LEADER 00950nam a22002531i 4500 001 991003730079707536 005 20040601112200.0 008 040802s1971 it a||||||||||||||||ita 035 $ab13118729-39ule_inst 035 $aARCHE-107133$9ExL 040 $aBiblioteca Interfacoltà$bita$cA.t.i. Arché s.c.r.l. Pandora Sicilia s.r.l. 082 04$a551.5 100 1 $aBernacca, Edmondo$0270743 245 10$aChe tempo farà :$bmanuale di meteorologia pratica /$cEdmondo Bernacca 260 $aMilano :$bA. Mondadori,$c1971 300 $a205 p., [8] c. di tav. :$bill. ;$c19 cm 440 0$aOscar casa 650 4$aMeteorologia 907 $a.b13118729$b01-07-21$c05-08-04 912 $a991003730079707536 945 $aLE002 Fondo Giudici P 1420$g1$iLE002G-15152$lle002$nC. 1$o-$pE0.00$q-$rn$so $t0$u0$v0$w0$x0$y.i13754105$z05-08-04 996 $aChe tempo fara$9308250 997 $aUNISALENTO 998 $ale002$b05-08-04$cm$da $e-$fita$git $h0$i1 LEADER 08232nam 2200553 450 001 996508571903316 005 20231005194608.0 010 $a9783031212406$b(electronic bk.) 010 $z9783031212390 024 7 $a10.1007/978-3-031-21240-6 035 $a(MiAaPQ)EBC7176393 035 $a(Au-PeEL)EBL7176393 035 $a(CKB)25997731400041 035 $a(DE-He213)978-3-031-21240-6 035 $a(PPN)267808259 035 $a(EXLCZ)9925997731400041 100 $a20230503d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLinear systems /$fGordon Blower 205 $a1st ed. 2022. 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2023] 210 4$d©2023 215 $a1 online resource (417 pages) 225 1 $aMathematical Engineering,$x2192-4740 311 08$aPrint version: Blower, Gordon Linear Systems Cham : Springer International Publishing AG,c2023 9783031212390 327 $aIntro -- Preface -- Contents -- 1 Linear Systems and Their Description -- 1.1 Linear Systems and Their Description -- 1.2 Feedback -- 1.3 Linear Differential Equations -- 1.4 Damped Harmonic Oscillator -- 1.5 Reduction of Order of Linear ODE -- 1.6 Exercises -- 2 Solving Linear Systems by Matrix Theory -- 2.1 Matrix Terminology -- 2.2 Characteristic Polynomial -- 2.3 Norm of a Vector -- 2.4 Cauchy-Schwarz Inequality -- 2.5 Matrix Exponential exp(A) or expm (A) -- 2.6 Exponential of a Diagonable Matrix -- 2.7 Solving MIMO (A,B,C,D) -- 2.8 Rational Functions -- 2.9 Block Matrices -- 2.10 The Transfer Function of (A,B,C,D) -- 2.11 Realization with a SISO -- 2.12 Exercises -- 3 Eigenvalues and Block Decompositions of Matrices -- 3.1 The Transfer Function of Similar SISOs (A,B,C,D) -- 3.2 Jordan Blocks -- 3.3 Exponentials and Eigenvalues of Complex Matrices -- 3.4 Exponentials and the Resolvent -- 3.5 Schur Complements -- 3.6 Self-adjoint Matrices -- 3.7 Positive Definite Matrices -- 3.8 Linear Fractional Transformations -- 3.9 Stable Matrices -- 3.10 Dissipative Matrices -- 3.11 A Determinant Formula -- 3.12 Observability and Controllability -- 3.13 Kalman's Decomposition -- 3.14 Kronecker Product of Matrices -- 3.15 Exercises -- 4 Laplace Transforms -- 4.1 Laplace Transforms -- 4.2 Laplace Convolution -- 4.3 Laplace Uniqueness Theorem -- 4.4 Laplace Transform of a Differential Equation -- 4.5 Solving MIMO by Laplace Transforms -- 4.6 Partial Fractions -- 4.7 Dirichlet's Integral and Heaviside's Expansions -- 4.8 Final Value Theorem -- 4.9 Laplace Transforms of Periodic Functions -- 4.10 Fourier Cosine Transform -- 4.11 Impulse Response -- 4.12 Transmitting Signals -- 4.13 Exercises -- 5 Transfer Functions, Frequency Response, Realization and Stability -- 5.1 Winding Numbers -- 5.2 Realization -- 5.3 Frequency Response -- 5.4 Nyquist's Locus. 327 $a5.5 Gain and Phase -- 5.6 BIBO Stability -- 5.7 Undamped Harmonic Oscillator: Marginal Stability and Resonance -- 5.8 BIBO Stability in Terms of Eigenvalues of A -- 5.9 Maxwell's Stability Problem -- 5.10 Stable Rational Transfer Functions -- 5.11 Nyquist's Criterion for Stability of T -- 5.12 Nyquist's Criterion Proof -- 5.13 M and N Circles -- 5.14 Exercises -- 6 Algebraic Characterizations of Stability -- 6.1 Feedback Control -- 6.2 PID Controllers -- 6.3 Stable Cubics -- 6.4 Hurwitz's Stability Criterion -- 6.5 Units and Factors -- 6.6 Euclidean Algorithm and Principal Ideal Domains -- 6.7 Ideals in the Complex Polynomials -- 6.8 Highest Common Factor and Common Zeros -- 6.9 Rings of Fractions -- 6.10 Coprime Factorization in the Stable Rational Functions -- 6.11 Controlling Rational Systems -- 6.12 Invariant Factors -- 6.13 Matrix Factorizations to Stabilize MIMO -- 6.14 Inverse Laplace Transforms of Strictly Proper Rational Functions -- 6.15 Differential Rings -- 6.16 Bessel Functions of Integral Order -- 6.17 Exercises -- 7 Stability and Transfer Functions via Linear Algebra -- 7.1 Lyapunov's Criterion -- 7.2 Sylvester's Equation AY+YB+C=0 -- 7.3 A Solution of Lyapunov's Equation AL+LA' +P=0 -- 7.4 Stable and Dissipative Linear Systems -- 7.5 Almost Stable Linear Systems -- 7.6 Simultaneous Diagonalization -- 7.7 A Linear Matrix Inequality -- 7.8 Differential Equations Relating to Sylvester's Equation -- 7.9 Transfer Functions tf -- 7.10 Small Groups of Matrices -- 7.11 How to Convert Complex Matrices into Real Matrices -- 7.12 Periods -- 7.13 Discrete Fourier Transform -- 7.14 Exercises -- 8 Discrete Time Systems -- 8.1 Discrete-Time Linear Systems -- 8.2 Transfer Function for a Discrete Time Linear System -- 8.3 Correspondence Between Continuous- and Discrete-Time Systems -- 8.4 Chebyshev Polynomials and Filters. 327 $a8.5 Hankel Matrices and Moments -- 8.6 Orthogonal Polynomials -- 8.7 Hankel Determinants -- 8.8 Laguerre Polynomials -- 8.9 Three-Term Recurrence Relation -- 8.10 Moments via Discrete Time Linear Systems -- 8.11 Floquet Multipliers -- 8.12 Exercises -- 9 Random Linear Systems and Green's Functions -- 9.1 ARMA Process -- 9.2 Distributions on a Bounded Interval -- 9.3 Cauchy Transforms -- 9.4 Herglotz Functions -- 9.5 Green's Functions -- 9.6 Random Diagonal Transformations -- 9.7 Wigner Matrices -- 9.8 Pastur's Theorem -- 9.9 May-Wigner Model -- 9.10 Semicircle Addition Law -- 9.11 Matrix Version of Pastur's Fixed Point Equation -- 9.12 Rank One Perturbations on Green's Functions -- 9.13 Exercises -- 10 Hilbert Spaces -- 10.1 Hilbert Sequence Space -- 10.2 Hardy Space on the Disc -- 10.3 Subspaces and Blocks -- 10.4 Shifts and Multiplication Operators -- 10.5 Canonical Model -- 10.6 Hardy Space on the Right Half-Plane -- 10.7 Paley-Wiener Theorem -- 10.8 Rational Filters -- 10.9 Shifts on L2 -- 10.10 The Telegraph Equation as a Linear System -- 10.11 Exercises -- 11 Wireless Transmission and Wavelets -- 11.1 Frequency Band Limited Functions and Sampling -- 11.2 The Shannon Wavelet -- 11.3 Telatar's Model of Wireless Communication -- 11.4 Exercises -- 12 Solutions to Selected Exercises -- Glossary of Linear Systems Terminology -- A MATLAB Commands for Matrices -- B SciLab Matrix Operations -- References -- Index. 330 $aThis textbook provides a mathematical introduction to linear systems, with a focus on the continuous-time models that arise in engineering applications such as electrical circuits and signal processing. The book introduces linear systems via block diagrams and the theory of the Laplace transform, using basic complex analysis. The book mainly covers linear systems with finite-dimensional state spaces. Graphical methods such as Nyquist plots and Bode plots are presented alongside computational tools such as MATLAB. Multiple-input multiple-output (MIMO) systems, which arise in modern telecommunication devices, are discussed in detail. The book also introduces orthogonal polynomials with important examples in signal processing and wireless communication, such as Telatar?s model for multiple antenna transmission. One of the later chapters introduces infinite-dimensional Hilbert space as a state space, with the canonical model of a linear system. The final chapter covers modern applications to signal processing, Whittaker?s sampling theorem for band-limited functions, and Shannon?s wavelet. Based on courses given for many years to upper undergraduate mathematics students, the book provides a systematic, mathematical account of linear systems theory, and as such will also be useful for students and researchers in engineering. The prerequisites are basic linear algebra and complex analysis. 410 0$aMathematical Engineering,$x2192-4740 606 $aAutomatic control 606 $aAutomatic control$xData processing 606 $aSistemes lineals$2thub 608 $aLlibres electrònics$2thub 615 0$aAutomatic control. 615 0$aAutomatic control$xData processing. 615 7$aSistemes lineals 676 $a629.8 700 $aBlower$b G$g(Gordon),$0321964 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996508571903316 996 $aLinear Systems$93004758 997 $aUNISA LEADER 07878nam 2201969Ia 450 001 9910781200803321 005 20200520144314.0 010 $a1-282-30380-5 010 $a9786612303807 010 $a1-4008-3106-7 024 7 $a10.1515/9781400831067 035 $a(CKB)2550000000002880 035 $a(EBL)475845 035 $a(OCoLC)507428541 035 $a(SSID)ssj0000337335 035 $a(PQKBManifestationID)11297311 035 $a(PQKBTitleCode)TC0000337335 035 $a(PQKBWorkID)10287892 035 $a(PQKB)10258020 035 $a(DE-B1597)446614 035 $a(OCoLC)979685624 035 $a(DE-B1597)9781400831067 035 $a(Au-PeEL)EBL475845 035 $a(CaPaEBR)ebr10333494 035 $a(CaONFJC)MIL230380 035 $a(MiAaPQ)EBC475845 035 $a(PPN)15099625X 035 $a(EXLCZ)992550000000002880 100 $a20090202d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe ergodic theory of lattice subgroups$b[electronic resource] /$fAlexander Gorodnik and Amos Nevo 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2009 215 $a1 online resource (136 p.) 225 1 $aAnnals of mathematics studies ;$vno. 172 300 $aDescription based upon print version of record. 311 $a0-691-14184-3 311 $a0-691-14185-1 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Main results: Semisimple Lie groups case -- $tChapter Two. Examples and applications -- $tChapter Three. Definitions, preliminaries, and basic tools -- $tChapter Four. Main results and an overview of the proofs -- $tChapter Five. Proof of ergodic theorems for S-algebraic groups -- $tChapter Six. Proof of ergodic theorems for lattice subgroups -- $tChapter Seven. Volume estimates and volume regularity -- $tChapter Eight. Comments and complements -- $tBibliography -- $tIndex 330 $aThe results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established. 410 0$aAnnals of mathematics studies ;$vno. 172. 606 $aErgodic theory 606 $aLie groups 606 $aLattice theory 606 $aHarmonic analysis 606 $aDynamics 610 $aAbsolute continuity. 610 $aAlgebraic group. 610 $aAmenable group. 610 $aAsymptote. 610 $aAsymptotic analysis. 610 $aAsymptotic expansion. 610 $aAutomorphism. 610 $aBorel set. 610 $aBounded function. 610 $aBounded operator. 610 $aBounded set (topological vector space). 610 $aCongruence subgroup. 610 $aContinuous function. 610 $aConvergence of random variables. 610 $aConvolution. 610 $aCoset. 610 $aCounting problem (complexity). 610 $aCounting. 610 $aDifferentiable function. 610 $aDimension (vector space). 610 $aDiophantine approximation. 610 $aDirect integral. 610 $aDirect product. 610 $aDiscrete group. 610 $aEmbedding. 610 $aEquidistribution theorem. 610 $aErgodic theory. 610 $aErgodicity. 610 $aEstimation. 610 $aExplicit formulae (L-function). 610 $aFamily of sets. 610 $aHaar measure. 610 $aHilbert space. 610 $aHyperbolic space. 610 $aInduced representation. 610 $aInfimum and supremum. 610 $aInitial condition. 610 $aInterpolation theorem. 610 $aInvariance principle (linguistics). 610 $aInvariant measure. 610 $aIrreducible representation. 610 $aIsometry group. 610 $aIwasawa group. 610 $aLattice (group). 610 $aLie algebra. 610 $aLinear algebraic group. 610 $aLinear space (geometry). 610 $aLipschitz continuity. 610 $aMass distribution. 610 $aMathematical induction. 610 $aMaximal compact subgroup. 610 $aMaximal ergodic theorem. 610 $aMeasure (mathematics). 610 $aMellin transform. 610 $aMetric space. 610 $aMonotonic function. 610 $aNeighbourhood (mathematics). 610 $aNormal subgroup. 610 $aNumber theory. 610 $aOne-parameter group. 610 $aOperator norm. 610 $aOrthogonal complement. 610 $aP-adic number. 610 $aParametrization. 610 $aParity (mathematics). 610 $aPointwise convergence. 610 $aPointwise. 610 $aPrincipal homogeneous space. 610 $aPrincipal series representation. 610 $aProbability measure. 610 $aProbability space. 610 $aProbability. 610 $aRate of convergence. 610 $aRegular representation. 610 $aRepresentation theory. 610 $aResolution of singularities. 610 $aSobolev space. 610 $aSpecial case. 610 $aSpectral gap. 610 $aSpectral method. 610 $aSpectral theory. 610 $aSquare (algebra). 610 $aSubgroup. 610 $aSubsequence. 610 $aSubset. 610 $aSymmetric space. 610 $aTensor algebra. 610 $aTensor product. 610 $aTheorem. 610 $aTransfer principle. 610 $aUnit sphere. 610 $aUnit vector. 610 $aUnitary group. 610 $aUnitary representation. 610 $aUpper and lower bounds. 610 $aVariable (mathematics). 610 $aVector group. 610 $aVector space. 610 $aVolume form. 610 $aWord metric. 615 0$aErgodic theory. 615 0$aLie groups. 615 0$aLattice theory. 615 0$aHarmonic analysis. 615 0$aDynamics. 676 $a515/.48 686 $aSI 830$2rvk 700 $aGorodnik$b Alexander$f1975-$01476747 701 $aNevo$b Amos$f1966-$01476748 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910781200803321 996 $aThe ergodic theory of lattice subgroups$93691524 997 $aUNINA