S The features of the low-lying spectrum and a complete set of quantum numbers for the (eeee) system have been deduced based on symmetry. The existence of a low odd-parity L=1 excited state with the two e coupled to s1 = 0, and two e + coupled to s2 = 1 (or s1 =1 and s2 =0) and a low evenparity L=0 excited state with s1 = s2 = 1 have been anticipated. A 2-dimensional (eeee) system has also been...

In this article, we establish a unilateral global bifurcation theorem from infinity for a class of N -dimensional p-Laplacian problems. As an application, we study the global behavior of the components of nodal solutions of the problem div(φp(∇u)) + λa(x)f(u) = 0, x ∈ B, u = 0, x ∈ ∂B, where 1 < p < ∞, φp(s) = |s|p−2s, B = {x ∈ RN : |x| < 1}, and a ∈ C(B̄, [0,∞)) is radially symmetric with a 6≡ ...

Let (S1,S2) be a bi-isometry, that is, pair of commuting isometries S1 and S2 on complex Hilbert space H. By the von Neumann-Wold decomposition, hyper-range H∞(S1):=∩n=0∞S1nH reduces to unitary operator. Although H∞(S1) is an invariant subspace for S2, in general, not reducing S2. We show isometry if only subspaces S2(ker⁡S1⁎) H are orthogonal. Further, we describe all bi-isometries satisfying ...

A bisection of a graph G is a bipartition S1, S2 of V (G) such that −1 ≤ |S1|− |S2| ≤ 1. It is NP-hard to find a bisection S1, S2 of a graph G maximizing e(S1, S2) (respectively, minimizing max{e(S1), e(S2)}), where e(S1, S2) denotes the number of edges of G between S1 and S2, and e(Si) denotes the number of edges of G with both ends in Si. There has been algorithmic work on bisections, but ver...

For an integer s1, s2, s3 > 0, let Ns1,s2,s3 denote the graph obtained by identifying each vertex of a K3 with an end vertex of three disjoint paths Ps1+1, Ps2+1, Ps3+1 of length s1, s2, and s3, respectively. We determine a family F of graphs such that, every 3-connected (K1,3, Ns1,s2,1)-free graph Γ with s1 + s2 + 1 ≤ 10 is hamiltonian if and only if the closure of Γ is L(G) for some graph G /...

We expose the recent extensions to the matrix case of classical results in the theory of the moment problem: the theorem of Riesz, the parametrization of Nevanlinna and properties of the N -extremal matrices of measures. 1. The classical theory The purpose of this survey is to show the recent extensions to the matrix case of classical results in the theory of the moment problem. The interest th...

We consider the nonlinear eigenvalue problems u ′′ rf u 0, 0 < t < 1, u 0 0, u 1 ∑m−2 i 1 αiu ηi , where m ≥ 3, ηi ∈ 0, 1 , and αi > 0 for i 1, . . . , m − 2, with ∑m−2 i 1 αi < 1; r ∈ R; f ∈ C1 R,R . There exist two constants s2 < 0 < s1 such that f s1 f s2 f 0 0 and f0 : limu→0 f u /u ∈ 0,∞ , f∞ : lim|u|→∞ f u /u ∈ 0,∞ . Using the global bifurcation techniques, we study the global behavior of...

The notation and terminology used here have been introduced in the following papers: [12], [2], [3], [7], [9], [11], [1], [4], [10], [13], [6], [17], [18], [15], [8], [16], [19], and [5]. For simplicity, we adopt the following rules: F denotes a non trivial real normed space, G denotes a real normed space, X denotes a set, x, x0, r, p denote real numbers, n, k denote elements of N, Y denotes a ...

Let S = (s1, s2, . . .) be any sequence of nonnegative integers and let Sk = ∑k i=1 si We then define the falling (rising) factorials relative to S by setting (x)↓k,S= (x−S1)(x−S2) · · · (x−Sk) and (x)↑k,S= (x+S1)(x+S2) · · · (x+Sk) if k ≥ 1 with (x)↓0,S= (x)↑0,S= 1. It follows that {(x)↓k,S}k≥0 and {(x)↑k,S}k≥0 are bases for the polynomial ring Q[x]. We use a rook theory model due to Miceli an...

For simplicity, we adopt the following convention: X is a complex unitary space, x, y, w, g, g1, g2 are points of X, z is a Complex, q, r, M are real numbers, s1, s2, s3, s4 are sequences of X, k, n, m are natural numbers, and N1 is an increasing sequence of naturals. Let us consider X, s1. We say that s1 is convergent if and only if: (Def. 1) There exists g such that for every r such that r > ...