On the calculation of multiplicities for representations of SU(n)

For some family of representations of SU(n) the explicit formulae for the multiplicity of a given representation in arbitrary tensor product are derived. The adjoint representation and the representations acting in the symmetrical and antisymmetrical tensors are contained in the considered family as the simplest cases.     

Macroion effective charge in complex plasmas with regard to microion correlations

In the present paper, features of high-charged macroions screening by microions are analysed in classical asymmetrically charged complex plasmas. We consider a two-component electroneutral system of classical macroions and oppositely charged microions in a spherically symmetrical electroneutral Wigner–Seitz cell with a central macroion in its centre. The present paper is devoted to a problem of a relation between the effective macroion charge and an initial one with regard to a non-linear screening effect and microions correlations. We show how this relation changes with the number of the central macroion charge value on the rise. Characteristics of two different parts of the relation between the effective charge and the initial one are calculated.     

Statistical and Visual Analysis of Audio,Text, and Image Features for Multi-Modal Music Genre Recognition

We present a multi-modal genre recognition framework that considers the modalities audio, text, and image by features extracted from audio signals, album cover images, and lyrics of music tracks. In contrast to pure learning of features by a neural network as done in the related work, handcrafted features designed for a respective modality are also integrated, allowing for higher interpretability of created models and further theoretical analysis of the impact of individual features on genre prediction. Genre recognition is performed by binary classification of a music track with respect to each genre based on combinations of elementary features. For feature combination a two-level technique is used, which combines aggregation into fixed-length feature vectors with confidence-based fusion of classification results. Extensive experiments have been conducted for three classifier models (Naïve Bayes, Support Vector Machine, and Random Forest) and numerous feature combinations. The results are presented visually, with data reduction for improved perceptibility achieved by multi-objective analysis and restriction to non-dominated data. Feature- and classifier-related hypotheses are formulated based on the data, and their statistical significance is formally analyzed. The statistical analysis shows that the combination of two modalities almost always leads to a significant increase of performance and the combination of three modalities in several cases.     

PEGylated Luminescent Gold Nanoclusters: Synthesis,Characterization, Bioconjugation,and Application to One‐ and Two‐Photon Cellular Imaging

Biocompatible, near‐infrared luminescent gold nanoclusters (AuNCs) are synthesized directly in water using poly(ethylene glycol)‐dithiolane ligands terminating in either a carboxyl, amine, azide, or methoxy group. The ≈1.5 nm diameter AuNCs fluoresce at ≈820 nm with quantum yields that range from 4–8%, depending on the terminal functional group present, and display average luminescence lifetimes approaching 1.5 μs. The two‐photon absorption (TPA) cross‐section and two‐photon excited fluorescence (TPEF) properties are also measured. Long‐term testing shows the poly(ethylene glycol) stabilized AuNCs maintain colloidal stability in a variety of media ranging from saline to tissue culture growth medium along with tolerating storage of up to 2 years. DNA and dye‐conjugation reactions confirm that the carboxyl, amine, and azide groups can be utilized on the AuNCs for carbodiimide, succinimidyl ester, and Cu^I‐assisted cycloaddition chemistry, respectively. High signal‐to‐noise one‐ and two‐photon cellular imaging is demonstrated. The AuNCs exhibit outstanding photophysical stability during continuous‐extended imaging. Concomitant cellular viability testing shows that the AuNCs also elicit minimal cytotoxicity. Further biological applications for these luminescent nanoclustered materials are discussed.     

The generalization of SU(3)-mass formulae for arbitrary reductive lie algebras

The analogues of Gell-Mann-Okubo and Coleman-Glashow mass formulae are derived for arbitrary reductive Lie algebras.     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.     

Results on Biorthogonal Filter Banks

For a maximally decimated nonuniform filter bank, the perfect reconstruction (PR) property is equivalent to biorthogonality. We start from this result and derive a number of properties of PR filter banks. For example, no two integer decimators in a biorthogonal system can be coprime; moreover, if all analysis and synthesis filters have unit energy, then perfect reconstruction is equivalent to orthonormality. We also generalize the Nyquist and power complementary properties of orthonormal filter banks, for the biorthogonal case. We then show that whenever the decimation ratios are such that biorthogonality is possible with rational filters, it is, in particular, possible to obtain orthonormality with rational filters. This is done by developing an orthonormalization procedure. While reminiscent of the Gram–Schmidt approach, the procedure converges in a finite number of steps and furthermore preserves the filter-bank-like form of the basis functions. We also show how this technique can be applied for the decorrelation of subband signals. We will consider the problem of alias cancellation and obtain a generalization of a previously known necessary condition called compatibility.     

Strong electromagnetic field localization near the surface of hemicylindrical particles

We theoretically study the forward and backward plane wave illuminations of hemicylindrical dielectric particles with different radii and refractive indices. Near field effects providing strong field enhancement and narrow beam width are obtained from hemicylindrical particles, which can be associated with whispering gallery modes (WGMs) and photonic nano-jets (PNJs). It should be noted that existence of PNJ and WGM effects depending on forward/backward light illuminations is studied for the first time in all-dielectric hemicylindrical particles. Compared to dielectric cylinders, hemicylindrical aided PNJs show relatively small influences of WGM regime, when exists, to PNJ behavior. Under the backward excitation, on the other hand, typical nano-jet is produced. The designed hemicylindrical structure could be implemented in high-resolution optical imaging and sensing applications.     

Atmospheric aerosol limb scanning based on the lunar eclipses photometry

The work is devoted to the analysis of the surface photometric observations of two total lunar eclipses in 2004. The lunar surface relative brightness distribution inside the umbra was used to retrieve the vertical distribution of aerosol extinction of the solar radiation expanding by a tangent path and its dependence on the location at the limb of the Earth. The upper altitude of troposphere aerosol layer was estimated for different latitude zones. The correlation between additional aerosol extinction in the upper troposphere and cyclones was investigated.