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  • 101.
    Hoque, MD. Anamul
    Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation.
    VOIP mobility over heterogeneous networks with focus on mobility issue2010Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [en]

    Abstract Multimedia on wireless networks and the integration with other cellular networks requires support for both mobility and quality of service. When mobile nodes move across different wireless networks, current session may be affected by the several factors like hand off delay, jitter and data loss. Voice over IP (VOIP) will be operated seamlessly across different wireless networks and that resulted few issues like mobility, signals and security. Mobile IP is proposed as a network layer host mobility solution. The problem associated with mobile IP makes it unsuitable for real time interactive solution like Voice over IP (VOIP). In this thesis paper we study the VOIP mobility in homogeneous wireless networks and cross layer mechanism for heterogeneous wireless networks which can support mobility in layer 2 of the network stack to get better VOIP performances and mobility. We describe the cross layer mechanism and the experimental results.

  • 102.
    Hua, Xiaoben
    et al.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Yang, Yuxia
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    A Fusion Model For Enhancement of Range Images2012Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [en]

    In this thesis, we would like to present a new way to enhance the “depth map” image which is called as the fusion of depth images. The goal of our thesis is to try to enhance the “depth images” through a fusion of different classification methods. For that, we will use three similar but different methodologies, the Graph-Cut, Super-Pixel and Principal Component Analysis algorithms to solve the enhancement and output of our result. After that, we will compare the effect of the enhancement of our result with the original depth images. This result indicates the effectiveness of our methodology.

  • 103.
    Hultgren, Anders
    et al.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för elektroteknik.
    Melin, Jan
    Ranstad, Per
    Asymmetric Limit Cycles in an Industrially Applied Controlled Resonant Converter2009Konferensbidrag (Refereegranskat)
    Abstract [sv]

    En industriellt använd LCC-kraftomvandlare är modellerad som ett hybrid-system. Det visas att för en given parameteruppsättning och olika begynnelsevillkor har systemet tre olika gränscykler, en stabil och två olika instabila assymmetriska gränscykler. Effekter för den industriella tillämpningen analyseras.

  • 104. Hultgren, Anders
    et al.
    Melin, Jan
    Ranstad, Per
    Limit Cycles in an Industrially Applied Hybrid System2010Konferensbidrag (Refereegranskat)
    Abstract [sv]

    En industriellt tillämpad LCC omvandlare är modellerad som ett hybridsystem. Det hybrida systemet modelleras med tre kontinuerliga tillstånd och ett logiskt tillstånd. Givet den industriella parameteruppsättningen och olika differentialvärden har systemet lösningar som bland annat en sluten bana och två gränscykler. Andra lösningar är inikerade.

  • 105.
    Husain, Syed Farzad
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Evaluation of Methods for 3D Environment Reconstruction with Respect to Navigation and Manipulation Tasks for Mobile Robots2010Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [sv]

    Fältet av 3-D-miljö återuppbyggnaden har varit föremål för olika forskningsinsatser under senare år. De ansökningar om mobila robotar är många. Först för navigering uppgifter (särskilt Slam), uppfattningen av 3-D-hinder har många fördelar jämfört navigering i 2-D-kartor, som det vanligtvis görs. Objekt som finns hänger över marken kan erkännas och dessutom robotarna vinna mycket mer information om dess verksamhet området vad som gör lokalisering lättare. För det andra, när det gäller tele-drift av robotar, hjälper en visualisering av miljön i tre dimensioner tele-aktör som utför uppgifter. Därför är en konsekvent, dynamiskt uppdaterade miljö modell avgörande. Tredje kan för mobila manipulation i en dynamisk miljö, en on-line hinder upptäcka och undvika kollisioner förverkligas, om miljön är känd. Under senare forskning, till 3-D-miljö återuppbyggnaden olika strategier har utvecklats. Två av de mest lovande metoderna är FastSLAM och 6-D-Slam. Båda kan bygga täta 3D-miljö kartor on-line. Det första man använder ett partikelfilter som tillämpas på extraherade funktioner i kombination med ett robotsystem modell och en mätning modell för att rekonstruera en karta. Den andra verk på 3-D data punktmoln och rekonstruerar en miljö med hjälp av ICP algoritm. Båda dessa metoder implementeras i GNU C. För det första är FastSLAM genomföras. Det objektorienterade programmering Tekniken används för att bygga upp Partikel-och Extended Kalman filter. För det andra är 6-D SLAM genomförs. Begreppet arv i C används för att göra genomförandet av ICP algoritm så mycket generisk som möjligt. För att testa vårt genomförande en mobil robot som heter Care-O-bot 3 används. Den mobila roboten är utrustad med en färg och en time-of-kamp kamera. Dataset tas som roboten rör sig i olika miljöer och vårt genomförande av FastSLAM och 6-D SLAM används för att rekonstruera kartorna.

  • 106.
    Hussain, Majid
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Fuzzy Relations2010Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [en]

    One of the most fundamental notions in pure and applied sciences is the concept of a relation. Science has been described as the discovery of relations between objects, states and events. Fuzzy relations generalize the concept of relations in the same manner as fuzzy sets generalize the fundamental idea of sets. This work presents an overview of comparison between classical and fuzzy relations. Some important compositions of fuzzy relations have been described and using these compositions a model for predicting score in cricket is developed. Finally it deals with the restoration and the identification of the causes (diagnosis) through the observed effects (symptoms) on the basis of fuzzy relations.

  • 107.
    Hussain, Zahid
    et al.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Sulaiman, Muhammad
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Sackey, Edward K. E.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Optimal System of Subalgebras and Invariant Solutions for the Black-Scholes Equation2009Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [en]

    The main purpose of this thesis is to use modern goal-oriented adaptive methods of Lie group analysis to construct the optimal sys- tem of Black-Scholes equation. We will show in this thesis how to obtain all invariant solutions by constructing what has now become so popular, optimal system of sub-algebras, the main Lie algebra admit- ted by the Black-Scholes equation. First, we obtain the commutator table of already calculated symmetries of the Black-Scholes equation. We then followed with the calculations of transformation of the gen- erators with the Lie algebra L6 which provides one-parameter group of linear transformations for the operators. Here we make use of the method of Lie equations to solve the partial di®erential equations. Next, we consider the construction of optimal systems of the Black- Scholes equation where the method requires a simpli¯cation of a vector to a general form to each of the transformations of the generators. Further, we construct the invariant solutions for each of the op- timal system. This study is motivated by the analysis of Lie groups which is being taken to another level by ALGA here in Blekinge In- stitute Technology, Sweden. We give a practical and in-depth steps and explanation of how to construct the commutator table, the calcu- lation of the transformation of the generators and the construction of the optimal system as well as their invariant solutions. Keywords: Black-Scholes Equation, commutators, commutator table, Lie equa- tions, invariant solution, optimal system, generators, Airy equation, structure constant,

  • 108.
    Ibeh, Elisabeth
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
    Detecting Abnormal Vibration in a Gearbox Using Time-Frequency Domain2012Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)
    Abstract [en]

    The gearbox of Volvo Construction Equipment vehicles may be considered as a critical mechanical component. Gear failures may cause costly down time while the gearbox is repaired. To improve uptime and reduce service costs, reliable and robust real time condition monitoring and diagnostics of gearboxes based on vibration data may be considered. This concerns the utilization of adequate feature extraction methods and classification methods. In this thesis project feature extraction methods have been considered for the purpose of enabling the detection of the slightest abnormal gear vibration in a gear test rig and a transmission test rig at Volvo CE. In particular a Time-Frequency Domain Averaging (TDFA) algorithm has been implemented for the extraction of gear box vibration features enabling the detection of abnormal gear vibration. Vibration has been measured for both test rigs during a test period of 2500 hours and a great number of vibration records were produced. Fluctuation in vibration could be observed as the experiment progressed using the TDFA method. The TDFA provide information on periodic components in a vibration signal related to the rotation speed it is synchronized and variations of them over time.

  • 109. Ibragimov, Nail
    A survey on integration of parabolic equations by reducing them to the heat equation2011Ingår i: Contemporary mathematics / [ed] Blázquez-Sanz, David; Morales-Ruiz, Juan J.; Lombardero, Jesús Rodríguez, AMS (American Mathematical society) , 2011Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The present paper is a survey of results [1], [2] on extension of Euler’s method for solving hyperbolic equations with one spatial variable to parabolic equations. The new method, based on the invariants of parabolic equations, allows one to identify all linear parabolic equations reducible to the heat equation and find their general solution. The method is illustrated by several examples.

  • 110. Ibragimov, Nail
    Archives of ALGA. Volume 32006Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 3 contains 6 articles: Lars Haikola, Louise Petrén-Overton, min mormor; Lars Haikola, Louise Petr´en-Overton, my grandmother. Traslations: Louise Petrén, Extension of Laplace's method to the equations...; E. Bessel-Hagen, On conservation laws of electrodynamics. Nail H. Ibragimov, The answer to the question put to me by L.V. Ovsyannikov 33 years ago; Nail H. Ibragimov, Raisa Khamitova, Bo Thidé, Adjoint system and conservation laws for symmetrized electromagnetic equations with a dual Ohm's law.

  • 111. Ibragimov, Nail
    Archives of ALGA, volume 52008Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 5 contains 3 articles by N.Ibragimov, an article by R. Khamitova and the English translation of V.P.Ermakov's article "Second order differential equations:conditions of complete integrability".

  • 112. Ibragimov, Nail
    Archives of ALGA. Volume 62009Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 6 contains 6 articles: Nail H. Ibragimov, Utilization of canonical variables for integration of systems of first-order differential equations; Nail H. Ibragimov and Ranis N. Ibragimov, Group analysis of nonlinear internal waves in oceans. I: Self-adjointness, conservation laws, invariant solutions; Nail H. Ibragimov, Ranis N. Ibragimov and Vladimir F. Kovalev, Group analysis of nonlinear internal waves in oceans. II: The symmetries and rotationally invariant solution; Nail H. Ibragimov and Ranis N. Ibragimov, Group analysis of nonlinear internal waves in oceans. III: Additional conservation laws; Nail H. Ibragimov Alternative presentation of Lagrange's method of variation of parameters; Nail H. Ibragimov Application of group analysis to liquid metal systems.

  • 113.
    Ibragimov, Nail
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Conservation laws and non-invariant solutions of anisotropic wave equations with a source2018Ingår i: Nonlinear Analysis, ISSN 1468-1218, Vol. 40, s. 82-94Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Linear and nonlinear waves in anisotropic media are used in various fields, e.g. in biomechanics, biomedical acoustics, etc. The present paper is devoted to discussion of nonlinear anisotropic wave equations with a source from point of view of their conservation laws and exact solutions associated with conservation laws. Nonlinearly self-adjoint wave equations with special source terms are singled out. The conservation laws associated with symmetries of the nonlinearly self-adjoint wave equations are computed and used for constructing exact solutions. The obtained solutions are different from group invariants solutions, in particular, from steady state and traveling wave solutions. The paper is designed for the application oriented readers. Its main goal is to introduce readers, interested in solutions of mathematical models having real world applications, to the recent method of conservation laws for constructing exact solutions of partial differential equations using conservation laws. © 2017 Elsevier Ltd

  • 114.
    Ibragimov, Nail
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för matematik och naturvetenskap.
    Construction of Conservation Laws Using Symmetries2014Konferensbidrag (Refereegranskat)
    Abstract [en]

    The concept of nonlinear self-adjointness of differential equations, introduced by the author in 2010, is discussed in detail. All linear equations and systems are nonlinearly self-adjoint. Moreover, the class of nonlinearly self-adjoint equations includes all nonlinear equations and systems having at least one local conservation law. It follows, in particular, that the integrable systems possessing infinite set of Lie-Backlund symmetries (higher-order tangent transformations) are nonlinearly self-adjoint. An explicit formula for conserved vectors associated with symmetries is provided for all nonlinearly self-adjoint differential equations and systems. The number of equations contained in the systems under consideration can be different from the number of dependent variables. A utilization of conservation laws for constructing exact solutions is discussed and illustrated by computing non-invariant solutions of the Chaplygin equations in gas dynamics.

  • 115.
    Ibragimov, Nail
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Integration of dynamical systems admitting nonlinear superposition2016Ingår i: JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS, ISSN 2330-152X, Vol. 4, nr 2, s. 91-106Artikel, forskningsöversikt (Refereegranskat)
    Abstract [en]

    A method of integration of non-stationary dynamical systems admitting nonlinear superpositions is presented. The method does not require knowledge of symmetries of the differential equations under consideration. The integration procedure is based on classification of Vessiot-Guldberg-Lie algebras associated with nonlinear superpositions. It is shown that the systems associated with one-and two-dimensional Lie algebras can be integrated by quadrature upon introducing Lie's canonical variables. It is not necessary to know symmetries of a system in question in this approach. Two-dimensional non-stationary dynamical systems with three-dimensional Vessiot-Guldberg-Lie algebras are classified into thirteen standard forms. Ten of them are integrable by quadrature. The remaining three standard forms lead to the Riccati equations. Integration of perturbed dynamical systems possessing approximate nonlinear superposition is discussed.

  • 116.
    Ibragimov, Nail
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Selected Works: Volume 52014Bok (Refereegranskat)
    Abstract [en]

    Advanced topics to be added to my textbook "A Practical Course in Differential Equations and Mathematical Modelling".

    This volume is dedicated to the memory of my teacher and friend Lev Vasilyevich Ovsyannikov (22.04.1919{23.05.2014).

    Volume V contains preprints written during 2008-2014 as advanced topics to be added to the textbook.  They include, e.g. a discussion of a wide class of linear ordinary differential equations whose integration is reducible to solution of algebraic equations. This class contains the constant coefficient equations and Euler’s equations as particular cases. The recent method of nonlinear self-adjointness for constructing conservations laws associated with symmetries of partial differential equations is also presented in this volume.

  • 117.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, Avdelningen för matematik och naturvetenskap.
    Avdonina, E.D.
    Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws2013Ingår i: Russian Mathematical Surveys, ISSN 0036-0279, E-ISSN 1468-4829, Vol. 68, nr 5, s. 889-921Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions.

  • 118.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, A. A.
    Ufa State Aviat Tech Univ, Rus.
    Three-dimensional dynamical systems admitting nonlinear superposition with three-dimensional Vessiot-Guldberg-Lie algebras2016Ingår i: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 52, s. 126-131Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The recent method of integration of non-stationary dynamical systems admitting nonlinear superpositions is applied to the three-dimensional dynamical systems associated with three-dimensional Vessiot-Guldberg-Lie algebras L-3. The investigation is based on Bianchi's classification of real three-dimensional Lie algebras and realizations of these algebras in the three-dimensional space. Enumeration of the Vessiot-Guldberg-Lie algebras L-3 allows to classify three-dimensional dynamical systems admitting nonlinear superpositions into thirty one standard types by introducing canonical variables. Twenty four of them are associated with solvable Vessiot-Guldberg-Lie algebras and can be reduced to systems of first-order linear equations. The remaining seven standard types are nonlinear. Integration of the latter types is an open problem. (C) 2015 Elsevier Ltd. All rights reserved.

  • 119.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, Aliya
    Ufimskij Gosudarstvennyj Aviacionnyj Tehniceskij Universitet, RUS.
    Three-dimensional dynamical systems with four-dimensional vessiot-guldberg-lie algebras2017Ingår i: The Journal of Applied Analysis and Computation, ISSN 2156-907X, E-ISSN 2158-5644, Vol. 7, nr 3, s. 872-883Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    - Dynamical systems attract much attention due to their wide applications. Many significant results have been obtained in this field from various points of view. The present paper is devoted to an algebraic method of integration of three-dimensional nonlinear time dependent dynamical systems admitting nonlinear superposition with four-dimensional Vessiot-Guldberg-Lie algebras L4. The invariance of the relation between a dynamical system admitting nonlinear superposition and its Vessiot-Guldberg-Lie algebra is the core of the integration method. It allows to simplify the dynamical systems in question by reducing them to standard forms. We reduce the three-dimensional dynamical systems with four-dimensional Vessiot-Guldberg-Lie algebras to 98 standard types and show that 86 of them are integrable by quadratures.

  • 120.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gainetdinova, Aliya. A.
    Ufa State Aviation Technical University, RUS.
    Classification and integration of four-dimensional dynamical systems admitting non-linear superposition2017Ingår i: International Journal of Non-Linear Mechanics, ISSN 0020-7462, Vol. 90, s. 50-71Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The method of integration of dynamical systems admitting non-linear superpositions is applied to four-dimensional non-linear dynamical systems. All four-dimensional dynamical systems admitting non-linear superpositions with four-dimensional Vessiot-Guldberg-Lie algebras are classified into 160 standard forms. The integration method is described and illustrated.

  • 121.
    Ibragimov, Nail
    et al.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Gandarias, M.L.
    Galiakberova, L.R.
    Bruzon, M.S.
    Avdonina, E.D.
    Group classification and conservation laws of anisotropic wave equations with a source2016Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 57, nr 8, artikel-id 083504Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.

  • 122. Ibragimov, Nail H.
    A Bridge Between Lie Symmetries and Galois Groups2009Konferensbidrag (Refereegranskat)
    Abstract [en]

    A bridge between Lie symmetry groups for differential equations and Galois groups for algebraic equations is suggested. It is based on calculation of Lie symmetries for algebraic equations and their restriction of the roots of the equations under consideration. The approach is illustrated by several examples. An alternative representation of Lie symmetries, called the Galois representation, is provided for differential equations.

  • 123. Ibragimov, Nail H.
    A discussion of conservation laws for over-determined systems with application to the Maxwell equations in vacuum.2007Ingår i: Archives of ALGA, ISSN 1652-4934, Vol. 4, s. 19-54Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The evolutionary part of Maxwell's equations has a Lagrangian written in terms of the electric and magnetic fields, but admit neither Lorentz nor conformal transformations. The additional equations on vanishing the divergences of the electric and magnetic fields guarantee the Lorentz and conformal invariance, but the resulting overdetermined system does not have a Lagrangian. The aim of the present paper is to attain a harmony between these two contradictory properties.

  • 124. Ibragimov, Nail H.
    A new conservation theorem2007Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 333, nr 1, s. 311-328Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Backlund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.

  • 125. Ibragimov, Nail H.
    A practical course in differential equations and mathematical modeling2009Bok (Övrigt vetenskapligt)
    Abstract [en]

    A practical course in differential equations and mathematical modelling is a unique blend of the traditional methods with Lie group analysis enriched by author’s own theoretical developments. The main objective of the book is to develop new mathematical curricula based on symmetry and invariance principles. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on author’s long-term experience of teaching at Novosibirsk and Moscow Universities in Russia, Collège de France, Georgia Tech and Stanford University in USA, Universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares the students for solving modern nonlinear problems and attracts essentially more students than the traditional way of teaching mathematics. The book can be used as a main textbook by undergraduate and graduate students and their teachers in applied mathematics, physics and engineering sciences.

  • 126. Ibragimov, Nail H.
    A practical course in differential equations and mathematical modelling: classical and new methods, nonlinear mathematical models, symmetry and invariance principles2006Bok (Övrigt vetenskapligt)
  • 127. Ibragimov, Nail H.
    A practical course in differential equations and mathematical modelling: Classical and new methods, nonlinear mathematical models, symmetry and invariance principles. 1st Ed.2004Bok (Övrigt vetenskapligt)
    Abstract [en]

    The present textbook on ordinary and partial differential equations is tailored to develop analytic skills and "working knowledge'' in both classical and Lie's methods for solving linear and nonlinear equations. It is based on lectures delivered by the author at Moscow Institute of Physics and Technology, and Blekinge Institute of Technology. The prerequisites are linear algebra and mathematical analysis with one and several variables including elements of ordinary differential equations.

  • 128. Ibragimov, Nail H.
    A Practical Course in Differential Equations and Mathematical Modelling: Classical and New Methods, Nonlinear Mathematical Models, Symmetry and Invariance Principles. 2nd ED2005Bok (Övrigt vetenskapligt)
    Abstract [en]

    The present textbook on ordinary and partial differential equations is tailored to develop analytic skills and "working knowledge'' in both classical and Lie's methods for solving linear and nonlinear equations. It is based on lectures delivered by the author at Moscow Institute of Physics and Technology, and Blekinge Institute of Technology. The prerequisites are linear algebra and mathematical analysis with one and several variables including elements of ordinary differential equations.

  • 129. Ibragimov, Nail H.
    An alternative presentation of the method of variation of parameters for higher-order equations2010Ingår i: Lobachevskii Journal of Mathematics, ISSN 1995-0802, Vol. 31, nr 2, s. 174-191Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An alternative approach to Lagrange's method of variation of parameters is presented. Explicit formulas for solutions of arbitrary initial value problems for linear equations of the first, second and third order are provided. These formulas are as simple for practical using as the formula for roots of quadratic equations.

  • 130. Ibragimov, Nail H.
    Applications of group invariance methods to problems of transport phenomena2008Konferensbidrag (Refereegranskat)
    Abstract [en]

    An overview is given of lie group analysis and symmetry methods applied to transport phenomena

  • 131. Ibragimov, Nail H.
    Approximate representation of the de Sitter group2007Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 333, nr 1, s. 329-346Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The purpose of this paper is to develop a theory of approximate representations of the de Sitter group considered as a perturbation of the Poincare group. This approach simplifies investigation of relativistic effects pertaining to the mechanics in the de Sitter universe. Utility of the approximate approach is manifest if one compares the transformations of the de Sitter group with their approximate representations.

  • 132.
    Ibragimov, Nail H.
    Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för matematik och naturvetenskap.
    Approximate transformation groups2008Bok (Övrigt vetenskapligt)
    Abstract [en]

    These notes provide an easy to follow introduction to the topic and are based on my talks at various conferences, in particular on the plenary lecture at the International Workshop on ``Differential equations and chaos" (University of Witwatersrand, Johannesburg, South Africa, January 1996). The book is prepared for the new graduate course ``Approximate transformation groups" that will be given at Blekinge Institute of Technology during January-March, 2009.

  • 133. Ibragimov, Nail H.
    Archives of ALGA, volume 12004Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 1 contains 3 articles: Nail H. Ibragimov, Equivalence groups and invariants of linear and non-linear equations; Nail H. Ibragimov and Sergey V. Meleshko, Linearization of third-order ordinary differential equations; Nail H. Ibragimov, Gazanfer Ünal and Claes Jogreús, Group analysis of stochastic differential systems: Approximate symmetries and conservation laws.

  • 134. Ibragimov, Nail H.
    Archives of ALGA. Volume 22005Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 2 contains 3 articles: Ilir Berisha, Translation of Bäcklunds paper ”Surfaces of constant negative curvature”; Johan Erlandsson, "Survey of mathematical models in biology from point of view of Lie group analysis"; Niklas Säfström, "Group analysis of a tumour growth model"

  • 135. Ibragimov, Nail H.
    Archives of ALGA. Volume 42007Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 4 contains articles: Nail H. Ibragimov, Ewald J.H. Wessels and George F.R. Ellis, Group classication of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time; Nail H. Ibragimov A discussion of conservation laws for over-determined systems with application to the Maxwell equations in vacuum; Nail H. Ibragimov, Quasi-self-adjoint differential equations; Nail H. Ibragimov and Salavat V. Khabirov, Existence of integrating factors for higher-order ordinary differential equations; Nail H. Ibragimov, Integration of second-order linear equations via linearization of Riccati's equations; Nail H. Ibragimov and Sergey V. Meleshko Linearization of second-order ordinary differential equations by changing the order; Nail H. Ibragimov and Sergey V. Meleshko Second-order ordinary differential equations equivalent to y''= H(y); Nail H. Ibragimov, Sergey V. Meleshko and Supaporn Suksern, Linearization of fourth-order ordinary differential equations by point transformations; Nail H. Ibragimov and Emrullah Yasar, Non-local conservation laws in fluid dynamics

  • 136. Ibragimov, Nail H.
    Archives of ALGA, volume 7/82010Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 7/8 contains 3 articles by N.H. Ibragimov, an article by N.H. Ibragimov, E. D. Avdonina and an article by N. H. Ibragimov , R. Khamitova.

  • 137.
    Ibragimov, Nail H.
    Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för matematik och naturvetenskap.
    Archives of ALGA: volume 92012Samlingsverk (redaktörskap) (Övrigt vetenskapligt)
    Abstract [en]

    Volume 9 contains articles of different authors.

  • 138.
    Ibragimov, Nail H.
    Blekinge Tekniska Högskola, Fakulteten för teknikvetenskaper, Institutionen för matematik och naturvetenskap.
    Comments on the paper "Conservation laws of the (2+1)-dimensional KP equation and Burgers equation with variable coefficients and cross terms" by Li-Hua Zhang2014Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 226, s. 1-2Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The recent paper mentioned in the title contains a confusing statement on computing conservation laws corresponding to symmetries of nonlinearly self-adjoint differential equations. The present brief article contains clarifying comments.

  • 139. Ibragimov, Nail H.
    Covariant method for solution of Cauchy's problem based on Lie group analysis and Leray's form2003Konferensbidrag (Refereegranskat)
    Abstract [en]

    The Lie group theory and Leray's form provide a covariant (i.e., independent of a coordinate system) method for the calculation of fundamental solutions for linear hyperbolic equations, and hence for the solution of Cauchy's problem. Here, the method is illustrated by the classical wave equation.

  • 140. Ibragimov, Nail H.
    Differentialekvationer och matematisk modellering2009Bok (Övrigt vetenskapligt)
    Abstract [sv]

    Differentialekvationer och matematisk modellering" är avsedd för högskolestuderande på nybörjarnivå, exempelvis inom ingenjörs- och naturvetarprogram. Den kombinerar klassiska lösningsmetoder med moderna metoder från gruppanalys. Texten är generös med exempel och övningsuppgifter, vissa med fullständiga lösningar. Många vanliga läroböcker är begränsade till ett antal speciella differentialekvationer som man råkar kunna lösa med enkla recept. De flesta matematiska modeller inom naturvetenskap och teknik leder dock till ickelinjära differentialekvationer som man inte kan lösa med traditionella metoder. Med de redskap som ges i denna bok ligger många intressanta tillämpningar inom räckhåll.

  • 141. Ibragimov, Nail H.
    Equivalence groups and invariants of linear and non-linear equations2004Ingår i: Archives of ALGA, ISSN 1652-4934, Vol. 1, s. 9-69Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Recently I developed a systematic method for determining invariants of families of equations. The method is based on the infinitesimal approach and is applicable to algebraic and differential equations possessing finite or infinite equivalence groups. Moreover, it does not depend on the assumption of linearity of equations. The method was applied to variety of ordinary and partial differential equations. The present paper is aimed at discussing the main principles of the method and its applications with emphasis on the use of infinite Lie groups.

  • 142. Ibragimov, Nail H.
    Extension of Euler's method to parabolic equations2009Ingår i: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, E-ISSN 1878-7274, Vol. 14, nr 4, s. 1157-1168Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Euler generalized d'Alembert's solution to a wide class of linear hyperbolic equations with two independent variables. He introduced in 1769 the quantities that were rediscovered by Laplace in 1773 and became known as the Laplace invariants. The present paper is devoted to an extension of Euler's method to linear parabolic equations with two independent variables. The new method allows one to derive an explicit formula for the general solution of a wide class of parabolic equations. In particular, the general solution of the Black-Scholes equation is obtained. (c) 2008 Elsevier B.V. All rights reserved.

  • 143. Ibragimov, Nail H.
    Extension of Laplace´s method2006Övrigt (Övrigt vetenskapligt)
    Abstract [en]

    Översättning av Louise Petréns doktorsavhandling vid Lunds universitet

  • 144. Ibragimov, Nail H.
    Generalization of Euler´s Equations2009Ingår i: Quarterly of Applied Mathematics, ISSN 0033-569X , Vol. 67, nr 2, s. 327-341Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A wide class of linear ordinary differential equations reducible to algebraic equations is studied. The method for solving all these equations is given. The new class depends essentially on two arbitrary functions and contains the constant coefficient equations and Euler's equations as particular cases.

  • 145. Ibragimov, Nail H.
    Integrating factors, adjoint equations and Lagrangians2006Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 318, nr 2, s. 742-757Artikel i tidskrift (Refereegranskat)
    Abstract [sv]

    Online: http://www.bth.se/ihn/alga.nsf/sidor/cc32aec8706331d0c125716b0041d97c!OpenDocume nt

  • 146. Ibragimov, Nail H.
    Integrating factors for higher-order equations2007Konferensbidrag (Refereegranskat)
    Abstract [en]

    Integrating factors are determined for ordinary differential equations of an arbitrary order. In the case of first-order equations the new definition coincides with the usual definition of integrating factor introduced by A. Clairaut in 1739. It is shown that higher-order equations, unlike the first-order equations, can have an integrating factor even when they do not admit Lie point symmetries. The method is illustrated by several examples.

  • 147.
    Ibragimov, Nail H.
    Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för matematik och naturvetenskap.
    Integration of second-order linear equations via linearization of Riccati's equations2007Ingår i: Archives of ALGA, ISSN 1652-4934, Vol. 4, s. 71-75Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The test for linearization of the Riccati equations by a change of the dependent variable, proved by the author in 1989, is utilized for integration of second-order linear equations by quadratures.

  • 148. Ibragimov, Nail H.
    INTEGRATION OF SYSTEMS OF FIRST-ORDER EQUATIONS ADMITTING NONLINEAR SUPERPOSITION2009Konferensbidrag (Refereegranskat)
    Abstract [en]

    Systems of two nonlinear ordinary differential equations of the first order admitting nonlinear superpositions are investigated using Lie's enumeration of groups on the plane. It is shown that the systems associated with two-dimensional Vessiot-Guldberg-Lie algebras can be integrated by quadrature upon introducing Lie's canonical variables. The knowledge of a symmetry group of a system in question is not needed in this approach. The systems associated with three-dimensional Vessiot-Guldberg-Lie algebras are classified into 13 standard forms 10 of which are integrable by quadratures and three are reduced to Riccati equations.

  • 149. Ibragimov, Nail H.
    Invariant Lagrangians and a new method of integration of nonlinear equations.2005Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 304, nr 1, s. 212-235Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A method for solving the inverse variational problem for differential equations admitting a Lie group is presented. The method is used for determining invariant Lagrangians and integration of second-order nonlinear differential equations admitting two-dimensional non-commutative Lie algebras. The method of integration suggested here is different from Lie's classical method of integration of second-order ordinary differential equations based on canonical forms of two-dimensional Lie algebras. The new method reveals existence and significance of one-parameter families of singular solutions to nonlinear equations of second order.

  • 150. Ibragimov, Nail H.
    et al.
    ,
    Invariants of evolution equations2004Övrigt (Övrigt vetenskapligt)
    Abstract [en]

    We investigate invariants of equations u_t=f(x,u)u_{xx}+g(x,u,u_x). We show that these equations have two functionally independent invariants of the second order.

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