| 1. |
- Silvestrov, D., et al.
(författare)
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Asymptotic Expansions for Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 37-66
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Bokkapitel (refereegranskat)abstract
- In Chapter 3, we introduce a model of perturbed semi-Markov processes, formulate basic perturbation conditions, describe a one-step time-space screening procedure of phase space reduction for perturbed semi-Markov processes, introduce hitting times, and prove an invariant property of them with respect to the procedure of phase space reduction. We, also, present algorithms for re-calculation of asymptotic expansions for transition characteristics of nonlinearly perturbed semi-Markov processes with reduced phase spaces and algorithms for sequential reduction of phase space for semi-Markov processes and construction of Laurent asymptotic expansions, without and with explicit upper bounds for remainders, for power moment of hitting times. © 2017, The Author(s).
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| 2. |
- Silvestrov, D., et al.
(författare)
-
Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes
- 2017
-
Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 67-79
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Bokkapitel (refereegranskat)abstract
- In Chapter 4, new algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on the technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit upper bounds for remainders. © 2017, The Author(s).
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| 3. |
- Silvestrov, D., et al.
(författare)
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Examples and Survey of Applied Perturbed Stochastic Models
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 107-121
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Bokkapitel (refereegranskat)abstract
- In Chapter 6, we present a background for construction of numerical examples for asymptotic results presented in Chapters 2 – 5, some numerical examples as well as a summary survey of applied perturbed stochastic systems. © 2017, The Author(s).
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| 4. |
- Silvestrov, D., et al.
(författare)
-
Introduction
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 1-15
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This book is devoted to the study of asymptotic expansions for moment of hitting times, stationary and conditional quasi-stationary distributions, and other functionals, for nonlinearly perturbed semi-Markov processes. The introduction intends to present in informal form the main problems, methods, and algorithms that constitute the content of the book. © 2017, The Author(s).
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| 5. |
- Silvestrov, D., et al.
(författare)
-
Laurent Asymptotic Expansions
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 17-35
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Bokkapitel (refereegranskat)abstract
- In Chapter 2, we present operational rules for Laurent asymptotic expansions given in two forms, with remainders given in the standard form o(⋅ ) and with explicit power-type upper bounds for remainders. In the former case, such rules should be possibly considered as generally known, while, in the latter case, asymptotic expansions have some novelty aspects. © 2017, The Author(s).
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| 6. |
- Silvestrov, D., et al.
(författare)
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Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - Cham : Springer Nature. - 9783319609881 ; , s. 81-106
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Bokkapitel (refereegranskat)abstract
- In Chapter 5, we present asymptotic expansions for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov processes, which play an important role in many applications. In this case, the corresponding expansions can be given in a more explicit form. © 2017, The Author(s).
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| 7. |
- Silvestrov, D., et al.
(författare)
-
Preface
- 2017
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Ingår i: Nonlinearly Perturbed Semi-Markov Processes. - : Springer Nature. - 9783319609881 ; , s. v-vii
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Casazza, P. G., et al.
(författare)
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Preface
- 2012
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Ingår i: Numerical Functional Analysis and Optimization. - : Informa UK Limited. - 0163-0563 .- 1532-2467. ; 33:7-9, s. 705-707
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 9. |
- Hellström, Lars, 1974-, et al.
(författare)
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Commuting Elements in Q-Deformed Heisenberg Algebras
- 2000
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Bok (refereegranskat)abstract
- Noncommutative algebras, rings and other noncommutative objects, along with their more classical commutative counterparts, have become a key part of modern mathematics, physics and many other fields. The q-deformed Heisenberg algebras defined by deformed Heisenberg canonical commutation relations of quantum mechanics play a distinguished role as important objects in pure mathematics and in many applications in physics. The structure of commuting elements in an algebra is of fundamental importance for its structure and representation theory as well as for its applications. The main objects studied in this monograph are q-deformed Heisenberg algebras — more specifically, commuting elements in q-deformed Heisenberg algebras.In this book the structure of commuting elements in q-deformed Heisenberg algebras is studied in a systematic way. Many new results are presented with complete proofs. Several appendices with some general theory used in other parts of the book include material on the Diamond lemma for ring theory, a theory of degree functions in arbitrary associative algebras, and some basic facts about q-combinatorial functions over an arbitrary field. The bibliography contains, in addition to references on q-deformed Heisenberg algebras, some selected references on related subjects and on existing and potential applications.The book is self-contained, as far as proofs and the background material are concerned. In addition to research and reference purposes, it can be used in a special course or a series of lectures on the subject or as complementary material to a general course on algebra. Specialists as well as doctoral and advanced undergraduate students in mathematics and physics will find this book useful in their research and study.Contents:Immediate Consequences of the Commutation RelationsBases and Normal Form in H(q) and H(q,J)Degree in and Gradation of H(q,J)Centralisers of Elements in H(q,J)Centralisers of Elements in H(q)Algebraic Dependence of Commuting Elements in H(q) and H(q,J)Representations of H(q,J) by q-Difference OperatorsThe Diamond LemmaDegree Functions and Gradationsq-Special CombinatoricsReadership: Researchers, graduate students and undergraduates in algebra and physics.
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| 10. |
- Javor, V., et al.
(författare)
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Modelling of measured lightning discharge currents to tall towers
- 2017
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Ingår i: Conference Proceedings - 2017 17th IEEE International Conference on Environment and Electrical Engineering and 2017 1st IEEE Industrial and Commercial Power Systems Europe, EEEIC / I and CPS Europe 2017. - : Institute of Electrical and Electronics Engineers Inc.. - 9781538639160
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Konferensbidrag (refereegranskat)abstract
- Lightning discharge currents and their derivatives have been measured at instrumented tall towers for a few decades already. Results of those measurements are used for lightning research purposes, modelling of lightning discharges and making improvements in lightning protection. Some of the measured lightning currents are represented in this paper by the multi-peaked analytically extended function (MP-AEF). The same function may be used for lightning current derivatives, thus providing their analytical integration.
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| 11. |
- Larsson, Daniel, et al.
(författare)
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On generalized N-complexes coming from twisted derivations
- 2009
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Ingår i: Generalized Lie theory in mathematics, physics and beyond. - Berlin, Heidelberg : Springer. - 9783540853329 - 9783540853312 ; , s. 81-88
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Bokkapitel (refereegranskat)abstract
- Inspired by a result of V. Abramov on q-differential graded algebras, we prove a theorem, analogous to Abramov's result but in a slightly different set-up, using a σ- (twisted) derivation as the differential-like map. As an application, we construct a generalized N-complex based on the ring of Laurent polynomials.
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| 12. |
- Larsson, Daniel, et al.
(författare)
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Quasi-Lie deformations on the algebra F[t]/(tn)
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:3, s. 201-205
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Tidskriftsartikel (refereegranskat)abstract
- This paper explores the quasi-deformation scheme devised by Hartwig, Larsson and Silvestrov as applied to the simple Lie algebra sl2(F). One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when the quasi-deformation method is applied to sl2(F) via representations by twisted derivations on the algebra F[t]/(tN) one obtains interesting new multi-parameter families of almost quadratic algebras.
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| 13. |
- Makhlouf, Abdenacer, et al.
(författare)
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Hom-algebra structures
- 2008
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Ingår i: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:2, s. 51-64
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Tidskriftsartikel (refereegranskat)abstract
- A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov in [4] and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras in [5, 6]. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic structures which generalize the well known associative, Leibniz and Lie admissible algebras. Also, we characterize the flexible Hom-algebras in this case. We also explain some connections between Hom-Lie algebras and Santilli’s isotopies of associative and Lie algebras.
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| 14. |
- Marinković, Sladjana D., et al.
(författare)
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Wallis Type Formula and a Few Versions of the Number π in q-Calculus
- 2023
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Ingår i: Non-commutative and Non-associative Algebra and Analysis Structures. - : Springer. - 9783031320088 ; , s. 741-759
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Konferensbidrag (refereegranskat)abstract
- In this paper, we expose a geometrical interpretation of the q-Wallis formula. We construct plane regions which consist of rectangles whose edges’ lengths are directly connected with factors in this formula. These regions are bounded by quarters of inside and outside circles from which we get estimates and conclusions about the number πq.
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| 15. |
- Mitrovic, Melanija, et al.
(författare)
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Constructive Semigroups with Apartness : Towards a New Algebraic Theory
- 2019
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Ingår i: Journal of Physics, Conference Series. - : Institute of Physics Publishing (IOPP). - 1742-6588 .- 1742-6596. ; 1194:1, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- The theory of constructive semigroups with apartness is a new approach tosemigroup theory, and not a new class of semigroups. Of course, our work is partly inspired byclassical semigroup theory, but, on the other hand, it is distinguished from it by two signicantaspects: rst, we use intuitionistic logic rather than classical, secondly, our work is based onthe notion of apartness (between elements, elements and sets). Here, the focus is on E. Bishop'sapproach to constructive mathematics (BISH)
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| 16. |
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| 17. |
- Richard, Lionel, et al.
(författare)
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Quasi-Lie structure of σ-derivations of C[t±1]
- 2008
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 319:3, s. 1285-1304
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Tidskriftsartikel (refereegranskat)abstract
- Hartwig, Larsson and Silvestrov in [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra 295 (2) (2006) 314–361] defined a bracket on σ-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain structural results providing new insights into σ-derivations on Laurent polynomials in one variable.
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| 18. |
- Öinert, Johan, et al.
(författare)
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Commutativity and ideals in pre-crystalline graded rings
- 2009
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 603-615
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Tidskriftsartikel (refereegranskat)abstract
- Pre-crystalline graded rings constitute a class of rings which share many properties with classical crossed products. Given a pre-crystalline graded ring A, we describe its center, the commutant CA(A0) of the degree zero grading part, and investigate the connection between maximal commutativity of A0 in A and the way in which two-sided ideals intersect A0.
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