On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

Defect-level analysis of semiconductors by a new differential evaluation ofn(1/T)-characteristics

A new method for the defect-level analysis of extrinsic semiconductors is described. Provided that the defect-level concentration is not too large and the temperature is not too low, the Fermi levelE _F is shifted with increasing temperature from a position near the conduction (or valence) band towards the middle of the forbidden gap monotonously. Thus majority carriers are emitted into the conduction (or valence) band from the defect levels successively. If for a small increment of the temperature the Fermi levelE _F is shifted by ΔE _F and the concentration of free majority carriers is increased by Δn, then the ratio Δn/ΔE _F is a measure of the defect-level concentration within ΔE _F . Furthermore we discuss how this analysis is influenced by additional defect levels outside the range over which the Fermi energy can be shifted by variation of the temperature.     

Suppression of Noise Effects in Color Correction by Spectral Sensitivities of Image Sensors

The accurate transformation of device responses to tristimulus values is important at an early stage in color management and this transformation is usually called color correction. In this paper it is shown that the influence of noise on color correction can be suppressed if the square of the singular values by the singular value decomposition (SVD) of a sensor matrix represented by surface reflectance, SLVA^1/2, is larger than the noise variance, where S is the M × N matrix of M channel spectral sensitivities, L is the N × N diagonal matrix for an recording illuminant, V is the N × N matrix which is composed of eigenvectors of an autocorrelation matrix for spectral reflectance of samples, A is the N × N diagonal matrix with eigenvalues of the autocorrelation matrix along the diagonal and N is the number of the dimension, respectively. A method to suppress the influence of noise on color correction by spectral sensitivities of sensors is presented for the first time.     

Multi-affinity and multi-fractality in systems of chaotic elements with long-wave forcing

Multi-scaling properties in quasi-continuous arrays of chaotic maps driven by long-wave random force are studied. The spatial pattern of the amplitude X(x,t) is characterized by multi-affinity, while the field defined by its coarse-grained spatial derivative exhibits multi-fractality. The strong behavioral similarity of the X- and Y-fields respectively to the velocity and energy dissipation fields in fully-developed fluid turbulence is remarkable, still our system is unique in that the scaling exponents are parameter-dependent and exhibit nontrivial q-phase transitions. A theory based on a random multiplicative process is developed to explain the multi-affinity of the X-field, and some attempts are made towards the understanding of the multi-fractality of the Y-field. Received 16 November 1998     

A Perturbative Approach for the Asymptotic Evaluation of the Neumann Value Corresponding to the Dirichlet Datum of a Single Periodic Exponential for the NLS

Boundary value problems for the nonlinear Schrödinger equation formulated on the half-line can be analyzed by the Fokas method. For the Dirichlet problem, the most difficult step of this method is the characterization of the unknown Neumann boundary value. For the case that the Dirichlet datum consists of a single periodic exponential, namely, a exp(iωt), a, ω real, it has been shown in [2–4] that if one assumes that the Neumann boundary value is given for large t by c exp(iωt), then c can be computed explicitly in terms of a and ω. Here, using the perturbative approach introduced in [16], it is shown that for typical initial conditions, it is indeed the case that at least up to third order in a perturbative expansion the Neumann boundary value is given by c exp(iωt) and the value of c is at least up to this order the value found in [2–4].     

Reply to a note by T. G. Shepherd

Summary In a recent note by Shepherd it is claimed that the main conclusions discussed in a paper by Petroniet al. about certain instability mechanisms for steady equivalent barotropic flows are incorrect and, although no criticism is made regarding the analytical treatment, two counterexamples are presented to support this thesis. In addition to this it is asserted that the envisaged necessity for energy and enstrophy to be transferred in both spatial directions in a normal-mode instability is ?extremely well known?. Here we demonstrate that Shepherd's conclusions are without foundation and confirm the validity and originality of Petroniet al. results by showing that:a) the first counterexample describes a situation that is in fact provided for by Petroniet al.'s analysis;b) the second counterexample is not dynamically realizable and, even if it were, the related conclusions would not apply to flows defined in doubly periodic or bounded domains such as those considered by Petroniet al.; c) the mechanism cited above is not known at all in the specific context dealt with by Petroniet al. We emphasize this by pointing out that for steady equivalent barotropic flows the range of parameters for which such an instability mechanism is allowed complements exactly the range for which the steady states are stable according to Benziet al.     

Modeling 1/f noise using moving averages

A model of 1/f noise is considered, based on moving averages of ordern. The coefficientsα _k defining the model are calculated numerically using Seidel iteration which turns out to converge rapidly. The convergence is independent ofn which seems to be caused by the fact that the nonlinear problem solved is defined by a self-similar matrix. The coefficientsα _k appear to approach, with indefinitely growingn, valuesα _k =1/√k and thus the model has a kind of Fourier invariance. Physical interpretation of the invariance is suggested as well as of coefficientsα _k describing long-range correlations. Fractal sets of dimensiond=2.5 are proposed to play certain role in explaining the latter. This work was partly supported by the Scientific Grant Agency of the Ministry of Education of Slovak Republic (VEGA) under the Grant No. 1/3143/96 and by the Slovak Literary Fund.     

Automorphisms of the affineSU(3) fusion rules

We classify the automorphisms of the (chiral) level-k affineSU(3) fusion rules, for any value ofk, by looking for all permutations that commute with the modular matricesS andT. This can be done by using the arithmetic of the cyclotomic extensions where the problem is naturally posed. Whenk is divisible by 3, the automorphism group (Z ₂) is generated by the charge conjugationC. Ifk is not divisible by 3, the automorphism group (Z ₂×Z ₂) is generated byC and the Altschüler-Lacki-Zaugg automorphism. Although the combinatorial analysis can become more involved, the techniques used here forSU(3) can be applied to other algebras.     

250步混沌强度解析混沌特征及其在心率研究中的应用

应用250步混沌强度分析Lorenz系统，分别对3维和x分量进行了计算表明，250步混沌强度与Lorenz系统的参数有明显关系.计算了正常人的窦性心率的250步混沌强度，得到了它与年龄的关系：y=6.4623-0.0496x，相关系数为-0.669，这一结果支持了Goldberger的观点，如果人的250步混沌强度照此规律衰减，将在130岁降到0.     

Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s ₀), where B is a Boolean algebra and s ₀ is a state on B.     

Induced Smectic-G Phase Through Intermolecular Hydrogen Bonding,Part XIII: Impact of a Nematogen on Phase Behaviour of Hydrogen-Bonded Liquid Crystals

A series of hydrogen-bonded mesogens, p-( p′-methoxybenzylidene)-cyanoaniline:p-n-alkoxybenzoic acids (MBCA:nABA), is synthesised by using liquid-crystalline p-n-alkoxybenzoic acids (nABA) (where n represents alkoxy carbon numbers, 3-10 and 12) and a nematogen, p-( p′-methoxybenzylidene)-cyanoaniline (MBCA). The thermal and phase behaviour of these compounds is studied by thermal microscopy (TM) and differential scanning calorimetry (DCS) techniques. These studies reveal the induction of smectic-G phase in all the compounds. The structural elucidation pertaining to the formation and stabilisation of intermolecular hydrogen bonding is carried out by a detailed IR spectral investigation. The impact of imino group of the nematogen, MBCA, on the liquid-crystallinity of the present series is realised from the comparative studies made on the reported analogous series, p-aminobenzonitrile:p-n-alkoxybenzoic acids (ABN:nABA).     

A quasi analytical method for the calculation of virial coefficients for realistic intermolecular potentials

The difficulties of accurately representing the Ursell function, f, for molecules interacting with a Lennard-Jones potential by a hard sphere core and a truncated exponential series are discussed. The range of R for which a hard sphere approximates f with negligible error is established and the range of arguments in f is determined. The accuracy with which the exponential series, S_k , truncated after k terms, represents the function is established for several ranges of arguments. It is shown that it is possible to represent f accurately by a hard sphere core and S ₄ or S ₆ for all values of R except over a short range of R.

Values of B and C, accurate to within a few per cent, can be obtained analytically through approximating f by S ₄ or S ₆ and a hard core whose diameter is determined by the range of arguments for which the series is valid. More accurate values of B and C required additional approximations for f. Two of these, the repulsive square well and the Barker-Henderson radius, give accurate values of B and C at all temperatures that were examined.     

On extending the applicability of the initial rise method for thermoluminescence glow peak analysis

We discuss an approach by which the initial rise (IR) method can be extended to evaluate the frequency factor (s) of a glow peak, in addition to activation energy (E) that is usually obtainable from it. The approach requires that the phosphor be irradiated to a dose near or equal to the saturation dose of the glow peak to be analyzed. By plotting ln(I) against 1/T for the thermoluminescence glow peak, one obtains a straight line whose gradient is ? E/k and intercept is ln(n ₀ s/β) from which E and s are determined respectively. The approach was used to analyze two numerically generated glow peaks and reproduce with reasonably good accuracy the E and s values used to generate the glow peaks. It is also shown that when it becomes necessary to include intensities above 10% of the maximum glow peak intensity, the error introduced into the calculated frequency factor by the assumption n? n ₀ is always negligible when the analysis is done by plotting ln(I/n) against 1/T. In this case the frequency factor is obtained from ln(s/β) which is now the intercept. Two experimental glow peaks were also analyzed using the new IR method approach and peak shape method. Good agreement, which again shows the validity and reliability of the present approach was observed between the values of E and s obtained by the two methods.     

One-step phase shift 3-D surface profilometry with grating projection

A 3-D profiling system has been developed using a grating projection approach and a one-step phase shift algorithm. In the system, a grating pattern projected on an object surface is acquired by a CCD camera, and the grating's phase deformation caused by the surface shape is extracted by spatial phase shift processing, which uses only one frame of digital image. One phase value can be calculated from a successive 3-pixel range if the fringe period is set to either 4-pixel width or 8-pixel width. The fixed phase distribution of the system is excluded by a standard plane calibration. With 8-bit input data, the system's RMS phase accuracy is developed up to 2π/60 in the experimental examinations.     

Counting operator analysis of the discrete spectrum of some model Hamiltonians

The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates operators R and R^† which share some of the properties of creation and annihilation operators, and are such that M becomes a counting operator. The spectrum of H is then decomposed into multiplets, not determined by symmetries of H, but by those of a reference Hamiltonian H_ref, which is defined by H_ref=H−R−R^†, and which commutes with M. Finally, we introduce the notion of stable eigenstates. It is shown that under rather weak conditions one stable eigenstate can be used to construct another one.     

Cantor–Bernstein Theorem for Pseudo-BCK-Algebras

We prove that if A and B are orthogonally σ-complete commutative pseudo-BCK-algebras such that A is isomorphic to a direct factor in B, and also B is isomorphic to a direct factor in A, then A and B are isomorphic. As a consequence we obtain previously known results for MV-algebras (by De Simone, Mundici and Navara), pseudo-MV-algebras (by Jakubík) and lattice-ordered groups (again by Jakubík). Supported by the Research and Development Council of the Czech Government, the research project MSM 6198959214.     

Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

Measurement of object height in emission electron microscopy

The possibility of measuring the height of an object in emission electron microscopy (EEM) is investigated. If the specimen is characterized by an equipotential surface with the relief h(x,y), the image is equivalent to a specimen with an ideal flat surface and a corresponding distribution of the electric potential φ(x,y)=−E _ext h(x,y). As a consequence of the interaction with the microfields grad φ(x,y), the trajectories of electrons forming the image become deformed, which leads to characteristic image distortion. From EEM, images obtained at different voltages of the extractor V _ext,φ(x,y) can be derived and thereby h(x,y) is reconstructed. If the surface of the specimen is characterized both by a distribution of the potential and in addition by a relief h(x,y), then for the reconstruction one needs an additional EEM image taken at a different voltage of the extractor. The maximal sensitivity to microfields/relief is exploited when using the electron microscope in the mirror operation mode. We illustrate the performance of the method by means of a test pattern of Au on Si. For quantitative comparison, the same structure was investigated by atomic force microscope.     

Analytic study of the Migdal-Kadanoff recursion formula

After proposing lattice gauge field models in which the Migdal renormalization group recursion formulas are exact, we study the recursion formulas analytically. IfD is less than 4, it is shown that the effective actions ofD-dimensionalU(1) lattice gauge models are uniformly driven to the high temperature region no matter how low the initial temperature is. If the initial temperature is large enough, this holds for anyD and gauge groupG. These are also the cases for the recursion formulas of Kadanoff type. It turns out, however, that the string tension forD=3 obtained by these methods is rather big compared with the one already obtained by Mack, Göpfert and by the present author. The reason is clarified.On leave of absence from: Dept. of Maths. Bedford College, Regents Park, London NW 1, England