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Showing 1 to 20 of 39 for “"Positive Real"”.
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Positive Real Functions
Made available in DSpace on 2014-12-05T21:50:13Z (GMT). No. of bitstreams: 1 5904534.pdf: 1452687 bytes, checksum: a4cf06aa0eb350fb4397362d08e0a636 (MD5) Previous issue date: 1959
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On Positive Real Functions
Made available in DSpace on 2014-12-05T21:50:13Z (GMT). No. of bitstreams: 1 5904511.pdf: 1582724 bytes, checksum: a679408150be81359765cf641b607e50 (MD5) Previous issue date: 1959
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Classifying expansions of the real field by complex subgroups
In this thesis, we study expansions of the real field by multiplicative subgroups of the complex numbers. We first consider expansions by a subgroup generated by an element of the unit circle and a positive real number. We then consider expansions by a subgroup generated by a complex number and a …
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The Construction and Applications of Modular Equations
… , where q3 is classical theta function. For any positive real numbers n and k, define hk,n=4e-p n/k k1/44e-p nk=q 30,-n/k k1/4q30, -nk and h'k,n=4 -e-2pn/k k1/44-e-2p nk =q30,1+2-n/ kk1/4q 30,1+2-nk . We show how they are connected with rk,n, r'k,n and Ramanujan-Weber class invariants and give …
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Optimum Semi-Iterative Methods for the Solution of Any Linear Algebraic System With a Square Matrix
… linear system, Ax = b, when the eigenvalues have positive real parts. The iterative parameters are reciprocals of the roots of a scaled and translated Chebyshev polynomial and depend upon an ellipse enclosing the spectrum of the system matrix.
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On Some Schroedinger Eigenvalue Problems From Mathematical Physics
… this implies that the eigenvalues are all positive real for the potentials alphaiz3 + beta z2 + gammaiz when alpha, beta, gamma ∈ R with alpha ≠ 0 and alphagamma ≥ 0, and with the boundary conditions that u(z) decays to zero as z tends to infinity along the positive and negative …
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The limits of Brune's impedance
… coined the term and then provided a proof that ``positive real"" is a necessary and sufficient condition for network synthesis using lumped elements. Brune's impedance, described using a ratio of polynomials, represents a fundamentally limited subset of impedance functions. Quite notably, all …
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Linear Discrete-time Dissipative Systems
… goal is to present versions of the discrete-time positive real and discrete-time bounded real lemmas that do not require the assumptions of controllability and observability, and in fact require no assumptions at all. The optimal control problem associated with passive systems is solved, likewise …
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Solution Of Linear Evolution Partial Differential Equations On The Half-Line
… boundary conditions and the Airy equation on the positive real line. Moreover, we observe how such problems give rise to new obstacles in the verification of potential solutions, and highlight the need for the development and implementation of new techniques, such as the Unified Transform method. …
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Schur-class of finitely connected planar domains: the test-function approach
… set of matrix-valued holomorphic functions with positive real part on a finitely-connected planar domain 𝐑 normalized to have value equal to the identity matrix at some prescribed point t₀ ∈ 𝐑. This leads to an integral representation for such functions more general than what would be expected …
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Arborescent numbers : higher arithmetic operations and division trees
… from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the …
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Performance and Robustness of Adaptive Controllers for Linear Stochastic Systems
… rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the …
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Local complex singularity exponents for isolated singularities
… c[sub]0(f) is defined as the supremum of all positive real number [lambda] for which 1/[magnitude of]f[to the power of][2 lambda] is integrable on some neighborhood of the origin. It has been conjectured that c[sub]0(f) should not decrease if f is deformed small enough. Using J. Mather and …
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Backward stochastic differential equations with jumps are stable
… the weak-convergence of finite measures on the positive real-line by means of relatively compact sets of the Skorokhod space endowed with the J1 −topology. We remain in the Skorokhod space, where we refine a classical result on convergence of the jump-times of a J1 −convergent sequence. More …
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Point processes of representation theoretic origin
… Z-measures are point processes on the punctured positive real line. They arise as interpolations of the spectral measures of a distinguished family of spherical representations of certain infinite-dimensional symmetric spaces. In representation-theoretic terms, our result solves the problem of …
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Accuracy of Computer Generated Approximations to Julia Sets
… Julia sets generated for the family λtan(z) for positive real λ are also accurate. We conclude with a cautionary example of a Julia set whose picture will be inaccurate for some apparently reasonable choices of parameters, demonstrating that some care must be exercised in using such algorithms. …
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On Observer-Based Control of Nonlinear Systems
… been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability …
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Study of an active RC line in the microwave region
… The combined effect of negative conductance and positive real resistance within the device makes it capable of being a microwave amplifier or oscillator. The advantage of this type of device is that it does not have to present a negative impedance to an external signal source (as is the case with …
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Matching problems in hypergraphs
… l with k >= 3 and k/2 < l <= k-1, there exists a positive real μ such that, for all sufficiently large integers m, n satisfying n/k - μn <= m <= n/k - 1 - (1 - l/k){ceil of (k - l)/(2l - k)}, if H is a k-uniform hypergraph on n vertices and the minimum l-degree of H is greater than {(n-l) choose …
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Synthesis of electrical and mechanical networks of restricted complexity
… is to gain a better understanding of minimal realisations within the simplest non-trivial class of networks of restricted complexity--the networks of the so-called "Ladenheim catalogue"--and thence establish more general results in the field of passive network synthesis. Practical motivation …
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