On the Algebraic Structure of Conditional Events

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

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Polymorphic Iterable Sequential Effect Systems

ACM Transactions on Programming Languages and Systems ◽

10.1145/3450272 ◽

2021 ◽

Vol 43 (1) ◽

pp. 1-79

Author(s):

Colin S. Gordon

Keyword(s):

Algebraic Structure ◽

Position Effect ◽

Type Systems ◽

Sequential Effect ◽

Prior Work ◽

Sequential Effects ◽

Wide Range ◽

The Relationship ◽

Categorical Semantics

Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden. But our general understanding of effect systems is limited primarily to systems where the order of effects is irrelevant. Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues and provides guidance when designing new effect systems. By contrast, sequential effect systems—where the order of effects is important—lack an established algebraic structure on effects. We present an abstract polymorphic effect system parameterized by an effect quantale—an algebraic structure with well-defined properties that can model the effects of a range of existing sequential effect systems. We define effect quantales, derive useful properties, and show how they cleanly model a variety of known sequential effect systems. We show that for most effect quantales, there is an induced notion of iterating a sequential effect; that for systems we consider the derived iteration agrees with the manually designed iteration operators in prior work; and that this induced notion of iteration is as precise as possible when defined. We also position effect quantales with respect to work on categorical semantics for sequential effect systems, clarifying the distinctions between these systems and our own in the course of giving a thorough survey of these frameworks. Our derived iteration construct should generalize to these semantic structures, addressing limitations of that work. Finally, we consider the relationship between sequential effects and Kleene Algebras, where the latter may be used as instances of the former.

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A Method to Avoid Underestimated Risks in Seismic SUPSA and MUPSA for Nuclear Power Plants Caused by Partitioning Events

Energies ◽

10.3390/en14082150 ◽

2021 ◽

Vol 14 (8) ◽

pp. 2150

Author(s):

Woo Sik Jung

Keyword(s):

Exact Solutions ◽

Nuclear Power ◽

Power Plants ◽

Nuclear Power Plants ◽

Fault Tree ◽

Ground Acceleration ◽

Special Operations ◽

Core Damage ◽

Full Power ◽

Conditional Events

Seismic probabilistic safety assessment (PSA) models for nuclear power plants (NPPs) have many non-rare events whose failure probabilities are proportional to the seismic ground acceleration. It has been widely accepted that minimal cut sets (MCSs) that are calculated from the seismic PSA fault tree should be converted into exact solutions, such as binary decision diagrams (BDDs), and that the accurate seismic core damage frequency (CDF) should be calculated from the exact solutions. If the seismic CDF is calculated directly from seismic MCSs, it is drastically overestimated. Seismic single-unit PSA (SUPSA) models have random failures of alternating operation systems that are combined with seismic failures of components and structures. Similarly, seismic multi-unit PSA (MUPSA) models have failures of NPPs that undergo alternating operations between full power and low power and shutdown (LPSD). Their failures for alternating operations are modeled using fraction or partitioning events in seismic SUPSA and MUPSA fault trees. Since partitioning events for one system are mutually exclusive, their combinations should be excluded in exact solutions. However, it is difficult to eliminate the combinations of mutually exclusive events without modifying PSA tools for generating MCSs from a fault tree and converting MCSs into exact solutions. If the combinations of mutually exclusive events are not deleted, seismic CDF is underestimated. To avoid CDF underestimation in seismic SUPSAs and MUPSAs, this paper introduces a process of converting partitioning events into conditional events, and conditional events are then inserted explicitly inside a fault tree. With this conversion, accurate CDF can be calculated without modifying PSA tools. That is, this process does not require any other special operations or tools. It is strongly recommended that the method in this paper be employed for avoiding CDF underestimation in seismic SUPSAs and MUPSAs.

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Two semigroups of continuous relations

Journal of the Australian Mathematical Society ◽

10.1017/s144678870001733x ◽

1977 ◽

Vol 23 (1) ◽

pp. 46-58 ◽

Cited By ~ 2

Author(s):

A. R. Bednarek ◽

Eugene M. Norris

Keyword(s):

Large Class ◽

Algebraic Structure ◽

Topological Spaces ◽

Hausdorff Spaces ◽

Completely Regular ◽

Topological Semigroups ◽

Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

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Equipping weak equivalences with algebraic structure

Mathematische Zeitschrift ◽

10.1007/s00209-019-02305-w ◽

2019 ◽

Vol 294 (3-4) ◽

pp. 995-1019 ◽

Cited By ~ 1

Author(s):

John Bourke

Keyword(s):

Algebraic Structure

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HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

International Journal of Modern Physics B ◽

10.1142/s0217979202011573 ◽

2002 ◽

Vol 16 (14n15) ◽

pp. 1867-1873 ◽

Cited By ~ 3

Author(s):

CHENG-MING BAI ◽

MO-LIN GE ◽

KANG XUE

Keyword(s):

Representation Theory ◽

Algebraic Structure ◽

Zeeman Effect ◽

Tensor Space ◽

Commutation Relations ◽

Raising And Lowering Operators ◽

Degenerate States ◽

Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

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