| 1. |
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| 2. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
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Expedited analytical hierarchical process for multicriteria decision making
- 2022
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Ingår i: ICIC Express Letters. - 1881-803X. ; 16:2, s. 145-151
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Tidskriftsartikel (refereegranskat)abstract
- In this study, a procedure to overcome analytical hierarchical process (AHP) limitations was developed and tested, and a tool created via pairwise comparison chart and weighted sum method hybridization was introduced. In addition, a multicriteria decision-making software was selected to validate the constructed hybrid decision-making tool. The software was formulated based on an established decision-making technique. Data for the comparison analysis were obtained from an ongoing research, and output from the comparison analysis provided evidence for the accuracy of the constructed tool. The proposed hybridized method aligned with AHP reasoning but demonstrated a faster process; hence, it was called ‘expedited AHP’.
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| 3. |
- Ni, Ying, 1976-
(författare)
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Nonlinearly Perturbed Renewal Equation with Perturbations of a Non-polynomial Type
- 2010
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Ingår i: Proceedings of the International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management, Beer Sheva, 2010.. - Beer Sheva : SCE - Shamoon College of Engineering. ; , s. 754-763
-
Konferensbidrag (refereegranskat)abstract
- The object of study is a model of nonlinearly perturbed continuous-time renewal equation with multivariate non-polynomial perturbations. The characteristics of the distribution generating the renewal equation are assumed to have expansions in the perturbation parameter with respect to a non-polynomial asymptotic scale which can be considered as a generalization of the standard polynomial scale. Exponential asymptotics for such a model are obtained and applications are given.
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| 4. |
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| 5. |
- Berndtsson, Bo, 1950
(författare)
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Probability measures associated to geodesics in the space of kähler metrics
- 2018
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 395-419
-
Konferensbidrag (refereegranskat)abstract
- We associate certain probability measures on R to geodesics in the space HL of positively curved metrics on a line bundle L, and to geodesics in the finite dimensional symmetric space of hermitian norms on H0(X, kL). We prove that the measures associated to the finite dimensional spaces converge weakly to the measures related to geodesics in HL as k goes to infinity. The convergence of second order moments implies a recent result of Chen and Sun on geodesic distances in the respective spaces, while the convergence of first order moments gives convergence of Donaldson’s Z-functional to the Aubin–Yau energy. We also include a result on approximation of infinite dimensional geodesics by Bergman kernels which generalizes work of Phong and Sturm.
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| 6. |
- Xia, Jiacheng, 1991
(författare)
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Vector-valued Eisenstein series of congruence types and their products
- 2019
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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| 7. |
- Sorooshian, Shahryar, 1980, et al.
(författare)
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Performance of the decision-making trial and evaluation laboratory
- 2023
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Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
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Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 8. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 9. |
- Aas, Erik, et al.
(författare)
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Limiting directions for random walks in classical affine Weyl groups
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Let be a finite Weyl group and the corresponding affine Weyl group. A random element of can be obtained as a reduced random walk on the alcoves of . By a theorem of Lam (Ann. Probab. 2015), such a walk almost surely approaches one of many directions. We compute these directions when is , and and the random walk is weighted by Kac and dual Kac labels. This settles Lam's questions for types and in the affirmative and for type in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process called the -TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.
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| 10. |
- Ameur, Yacin, et al.
(författare)
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FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES
- 2011
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Ingår i: Duke mathematical journal. - : Duke University Press. - 0012-7094 .- 1547-7398. ; 159:1, s. 31-81
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane-the "droplet." We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.
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| 11. |
- Jain, P., et al.
(författare)
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Inequalities and properties of some generalized Orlicz classes and spaces
- 2007
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Ingår i: Acta Mathematica Hungarica. - : Springer Science and Business Media LLC. - 0236-5294 .- 1588-2632. ; 117:1-2, s. 161-174
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Tidskriftsartikel (refereegranskat)abstract
- We discuss and complement the knowledge about generalized Orlicz classes and Orlicz spaces X Φ obtained by replacing the space L 1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also natural generalizations of some classical ones (e.g., Minkowski’s, Hölder’s and Young’s inequalities). Moreover, a number of other basic facts for further study of inequalities and function spaces are included.
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| 12. |
- Kuliev, K., et al.
(författare)
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An extension of Rothe´s method to noncylindrical domains
- 2007
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Ingår i: Applications of Mathematics. - : Institute of Mathematics, Czech Academy of Sciences. - 0862-7940 .- 1572-9109. ; 52:5, s. 365-389
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Tidskriftsartikel (refereegranskat)abstract
- In this paper Rothe's classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
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| 13. |
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| 14. |
- Okpoti, Christopher, et al.
(författare)
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An equivalence theorem for some integral conditions with general measures related to Hardy´s inequality
- 2007
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 326:1, s. 398-413
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Tidskriftsartikel (refereegranskat)abstract
- It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<pq<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.
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| 15. |
- Persson, Lars-Erik, et al.
(författare)
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Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:2, s. 267-279
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the weighted Hardy inequality 1/q 1/p q ∞ ∞ x f p (x)v(x)dx f (t)dt u(x)dx C 0 0 0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x) 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.
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| 16. |
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| 17. |
- Persson, Lars-Erik, et al.
(författare)
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Weighted inequalities of Hardy type for matrix operators: The case q
- 2007
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:4, s. 843-861
-
Tidskriftsartikel (refereegranskat)abstract
- A non-negative triangular matrix operator is considered in weighted Lebesgue spaces ofsequences. Under some additional conditions on the matrix, some new weight characterizationsfor discrete Hardy type inequalities with matrix operator are proved for the case 1 < q < p < ∞.Some further results are pointed out.
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| 18. |
- Önskog, Thomas, 1979-, et al.
(författare)
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Pricing and hedging of financial derivatives using a posteriori error estimates and adaptive methods for stochastic differential equations
- 2010
-
Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 235, s. 563-592
-
Tidskriftsartikel (refereegranskat)abstract
- The efficient and accurate calculation of sensitivities of the price of financial derivatives with respect to perturbations of the parameters in the underlying model, the so-called `Greeks', remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial differential equations or stochastic differential equations (Monte Carlo techniques) are being used. The computation of the `Greeks' is essential to risk management and to the hedging of financial derivatives and typically requires substantially more computing time as compared to simply pricing the derivatives. Any numerical algorithm (Monte Carlo algorithm) for stochastic differential equations produces a time-discretization error and a statistical error in the process of pricing financial derivatives and calculating the associated `Greeks'. In this article we show how a posteriori error estimates and adaptive methods for stochastic differential equations can be used to control both these errors in the context of pricing and hedging of financial derivatives. In particular, we derive expansions, with leading order terms which are computable in a posteriori form, of the time-discretization errors for the price and the associated `Greeks'. These expansions allow the user to simultaneously first control the time-discretization errors in an adaptive fashion, when calculating the price, sensitivities and hedging parameters with respect to a large number of parameters, and then subsequently to ensure that the total errors are, with prescribed probability, within tolerance.
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| 19. |
- Eriksson, Kimmo, et al.
(författare)
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Bentley’s conjecture on popularity toplist turnover under random copying
- 2010
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Ingår i: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
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Tidskriftsartikel (refereegranskat)abstract
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
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| 20. |
- Önskog, Thomas, 1979-, et al.
(författare)
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Weak approximation of obliquely reflected diffusions in time-dependent domains
- 2010
-
Ingår i: Journal of Computational Mathematics. - : Global Science Press. - 0254-9409 .- 1991-7139. ; 28:5, s. 579-605
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Tidskriftsartikel (refereegranskat)abstract
- In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in R^d, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.
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| 21. |
- Önskog, Thomas, 1979-, et al.
(författare)
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The Skorohod oblique reflection problem in time-dependent domains
- 2010
-
Ingår i: Annals of Probability. - : Project Euclid. - 0091-1798 .- 2168-894X. ; 38:6, s. 2170-2223
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Tidskriftsartikel (refereegranskat)abstract
- The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains, by H. Tanaka and further investigated by P.-L. Lions and A.-S. Sznitman in their celebrated article. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In this article we conduct a thorough study of the multidimensional Skorohod problem in time-dependent domains. In particular, we prove the existence of càdlàg solutions (x, λ) to the Skorohod problem, with oblique reflection, for (D,,w) assuming, in particular, that D is a time-dependent domain (Theorem 1.2). In addition, we prove that if w is continuous, then x is continuous as well (Theorem 1.3). Subsequently, we use the established existence results to construct solutions to stochastic differential equations with oblique reflection (Theorem 1.9) in time-dependent domains. In the process of proving these results we establish a number of estimates for solutions to the Skorohod problem with bounded jumps and, in addition, several results concerning the convergence of sequences of solutions to Skorohod problems in the setting of time-dependent domains.
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| 22. |
- Andersson, Fredrik K., et al.
(författare)
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The mathematics of internet search engines
- 2008
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Ingår i: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 104:2, s. 211-242
-
Tidskriftsartikel (refereegranskat)abstract
- This article presents a survey of techniques for ranking results in search engines, with emphasis on link-based ranking methods and the PageRank algorithm. The problem of selecting, in relation to a user search query, the most relevant documents from an unstructured source such as the WWW is discussed in detail. The need for extending classical information retrieval techniques such as boolean searching and vector space models with link-based ranking methods is demonstrated. The PageRank algorithm is introduced, and its numerical and spectral properties are discussed. The article concludes with an alternative means of computing PageRank, along with some example applications of this new method.
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| 23. |
- Asratian, Armen, et al.
(författare)
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Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs
- 2009
-
Ingår i: Journal of Graph Theory. - : Wiley Periodicals Inc.. - 0364-9024 .- 1097-0118. ; 61:2, s. 88-97
-
Tidskriftsartikel (refereegranskat)abstract
- An interval coloring of a graph G is a proper coloring of E(G) by positive integers such that the colors on the edges incident to any vertex are consecutive. A (3,4)-biregular bigraph is a bipartite graph in which each vertex of one part has degree 3 and each vertex of the other has degree 4; it is unknown whether these all have interval colorings. We prove that G has an interval coloring using 6 colors when G is a (3,4)-biregular bigraph having a spanning subgraph whose components are paths with endpoints at 3-valent vertices and lengths in {2, 4, 6, 8}. We provide several sufficient conditions for the existence of such a subgraph.
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| 24. |
- Geli, Patricia
(författare)
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Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens
- 2009
-
Ingår i: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:5, s. 1416-1432
-
Tidskriftsartikel (refereegranskat)abstract
- A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.
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| 25. |
- Gaidashev, Denis, 1973-, et al.
(författare)
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A numerical study of infinitely renormalizable area-preserving maps
- 2012
-
Ingår i: Dynamical systems. - : Informa UK Limited. - 1468-9367 .- 1468-9375. ; 27:3, s. 283-301
-
Tidskriftsartikel (refereegranskat)abstract
- It has been shown in Gaidashev and Johnson [D. Gaidashev and T. Johnson, Dynamics of the universal area-preserving map associated with period doubling: stable sets, J. Mod. Dyn. 3(4) (2009), pp. 555–587.] and Gaidashev et al. [D. Gaidashev, T. Johnson, and M. Martens, Rigidity for infinitely renormalizable area-preserving maps, in preparation.] that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Hölder continuous of exponent α > 0. In this article we investigate numerically the specific value of α. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real.
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| 26. |
- Lundengård, Karl, 1987-
(författare)
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Generalized Vandermonde matrices and determinants in electromagnetic compatibility
- 2017
-
Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.
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| 27. |
- Arnlind, Joakim, et al.
(författare)
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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
-
Tidskriftsartikel (refereegranskat)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 28. |
-
Discrete Geometry and Mathematical Morphology : First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24–27, 2021, Proceedings
- 2021
-
Samlingsverk (redaktörskap) (refereegranskat)abstract
- This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden.The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM.The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering.The book also contains 3 invited keynote papers.
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| 29. |
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| 30. |
- Gäfvert, Oliver, 1991-
(författare)
-
Topological and geometrical methods in data analysis
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns two related data analysis pipelines, using topological and geometrical methods respectively, to extract relevant information. The first pipeline, referred to as the topological data analysis (TDA) pipeline, constructs a filtered simplicial complex on a given data set in order to describe its shape. The shape is described using a persistence module, which characterizes the topological features of the filtration, and the final step of the pipeline extracts algebraic invariants from this object. The second pipeline, referred to as the geometric data analysis (GDA) pipeline, associates an algebraic variety to a given data set and aims to describe the structure of this variety. Its structure is described using homology, an invariant which for most algebraic varieties can only be computed numerically using sampling methods.In Paper A we consider invariants on multi-parameter persistence modules. We explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.In Paper B we introduce an efficient algorithm to compute a minimal presentation of a multi-parameter persistent homology module, given a chain complex of free modules as input. Our approach extends previous work on this problem in the 2-parameter case, and draws on ideas underlying the F4 and F5 algorithms for Gröbner basis computation. In the r-parameter case, our algorithm computes a presentation for the homology of C ->F A ->G B, with modules of rank l,n,m respectively, in O(r2nr+1 + nrm + nr-1m2 + rn2 l) arithmetic operations. We implement this approach in our new software Muphasa, written in C++. In preliminary computational experiments on synthetic TDA examples, we compare our approach to a version of a classical approach based on Schreyer's algorithm, and find that ours is substantially faster and more memory efficient. In the course of developing our algorithm for computing presentations, we also introduce algorithms for the closely related problems of computing Gröbner bases for the image and kernel of the morphism G. This algorithm runs in time O(nrm + nr-1m2) and memory O(n2 + mn + nr + K), where K is the size of the output.Paper C analyzes the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in RN. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDD) of a certain variety called the hypothesis variety as the number of points in the configuration increases. Finally, we establish a connection to complexity of architectures of polynomial neural networks. For the problem of fitting an (N-1)-sphere to a configuration of m points in RN, we give a closed formula for the algebraic complexity of the hypothesis variety as m grows for the case of N=1. For the case N>1 we conjecture a generalization of this formula supported by numerical experiments.In Paper D we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing bottlenecks of the variety. Using geometric information such as the bottlenecks and the local reach we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et. al. (2019).
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| 31. |
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| 32. |
- Lundin, Sverker, 1975
(författare)
-
Skolans matematik : En kritisk analys av den svenska skolmatematikens förhistoria, uppkomst och utveckling
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- I argue that common beliefs regarding mathematics originate in the practices of elementary mathematics instruction rather than in science. While learning how to solve mathematical problems in school, we come to believe that mathematics has a set of properties in itself, for instance that it is useful in everyday life, even though this is not necessarily so. I call this object of belief the mathematics of schooling (skolans matematik), while the system of practices by which the belief is produced is called mathematics education (skolmatematik). I introduce a terminology inspired by psychoanalytic theory to describe the peculiar properties of the mathematics of schooling and suggest that it can be understood as a sublime object of an ideology propagated by the system of education. To substantiate this claim I give an overview of the history of Swedish mathematics education, based on curricula, textbooks, discussions in teacher magazines, and other published material – covering in general terms the eighteenth to the twenty-first century. The historical narrative moves between social factors determining the practices of mathematics education, the changing ideas about mathematics expressed in these contexts, and the interplay between external social factors and internal “ideological” meaning. My conclusion is that while elementary arithmetics is, and should be, a part of common knowledge, the mathematics of schooling is something quite different. This object is thoroughly ideological and plays a central part in society mainly by making the social effects of mathematics education – keeping children away from production while sorting them – to appear as something else, namely as most often failed attempts to give children a necessary knowledge of mathematics.
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| 33. |
- van Bommel, Jorryt, 1974-
(författare)
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Att formulera problem 4-6
- 2021
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Att formulera problemuppgifter är en del av problemlösning, en del som dock skiljer sig från att lösa problemuppgifter. Denna text inriktas på hur undervisning med fokus på problemformulering kan utformas, varför det är viktigt att elever i samband med problemlösning ges möjlighet att formulera egna uppgifter samt vad eleverna då kan lära
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| 34. |
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| 35. |
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| 36. |
- Fotedar, Sunney, 1989, et al.
(författare)
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A criterion space decomposition approach to generalized tri-objective tactical resource allocation
- 2023
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Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20:1
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Tidskriftsartikel (refereegranskat)abstract
- We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the generalized tactical resource allocation problem (GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the quadrant shrinking method (QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances.
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| 37. |
- Fotedar, Sunney, 1989
(författare)
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Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers and to maintain control of the tied-up working capital. We introduce new multi-item , multi-level capacitated resource allocation models with a medium--to--long--term planning horizon. The model refers to functional workshops where costly and/or time- and resource-demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimize the maximum excess resource loading above a given loading threshold while incurring as low qualification costs as possible and minimizing the inventory. In Paper I , we propose a new bi-objective mixed-integer (linear) optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. In Paper II , we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. In Paper III , we extend the TRAP with an inventory of semi-finished as well as finished parts, resulting in a tri-objective mixed-integer (linear) programming model. We create a criterion space partitioning approach that enables solving sub-problems simultaneously. In Paper IV , using our knowledge from our previous work we embarked upon a task to generalize our findings to develop an approach for any discrete tri-objective optimization problem. The focus is on identifying a representative set of non-dominated points with a pre-defined desired coverage gap .
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| 38. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model
- 2024
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Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101
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Tidskriftsartikel (refereegranskat)abstract
- Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
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| 39. |
- Lindwall, Katrin, 1959-, et al.
(författare)
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Maker Tour - Mot nya höjder : Make IT flow, del 2
- 2018
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Annan publikation (populärvet., debatt m.m.)abstract
- Utmaningarna är en del av projektet Maker tour - Mot nya höjder ( tidigare Mot nya höjder). Projektets mål är att öka intresset för naturvetenskap, teknik och matematik bland skolelever.Läs gärna mer på http://motnyahojder.com/
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| 40. |
- Lindwall, Katrin, 1959-, et al.
(författare)
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Maker tour: mot nya höjder : make space HT-19
- 2019
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Annan publikation (populärvet., debatt m.m.)abstract
- Utmaningarna är en del av projektet Maker tour - Mot nya höjder (tidigare Mot nya höjder). Projektets mål är att öka intresset för naturvetenskap, teknik och matematik bland skolelever.
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| 41. |
- Lindwall, Katrin, 1959-, et al.
(författare)
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Maker tour: mot nya höjder : make IT shine HT-18
- 2018
-
Annan publikation (populärvet., debatt m.m.)abstract
- Utmaningarna är en del av projektet Maker tour - Mot nya höjder (tidigare Mot nya höjder). Projektets mål är att öka intresset för naturvetenskap, teknik och matematik bland skolelever.
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| 42. |
- Lindwall, Katrin, 1959-, et al.
(författare)
-
Mot nya höjder : Make IT happen våren 2016
- 2016
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Annan publikation (populärvet., debatt m.m.)abstract
- Utmaningarna är en del av projektet Mot nya höjder ( från 2018 Maker tour - Mot nya höjder). Projektets mål är att öka intresset för naturvetenskap, teknik och matematik bland skolelever.Läs gärna mer på www.motnyahojder.com
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| 43. |
- Tyrberg, Barbro, et al.
(författare)
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Mot nya höjder : Make it taste (Make it move)
- 2017
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Annan publikation (populärvet., debatt m.m.)abstract
- Utmaningarna är en del av projektet Mot nya höjder. Projektets mål är att öka intresset för naturvetenskap, teknik och matematik bland skolelever.
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| 44. |
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| 45. |
- Accardi, Luigi, et al.
(författare)
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Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology
- 2009
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Ingår i: Open systems & information dynamics. - Singapore : WSP. - 1230-1612 .- 1573-1324. ; 16:4, s. 371-385
-
Tidskriftsartikel (refereegranskat)abstract
- We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.
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| 46. |
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| 47. |
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| 48. |
- Albeverio, Sergio, et al.
(författare)
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Estimates uniform in time for the transition probability ofdiusions with small drift and for stochastically perturbed Newton equations
- 1999
-
Ingår i: Journal of theoretical probability. - 0894-9840 .- 1572-9230. ; 12:2, s. 293-300
-
Tidskriftsartikel (refereegranskat)abstract
- An estimate uniform in time for the transition probability of di®usion processes with small drift is given. This also covers the case of a degenerate di®usion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a su±ciently small drift.
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| 49. |
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| 50. |
- Albeverio, S., et al.
(författare)
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Operator calculus for p-adic valued symbols and quantization
- 2009
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Ingår i: Rendicoti Del Seminario Matematico. - 0373-1243. ; 67:2, s. 137-150
-
Tidskriftsartikel (refereegranskat)abstract
- The aim of this short review is to attract the attention of the pseudo-differentialcommunity to possibilities in the development of operator calculus for symbols (dependingon p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of thiscalculus were presented in works of the authors of this paper in order to perform p-adic valuedquantization. Unfortunately, this calculus still has not attracted a great deal of attentionfrom pure mathematicians, although it opens new and interesting domains for the theory ofpseudo-differential operators.
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