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Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of sub-critical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here, we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them. [ABSTRACT FROM AUTHOR]

Line mixing effects in the Q branch of pure N2 isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N2 molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of the results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems. [ABSTRACT FROM AUTHOR]

We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559] for spectral measures of classical ensembles (Gauss–Hermite, Laguerre, Jacobi) and it was extended to spectral matrix measures of the Hermite and Laguerre ensemble in [Sum rules and large deviations for spectral matrix measures, Bernoulli 25(1) (2018) 712–741]. In this paper, we consider the remaining case of spectral matrix measures of the Jacobi ensemble. Our main results are a large deviation principle for such measures and a sum rule for matrix measures with reference measure the Kesten–McKay law. As an important intermediate step, we derive the distribution of matricial canonical moments of the Jacobi ensemble. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulation has been applied for water to compare the isotropic periodic sum (IPS) method [X. Wu and B. R. Brooks, J. Chem. Phys. 122, 044107 (2005)] with the Ewald sum based on the diffusion coefficient and liquid structure. The IPS method gives a good estimation for the self-diffusion coefficient at a cutoff radius, rc, greater than 2.2 nm; however, the radial distribution function g(r) has a notable deviation. The peak of this deviation appears at specific intermolecular distances which are near each cutoff radius and decrease in proportion to the inverse of the cube of rc. Thus the deviation becomes insignificant (less than 1%) at rc greater than 2.2 nm. The distance dependent Kirkwood factor Gk(r) was also calculated, and since the truncation of a long-range interaction of the cutofflike method (such as cutoff with or without the switch function and the reaction field) shows serious shortcomings for dipole-dipole correlations in bulk water systems, this was observed by comparing the shape to that of the Ewald sum [Y. Yonetani, J. Chem. Phys. 124, 204501 (2006); D. van der Spoel and P. J. van Maaren, J. Chem. Theory Comput. 2, 1 (2006)]. The Gk(r) of cutofflike method greatly deviate from that of the Ewald sum. However, the discrepancy of Gk(r) for the IPS method was found to be much less than that of other typical cutofflike methods. In conclusion, the IPS method is an adequately accurate technique for estimating transport coefficients and the liquid structure of water in a homogeneous system at long cutoff distances. [ABSTRACT FROM AUTHOR]

We present an analysis of the physics of intersubband transitions in a patterned inverse quantum dot (IQD) array. Numerical techniques for computing the oscillator strength for intersubband transitions are outlined along with the selection and sum rules. It is demonstrated that the polarization dependence of intersubband absorption can be controlled through appropriate design of the IQD array geometry. [ABSTRACT FROM AUTHOR]

The transmittance of silicon monoxide films prepared by thermal evaporation was measured from 7.1 to 800 eV and used to determine the optical constants of the material. SiO films deposited onto C-coated microgrids in ultrahigh vacuum conditions were measured in situ from 7.1 to 23.1 eV. Grid-supported SiO films deposited in high vacuum conditions were characterized ex situ from 28.5 to 800 eV. At each photon energy, transmittance, and thickness data were used to calculate the extinction coefficient k. The obtained k values combined with data from the literature, and with interpolations and extrapolations in the rest of the electromagnetic spectrum provided a complete set of k values that was used in a Kramers–Kronig analysis to obtain the real part of the index of refraction, n. Two different sum-rule tests were performed that indicated good consistency of the data. [ABSTRACT FROM AUTHOR]

New experimental data have been obtained for the methoxy radical by observing at high-resolution laser-induced fluorescence (LIF) and stimulated emission pumping (SEP) transitions between the X 2E and lowest excited à 2A1 state. The SEP transitions were from the à state (pumped from the X 2E3/2 spin-orbit component) to the X 2E1/2 spin-orbit component. These data for the first time directly connect with high precision the spin-orbit components of the X 2E ground state of CH3O. Surprisingly these new SEP observations are inconsistent with predictions of the X state structure based on long-standing analyses primarily based on the microwave spectra of ground state CH3O. It is found that all the experimental data can be understood consistently when the previously accepted value of the spin-orbit coupling constant is adjusted and the reflection parity assignments in the X state are reversed. The latter action changes the sign of a number of reflection-parity-dependent parameters in the X state. The ramifications of the changes and the physical interpretation of the resulting parameters are discussed in some detail. [ABSTRACT FROM AUTHOR]

A cavity ring-down spectrometer designed to investigate optical properties of size-selected clusters on surfaces under ultrahigh vacuum (UHV) conditions is presented. Clusters are produced using a laser vaporization cluster source with typical size-selected cluster currents of about 100 pA. The size of the deposition area can be controlled by means of a focusing octopole. Using the UHV compatible mirror exchanger, it is possible to have up to ten ring-down cavities and to adjust them while in vacuum. With ten cavities it is possible to cover a continuous spectral range as broad as 600 nm. The sensitivity of the method is shown to be about 5 ppm, which is two orders of magnitude better than commercial techniques. The optical spectra of small NiN clusters (N=7, 10, and 20) supported at amorphous SiO2 in the range between 417 and 669 nm are presented. Simple Mie theory calculations and oscillator-strength sum rule are in good agreement with the experimental data. The method proved to be sensitive enough for detection of defect sites and therefore makes it possible to study the interaction between the clusters and different surface defects. Furthermore the cryogenic sample holder can be used to perform cavity ring-down spectroscopy at low temperatures. [ABSTRACT FROM AUTHOR]

The maximum entropy analytic continuation (MEAC) and ring polymer molecular dynamics (RPMD) methods provide complementary approaches to the calculation of real time quantum correlation functions. RPMD becomes exact in the high temperature limit, where the thermal time βh tends to zero and the ring polymer collapses to a single classical bead. MEAC becomes most reliable at low temperatures, where βh exceeds the correlation time of interest and the numerical imaginary time correlation function contains essentially all of the information that is needed to recover the real time dynamics. We show here that this situation can be exploited by combining the two methods to give an improved approximation that is better than either of its parts. In particular, the MEAC method provides an ideal way to impose exact moment (or sum rule) constraints on a prior RPMD spectrum. The resulting scheme is shown to provide a practical solution to the “nonlinear operator problem” of RPMD, and to give good agreement with recent exact results for the short-time velocity autocorrelation function of liquid parahydrogen. Moreover these improvements are obtained with little extra effort, because the imaginary time correlation function that is used in the MEAC procedure can be computed at the same time as the RPMD approximation to the real time correlation function. However, there are still some problems involving long-time dynamics for which the RPMD+MEAC combination is inadequate, as we illustrate with an example application to the collective density fluctuations in liquid orthodeuterium. [ABSTRACT FROM AUTHOR]

The third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated at the Hartree–Fock level of theory in the Hellmann–Feynman approximation. The nuclear electric hypershieldings are closely related to molecular vibrational absorption intensities and a generalization of the atomic polar tensors (expanded in powers of the electric field strength) is proposed to rationalize these intensities. It is shown that the sum rules for rototranslational invariance and the constraints imposed by the virial theorem provide useful criteria for basis-set completeness and for near Hartree–Fock quality of nuclear shieldings and hypershieldings evaluated in the Hellmann–Feynman approximation. Twelve basis sets of different size and quality have been employed for the water molecule in an extended numerical test on the practicality of the proposed scheme. The best results are obtained with the R12 and R12+ basis sets, designed for the calculation of electronic energies by the explicitly correlated R12 method. The R12 basis set is subsequently used to investigate three other molecules, CO, N[sub 2], and NH[sub 3], verifying that the R12 basis consistently performs very well. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the connection between the spectral condition of an Hermite subdivision operator and polynomial reproduction properties of the associated subdivision scheme. While it is known that in general the spectral condition does not imply the reproduction of polynomials, we here prove that a special spectral condition (defined by shifted monomials) is actually equivalent to the reproduction of polynomials. We further put into evidence that the sum rule of order ℓ > d associated with an Hermite subdivision operator of order d does not imply that the spectral condition of order ℓ is satisfied, while it is known that these two concepts are equivalent in the case ℓ = d. Highlights • Certain spectral and polynomial reproduction properties of Hermite schemes are equivalent. • High order sum rules do not imply spectral conditions of the same order. • Polynomial generation implies spectral conditions. [ABSTRACT FROM AUTHOR]

This is an extension of the prediction of strange baryon decays to the decays of charmed baryons using QCD sum rules. Using QCD sum rules, we estimate the decay Λ c + (u d c) → Λ s o (u d s) + π + . Although some weak decays of the Λ c + have been measured, since it is difficult to measure Λ c + → Λ s o + π + our estimates should be useful for future experiments. [ABSTRACT FROM AUTHOR]

The strong coupling constant is an important parameter that can help us understand the strong decay behaviors of baryons. In our previous work, we have analyzed the strong vertices Σ c ∗ N D , Σ b ∗ N B , Σ c N D and Σ b N B in QCD sum rules. Following these works, we further analyze the strong vertices Σ c N D ∗ and Σ b N B ∗ using the three-point QCD sum rules under Dirac structures q / p / γ α and q / p / p α . In this work, we first calculate strong form-factors considering contributions of the perturbative part and the condensate terms 〈 q ̄ q 〉 , 〈 α s π G G 〉 and 〈 q ̄ g s σ G q 〉. Then, these form-factors are used to fit into analytical functions. According to these functions, we finally determine the values of the strong coupling constants for these two vertices Σ c N D ∗ and Σ b N B ∗ . [ABSTRACT FROM AUTHOR]

Abstract How to identify influential nodes in complex networks continues to be an open issue. A number of centrality measures have been presented to address this problem. However, these studies focus only on a centrality measure and each centrality measure has its own shortcomings and limitations. To solve problems above, in this paper, a novel method is proposed to identify influential nodes based on the inverse-square law. The mutual attraction between different nodes has been defined in complex network, which is inversely proportional to the square of the distance between two nodes. Then, the definition of intensity of node in a complex network is proposed and described as the sum of attraction between a pair of nodes in the network. The ranking method is presented based on the intensity of node, which can be considered as the influence of the node. In order to illustrate the effectiveness of the proposed method, several experiments are conducted to identify vital nodes simulations on four real networks, and the superiority of the proposed method can be demonstrated by the results of comparison experiments. Highlights • A novel method is proposed to identify influential nodes based on the inverse-square law. • The mutual attraction between two nodes is inversely proportional to the square of their distance. • The influence of a node is determined as based on its intensity. [ABSTRACT FROM AUTHOR]

We introduce an algebra model to study higher-order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum rules involving a Hall-Littlewood type polynomial. By this expression, we recover an earlier result by Golinskii and Zlatoš and prove a new case - half of the Lukic conjecture in the case of a single critical point with arbitrary order. [ABSTRACT FROM AUTHOR]

Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one‐component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self‐consistent method of moments, recently developed in Phys. Rev. Lett., 2017, 119, 045001, that provides a neat expression for the loss function valid at strong couplings. An input value of the method in its classical version is the static structure factor, whose accuracy is shown to insignificantly affect the resulting numerical data. Starting from the Cauchy‐Bunyakovsky‐Schwarz inequality, a criterion is proposed to verify the quality of various approaches to the evaluation of the static characteristics of one‐component, strongly coupled plasmas. [ABSTRACT FROM AUTHOR]

10 and 27 SU(3) multiplets of hexaquarks states with baryon number B = 2 , known as dibaryons, are considered. Previous analyses are complemented and sum rules for strong decay amplitudes with SU(3) symmetry violation up to the first order are determined for the 10 and 27 dibaryon multiplets into a baryon octet plus a baryon decuplet and for the dibaryon 27 into two baryon octets. [ABSTRACT FROM AUTHOR]

In this article, we construct the axialvector-diquark-scalar-antidiquarktype currents to interpolate the axialvector doubly heavy tetraquark states, and study them with the QCD sum rules in details by carrying out the operator product expansion up to the vacuum condensates of dimension 10. [ABSTRACT FROM AUTHOR]

General constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random-phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The second order polarization propagator approximation (SOPPA) has been applied to the calculation of the dynamic dipole polarizability, α(ω), of the molecules N2, C2H2, CO, and HCN. The dipole oscillator sum rules S(-4) and S(-6), which are the leading contributions to the Cauchy expansion of the polarizability, have also been evaluated at SOPPA level, using a polynomial fit to this expansion. These are the first reported values of the higher sum rules obtained using the SOPPA approach, and we observe excellent agreement with experiment. We also discuss the applicability of scaling or additivity expressions for obtaining the correlated polarizability from static correlated and dynamic uncorrelated quantities. [ABSTRACT FROM AUTHOR]

4D CFTs have a scale anomaly characterized by the coefficient c, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for c in terms of TTO OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the hTTTTi correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives c as a sum of positive terms, and therefore implies a lower bound on c given any lower bound on TTO OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor. [ABSTRACT FROM AUTHOR]

We put forward a new phenomenological method for calculating the slope of radial trajectories from values of ground states and vacuum condensates. The method is based on a large- extension of borelized spectral sum rules. The approach is applied to the light nonstrange vector, axial and scalar mesons. The extracted values of slopes proved to be approximately universal and are in the interval GeV2. As a by-product, the given method leads to prediction of the second radial trajectory with ground state mass lying near 0.6 GeV. [ABSTRACT FROM AUTHOR]

We investigate the polarized Bjorken sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2anQCD) and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3anQCD, 4l3anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e. and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2 and 3) are in good agreement with the experimental data for already when only one higher-twist term is used. In the low- regime , we use PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature. [ABSTRACT FROM AUTHOR]

The strong coupling constants of newly observed Ωc0 baryons with spins J=1/2 and J=3/2 decaying into Ξc+K- are estimated within light cone QCD sum rules. The calculations are performed within two different scenarios on quantum numbers of Ωc baryons: (a) all newly observed Ωc baryons are negative parity baryons; that is, the Ωc(3000), Ωc(3050), Ωc(3066), and Ωc(3090) have quantum numbers JP=1/2- and JP=3/2- states, respectively; (b) the states Ωc(3000) and Ωc(3050) have quantum numbers JP=1/2- and JP=1/2+, while the states Ωc(3066) and Ωc(3090) have the quantum numbers JP=3/2- and JP=3/2+, respectively. By using the obtained results on the coupling constants, we calculate the decay widths of the corresponding decay. The results on decay widths are compared with the experimental data of LHC Collaboration. We found out that the predictions on decay widths within these scenarios are considerably different from the experimental data; that is, both considered scenarios are ruled out. [ABSTRACT FROM AUTHOR]

The large- masses of light vector, axial, scalar and pseudoscalar mesons are calculated from QCD spectral sum rules for a particular ansatz interpolating the radial Regge trajectories. The ansatz includes a linear part plus exponentially degreasing corrections to the meson masses and residues. The form of corrections was proposed some time ago for consistency with analytical structure of Operator Product Expansion of the two-point correlation functions. We revised that original analysis and found the second solution for the proposed sum rules. The given solution describes better the spectrum of vector and axial mesons. [ABSTRACT FROM AUTHOR]

The strong coupling constants not only are important to understand the strong interactions of the heavy baryons, but can also help us reveal the nature and structure of these baryons. Additionally, researchers indeed have made great efforts to calculate some of the strong coupling constants, , , , , , , , , , , , , , , , etc. In this paper, we analyze the strong vertices and using the three-point QCD sum rules under the Dirac structure of . We perform our analysis by considering the contributions of the perturbative part and the condensate terms of and . After the form factors are calculated, they are then fitted into analytical functions which are used to get the strong coupling constants for these two vertices. The final results are and . [ABSTRACT FROM AUTHOR]

In this paper, we developed a combining classifier model based on tree-based algorithms for network intrusion detection. The NSL-KDD dataset, a much improved version of the original KDDCUP'99 dataset, was used to evaluate the performance of our detection algorithm. The task of our detection algorithm was to classify whether the incoming network traffics are normal or an attack, based on 41 features describing every pattern of network traffic. The detection accuracy of 89.24 % was achieved using the combination of random tree and NBTree algorithms based on the sum rule scheme, outperforming the individual random tree algorithm. This result represents the highest result achieved so far using the complete NSL-KDD dataset. Therefore, combining classifier approach based on the sum rule scheme can yield better results than individual classifiers, giving us hope of better anomaly based intrusion detection systems in the future. [ABSTRACT FROM AUTHOR]

We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tensors of the CFT ( t and t). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just $$ \frac{d}{2\left(d+1\right)} $$ . This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in AdS black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in AdS black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in d ≥ 4. Evaluating the parameters t and t for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms. [ABSTRACT FROM AUTHOR]

The hadronic matrix elements of dimension-six ∆ F = 0, 2 operators are crucial inputs for the theory predictions of mixing observables and lifetime ratios in the B and D system. We determine them using HQET sum rules for three-point correlators. The results of the required three-loop computation of the correlators and the one-loop computation of the QCD-HQET matching are given in analytic form. For mixing matrix elements we find very good agreement with recent lattice results and comparable theoretical uncertainties. For lifetime matrix elements we present the first ever determination in the D meson sector and the first determination of ∆ B = 0 matrix elements with uncertainties under control - superseeding preliminary lattice studies stemming from 2001 and earlier. With our state-of-the-art determination of the bag parameters we predict: τ( B )/ τ( B ) = 1.082, τ( B )/ τ( B ) = 0.9994 ± 0.0025, τ( D )/ τ( D ) = 2. 7 and the mixing-observables in the B and B system, in good agreement with the most recent experimental averages. [ABSTRACT FROM AUTHOR]

The problem of determining the magnitude of the atomic magnetic moments in compounds with rare-earth and transition elements using the X-ray magnetic circular dichroism (XMCD) is investigated. The standard sum rules approach usually gives the moment values by several times smaller than their bulk values obtained from the direct magnetic measurements. We attribute this to the strong spin fluctuations in the surface layer which actually formed the soft XMCD signal. A method of determining the value of the local magnetic moments in the presence of strong fluctuations is proposed. The magnetic interactions in La 0.5 Pr 0.2 Ca 0.3 MnO 3 are investigated by x-ray absorption spectroscopy, XMCD and bulk magnetization measurements. The proposed procedure is used to determine the values of atomic magnetic moments of transition and rare-earth elements as well as net magnetization on the surface and in the bulk from experimental Mn L 2,3 and Pr M 4,5 XMCD spectra. [ABSTRACT FROM AUTHOR]

The Principle of Maximum Conformality (PMC) provides scale-fixed perturbative QCD predictions which are independent of the choice of the renormalization scheme, as well as the choice of the initial renormalization scale. In this article, we will test the PMC by comparing its predictions for the strong coupling α g 1 s ( Q ) , defined from the Bjorken sum rule, with predictions using conventional pQCD scale-setting. The two results are found to be compatible with each other and with the available experimental data. However, the PMC provides a significantly more precise determination, although its domain of applicability ( Q ≳ 1.5 GeV) does not extend to as small values of momentum transfer as that of a conventional pQCD analysis ( Q ≳ 1 GeV). We suggest that the PMC range of applicability could be improved by a modified intermediate scheme choice or using a single effective PMC scale. [ABSTRACT FROM AUTHOR]

Numerically exact nonadiabatic eigenfunctions are computed for a two-dimensional conical intersection with circular symmetry, for which a pseudorotation quantum number is conserved and all eigenstates are doubly degenerate. In the calculations reported here, the conical intersection is submerged, with energy below the zero point level. The complete real-valued vibrational-electronic eigenfunctions are visualized using Hunter's exact factorization for the total vibrational amplitude factor and color for the electronic factor. The zero-point levels have nonzero amplitude at the conical intersection. Nodes in the degenerate nonadiabatic eigenfunctions are classified as accidental if they can be moved or removed by a change in degenerate basis and as essential if they cannot. An integer electronic index defines the order of the nodes for nonadiabatic eigenfunctions by simple closed counterclockwise line integrals. Higher eigenstates can have accidental conical nodes around the conical intersection and essential nodes of varying circular orders at the conical intersection. The signs of the essential nodes are all opposite the sign of the conical intersection and the signed node orders obey sum rules. Even for submerged conical intersections, the appearance of the exact eigenstates motivates use of signed, half-odd-integral, pseudorotation quantum numbers j. Essential nodes of absolute order (|j| - 1/2) are located on the conical intersection for |j| greater than or equal to 3/2. The eigenfunctions around essential first order nodes are right circular cones with their vertex at the conical intersection. [ABSTRACT FROM AUTHOR]

We present a model to calculate the electrical and thermal electronic conductivities in plasmas using the Chester-Thellung-Kubo-Greenwood approach coupled with the Kramers approximation. The divergence in photon energy at low values is eliminated using a regularization scheme with an effective energy-dependent electron-ion collision-frequency. Doing so, we interpolate smoothly between the Drude-like and the Spitzer-like regularizations. The model still satisfies the well-known sum rule over the electrical conductivity. Such kind of approximation is also naturally extended to the average-atom model. A particular attention is paid to the Lorenz number. Its nondegenerate and degenerate limits are given and the transition towards the Drude-like limit is proved in the Kramers approximation. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the family of Deslauriers-Dubuc's interpolatory masks from dimension one to arbitrary dimensions with respect to the quincunx dilation matrices, thereby providing a family of quincunx fundamental refinable functions in arbitrary dimensions. We show that a family of unique quincunx interpolatory masks exists and such a family of masks is of real value and has the full-axis symmetry property. In dimension d = 2, we give the explicit form of such unique quincunx interpolatory masks, which implies the nonnegativity property of such a family of masks. [ABSTRACT FROM AUTHOR]

The electric field dependence of the dielectric properties below 50 K along the chain direction of o -TaS 3 has been investigated. Under a dc bias field exceeding the lower threshold E ′ T , the real part of dielectric constant ϵ 1 ( ω ) decreases possibly due to the decreasing concentration of bound solitons. We propose that the delocalization of bound solitons with the increasing applied electric field could be used to explain the reduction of ϵ 1 ( ω ) and the enhancement of the dc conductivity. This has also been confirmed by the quantitative comparison between the enhancement of the dc conductivity and the change of the dielectric spectral weight. [ABSTRACT FROM AUTHOR]