vector spaces and linear systems
Báo cáo toán học: "Finite vector spaces and certain lattices" pps
... the number of r-dimensional vector subspaces of the n-dimensional vector space Vn (q) over the finite field GF (q) We let Gn = Gn (q) denote the total number of vector subspaces of Vn (q) The numbers ... the pair of lattices which are solution spaces of Bx ≡ mod r and Cx ≡ mod s, (5) where the matrices B and C are defined by A ≡ B mod r and A ≡ C mod s; (6) and conversely, given (5) we define a matrix ... the systems Bi x ≡ mod r, ≤ i ≤ Lm (r), and every m-dimensional mod s lattice is the solution space of exactly one of the systems Cj x ≡ mod s, ≤ j ≤ Lm (s) Since gcd(r, s) = 1, the theory of linear...
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Báo cáo toán học: "Vector spaces and the Petersen graph" pdf
... of the linear space of the graph Each vector space considered in this paper is over the field GF (2), has sets of edges as vectors and has symmetric difference as the addition operation The linear ... described earlier by relating the dimensions of the spaces L(G), C(G), E(G) and A(G) An argument using vector spaces Every generating set for a vector space over any field includes a basis In particular, ... how the dimensions of the cycle and even spaces are related for a 2-connected non-bipartite graph We now derive an analogous result for the linear and alternating spaces in a graph with a 1-factor...
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Báo cáo khoa học: "Orthogonal Negation in Vector Spaces for Modelling Word-Meanings and Document Retrieval" ppt
... benefits and drawbacks of vector negation compared with two other methods for negation Negation and Disjunction in Vector Spaces In this section we use well-known linear algebra to define vector ... single vector This is exactly what vector negation accomplishes, and also determines a suitable value of λ from a and b Thus a second benefit for vector negation is that it produces a combined vector ... (Birkhoff and von Neumann, 1936), a development which is discussed in much more detail in (Widdows and Peters, 2003) Because of its simplicity, our model is easy to understand and to implement Vector...
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Báo cáo toán học: " An introduction to 2-fuzzy n-normed linear spaces and a new perspective to the Mazur-Ulam problem" docx
... of fuzzy norms on a linear space Cheng and Mordeson [7] and Bag and Samanta [8] introduced a concept of fuzzy norm on a linear space The concept of fuzzy n-normed linear spaces has been studied ... (X) and α, β ∈ (0, 1) The smallest such κ is called the n-Lipschitz constant Lemma 4.3 Assume that if f0 , f1 , and f2 are -collinear then Ψ (f0 ) , Ψ (f1 ) and Ψ (f2 ) are 2-collinear, and that ... contradicts the fact that A contains n linearly independent vectors And so on, Ψ(f1 )−Ψ(f0 ), Ψ(f2 )−Ψ(f0 ) are linearly dependent Thus Ψ(f0 ), Ψ(f1 ), and Ψ(f2 ) are 2-collinear Theorem 4.2 Every n-isometry...
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Báo cáo hóa học: " Research Article Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems" doc
... needed Lemma 2.5 (a) If u v and v w, then u w (b) If u v and v w, then u w (c) If u v and v w, then u w c, and (d) Let x ∈ X, {xn } and {bn } be two sequences in X and E, respectively, θ bn for ... 1, and q r or s t If f X ∪ g X ⊂ h X and h X is a complete subspace of X, then f, g, and h have a unique point of coincidence Moreover, if f, h and g, h are weakly compatible, then f, g, and ... γ ≥ and α 2β 2γ < If f X ∪ g X ⊂ h X and h X is a complete subspace of X, then f, g, and h have a unique point of coincidence Moreover, if f, h and g, h are weakly compatible, then f, g, and...
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Báo cáo hóa học: " COMMON FIXED POINT AND INVARIANT APPROXIMATION RESULTS IN CERTAIN METRIZABLE TOPOLOGICAL VECTOR SPACES" pptx
... topological vector spaces, locally convex topological vector spaces and metric linear spaces We apply a new theorem to derive some results on the existence of best approximations Our results unify and ... I and T be selfmaps of a Banach space X with u ∈ F(I) ∩ F(T), M ⊂ X with T(∂M ∩ M) ⊂ M Suppose that D is closed and q-starshaped with q ∈ F(I), I(D) = D, I is linear and continuous on D If I and ... 1.3 Let I and T be selfmaps of a normed space X with u ∈ F(I) ∩ F(T), M ⊂ X with T(∂M) ⊂ M, and q ∈ F(I) If PM (u) is compact and q-starshaped, I(PM (u)) = PM (u), I is continuous and linear on...
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Báo cáo hóa học: " TRANSFER POSITIVE HEMICONTINUITY AND ZEROS, COINCIDENCES, AND FIXED POINTS OF MAPS IN TOPOLOGICAL VECTOR SPACES" pdf
... coincidences, and fixed points and [6, Theorems and 5], Fan [6, 9], [10, Theorem 5] and [8, Theorem 1], Glicksberg [14], Kakutani [18], Bohnenblust and Karlin [3], Halpern and Bergman [15], and others) ... compact and convex and F3 and G3 are s.t.p.h.c and t.p.h.c on C (thus also s.t.h.c and t.h.c by Proposition 2.4, Remark 2.2 and Definitions 2.1 and 2.3) but not u.h.c on C Examples and remarks Let ... ) and the maps Fi and Gi satisfy the assumptions of Theorems 2.9(iii) and 2.9(iv), respectively, i = − The pair (Fi ,Gi ) and the maps Fi and Gi satisfy the assumptions of Theorems 2.10(iii) and...
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Báo cáo toán học: "Controllability Radii and Stabilizability Radii of Time-Invariant Linear Systems" pot
... where K B and K λ are the matrices representing KerB and Ker(A∗ − λI), and the formula of rAB is the result obtained in [4] By the definitions, it is clear that rAB ≤ min{rA , rB }, and the strict ... obtain Controllability Radii and Stabilizability Radii of Time-Invariant Linear Systems rAB = 499 √ 2, rA = 2, rB = 2, rF = References John S Bay, Fundamentals of Linear State Space System, McGraw-Hill, ... Between controllable and uncontrollable, System & Control Letters (1984) 263–264 N K Son and N D Huy, Maximizing the stability radius of discrete-time linear positive system by linear feedbacks,...
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Báo cáo toán học: "On the number of orthogonal systems in vector spaces over finite fields" ppsx
... Sudakov, Pseudo-random graphs, Conference on Finite and Infinite Sets Budapest, Bolyai Society Mathematical Studies X, pp 1–64 [3] A Iosevich and S Senger, Orthogonal systems in vector spaces over ... hospitality and financial support during his visit References [1] N Alon and M Krivelevich, Constructive bounds for a Ramsey-type problem, Graphs and Combinatorics 13 (1997), 217–225 [2] M Krivelevich and ... denote the graph whose vertices are the points of d − (0, , 0) and two (not necessarily distinct) vertices x q and y are adjacent if and only if they are orthogonal, i.e x1 y1 + + xd yd = Then...
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Báo cáo toán học: "Orthogonal systems in vector spaces over finite fields" pot
... of vector spaces over finite fields, Analysis Mathematika, 34, (2007) [7] D Hart, A Iosevich, D Koh and M Rudnev Averages over hyperplanes, sum-product theory in vector spaces over finite fields and ... publication (2007) [8] D Hart, A Iosevich, D Koh S Senger and I Uriarte-Tuero, Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness, (submitted for publication), (2008) [9] ... Proceedings and Lecture Notes (2007) [10] M Krivelevich and B Sudakov, Pseudo-random graphs, Conference on Finite and Infinite Sets Budapest, Bolyai Society Mathematical Studies X, pp 1–64 [11] R Lidl and...
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Analysis and Control of Linear Systems - Chapter 0 pptx
... and linear discrete systems 2.4 Controllability of systems 2.4.1 General definitions 2.4.2 Controllability of linear and invariant systems ... chapters (1 and 2) Discrete-time systems are, for more clarity, explained in Chapter Chapter explains the structural properties of linear systems Chapter xvi Analysis and Control of Linear Systems ... Designs and Patents Act 1988 Library of Congress Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires eng] Analysis and control of linear systems analysis and...
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Analysis and Control of Linear Systems - Chapter 1 pptx
... continuous systems which will have only one input and one output, modeled by continuous signals Chapter written by Dominique BEAUVOIS and Yves TANGUY 4 Analysis and Control of Linear Systems 1.2 ... overflow and the terms ω t r ( t r is the establishment time at 5%) and ω t m according to the damping ξ Figure 1.21 ω0 tr and ω0 tm according to the damping ξ 30 Analysis and Control of Linear Systems ... ) (t ) 16 Analysis and Control of Linear Systems By supposing that x(t ) and y(t ) are continuous functions defined from −∞ to +∞ , continuously differentiable of order m and n, by a two-sided...
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Analysis and Control of Linear Systems - Chapter 3 pps
... distinct parts The analysis and manipulation of signals and discrete-time systems are presented in sections 3.2 and 3.3 The discretization of continuous-time systems and certain concepts of the ... Analysis and Control of Linear Systems 3.2.2 Delay and lead operators The concept of an operator is interesting because it enables a compact formulation of the description of signals and systems ... between u(k ) and the sampled output and state vectors x(k ) = x a (kT ) and y(k ) = y a (kT ) We have, between the sampling instants tk = kT and tk +1 = (k + 1) T , ua (t ) = u(k ) and consequently...
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Analysis and Control of Linear Systems - Chapter 4 ppt
... the main references 4.1.1 Vector spaces, linear applications Let X and Y be real vector spaces of finite dimension and V ⊂ X and W ⊂ Y, two sub -spaces Let L: X → Y be a linear application LV designates ... with E and H as linear applications of X toward X and two isomorphic spaces of size n, will also have finite and infinite zeros Among the most compact methods to illustrate these finite and infinite ... infinite zeros, [pE-H] also has a non-trivial core and co-core Polynomial vectors and co-vectors, x(p) and xT(p) then exist such that: [pE-H] x(p) = and/ or xT(p) [pE-H] = The various possible solutions...
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Analysis and Control of Linear Systems - Chapter 5 pptx
... integral is the product of transforms: (y1 ⊗ y2 ) = y1 y2 [5.9] 144 Analysis and Control of Linear Systems On the other hand, the Fourier transform preserves the energy (Parseval theorem) Indeed, ... with the first and second order moments, i.e the mean and the autocorrelation function A discrete-time random signal y[k], k ∈ Z is called stationary in the broad sense if its mean my and its autocorrelation ... instant k and the signal at instant k + κ It is traditional to remain limited only to the mean and the autocorrelation function in order to characterize a stationary random signal and this even...
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Analysis and Control of Linear Systems - Chapter 6 ppsx
... listed in section 6.1 can thus be applied here by replacing matrices A and B (or F and G ) by AT and C T (or F T and CT) and the state feedback K by LT Based on Theorem 6.1, we infer that matrix ... [6.35] are verified and also if: ⎧( F , G ) is stabilizable ⎨ ⎩ ( H , F ) is detectable [6.41] 174 Analysis and Control of Linear Systems there is a unique matrix P , symmetric and positive semi-defined, ... between stabilizability and detectability, we immediately obtain the following result 178 Analysis and Control of Linear Systems THEOREM 6.4.– if conditions [6.52] are verified and also if: ⎧( AT...
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Analysis and Control of Linear Systems - Chapter 7 docx
... one hand, the problem of identification (and also the problem of simulation and control) is made much easier by the computing tool and is already well known in data analysis (linear or non -linear ... fact be used on non -linear representations and that is why we also use it in order to parameterize the knowledge methods mentioned above 198 Analysis and Control of Linear Systems 7.2 Modeling ... problems directly as they stand, by using only the state representation: xt+1 = Axt+1 + But [7.52] y = Cxt where ut is the vector input, yt the vector output and xt the state vector The parameters...
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Analysis and Control of Linear Systems - Chapter 8 ppsx
... speed and accuracy accessible in simulation 8.2 Standard linear equations 8.2.1 Definition of the problem We will adopt the notations usually used to describe the state forms and linear dynamic systems ... elegant and robust solution consists of obtaining simultaneously Φ and Γ through the relation: Φ Γ A B h [8.7] = exp I 0 230 Analysis and Control of Linear Systems The sizes of blocks and I are ... B and C are constant and verify A ∈ Rn×n , B ∈ Rn×m As for X and U , their size is given by X ∈ Rn×m and U ∈ Rm×m To establish the solution of these equations, we examine the free state, and...
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Analysis and Control of Linear Systems - Chapter 9 pot
... E and ω : E0 = vM γM and ω = γM vM [9.53] 278 Analysis and Control of Linear Systems hence the condition: µ1 µ β p= j γM vM ≤ ε d max vM [9.54] γM We note that this condition is necessary and, ... with this latter transformation and we will study the case of open loop stable systems, that of integrator systems and finally the case of open loop unstable systems Analysis by Classic Scalar ... reaches –180° These margins, noted by ∆φ and ∆G , are represented in Bode, Nyquist and Black-Nichols planes in Figure 9.13 268 Analysis and Control of Linear Systems Figure 9.13 Bode plane (a), Nyquist...
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