We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

For linear operators L , T and nonlinear maps P we describe classes of simple F = I ? between Banach Hilbert spaces, for which no point has more than two preimages. The encompass known examples (homeomorphisms, global folds) the weaker, geometric, hypotheses suggest new ones. operator may be Laplacian with various boundary conditions, as in original Ambrosetti-Prodi theorem, or associated quant...

A walk W between two non-adjacent vertices in a graph G is called tolled if the first vertex of W is among vertices from W adjacent only to the second vertex ofW , and the last vertex ofW is among vertices fromW adjacent only to the second-last vertex of W . In the resulting interval convexity, a set S ⊂ V (G) is toll convex if for any two non-adjacent vertices x, y ∈ S any vertex in a tolled w...

In this paper we first describe a new deviation inequality for sums of independent random variables which uses the precise constants appearing in the tails of their distributions, and can reflect in full their concentration properties. In the proof we make use of Chernoff’s bounds. We then apply this inequality to prove a global diameter reduction theorem for abstract families of linear operato...

The main purpose of this paper is to investigate the formal deficiency indices N±(I) of a symmetric first order system Jf ′ +Bf = λH f on an interval I, where I = R or I = R±. Here J,B,H are n × n matrix valued functions and the Hamiltonian H ≥ 0 may be singular even everywhere. We obtain two results for such a system to have minimal numbers N±(R) = 0 (resp. N±(R±) = n) and a criterion for thei...

We give an example of a positive operator B in a Krein space with the following properties: the nonzero spectrum of B consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of B are uniformly bounded and the point ∞ is a singular critical point of B. An operator A in the Krein space (K, [ · , · ]) is said to be positive ...

We study the rank one Harish-Chandra-Itzykson-Zuber integral in limit where \frac{N\beta}{2} \to c N?2?c , called high-temperature regime and show that it can be ...

Two concepts, evidently very different in nature, have proved to be useful in analytical and numerical studies of spectral stability in nonlinear wave theory: (i) the Krein signature of an eigenvalue, a quantity usually defined in terms of the relative orientation of certain subspaces that is capable of detecting the structural instability of imaginary eigenvalues and, hence, their potential fo...

We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u 4 t f t, u t , u′′ t , t ∈ 0, 1 , u 0 ∫1 0 g s u s ds, u 1 0, u′′ 0 ∫1 0 h s u ′′ s ds, u′′ 1 0, where f : 0, 1 × 0, ∞ × −∞, 0 → 0, ∞ is continuous, g, h ∈ L1 0, 1 are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the globa...

We give a short argument that for some C > 0, every n-dimensional Banach ball K admits a 256-round subquotient of dimension at least Cn/(logn). This is a weak version of Milman’s quotient of subspace theorem, which lacks the logarithmic factor. Let V be a finite-dimensional vector space over R and let V ∗ denote the dual vector space. A symmetric convex body or (Banach) ball is a compact convex...