On Real Solutions of the Equation Φ\u3csup\u3e\u3cem\u3et\u3c/em\u3e\u3c/sup\u3e (\u3cem\u3eA\u3c/em\u3e) = 1/\u3cem\u3en\u3c/em\u3e J\u3csub\u3e\u3cem\u3en\u3c/em\u3e\u3c/sub\u3e

For a class of n × n-matrices, we get related real solutions to the matrix equation Φt (A) = 1/n Jn by generalizing the approach of and applying the results of Zhang, Yang, and Cao [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 642–645]. These solutions contain not only those obtained by Zhang, Yang, and Cao but also some which are neither diagonally nor permutation equivalent to those obtained by Zhang, Yang, and Cao. Therefore, the open problem proposed by Zhang, Yang, and Cao in the cited paper is solved

Erratum to “The lollipop graph is determined by its Q-spectrum”

AbstractThe proof of Theorem 3.3 in [Y. Zhang, X. Liu, B. Zhang, X. Yong, The lollipop graph is determined by its Q-spectrum, Discrete Math. 309 (2009) 3364–3369] is not correct. Actually, in the development of PA(G1)(λ), the authors missed several products into addition, which makes the rest of the proof invalid. Note that the statement of the theorem is true. Here, we give a correct proof

Systematic X-ray absorption study of hole doping in BSCCO - phases

X-ray absorption spectroscopy (XAS) on the O 1s threshold was applied to Bi-based, single crystalline high temperature superconductors (HTc's), whose hole densities in the CuO2 planes was varied by different methods. XAS gives the intensity of the so-called pre-peak of the O 1s line due to the unoccupied part of the Zhang-Rice (ZR) singlet state. The effects of variation of the number n of CuO2 - planes per unit cell (n = 1,2,3) and the effect of La-substitution for Sr for the n = 1 and n = 2 phase were studied systematically. Furthermore the symmetry of the states could be probed by the polarization of the impinging radiation.Comment: 4 pages, 2 figures, to appear in the proceedings of SCES2001, Ann Arbor, August 6-10, 200

Zero energy correction method for non-Hermitian Harmonic oscillator with simultaneous transformation of co-ordinate and momentum: Wave function analysis under Iso-spectral condition

We present a complete analysis on energy and wave function of Harmonic oscillator with simultaneous non-hermitian transformation of co-ordinate ($(x \rightarrow \frac{(x+ i\lambda p)}{\sqrt{(1+\beta \lambda)}}$ and momentum $(p \rightarrow \frac{(p+ i\beta x)}{\sqrt{(1+\beta \lambda)}}$ for getting energy eigenvalue using perturbation theory under iso-spectral condition. Further we notice that two different frequency of oscillation ($w_{1}, w_{2}$)correspond to same energy eigenvalue, which can also be verified using Lie algebraic approach [Zhang et.al J.Math.Phys 56 ,072103 (2015)]. Interestingly wave function analysis using similarity transformation [F.M. Fernandez, Int. J. Theo. Phys. (2015)(in Press)] refers to a very special case.Comment: This paper for replacement .(i) Minor change in title reflecting wave function analysis(ii) Abstract-chaed suitably to refect wave function (iii) Text original work with information on wave function ,comparison and slight modification in references.Kindly accep

Nonbonding oxygen holes and spinless scenario of magnetic response in doped cuprates

Both theoretical considerations and experimental data point to a more complicated nature of the valence hole states in doped cuprates than it is predicted by Zhang-Rice model. Actually, we deal with a competition of conventional hybrid Cu 3d-O 2p $b_{1g}\propto d_{x^2 -y^2}$ state and purely oxygen nonbonding state with $e_{u}x,y \propto p_{x,y}$ symmetry. The latter reveals a non-quenched Ising-like orbital moment that gives rise to a novel spinless purely oxygen scenario of the magnetic response in doped cuprates with the oxygen localized orbital magnetic moments of the order of tenths of Bohr magneton. We consider the mechanism of ${}^{63,65}$Cu-O 2p transferred orbital hyperfine interactions due to the mixing of the oxygen O 2p orbitals with Cu 3p semicore orbitals. Quantitative estimates point to a large magnitude of the respective contributions both to local field and electric field gradient, and their correlated character.Comment: 7 pages, 1 figur

Theory of Four-dimensional Fractional Quantum Hall States

We propose a pseudo-potential Hamiltonian for the Zhang-Hu's generalized fractional quantum Hall states to be the exact and unique ground states. Analogously to Laughlin's quasi-hole (quasi-particle), the excitations in the generalized fractional quantum Hall states are extended objects. They are vortex-like excitations with fractional charges $+(-)1/m^3$ in the total configuration space CP$^3$. The density correlation function of the Zhang-Hu states indicates that they are incompressible liquid.Comment: 4 page