Let Γ be a regular graph with n vertices, diameter D, and d + 1 different eigenvalues λ > λ1 > · · · > λd. In a previous paper, the authors showed that if P (λ) > n − 1, then D ≤ d − 1, where P is the polynomial of degree d−1 which takes alternating values±1 atλ1, . . . , λd. The graphs satisfying P (λ) = n − 1, called boundary graphs, have shown to deserve some attention because of their rich ...

In this paper we first present a CG-type method for inverse eigenvalue problem of constructing real and symmetric matrices M, D and K for the quadratic pencil Q(λ) = λ2M + λD + K, so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors. This method can determine the solvability of the inverse eigenvalue problem automatically. We then consider the least squares model for updating a ...

The triviality of the scalar sector of the standard one-doublet Higgs model implies that it is only an effective low-energy theory valid below some cut-off scale Λ. In this note we show that the experimental constraint on the amount of custodial symmetry violation, |∆ρ∗| = α|T | ≤ 0.4%, implies that the scale Λ must be greater than of order 7.5 TeV. For theories defined about the infraredstable...

We investigate the rotating D3-brane solution with maximum number of angular momentum parameters. After determining the angular velocities, Hawking temperature, ADM mass and entropy, we use this geometry to construct general three-parameter models of non-supersymmetric pure SU(N) Yang–Mills theories in 2+1 dimensions. We calculate glueball masses in the WKB approximation and obtain closed analy...

In this paper we investigate how the phase diagram of a U(1) symmetric HiggsYukawa system depends on the scalar self coupling λ. The phase diagram of similar models with continuous symmetry were extensively studied in the infinite scalar self coupling λ = ∞ limit. Recent analytical and numerical calculations at zero self coupling showed qualitatively different phase diagram, raising the questio...

We present a resonant cavity approach for non-invasive, pulse-to-pulse, beam emittance measurements of non-circular multi-bunch beams. In a resonant cavity, desired field components can be enhanced up to π λ / L Q , where λ L Q is the loaded quality factor of the resonant mode λ , when the cavity resonant mode matches the bunch frequency of a bunch-train beam pulse. In particular, a quad-cavity...

I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the eigenvalues λi should behave as z(i)/V for large volume V , where z(i) is the i-th zero of the Bessel function. With neither chiral nor λ extrapolation, one can ...

We study new physics effects to the quartic gauge boson couplings formulated by the electroweak chiral Lagrangian. Five next-to-leading order operators characterize the anomalous quartic gauge interactions which involve pure Goldstone boson dynamics for the electroweak symmetry breaking. We estimate the typical size of these couplings in different strongly-interacting models and examine the sen...

The triviality of the scalar sector of the standard one-doublet Higgs model implies that it is only an effective low-energy theory valid below some cut-off scale Λ. In this note we show that the experimental constraint on the amount of custodial symmetry violation, |∆ρ∗| = α|T | ≤ 0.4%, implies that the scale Λ must be greater than of order 7.5 TeV. For theories defined about the infraredstable...

We explore the Higgs sector of the NMSSM in the limit when the Peccei–Quinn symmetry is exact or only slightly broken. In this case the Higgs spectrum has a hierarchical structure which is caused by the stability of the physical vacuum. We find a strong correlation between the parameters of the NMSSM if κ = 0 or κ λ 2. It allows one to distinguish the NMSSM with exact or softly broken PQ-symmet...