Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution

The multi-phase particle swarm optimization (MPPSO) technique is applied to retrieve the particle size distribution (PSD) under dependent model.Based on the Mie theory and the Lambert-Beer theory, three PSDs, i.e., the Rosin-Rammer (R-R) distribution, the normal distribution, and the logarithmic normal distribution, are estimated by MPPSO algorithm.The results confirm the potential of the proposed approach and show its effectiveness.It may provide a new technique to improve the accuracy and reliability of the PSD inverse calculation.     

On Nonnormal Numbers

Mathematical Notes -     

An oscillation phenomenon of low frequency reverberation in the shallow water and its physical explanation

~~An oscillation phenomenon of low frequency reverberation in the shallow water and its physical explanation1 Zhang, R.. Jin. G. Normal-mode theory of average reverberation intensity in shallow water, Journal of Sound and Vibration, 1987 19(2):215-223 2. Ellis, D. D., A shallow-water normal-mode reverberation model, J. Acoust. Soc, Am., 1995, 97(5): 2804-2814. 3. McDaniel, S. T., Seafloor reverberation fluctuations, J. Acoust. Soc. Am., 1990, 88(3): 1530-1535. 4. Abraham, …     

UCN production in superfluid helium

Ultra-cold neutrons (UCN) are produced in superfluid helium by single- and multi-phonon excitation. The UCN production rate density R _II via multiphonons can be larger than that by one-phonon excitation R _I being due to the dependence of the incident neutron spectral flux density dφ/dλ on the wavelength λ. Received: 28 March 2002 / Accepted: 19 December 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: wschott@e18.physik.tu-muenchen.de RID="b" ID="b"On leave of absence from PNPI, Gatchina, Russia Communicated by T. Walcher     

On the Approximability by Finite p-Groups of Free Products of Groups with Normal Amalgamation

A sufficient condition for the residual p-finiteness (approximability by the class of finite p-groups) of a free product G = (A * B; H) of groups A and B with a normal amalgamated subgroup H is obtained. This condition is used to prove that if A and B are extensions of residually -groups by -groups, where stands for the class of finitely generated torsion-free nilpotent groups, and if H is a normal p′-isolated polycyclic subgroup, then the group G is residually p-finite (i.e., residually -group), provided the quotient group G/H ^p H′ is residually p-finite.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 125–131.Original Russian Text Copyright © 2005 by E. V. Sokolov.     

The Exact Value of Normal Structure Coefficients and WCS coefficients in a Class of Orlicz Function Spaces

Let φ be an N-function. Then the normal structure coefficients N and the weakly convergent sequence coefficients WCS of the Orlicz function spaces L ^φ[0, 1] generated by φ and equipped with the Luxemburg and Orlicz norms have the following exact values. (i) If F _φ(t) = t _?(t)/φ(t) is decreasing and 1 < C _φ < 2 (where \(C_\Phi = \lim _{t \to + \infty } t\varphi (t)/\Phi (t)\)), then N(L ^(φ)[0, 1]) = N(L ^φ[0, 1]) = WCS(L ^(φ)[0, 1]) = WCS(L ^φ[0, 1]) = 2^1?1/Cφ. (ii) If F _φ(t) is increasing and C _φ > 2, then N(L ^(φ)[0, 1]) = N(L ^φ[0, 1]) = WCS(L ^(φ)[0, 1]) = WCS(L ^φ[0, 1]) = 2^1/Cφ.     

Normal cirulant graphs with noncyclic regular subroups

We prove that any circulant graph of order n with connection set S such that n and the order of ?(S), the subgroup of ? that fixes S set‐wise, are relatively prime, is also a Cayley graph on some noncyclic group, and shows that the converse does not hold in general. In the special case of normal circulants whose order is not divisible by 4, we classify all such graphs that are also Cayley graphs of a noncyclic group, and show that the noncyclic group must be metacyclic, generated by two cyclic groups whose orders are relatively prime. We construct an infinite family of normal circulants whose order is divisible by 4 that are also normal Cayley graphs on dihedral and noncyclic abelian groups. © 2005 Wiley Periodicals, Inc. J Graph Theory     

The classical monotone convergence theorem of Beppo Levi fails in noncommutative -spaces

Let be a complex Hilbert space and let be a von Neumann algebra over equipped with a faithful, normal state . Then is a prehilbert space with respect to the inner product , whose completion is given by the Gelfand-Naimark-Segal representation theorem, according to which there exist a one-to-one -homomorphism of into the algebra of all bounded linear operators acting on and a cyclic, separating vector such that for all . Given any separable Hilbert space , we construct a faithful, normal state on and an increasing sequence of positive operators acting on such that is bounded, but fails to converge both bundlewise and in -norm. We also present an example of an increasing sequence of positive operators which has a subsequence converging both bundlewise and in -norm, but the whole sequence fails to converge in either sense. Finally, we observe that our results are linked to a previous one by R. V. Kadison.

     

Existence of Positive Solutions for N-term Non-autonomous Fractional Differential Equations

Existence of positive solutions for the nonlinear fractional differential equation D ^αu = f(x,u), 0 < α < 1 has been given (S. Zhang. J. Math. Anal. Appl. 252 (2000), 804–812) where D ^α denotes Riemann–Liouville fractional derivative. In the present work we extend this analysis for n-term non autonomous fractional differential equations. We investigate existence of positive solutions for the following initial value problem

Anharmonic resonances in the vibrational spectra of pyrazine

The quartic force field of pyrazine has been calculated in the B3LYP/6-31G(d) hybrid density-functional approximation. Based on the results of this calculation, the total IR (250–3800 cm^–1) and Raman (400–3200 cm^–1) spectra of pyrazine have been interpreted with consideration for the Fermi and Darling-Dennison resonances and their spectral manifestations. A precision method is proposed for anharmonic analysis of the vibrational states of polyatomic molecules on the basis of consideration of their theoretical anharmonicity constants in combination with the corresponding experimental frequencies. The method of linear scaling of frequencies has been theoretically substantiated.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 13–22, January–February, 2005.