Lie groups, Lie algebras, and some of their applications by Robert Gilmore

By Robert Gilmore

With rigor and readability, this upper-level undergraduate textual content employs quite a few workouts, solved difficulties, and figures to introduce upper-level undergraduates to Lie workforce conception and actual functions. It extra illustrates Lie crew theory's position in expressing suggestions and effects from numerous fields of physics. 1974 variation. comprises seventy five figures and 17 tables.

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Representation of Lie Groups and Special Functions: Volume by N.Ja. Vilenkin, A.U. Klimyk

By N.Ja. Vilenkin, A.U. Klimyk

This is often the 1st of 3 significant volumes which current a accomplished therapy of the idea of the most periods of targeted services from the perspective of the idea of team representations. This quantity offers with the homes of classical orthogonal polynomials and distinct services that are concerning representations of teams of matrices of moment order and of teams of triangular matrices of 3rd order. This fabric varieties the root of many effects bearing on classical unique services comparable to Bessel, MacDonald, Hankel, Whittaker, hypergeometric, and confluent hypergeometric services, and varied periods of orthogonal polynomials, together with these having a discrete variable. Many new effects are given. the quantity is self-contained, considering an introductory part provides simple required fabric from algebra, topology, practical research and crew idea. For study mathematicians, physicists and engineers.

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Quaternions and rotation sequences: a primer with by J. B. Kuipers

By J. B. Kuipers

Ever because the Irish mathematician William Rowan Hamilton brought quaternions within the 19th century--a feat he celebrated through carving the founding equations right into a stone bridge--mathematicians and engineers were fascinated with those mathematical gadgets. this present day, they're utilized in purposes as numerous as describing the geometry of spacetime, guiding the distance travel, and constructing machine functions in digital truth. during this e-book, J. B. Kuipers introduces quaternions for scientists and engineers who've now not encountered them prior to and indicates how they are often utilized in a number of functional occasions.

The booklet is basically an exposition of the quaternion, a 4-tuple, and its fundamental program in a rotation operator. yet Kuipers additionally offers the extra traditional and well-known three x three (9-element) matrix rotation operator. those parallel displays permit the reader to pass judgement on which techniques are most excellent for particular functions. the quantity is split into 3 major components. the outlet chapters current introductory fabric and determine the book's terminology and notation. the subsequent half provides the mathematical homes of quaternions, together with quaternion algebra and geometry. It comprises extra complicated certain issues in round trigonometry, besides an advent to quaternion calculus and perturbation thought, required in lots of occasions concerning dynamics and kinematics. within the ultimate part, Kuipers discusses cutting-edge purposes. He provides a six degree-of-freedom electromagnetic place and orientation transducer and concludes by means of discussing the pc photographs priceless for the advance of functions in digital fact.

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Linear Triatomic Molecules - OCO+, FeCO - NCO- by G. Guelachvili, K. Narahari Rao (auth.), G. Guelachvili

By G. Guelachvili, K. Narahari Rao (auth.), G. Guelachvili (eds.)

Volume II/20 presents severely evaluated info on unfastened molecules, acquired from infrared spectroscopy and comparable experimental and theoretical investigations.
The quantity is split into 4 subvolumes, A: Diatomic Molecules, B: Linear Triatomic Molecules, C: Nonlinear Triatomic Molecules, D: Polyatomic Molecules.
All volumes include a CD-ROM, additional subvolumes are in preparation.

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Positive linear systems : theory and applications by Lorenzo Farina

By Lorenzo Farina

"This reference is split into 3 major components: the 1st half comprises the definitions and uncomplicated homes of confident linear platforms. the second one half, following the theoretical exposition, experiences the most conceptual effects, contemplating appropriate examples taken from a few generic types. The 3rd half is dedicated to the research of a few sessions of optimistic linear platforms of specific relevance in functions (such because the Leontief version, the Leslie version, the Markov chains, the compartmental structures, and the queueing systems). Readers acquainted with linear algebra and linear platforms thought will have fun with the best way arguments are handled and presented."--BOOK JACKET. learn more... 2 Definitions and stipulations of Positivity 7 -- three effect Graphs 17 -- four Irreducibility, Excitability, and Transparency 23 -- half II homes 33 -- five balance 35 -- 6 Spectral Characterization of Irreducible structures forty nine -- 7 Positivity of Equilibria fifty seven -- eight Reachability and Observability sixty five -- nine cognizance eighty one -- 10 minimal section ninety one -- eleven Interconnected platforms a hundred and one -- half III purposes 107 -- 12 Input-Output research 109 -- thirteen Age-Structured inhabitants versions 117 -- 14 Markov Chains 131 -- 15 Compartmental platforms one hundred forty five -- sixteen Queueing platforms a hundred and fifty five -- Appendix A components of Linear Algebra and Matrix conception 187 -- A.1 actual Vectors and Matrices 187 -- A.2 Vector areas 189 -- A.3 measurement of a Vector house 193 -- A.4 switch of foundation 195 -- A.5 Linear adjustments and Matrices 196 -- A.6 photograph and Null house 198 -- A.7 Invariant Subspaces, Eigenvectors, and Eigenvalues 201 -- A.8 Jordan Canonical shape 207 -- A.9 Annihilating Polynomial and minimum Polynomial 210 -- A.10 Normed areas 212 -- A.11 Scalar Product and Orthogonality 216 -- A.12 Adjoint changes 221 -- Appendix B components of Linear platforms idea 225 -- B.1 Definition of Linear platforms 225 -- B.2 ARMA version and move functionality 228 -- B.3 Computation of move features and attention 231 -- B.4 Interconnected Subsystems and Mason's formulation 234 -- B.5 switch of Coordinates and an identical platforms 237 -- B.6 movement, Trajectory, and Equilibrium 238 -- B.7 Lagrange's formulation and Transition Matrix 241 -- B.8 Reversibility 244 -- B.9 Sampled-Data structures 244 -- B.10 inner balance: Definitions 248 -- B.11 Eigenvalues and balance 248 -- B.12 exams of Asymptotic balance 251 -- B.13 power and balance 256 -- B.14 Dominant Eigenvalue and Eigenvector 259 -- B.15 Reachability and keep an eye on legislation 260 -- B.16 Observability and country Reconstruction 264 -- B.17 Decomposition Theorem 268 -- B.18 choice of the ARMA types 272 -- B.19 Poles and Zeros of the move functionality 279 -- B.20 Poles and Zeros of Interconnected platforms 282 -- B.21 Impulse reaction 286 -- B.22 Frequency reaction 288 -- B.23 Fourier rework 293 -- B.24 Laplace remodel 296 -- B.25 Z-Transform 298 -- B.26 Laplace and Z-Transforms and move features three hundred

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