Castro (2010). On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy. Foundations of Physics 40 (11):1712-1730.score: 54.0
    A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation (...)
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  27. Bill Poirier (2001). Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces. [REVIEW] Foundations of Physics 31 (11):1581-1610.score: 54.0
    In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, (...)
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  28. Gilles Fauconnier & Mark Turner, Conceptual Projection and Middle Spaces.score: 54.0
    Conceptual projection from one mental space to another always involves projection to "middle" spaces-abstract "generic" middle spaces or richer "blended" middle spaces. Projection to a middle space is a general cognitive process, operating uniformly at different levels of abstraction and under superficially divergent contextual circumstances. Middle spaces are indispensable sites for central mental and linguistic work. The process of blending is in particular a fundamental and general cognitive process, running over many (conceivably all) cognitive phenomena, including (...)
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  29. Matthew A. Graydon (2013). Quaternionic Quantum Dynamics on Complex Hilbert Spaces. Foundations of Physics 43 (5):656-664.score: 54.0
    We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum measurements with positive operator valued measures on complex Hilbert spaces. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex matrices. These novel results map all quaternionic quantum processes to algorithms in usual quantum information theory.
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  30. Gerd Niestegge (2008). A Representation of Quantum Measurement in Order-Unit Spaces. Foundations of Physics 38 (9):783-795.score: 54.0
    A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this (...)
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  31. Hans A. Keller (1990). Measures on Infinite-Dimensional Orthomodular Spaces. Foundations of Physics 20 (5):575-604.score: 54.0
    We classify the measures on the lattice ℒ of all closed subspaces of infinite-dimensional orthomodular spaces (E, Ψ) over fields of generalized power series with coefficients in ℝ. We prove that every σ-additive measure on ℒ can be obtained by lifting measures from the residual spaces of (E, Ψ). The measures being lifted are known, for the residual spaces are Euclidean. From the classification we deduce, among other things, that the set of all measures on ℒ (...)
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  32. Shimon Edelman (2001). Neural Spaces: A General Framework for the Understanding of Cognition? Behavioral and Brain Sciences 24 (4):664-665.score: 54.0
    A view is put forward, according to which various aspects of the structure of the world as internalized by the brain take the form of “neural spaces,” a concrete counterpart for Shepard's “abstract” ones. Neural spaces may help us understand better both the representational substrate of cognition and the processes that operate on it. [Shepard].
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  33. Anatolij Dvurečenskij, Tibor Neubrunn & Sylvia Pulmannová (1990). Finitely Additive States and Completeness of Inner Product Spaces. Foundations of Physics 20 (9):1091-1102.score: 54.0
    For any unit vector in an inner product space S, we define a mapping on the system of all ⊥-closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. (...)
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  34. Jarosław Achinger (1986). On a Problem of P(Α, Δ, Π) Concerning Generalized Alexandroff S Cube. Studia Logica 45 (3):293 - 300.score: 54.0
    Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ).
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  35. D. Bohm & B. J. Hiley (1981). On a Quantum Algebraic Approach to a Generalized Phase Space. Foundations of Physics 11 (3-4):179-203.score: 52.0
    We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of “negative probabilities” by regarding (...)
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  36. James D. Edmonds Jr (1977). Generalized Quaternion Formulation of Relativistic Quantum Theory in Curved Space. Foundations of Physics 7 (11-12):835-859.score: 50.0
    A survey is presented of the essential principles for formulating relativistic wave equations in curved spacetime. The approach is relatively simple and avoids much of the philosophical debate about covariance principles, which is also indicated. Hypercomplex numbers provide a natural language for covariance symmetry and the two important kinds of covariant derivative.
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  37. Anatolij Dvurečenskij & Jiří Janda (2013). On Bilinear Forms From the Point of View of Generalized Effect Algebras. Foundations of Physics 43 (9):1136-1152.score: 50.0
    We study positive bilinear forms on a Hilbert space which are not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) σ-complete generalized effect algebras.
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  38. Georg Gottlob (1997). Relativized Logspace and Generalized Quantifiers Over Finite Ordered Structures. Journal of Symbolic Logic 62 (2):545-574.score: 50.0
    We here examine the expressive power of first order logic with generalized quantifiers over finite ordered structures. In particular, we address the following problem: Given a family Q of generalized quantifiers expressing a complexity class C, what is the expressive power of first order logic FO(Q) extended by the quantifiers in Q? From previously studied examples, one would expect that FO(Q) captures L C , i.e., logarithmic space relativized to an oracle in C. We show that this is (...)
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  39. Dag Normann (1995). Review: Dimiter G. Skordev, Computability in Combinatory Spaces. An Algebraic Generalization of Abstract First Order Computability. [REVIEW] Journal of Symbolic Logic 60 (2):695-696.score: 50.0
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  40. Luca Lusanna & Massimo Pauri, General Covariance and the Objectivity of Space-Time Point-Events.score: 48.0
    "The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that represent - as it were - the "ontic" part of the metric field. The physical role of the "epistemic" part (viz. the "gauge" variables) is likewise clarified. At the end, a (...)
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  41. Matej Pavšič (2005). Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings. [REVIEW] Foundations of Physics 35 (9):1617-1642.score: 48.0
    The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is (...)
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  42. Alexey A. Kryukov (2006). Quantum Mechanics on Hilbert Manifolds: The Principle of Functional Relativity. [REVIEW] Foundations of Physics 36 (2):175-226.score: 48.0
    Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory (QT) is indeed a functional tensor theory, i.e., it can be (...)
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  43. Michael Freenor & Clark Glymour, Searching the DCM Model Space, and Some Generalizations.score: 48.0
    We describe the (enormous) size of the search space for Dynamic Casual Models and generalizations of them.
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  44. Abraham Stone, On the Completion and Generalization of Intuitive Space in der Raum: Husserlian and Drieschian Elements.score: 48.0
    The paper focuses on some puzzles about Carnap's intended epistemological point in the "completion" and "generalization" of the Anschauungsraum in sec. II of Der Raum (leaving aside the technical problems which also arise). Since any global structure at all requires that eidetic intuition be supplemented with freely-chosen postulates and/or intuitively unmotivated generalizations, it is unclear, as several authors have pointed out, how and in what sense "intuitive space" as a whole represents a distinctive, a priori contribution to our knowledge. I (...)
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  45. Luca Lusanna & Massimo Pauri, General Covariance and the Objectivity of Space-Time Point-Events: The Physical Role of Gravitational and Gauge Degrees of Freedom - DRAFT.score: 48.0
    This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...)
     
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  46. Victor Pambuccian (2009). A Reverse Analysis of the Sylvester-Gallai Theorem. Notre Dame Journal of Formal Logic 50 (3):245-260.score: 48.0
    Reverse analyses of three proofs of the Sylvester-Gallai theorem lead to three different and incompatible axiom systems. In particular, we show that proofs respecting the purity of the method, using only notions considered to be part of the statement of the theorem to be proved, are not always the simplest, as they may require axioms which proofs using extraneous predicates do not rely upon.
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  47. Daniel R. Patten (2013). Mereology on Topological and Convergence Spaces. Notre Dame Journal of Formal Logic 54 (1):21-31.score: 46.0
    We show that a standard axiomatization of mereology is equivalent to the condition that a topological space is discrete, and consequently, any model of general extensional mereology is indistinguishable from a model of set theory. We generalize these results to the Cartesian closed category of convergence spaces.
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  48. Arthur Stanley Eddington (1920/1966). Space, Time, and Gravitation: An Outline of the General Relativity Theory. Cambridge [Eng.]University Press.score: 44.0
    The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.
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  49. David J. Foulis & Sylvia Pulmannová (2009). Spin Factors as Generalized Hermitian Algebras. Foundations of Physics 39 (3):237-255.score: 44.0
    We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.
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