On the way towards a generalized entropy maximization procedure

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptotically for q∈(0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.     

Fuzzy Kaluza-Klein induced M2?s from a single M5

We propose an algorithmic procedure of obtaining multiple M2 brane dynamics starting with an action of a single M5 brane. The procedure involves a novel Kaluza-Klein reduction. First, the M5 brane action is truncated to keep a few leading terms in the derivative expansion. Then 3+3 splitting of dimensions is carried out. With expansion in terms of the S² spherical harmonics, the fields are associated with SU(N) (or its infinite extension) gauge algebra. We present an elaborate reduction procedure that leads to ABJM theory when the fuzzy spherical harmonics are replaced by SU(N) gauge generators.     

Selection of jets in multihadron final states produced bye + e −-annihilation

Fore ⁺ e ^?-annihilations a procedure is described to select events of a given multiplicity of jets. The procedure is demonstrated by applying it to a Monte-Carlo sample ofe ⁺ e ^? multihadron final states. Selection of three jet events is shown to be somewhat better than more conventional techniques.     

A method of three-jet analysis ine + e − annihilation

For three-jet events ine ⁺ e ^? annihilation, a procedure is described to determine all three jet axes by minimizing the sum of squares of transverse momenta. Computations with this procedure show that at high energies the result is quite insensitive to missing particles, such as neurals.     

The Quantum N-Body Problem and the Auxiliary Field Method: New Developments

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and a connection is presented between the method and the generalized virial theorem. The procedure is applied to the case of baryons in the large-N _c limit.     

QCD analysis of the semi-inclusive COMPASS and HERMES data

The first moments of polarized valence parton distribution functions truncated to the wide Bjorken x region 0.004 < x < 0.7 are directly (without any fitting procedure) extracted in the NLO QCD from combined semi-inclusive DIS data of COMPASS and HERMES collaborations. Two scenarios for fragmentation functions are considered. Applying the proposed original procedure to these results we estimate the contributions of sea u and d quarks to the proton spin, which turn out to be simply zero within the errors.     

A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

A simple procedure for electroluminescent phosphor assessment

A simple assessment procedure is described which facilitates optimal selection of an electroluminescent phosphor based on the measurement of two optically deduced energies—absorption and emission. These two energies are used as input for an appraisal analysis based on a classical configuration-coordinate diagram model of the phosphor. A phosphor performance figure-of-merit is proposed as a consequence of the formulation of this assessment procedure. This procedure is then used to rationalize the relative performance of five electroluminescent phosphors (ZnS:Mn, BaAl₂S₄:Eu, SrS:Ce, SrGa₂S₄:Ce, CaGa₂S₄:Ce). Additionally, two cathodoluminescent phosphors (ZnS:Ag and ZnS:Cu) are appraised using this methodology, suggesting that this procedure may be of some utility in the evaluation of other types of phosphors.     

On the Renormalized Volume of Hyperbolic 3-Manifolds

The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main aim of the present paper is to elucidate its geometrical meaning. We use another regularization procedure based on surfaces equidistant to a given convex surface ?N. The renormalized volume computed via this procedure is equal to what we call the W-volume of the convex region N given by the usual volume of N minus the quarter of the integral of the mean curvature over ?N. The W-volume satisfies some remarkable properties. First, this quantity is self-dual in the sense explained in the paper. Second, it verifies some simple variational formulas analogous to the classical geometrical Schläfli identities. These variational formulas are invariant under a certain transformation that replaces the data at ?N by those at infinity of M. We use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of Takhtajan et al on the Kähler potential on various moduli spaces.     

The exactness of the GCM description of the j3 and j4 systems

Under the single-j shell assumption, some typical cases of j³ and j⁴ are introduced as examples of the way in which the validity and exactness of the GCM (generator coordinate method) can be demonstrated. The exact solutions, equivalent to those from the shell model and exact NFT (nuclear field theory), are obtained within the actual procedure of effective GCM hamiltonian derivation, while the unphysical states are identified and discarded in this procedure naturally through performing diagonalization of the N-operator matrix.     

Solution based, RuHCl(CO)(PPh3)3 catalyzed hydrosilylation of alkynes onto Si(1 0 0) surfaces

In this communication we report a novel, technologically promising procedure able to graft alkynes onto Si(1 0 0) through the formation of direct Si-C bond. It results in the formation of grafted layers as FTIR measurements demonstrates. The advantages of this procedure compared to other available routes are that chemicals used are relatively harmless compared to those used in other wet chemical procedures; and that no surface pre-activation is required, the overall process being surface preserving, i.e. leading to no increase of surface roughness. Furthermore, the reaction mechanism guarantees full stereoselectivity. Therefore, gas sensors built using such a procedure are expected to show higher reliability and more stable electrical behavior.     

Extraction of optical constants from mid-IR spectra of small aerosol particles

A direct method for extracting optical constants in the mid-infrared (IR), using small particle's spectra is presented. The method is based on the direct extraction of the optical constants from the measured spectra using the Rayleigh approach for absorbance cross section of small particles. This was achieved by using an experimental system combining a scanning mobility particle sizing system attached to a long-path IR cell, allowing simultaneous measurements of aerosol size distribution and their IR spectra.The inversion procedure was tested on crystalline ammonium sulfate aerosols, for which high resolution set of optical constants was obtained and were found to be in good agreement with recently published data. Since the extraction of the k and n spectra is deduced from the refractive index dependent complex function, the exact band features can be obtained, unlike the commonly used iterative methods that modify simultaneously both band features and scale of k and n during the calculation procedure. The suggested procedure is simple to apply; nevertheless, it is sensitive to scaling errors of the final constants resulting from uncertainties in total particle volume measurements.     

RKR potentials and semiclassical centrifugal constants of diatomic molecules

Semiclassical formulas are obtained for the centrifugal constants D_v and H_v of a diatomic molecule by differentiation of the WKB quantization condition, and a numerical procedure is presented for the computation of these constants from the RKR turning points. A similar procedure also provides a simple and rapid method for the determination of the RKR turning points from the vibrational term values and rotational constants. Applications to carbon monoxide and iodine are discussed.     

Calculation of Coefficients of Fractional Parentage for Large-Basis Harmonic-Oscillator Shell Model

A new procedure for large-scale calculations of the coefficients of fractional parentage (CFPs) for a single j-orbit with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient method for constructing the eigenvectors of an idempotent matrix. We investigate the characteristics of the introduced CFP basis and the application of this procedure to the ab initio harmonic-oscillator shell-model approach. The results of CFP calculations for the j=1/2,…,41/2 orbits are presented (the full sets of one-particle and two-particle CFPs up to the j=9/2 orbit are obtained). The new computer code for calculation of the CFPs proves to be very quick, efficient, and numerically stable and produces results possessing only small numerical uncertainties.     

Application of infinite oscillator shell model calculations to the description of nuclear reactions

A simple R-matrix procedure is proposed to provide a means of using nuclear structure information, from calculations in an infinite oscillator well, to describe reaction cross sections. The procedure uses values for the channel radius parameters of the R-matrix theory that are extracted from knowledge of the structure and reaction properties of the neighbouring closed shell nucleus answering one of the main criticisms expressed concerning the dependence of the R-matrix on unphysical parameters. Application of the model to the scattering of neutrons from ¹⁵N and comparison to previous theoretical predictions are considered.     

On the phenomenological approach to dual resonance models for deep inelastic electroproduction

We outline a systematic procedure for constructing a dual resonance model for deep inelastic electroproduction which incorporates locality, current algebra, Regge behaviour, Bjorken scaling and the Dashen — Fubini — Gell-Mann sum rule. We illustrate the procedure in terms of a simple Ansatz for theW ₂ electroproduction structure function.     

Bag Scattering Theory

We reanalyze the procedure used thus far for the study of collision processes in the Chiral Bag Model from the point of view of scattering theory. In the present formalism thein andout states are free waves with no memory of the cavity. This feature gives rise to an observable effect consisting in a peculiar momentum dependence of the scattering amplitudes, which differs from that of previous calculations. The new procedure however does not change the magnitude of the pion-baryon coupling constants.     

Synthesis of new 1,5-diaryl-3-(arylamino)-1H-pyrrol-2(5H)-ones under catalyst-free and solvent-free conditions

Several new 1,5-diaryl-3-(arylamino)-1H-pyrrol-2(5H)-ones were synthesized via the three-component condensation reaction of aldehydes, aromatic amines, and ethyl pyruvate under catalyst-free and solvent-free conditions. Also, 5-(4-hydroxyl-3-nitrophenyl)-1-(4-methoxy-phenyl)-3-(4-methoxyphenylamino)-1,5-dihydro-pyrrol-2-one was synthesized using oxime instead of aldehyde. The eco-friendly, simple procedure, green procedure, catalyst-free and solvent-free conditions, short reaction times, and high yields of the products are the advantages of this method.     

Ultrasonic sizing of short surface cracks

This paper presents a method for ultrasonic sizing of surface cracks based on time domain and frequency domain Rayleigh wave near-field analysis. The procedure allows for the entire range of ratio of crack depth to Rayleigh wavelength a/λ to be covered with one single measurement. In the time domain the time-of-flight method was extended to cracks smaller than the wavelength by correlation of the time delay of the transmitted Rayleigh wave with the crack depth. In the frequency domain, the inverse scattering problem was solved by comparison of the measured scattering coefficients and central frequencies of the reflected and transmitted Rayleigh waves with theoretical curves. The sizing procedure was demonstrated experimentally with narrow slots and real fatigue cracks. The out-of-plane displacement component was measured pointwise in the scattered near field by means of laser interferometry. The determination of the scattering parameters in the near field was enabled by a procedure that allows for the Rayleigh wave to be separated from the other modes scattered at the defect. The experimental results showed good accuracy and repeatability down to the smallest available ratio of crack depth to Rayleigh wavelength a/λ = 0.15.     

Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multiscaling

We develop a consistent closure procedure for the calculation of the scaling exponents ζ _n of the nth-order correlation functions in fully developed hydro-dynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ _n . This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest non-trivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier–Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to non-Kolmogorov values of the scaling exponents ζ _n . Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.