A detailed development of the principal component proxy method of dynamical tracer reconstruction is presented, including error analysis. The method works by correlating the largest principal ...components of a matrix representation of the transport dynamics with a set of sparse measurements. The Lyapunov spectrum was measured and used to quantify the lifetime of each principal component. The method was tested on the 500 K isentropic surface with stratospheric ozone concentration measurements from the Polar Aerosol and Ozone Measurement III satellite instrument during October and November 1998 and compared with the older proxy tracer method which works by correlating measurements with a single other tracer or proxy. Using a 60 day integration time and five (5) principal components, cross validation of globally reconstructed ozone and comparison with ozone sondes returned root-mean-square errors of 0.16 and 0.36 ppmv, respectively. This compares favourably with the classic proxy tracer method in which a passive tracer equivalent latitude field was used for the proxy and which returned RMS errors of 0.22 and 0.59 ppmv for cross-validation and sonde validation respectively. The method seems especially effective for shorter lived tracers and was far more accurate than the classic method at predicting ozone concentration in the Southern hemisphere over the same time period. It is also more effective when reconstruction is performed over the entire Earth rather than a single hemisphere allowing for seamless reconstruction of global fields.
We analyze differences between BL–algebras and MV–algebras. The study has application in mathematical fuzzy logic as the Lindenbaum algebras of Lukasiewicz logic or Hájek’s BL–logics are MV–algebras ...or BL–algebras, respectively. We focus on possible generalizations of Boolean elements of a general BL–algebra L; we prove that an element x ∈ L is Boolean iff x ∨ x ∗ = 1. L is called semi–Boolean if, for all x ∈ L, x ∗ is Boolean. We prove that an MV–algebra L is semi–Boolean iff L is a Boolean algebra. A BL–algebra L is semi–Boolean iff L is a SBL–algebra. A BL–algebra L is called hyper–Archimedean if, for all x ∈ L, there is an n ≥ 1 such that xn is Boolean. We prove that hyper–Archimedean BL–algebras are MV–algebras. We discuss briefly the applications of our results in mathematical fuzzy logic.
This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection ...cohomology, anddetailed information on representations of Weylgroups.
Policy composition is an essential requirement of grid access control, not only because of the integrity of local and global policies, but also the dynamic collaboration under jointly controlled ...policies among multiple partners across different domains. In this paper, we propose an algebra for compositing attribute-based access control policies. Traditional arithmetic operators are extended and semantically redefined, as well as new operators are introduced to satisfy unique grid scenarios. The powerful expressiveness of our proposed algebra is illustrated by applying to scenarios and comparing with related works.
In this paper we demonstrate how one can reformulate the MPC problem for LPV systems to a series of mpLPs by a closed-loop minimax MPC algorithm based on dynamic programming. A relaxation technique ...is employed to reformulate constraints which are polynomial in the scheduling parameters to parameter-independent constraints. The algorithm allows the computation of explicit control laws for linear parameter-varying systems and enables the controller to exploit information about the scheduling parameter. This improves the control performance compared to a standard robust approach where no uncertainty knowledge is used, while keeping the benefits of fast online computations. The off-line computational burden is similar to what is required for computing explicit control laws for uncertain or nominal LTI systems. The proposed control strategy is applied to an example to compare the complexity of the resulting explicit control law to the robust controller.
INTERVAL SHEFFER STROKE BASIC ALGEBRAS Oner, T; Katican, T; Ulker, A
TWMS journal of applied and engineering mathematics,
01/2019, Volume:
9, Issue:
1 SI
Journal Article
Peer reviewed
Open access
In this paper we deal with Sheffer stroke basic algebras A = (A; |), and we define the operations mathematical expression not reproducible for any elements a, b member of A in such a way that (a, ...1;|.sub.a), (0, b;|.sup.b), mathematical expression not reproducible become also Sheffer Stroke basic algebras, respectively. Subsequeutly, we show that these interval Sheffer Stroke basic algebras on a given Sheffer Stroke basic algebra A = ( A; | ) verify the patchwork condition.Keywords: Basic algrebras, interval basic algebra, patchwork condition.AMS Subject Classification: 06D15, 06B05, 03G25
Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate ...students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite ...rules, and to demonstrate that a logic can be built on this to allow the formalisation of inductive proofs in the string diagrams of compact closed and traced symmetric monoidal categories. String diagrams provide an intuitive method for reasoning about monoidal categories. However, this does not negate the ability for those using them to make mistakes in proofs. To this end, there is a project (Quantomatic) to build a proof assistant for string diagrams, at least for those based on categories with a notion of trace. The development of string graphs has provided a combinatorial formalisation of string diagrams, laying the foundations for this project. The prevalence of commutative Frobenius algebras (CFAs) in quantum information theory, a major application area of these diagrams, has led to the use of variable-arity nodes as a shorthand for normalised networks of Frobenius algebra morphisms, so-called "spider notation". This notation greatly eases reasoning with CFAs, but string graphs are inadequate to properly encode this reasoning. This dissertation firstly extends string graphs to allow for variable-arity nodes to be represented at all, and then introduces !-box notation – and structures to encode it – to represent string graph equations containing repeated subgraphs, where the number of repetitions is abitrary. This can be used to represent, for example, the "spider law" of CFAs, allowing two spiders to be merged, as well as the much more complex generalised bialgebra law that can arise from two interacting CFAs. This work then demonstrates how we can reason directly about !-graphs, viewed as (typically infinite) families of string graphs. Of particular note is the presentation of a form of graph-based induction, allowing the formal encoding of proofs that previously could only be represented as a mix of string diagrams and explanatory text.
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