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  • 1.
    Abidin, Aysajan
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Weaknesses of Authentication in Quantum Cryptography and Strongly Universal Hash Functions2010Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Authentication is an indispensable part of Quantum Cryptography, which is an unconditionally secure key distribution technique based on the laws of nature. Without proper authentication, Quantum Cryptography is vulnerable to “man-in-the-middle” attacks. Therefore, to guarantee unconditional security of any Quantum Cryptographic protocols, the authentication used must also be unconditionally secure. The standard in Quantum Cryptography is to use theWegman-Carter authentication, which is unconditionally secure and is based on the idea of universal hashing.

    In this thesis, we first investigate properties of a Strongly Universal hash function family to facilitate understanding the properties of (classical) authentication used in Quantum Cryptography. Then, we study vulnerabilities of a recently proposed authentication protocol intended to rule out a "man-in-the-middle" attack on Quantum Cryptography. Here, we point out that the proposed authentication primitive is not secure when used in a generic Quantum Cryptographic protocol. Lastly, we estimate the lifetime of authentication using encrypted tags when the encryption key is partially known. Under simplifying assumptions, we derive that the lifetime is linearly dependent on the length of the authentication key. Experimental results that support the theoretical results are also presented.

    List of papers
    1. Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    Open this publication in new window or tab >>Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography
    2009 (English)In: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, 289-293 p.Conference paper, Published paper (Refereed)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

    Place, publisher, year, edition, pages
    New York: American Institute of Physics, 2009
    Keyword
    Quantum cryptography, Quantum theory, Probability
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-18738 (URN)10.1063/1.3109951 (DOI)
    Conference
    Foundations of Probability and Physics—5, Växjö, augusti 2008
    Projects
    ICG QC
    Available from: 2009-06-03 Created: 2009-06-03 Last updated: 2016-08-31
    2. Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    Open this publication in new window or tab >>Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"
    2009 (English)In: International Journal of Quantum Information, ISSN 0219-7499, Vol. 7, no 5, 1047-1052 p.Article in journal (Refereed) Published
    Abstract [en]

    In this paper, we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography" [M. Peev et al., Int. J. Quant. Inf. 3 (2005) 225]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.

    Keyword
    Quantum cryptography, quantum key distribution, authentication
    National Category
    Natural Sciences
    Identifiers
    urn:nbn:se:liu:diva-20405 (URN)10.1142/S0219749909005754 (DOI)
    Projects
    ICG QC
    Available from: 2009-09-08 Created: 2009-09-07 Last updated: 2016-08-31Bibliographically approved
    3. Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially Known
    Open this publication in new window or tab >>Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially Known
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    Quantum cryptography is an unconditionally secure key growing technique provided that an unconditionally secure authentication protocol is combined with it. This paper is about the study of the lifetime of a message authentication scheme, where a message to be authenticated is first hashed by a secret–but fixed–Strongly Universal hash function then the output is encrypted with a one-time-pad key to generate a tag for the message. If the onetime-pad is completely secret, then the lifetime is exponential in the tag length. If, however, the one-time-pad key is partially known in each authentication round, as is the case in practical quantum key distribution protocols, then the picture is different; because the adversary’s partial knowledge of the one-time-pad key in each authentication round contributes to his/her ability to identify the secret hash function. We estimate the lifetime of this type of authentication. Here the parameters are the length of the key identifying the secret hash function and the amount of knowledge that Eve has on the one-time-pad. A theoretical estimate is presented, along with experimental results that support it.

    Keyword
    Quantum cryptography, quantum key distribution, authentication, strongly universal hash functions, lifetime
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-57289 (URN)
    Projects
    ICG QC
    Available from: 2010-06-16 Created: 2010-06-16 Last updated: 2016-08-31
  • 2.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Lifetime of Authentication Using Encrypted Tags When the Encryption Key is Partially KnownManuscript (preprint) (Other academic)
    Abstract [en]

    Quantum cryptography is an unconditionally secure key growing technique provided that an unconditionally secure authentication protocol is combined with it. This paper is about the study of the lifetime of a message authentication scheme, where a message to be authenticated is first hashed by a secret–but fixed–Strongly Universal hash function then the output is encrypted with a one-time-pad key to generate a tag for the message. If the onetime-pad is completely secret, then the lifetime is exponential in the tag length. If, however, the one-time-pad key is partially known in each authentication round, as is the case in practical quantum key distribution protocols, then the picture is different; because the adversary’s partial knowledge of the one-time-pad key in each authentication round contributes to his/her ability to identify the secret hash function. We estimate the lifetime of this type of authentication. Here the parameters are the length of the key identifying the secret hash function and the amount of knowledge that Eve has on the one-time-pad. A theoretical estimate is presented, along with experimental results that support it.

  • 3.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography2009In: AIP Conference Proceedings, ISSN 0094-243X, Foundations of Probability and Physics—5, Växjö, augusti 2008, New York: American Institute of Physics , 2009, Vol. 1101, 289-293 p.Conference paper (Refereed)
    Abstract [en]

    Secure message authentication is an important part of Quantum Key Distribution. In this paper we analyze special properties of a Strongly Universal2 hash function family, an understanding of which is important in the security analysis of the authentication used in Quantum Cryptography. We answer the following question: How much of Alices message does Eve need to influence so that the message along with its tag will give her enough information to create the correct tag for her message?

  • 4.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography"2009In: International Journal of Quantum Information, ISSN 0219-7499, Vol. 7, no 5, 1047-1052 p.Article in journal (Refereed)
    Abstract [en]

    In this paper, we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography" [M. Peev et al., Int. J. Quant. Inf. 3 (2005) 225]. In particular, we point out that the proposed primitive is not secure when used in a generic protocol, and needs additional authenticating properties of the surrounding quantum-cryptographic protocol.

  • 5. Accardi, L
    et al.
    Brody, DC
    Belavkin, VP
    Kent, JT
    Bingham, NH
    Frey, JG
    Helland, IS
    Larsson, Jan-Åke
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Majumdar, NK
    Minozzo, M
    Thompson, JW
    Discussion on "On quantum statistical inference" by Barndorff-Nielsen, Gill and Jupp2003In: Journal of The Royal Statistical Society Series B-statistical Methodology, ISSN 1369-7412, E-ISSN 1467-9868, Vol. 65, no 4, 805-816 p.805-816 p.Article in journal (Refereed)
  • 6.
    Aerts, S
    et al.
    Free Univ Brussels, Fundamenten Exacte Wetenschappen, B-1050 Brussels, Belgium Los Alamos Natl Lab, Los Alamos, NM 87545 USA Linkoping Univ, Matemat Inst, SE-58183 Linkoping, Sweden Univ Gdansk, Inst Theoret Phys & Astrophys, PL-80952 Gdansk, Poland.
    Kwiat, P
    Free Univ Brussels, Fundamenten Exacte Wetenschappen, B-1050 Brussels, Belgium Los Alamos Natl Lab, Los Alamos, NM 87545 USA Linkoping Univ, Matemat Inst, SE-58183 Linkoping, Sweden Univ Gdansk, Inst Theoret Phys & Astrophys, PL-80952 Gdansk, Poland.
    Larsson, Jan-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Zukowski, M
    Free Univ Brussels, Fundamenten Exacte Wetenschappen, B-1050 Brussels, Belgium Los Alamos Natl Lab, Los Alamos, NM 87545 USA Linkoping Univ, Matemat Inst, SE-58183 Linkoping, Sweden Univ Gdansk, Inst Theoret Phys & Astrophys, PL-80952 Gdansk, Poland.
    Comment on "Two-photon Franson-type experiment and local realism" - Reply2001In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 86, no 9, 1909-1909 p.Article in journal (Refereed)
  • 7.
    Aerts, Sven
    et al.
    Fundamenten van de Exacte Wetenschappen Vrije Universiteit Brussel.
    Larsson, Jan-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Kwiat, Paul
    Los Alamos National Laboratory.
    Zukowski, Marek
    Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdanski.
    Aerts et al. Reply2001In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 86, no 9, 1909-1909 p.Article in journal (Refereed)
  • 8.
    Aghapournahr, M
    et al.
    Arak University.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Finiteness properties of minimax and coatomic local cohomology modules2010In: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 94, no 6, 519-528 p.Article in journal (Refereed)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R, and M an R-module. We prove that for a finite module M, if H-alpha(i)(M) is minimax for all i andgt;= r andgt;= 1, then H-alpha(i)(M) is artinian for i andgt;= r. A local-global principle for minimax local cohomology modules is shown. If H-alpha(i)(M) is coatomic for i andlt;= r (M finite) then H-alpha(i)(M) is finite for i andlt;= r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing theorems are proved for local cohomology modules.

  • 9.
    Aghapournahr, Moharram
    et al.
    Arak University.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A natural map in local cohomology2010In: ARKIV FOR MATEMATIK, ISSN 0004-2080, Vol. 48, no 2, 243-251 p.Article in journal (Refereed)
    Abstract [en]

    Let R be a Noetherian ring, a an ideal of R, M an R-module and n a non-negative integer. In this paper we first study the finiteness properties of the kernel and the cokernel of the natural map f: Ext(R)(n) (R/alpha, M) -andgt; Hom(R)(R/alpha, H-alpha(n) (M)), under some conditions on the previous local cohomology modules. Then we get some corollaries about the associated primes and Artinianness of local cohomology modules. Finally we will study the asymptotic behavior of the kernel and the cokernel of the natural map in the graded case.

  • 10.
    Aghapournahr, Moharram
    et al.
    Arak Univ, Arak, Iran.
    Melkersson, Leif
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES2009In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 105, no 2, 161-170 p.Article in journal (Refereed)
    Abstract [en]

    Let R be a noetherian ring, alpha an ideal of R such that dim R/alpha = 1 and M a finite R-module. We will study cofiniteness and some other properties of the local cohomology modules H-alpha(i)(M). For an arbitrary ideal alpha and an R-module M (not necessarily finite), we will characterize alpha-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

  • 11.
    Aghapournahr, Moharram
    et al.
    Teacher Training Univ, Fac Math Sci, Tehran 15614, Iran.
    Melkersson, Leif
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Local cohomology and Serre subcategories2008In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 320, no 3, 1275-1287 p.Article in journal (Refereed)
    Abstract [en]

    The membership of the local cohomology modules H-a(n) (M) of a module M in certain Serre subcategories of the category of modules is studied from below (i < n) and from above (i > n). Generalizations of depth and regular sequences are defined. The relation of these notions to local cohomology are found. It is shown that the membership of the local cohomology modules of a finite module in a Serre subcategory in the upper range just depends on the support of the module. (C) 2008 Elsevier Inc. All rights reserved.

  • 12.
    Aigner, Mats
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Existence of the Ginzburg-Landau vortex number2001In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 216, no 1, 17-22 p.Article in journal (Refereed)
    Abstract [en]

    The existence of the Ginzburg-Landau vortex number is established for any configuration with finite action. As a consequence, Bogomol'nyi's formula for the critical action is valid for any finite action configuration.

  • 13.
    Alfonseca, M Angeles
    et al.
    N Dakota State University.
    Auscher, Pascal
    University Paris 11.
    Axelsson Rosén, Andreas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Hofmann, Steve
    University of Missouri.
    Kim, Seick
    Yonsei University.
    Analyticity of layer potentials and L-2 solvability of boundary value problems for divergence form elliptic equations with complex L-infinity coefficients2011In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 226, no 5, 4533-4606 p.Article in journal (Refereed)
    Abstract [en]

    We consider divergence form elliptic operators of the form L = -div A (x)del, defined in Rn+1 = {(x, t) is an element of R-n x R}, n andgt;= 2, where the L-infinity coefficient matrix A is (n + 1) x (n + 1), uniformly elliptic, complex and t-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on L-2 (R-n) = L-2(partial derivative R-+(n+1)) is stable under complex, L-infinity perturbations of the coefficient matrix. Using a variant of the Tb Theorem, we also prove that the layer potentials are bounded and invertible on L-2(R-n) whenever A (x) is real and symmetric (and thus, by our stability result, also when A is complex, parallel to A - A(0)parallel to(infinity) is small enough and A(0) is real, symmetric, L-infinity and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with L-2 (resp. (L) over dot(1)(2)) data, for small complex perturbations of a real symmetric matrix. Previously, L-2 solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients A (j,n+1)= 0 = A(n+1,j), 1 andlt;= j andlt;= n, which corresponds to the Kato square root problem.

  • 14.
    Alvarado, Ryan
    et al.
    University of Missouri.
    Brigham, Dan
    University of Missouri.
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mitrea, Marius
    University of Missouri.
    Ziade, Elia
    University of Missouri.
    Sharp Geometric Maximum Principles for Semi-Elliptic Operators with Singular Drift2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 4, 613-620 p.Article in journal (Refereed)
    Abstract [en]

    We discuss a sharp generalization of the Hopf-Oleinik boundary point principle (BPP) for domains satisfying an interior pseudo-ball condition, for non-divergence form, semi-elliptic operators with singular drift. In turn, this result is used to derive a version of the strong maximum principle under optimal pointwise blow-up conditions for the coefficients of the differential operator involved. We also explain how a uniform two-sided pseudo-ball condition may be used to provide a purely geometric characterization of Lyapunov domains, and clarify the role this class of domains plays vis-a-vis to the BPP.

  • 15.
    Alvino, Angelo
    et al.
    University Napoli Federico II.
    Cianchi, Andrea
    University Florence.
    Maz´ya, Vladimir
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mercaldo, Anna
    University Napoli Federico II.
    Well-posed elliptic Neumann problems involving irregular data and domains2010In: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, ISSN 0294-1449, Vol. 27, no 4, 1017-1054 p.Article in journal (Refereed)
    Abstract [en]

    Non-linear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are established under a suitable balance between the integrability of the datum and the (ir)regularity of the domain. The latter is described in terms of isocapacitary inequalities. Applications to various classes of domains are also presented. (C) 2010 Elsevier Masson SAS. All rights reserved.

  • 16.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A Duality-Based Derivation of the Maximum Flow Formulation of the Open-Pit Design ProblemManuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit mining is a surface mining operation whereby ore, or waste, is excavated from the surface of the land. The open-pit design problem is deciding on which blocks of an ore deposit to mine in order to maximize the total profit, while obeying digging constraints concerning pit slope and block precedence. The open-pit design problem can be formulated as a maximum flow problem in a certain capacitated network, as first shown by Picard in 1976. His derivation is based on a restatement of the problem as a quadratic binary program. We give an alternative derivation of the maximum flow formulation, which uses only linear programming duality.

  • 17.
    Amankwah, Henry
    et al.
    University of Cape Coast, Ghana .
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A maximum flow formulation of a multi-period open-pit mining problem2014In: Operational Research, ISSN 1109-2858, E-ISSN 1866-1505, Vol. 14, no 1, 1-10 p.Article in journal (Refereed)
    Abstract [en]

    We consider the problem of finding an optimal mining sequence for an open pit during a number of time periods subject to only spatial and temporal precedence constraints. This problem is of interest because such constraints are generic to any open-pit scheduling problem and, in particular, because it arises as a Lagrangean relaxation of an open-pit scheduling problem. We show that this multi-period open-pit mining problem can be solved as a maximum flow problem in a time-expanded mine graph. Further, the minimum cut in this graph will define an optimal sequence of pits. This result extends a well-known result of J.-C. Picard from 1976 for the open-pit mine design problem, that is, the single-period case, to the case of multiple time periods.

  • 18.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    A Multi-Parametric Maximum Flow Characterization of the Open-Pit Scheduling ProblemManuscript (preprint) (Other academic)
    Abstract [en]

    We consider the problem of finding an optimal mining schedule for an openpit during a number of time periods, subject to a mining capacity restriction for each time period. By applying Lagrangian relaxation to the capacities, a multi-parametric formulation is obtained. We show that this formulation can be restated as a maximum flow problem in a time-expanded network. This result extends a well-known result of Picard from 1976 for the open-pit design problem, that is, the single-period case, to the case of multiple time periods.

  • 19.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    On the use of Parametric Open-Pit Design Models for Mine Scheduling - Pitfalls and CounterexamplesManuscript (preprint) (Other academic)
    Abstract [en]

    This paper discusses a Lagrangian relaxation interpretation of the Picard and Smith (2004) parametric approach to open-pit mining, which finds a sequence of intermediate contours leading to an ultimate one. This method is similar to the well known parametric approach of Lerchs and Grossmann (1965). We give examples of worst case performance, as well as best case performance of the Picard-Smith approach. The worst case behaviour can be very poor in that we might not obtain any intermediate contours at all. We also discuss alternative parametric methods for finding intermediate contours, but conclude that such methods seem to have inherent weaknesses.

  • 20.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Open-Pit Mining with Uncertainty - A Conditional Value-at-Risk ApproachManuscript (preprint) (Other academic)
    Abstract [en]

    The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty, and also the future market behaviour of metal prices and foreign exchange rates, which are impossible to be known with certainty, make mining a high risk business.

    Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does however have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev (2000) introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex problem.

    An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and price uncertainties.

  • 21.
    Amankwah, Henry
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Textorius, Björn
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Open-Pit Production Scheduling - Suggestions for Lagrangian Dual Heuristic and Time Aggregation ApproachesManuscript (preprint) (Other academic)
    Abstract [en]

    Open-pit production scheduling deals with the problem of deciding what and when to mine from an open-pit, given potential profits of the different fractions of the mining volume, pit-slope restrictions, and mining capacity restrictions for successive time periods. We give suggestions for Lagrangian dual heuristic approaches for the open-pit production scheduling problem. First, the case with a single mining capacity restriction per time period is considered. For this case, linear programming relaxations are solved to find values of the multipliers for the capacity restrictions, to be used in a Lagrangian relaxation of the constraints. The solution to the relaxed problem will not in general satisfy the capacity restrictions, but can be made feasible by adjusting the multiplier values for one time period at a time. Further, a time aggregation approach is suggested as a way of reducing the computational burden of solving linear programming relaxations, especially for largescale real-life mine problems. For the case with multiple capacity restrictions per time period we apply newly developed conditions for optimality and nearoptimality in general discrete optimization problems to construct a procedure for heuristically constructing near-optimal intermediate pits.

  • 22.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, S.B.
    Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor2001In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, no 12, 2297-2304 p.Article in journal (Refereed)
    Abstract [en]

    A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.

  • 23.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, S.B.
    Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times2001In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 37, no 4, 273-290 p.Article in journal (Refereed)
    Abstract [en]

    We investigate the possibility of existence of a symmetric potential HABA'B'=H(AB)(A'B') for a symmetric (3,1)-spinor LABCA', e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA'=?(AB'H BC)A'B'. We prove that in all Einstein space-times such a symmetric potential HABA'B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time. © 2001 Elsevier Science B.V.

  • 24.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, SB
    Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Spin coefficients as Lanczos scalars: Underlying spinor relations2000In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 41, no 5, 2990-3001 p.Article in journal (Refereed)
    Abstract [en]

    It has been conjectured by Lopez-Bonilla and co-workers that there is some linear relationship between the NP spin coefficients and the Lanczos scalars, and examples have been given for a number of different classes of space-times. We show that in each of those examples a Lanczos potential can be defined in a very simple way directly from the spinor dyad. Although some of these examples seem to have no deeper geometric meaning, we emphasize that there are structural links between Lanczos potential and spin coefficients which we highlight in some other examples. In particular we show that the direct identification of Lanczos potentials with spin coefficients is possible for some important classes of space-times while the direct identification of Lanczos potentials with the properly weighted spin coefficients is also possible for several important classes of space-times. In both of these cases we obtain the necessary and sufficient conditions on the spin coefficients for such identifications to be possible, which enables us to test space-times directly. (C) 2000 American Institute of Physics. [S0022-2488(00)03104-2].

  • 25.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A quasistatic frictional problem with normal compliance penalization term1999In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 37, 689-705 p.Article in journal (Refereed)
  • 26.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Existence results for quasistatic contact problems with Coulomb friction2000In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 42, no 2, 169-202 p.Article in journal (Refereed)
    Abstract [en]

    We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique.

  • 27.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Quasistatic frictional contact problems with finitely many degrees of freedom.1999Report (Other academic)
    Abstract [en]

    In the present paper results on existence and uniqueness of solutions to discrete frictional quasi-static unilateral contact problems are given under a condition that the coefficients of friction are smaller than a certain upper bound. This upper bound is defined in terms of an influence matrix for the contact nodes. The results of existence and uniqueness may be ordered into two classes depending on whether regularity conditions for the applied forces are imposed or not. For general loading which has a time derivative almost everywhere it is shown that a solution exists which satisfies governing equations for almost all times. Uniqueness of the solution has been shown only when the problem is restricted to two degrees of freedom. For a loading which is right piecewise analytic, additional results can be obtained. For instance, if each contact node has only two degrees of freedom a unique solution which satisfies governing equeations for all times exists. For the constructed solutions a priori estimates of the displacement field and its time derivate in terms of the applied forces are also given.

  • 28.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Quasistatic frictional contact problems with finitely many degrees of freedom. Existence and uniqueness2002In: WE-Hereus Seminar on Contact and Fracture Problems,2002, 2002Conference paper (Other academic)
  • 29.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Khludnev, Alexander
    Lavrentiev Institute of Hydrodynamics Russian Academie of Sciences, Novosibirsk.
    On crack crossing a contact boundary. Fictitious domain method and invariant integrals (Russian) .2008In: Siberian journal of industrial mathematics, ISSN 1560-7518, Vol. 11, no 3, 15-29 p.Article in journal (Refereed)
    Abstract [en]

        

  • 30.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    A review of the theory of static and quasi-static frictional contact problems in elasticity2001In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 359, 2519-2539 p.Article in journal (Refereed)
  • 31.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    A Survey of Basic Mathematical Results for Frictional Contact Problems2001In: From Convexity to Nonconvexity / [ed] Robert P Gilbert; P D Panagiotopoulos; P M Pardalos, Dordrecht/Boston/London: Kluwer , 2001, -392 p.Chapter in book (Other academic)
    Abstract [en]

    Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.

  • 32.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Existence and uniqueness for quasistatic contact problems with friction2001In: CMIS 2001, third Contact Mechanics International Symposiium,2001, Dordrecht: Kluwer , 2001, 245- p.Conference paper (Refereed)
  • 33.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating2004In: International Congress of Theoretical and Applied Mechanics,2004, 2004, 215-215 p.Conference paper (Refereed)
  • 34.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Quasi-static Frictional Contact of Discrete Mechanical Structures2000In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 19, S61-S67 p.Article in journal (Refereed)
  • 35.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Barber, J.R.
    Department of Mechanical Engineering University of Michigan.
    Ciavarella, M.
    CEMEC-PoliBA.
    On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating2005In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 461, no 2057, 1261-1282 p.Article in journal (Refereed)
    Abstract [en]

    It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.

  • 36.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Barber, J.R.
    University of Michigan.
    Ciavarella, M.
    Politecnio di Bari.
    Thermoelastic Contact with Frictional Heating2006In: Nonsmooth Mechanics and Analysis,2003, New York: Springer Science+business Media, inc. , 2006, 61- p.Conference paper (Refereed)
  • 37.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Peters, T.J.
    Computer Science Engineering University of Connecticut.
    Stewart, N.F.
    Dept IRO Universite de Montreal.
    Equivalence of topological form for curvilinear geometric objects2000In: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 10, no 6, 609-622 p.Article in journal (Refereed)
    Abstract [en]

    Given a curvilinear geometric object in R3, made up of properly-joined parametric patches defined in terms of control points, it is of interest to know under what conditions the object will retain its original topological form when the control points are perturbed. For example, the patches might be triangular BΘzier surface patches, and the geometric object may represent the boundary of a solid in a solid-modeling application. In this paper we give sufficient conditions guaranteeing that topological form is preserved by an ambient isotopy. The main conditions to be satisfied are that the original object should be continuously perturbed in a way that introduces no self-intersections of any patch, and such that the patches remain properly joined. The patches need only have C0 continuity along the boundaries joining adjacent patches. The results apply directly to most surface modeling schemes, and they are of interest in several areas of application.

  • 38.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Rietz, Andreas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Existence theorems for noncoercive incremental contact problems with Coulomb friction2006In: Analysis and Simulation of Contact Problems / [ed] Peter Wriggers and Udo Nackenhorst, Springer Berlin/Heidelberg, 2006, 121-128 p.Chapter in book (Other academic)
    Abstract [en]

    For static or incremental contact problems with Coulomb friction there are satisfactory and well known existence results for the coercive case, i.e., when the elastic body is anchored so that rigid body motions are not possible, see [3, 1, 6, 7, 2]. The articles by Jaruusek and Cocu, [7, 2] indeed contain results for the noncoercive case, i.e., when rigid body motions are possible. However, the compatibility conditions which are used to ensure the existence of a solution, are the same that guarantee that the corresponding contact problem without friction has a solution. The condition is essentially that the applied force field should push the elastic body towards the obstacle. One of few previous articles containing friction-dependent compatibility conditions is.

  • 39.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, Neil F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Conditions for use of a non-selfintersection conjecture2006In: Computer Aided Geometric Design, ISSN 0167-8396, E-ISSN 1879-2332, Vol. 23, no 7, 599-611 p.Article in journal (Refereed)
    Abstract [en]

    Volino and Thalmann have published a conjecture proposing sufficient conditions for non-selfintersection of surfaces. Such conditions may be used in solid modeling, computer graphics, and other application areas, as a basis for collision-detection algorithms. In this paper we clarify certain of the hypotheses of the proposed theorem, and give a proof. A brief summary of possible pitfalls related to using the conditions, when the hypotheses of the formal theorem given here are not satisfied, is also given. We also give examples, and show that the theorem can be extended to domains that are not simply connected. © 2006 Elsevier B.V. All rights reserved.

  • 40.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, Neil F.
    Departement IRO Universite de Montreal.
    Zidani, Malika
    Departement IRO Universite de Montreal.
    Error analysis for operations in solid modeling in the presence of uncertainty2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 29, no 2, 811-826 p.Article in journal (Refereed)
    Abstract [en]

    The problem of maintaining consistent representations of solids in computer-aided design and of giving rigorous proofs of error bounds for operations such as regularized Boolean intersection has been widely studied for at least two decades. One of the major difficulties is that the representations used in practice not only are in error but are fundamentally inconsistent. Such inconsistency is one of the main bottlenecks in downstream applications. This paper provides a framework for error analysis in the context of solid modeling, in the case where the data is represented using the standard representational method, and where the data may be uncertain. Included are discussions of ill-condition, error measurement, stability of algorithms, inconsistency of defining data, and the question of when we should invoke methods outside the scope of numerical analysis. A solution to the inconsistency problem is proposed and supported by theorems: it is based on the use of Whitney extension to define sets, called Quasi-NURBS sets, which are viewed as realizations of the inconsistent data provided to the numerical method. A detailed example illustrating the problem of regularized Boolean intersection is also given.    

  • 41.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, N.F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Proof of a non-selfintersection conjecture2006Report (Other academic)
  • 42. Andreev, A.
    et al.
    Nikoltjeva-Hedberg, Margarita
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Averaged Moduli of Smoothness and Runge-Kutta Methods2005In: Mathematica Balkanica, ISSN 0350-2007, Vol. 19, 293-304 p.Article in journal (Refereed)
  • 43.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Jonsson, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Linusson, Svante
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Determining the Number of Solutions to Binary CSP Instances2002In: Principles and Practice of Constraint Programming, 8th International Conference CP-2002,2002, Heidelberg: Springer Verlag , 2002, 327- p.Conference paper (Refereed)
    Abstract [en]

    Counting the number of solutions to CSP instances has applications in several areas, ranging from statistical physics to artificial intelligence. We give an algorithm for counting the number of solutions to binary CSPs, which works by transforming the problem into a number of 2-SAT instances, where the total number of solutions to these instances is the same as those of the original problem. The algorithm consists of two main cases, depending on whether the domain size d is even, in which case the algorithm runs in O(1.3247^n*(d/2)^n) time, or odd, in which case it runs in O(1.3247^n*((d^2+d+2)/4)^(n/2)) if d=4*k+1, and O(1.3247^n*((d^2+d)/4)^(n/2)) if d=4*k+3. We also give an algorithm for counting the number of possible 3-colourings of a given graph, which runs in O(1.8171^n), an improvement over our general algorithm gained by using problem specific knowledge. 

  • 44.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A Microstructure Based Approach to Constraint Satisfaction Optimisation Problems2005In: The 18th International FLAIRS Conference,2005, Menlo Park, CA, USA: AAAI Press , 2005, 155- p.Conference paper (Refereed)
    Abstract [en]

    We study two constraint satisfaction optimisation problems: The Max Value problem for CSPs, which, somewhat simplified, aims at maximising the sum of the (weighted) variable values in the solution, and the Max Ind problem, where the goal is to find a satisfiable subinstance of the original instance containing as many variables as possible. Both problems are NP-hard to approximate within n^(1-e), e>0, where n is the number of variables in the problems, which implies that it is of interest to find exact algorithms. By exploiting properties of the microstructure, we construct algorithms for solving instances of these problems with small domain sizes, and then, using a probabilistic reasoning, we show how to get algorithms for more general versions of the problems. The resulting algorithms have running times of O((0.585d)^n) for Max Value (d,2)-CSP, and O((0.503d)^n) for MaxInd (d,2)-CSP. Both algorithms represent the best known theoretical bounds for their respective problem, and, more importantly, the methods used are applicable to a wide range of optimisation problems. 

  • 45.
    Angelsmark, Ola
    et al.
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Thapper, Johan
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Algorithms for the Maximum Hamming Distance Problem2006In: Recent Advances in Constraints: Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2004, Lausanne, Switzerland, June 23-25, 2004, Revised Selected and Invited Papers / [ed] Boi V. Faltings, Adrian Petcu, François Fages and Francesca Rossi, Springer Berlin/Heidelberg, 2006, 128-141 p.Chapter in book (Refereed)
    Abstract [en]

    This book constitutes the thoroughly refereed and extended post-proceedings of the Joint ERCIM/CoLogNet International Workshop on Constraint Solving and Constraint Logic Programming, CSCLP 2005, held in Uppsala, Sweden in June 2005.

    Besides papers taken from the workshop, others are submitted in response to an open call for papers after the workshop.

    The 12 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on global constraints, search and heuristics, language and implementation issues, and modeling.

  • 46.
    Angelsmark, Ola
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
    Thapper, Johan
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    New Algorithms for the Maximum Hamming Distance Problem2004In: Joint Annual Workshop of ERCIMCoLogNet on Constraint Solving and Constraint Logic Programming,2004, 2004, 271-285 p.Conference paper (Refereed)
  • 47.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Examples of infinity harmonic functions having singular lines2006Report (Other academic)
  • 48.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Five Geometric Principles for Injection Molding2003In: International polymer processing, ISSN 0930-777X, E-ISSN 2195-8602, Vol. 18, no 1, 91-94 p.Article in journal (Refereed)
    Abstract [en]

    A condensed presentation of some results of a geometric character, concerning the injection molding of plastics, is given here. The author has derived these results from mathematical arguments and some simplifying assumptions, besides the usual Hele-Shaw flow conditions.

    The presentation here is intended for readers with an interest in polymer processing, rather than mathematics, so that the mathematical derivations are omitted in some cases, and sketchy in other cases. Instead we try to explain the results using figures, intuitive arguments and a few inevitable formulas. Since the experimental verification of the results is still very incomplete, we prefer to present them as proposed principles. Comments and suggestions for improvement are very welcome.

  • 49.
    Aronsson, Gunnar
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    INTERPOLATION UNDER A GRADIENT BOUND2009In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, Vol. 87, no 1, 19-35 p.Article in journal (Refereed)
    Abstract [en]

    This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (ail inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.

  • 50.
    Aronsson, Gunnar
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Interpolation under a gradient bound and infimal convolutions2007Report (Other academic)
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