In this paper we complement some results of [L. Marconi, L. Praly, and A. Isidori, SIAM J. Control Optim., 45 (2007), pp. 2277–2298] by presenting a sufficient condition under which the output feedback controller proposed in that paper can be designed to be locally Lipschitz. The condition in question consists in a regularity property of the observable part of an autonomous system with output t...

Chvátal (J Combin Theory Ser B 12:163–168, 1972) gave a well-known sufficient condition for graphical sequence to be forcibly hamiltonian, and showed that in some sense his is best possible. Nash-Williams (Recent Trends Graph Theory. Springer, Berlin, pp. 197–210, 1971) examples of hamiltonian n-sequences do not satisfy Chvátal’s condition, every \(n\ge 5\). In this note we generalize the examp...

An interesting feature of the finite-dimensional real spectral triple (A,H,D,J) Standard Model is that it satisfies a ``second-order'' condition: conjugation by J maps Clifford algebra Cl_D(A) into its commutant, which in fact isomorphic to itself (H self-Morita equivalence Cl_D(A)-bimodule). This resembles property canonical closed oriented Riemannian manifold: there dense subspace H Cl_D(A)-b...

For an elliptic curve E over ℚ, putting K=ℚ(E[p]) which is the p-th division field of for odd prime p, we study ideal class group ClK K as a Gal(K/ℚ)-module. More precisely, any j with 1⩽j⩽p-2, give condition that ClK⊗Fp has symmetric power SymjE[p] E[p] its quotient Gal(K/ℚ)-module, in terms Bloch-Kato’s Tate-Shafarevich SymjVpE. Here VpE denotes rational p-adic Tate module E. This partial gen...

Let $\{b_{j}\}_{j=1}^{k}$ be meromorphic functions, and let $w$ admissible solutions of delay differential equation $$w'(z)=w(z)\left[\frac{P(z, w(z))}{Q(z,w(z))}+\sum_{j=1}^{k}b_{j}(z)w(z-c_{j})\right]$$ with distinct delays $c_{1}, \ldots, c_{k}\in\mathbb{C}\setminus\{0\},$ where the two nonzero polynomials $P(z, w(z))$ $Q(z, in coefficients are prime each other. We obtain that if $\limsup_{r...

We study model theoretical stability for Banach spaces and structures based on Banach spaces, e.g., Banach lattices or C∗-algebras. We prove that a theory is stable if and only if the following condition is true in every model E of the theory: If (ām ) and (b̄n) are bounded sequences in Ek and El (respectively) and R : Ek × El → R is definable, then there exist subsequences (āmi ) and (b̄n j ) su...

In this very short note we prove that the pseudo-random index j of RC4 is indeed not pseudo-random. This is a simple result that missed our attention for quite a long time. We show that in long term Pr(j = i + 1) = 1 N − 1 N2 , instead of the random association 1 N and this happens for the non-existence of the condition S[i] = 1 and j = i + 1 that is mandatory for the non-existence of the Finne...

In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich’s and Nourein’s iterations. Our theorems generalize and improve recent results of Zheng and Huang [J. Comput. Math. 18 (2000), 113– 122], Petković and Herceg [J. Comput. Appl. Math. 136 (2001), 283–307] and Nedić [Novi Sad J. ...

We discuss the proof of and systematic application of Case’s sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J − J0 is Hilbert–Schmidt, and a proof of Nevai’s conjecture that the Szegő condition holds if...