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In this paper, the issue of exponential stabilization and sampled-data controller design for Takagi–Sugeno fuzzy large-scale networked control systems is studied by using the reduction-based ordinary differential equation prediction method. For the problem that matrices cannot be multiplied directly during the process of designing the sampled-data controller in this paper, a matrix dimensional transformation method is proposed. Firstly, a type of two-sided mode-dependent loop-based Lyapunov–Krasovskii functional is constructed, which compensates for the large delay and makes fuller use of the information in sampled-data interval. Secondly, the proposed method is used to give the design scheme of an aperiodic sampled-data controller, and furthermore, an iterative algorithm to verify the effectiveness of the requested control gains is provided. Finally, two coupled vehicle pendulum systems and two-area interconnected power systems are applied to demonstrate the efficiency of the presented approach. [ABSTRACT FROM AUTHOR]

We utilize a previously constructed thermodynamic T-matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T-matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results. [ABSTRACT FROM AUTHOR]

A solution to the electrostatic problem for the spheroidal particle with a spherical core is constructed. To involve the problem geometry in a full manner, in a vicinity of the particle surface the potentials of the fields are represented by their expansions in terms of spheroidal harmonics of Laplace equation, while in a vicinity of the core surface by the expansions in terms of spherical harmonics. Matching of the fields inside the particle shell is made by using the relations between the spheroidal and spherical harmonics. The T-matrix relates the coefficients of expansions of the incident and "scattered" fields. In the present paper, both the particle polarizability related to the main matrix element T11, and the whole T-matrix are considered. The symmetry of the matrix as well as its dependence on the size of the layered particle are shown. A relationship between the T-matrices in the spherical and spheroidal systems was also found. Numerical calculations made for particles of small and large aspect ratios (a/b = 1.5 − 5.0) confirmed high efficiency of the suggested solution in contrast to the methods that use a single spherical basis. [ABSTRACT FROM AUTHOR]

The relations between the T-matrices emerging when solving the problem of light scattering by a spheroid by applying the expansions of the electro-magnetic fields in the employing spheroidal and spherical bases are found. The behavior of the obtained relations is numerically studied, and it is noted that in a wide range of the task parameter values the calculation of the spheroidal T-matrix and its corresponding transformation is the only practical way to derive the spherical T-matrix often used in applications. [ABSTRACT FROM AUTHOR]

The rough hailstone scattering library is created to fill the need for results of non-spheroidal hailstone backscattering characteristics. The listed backscattering coefficients at the S-band (2.8 GHZ) are specifically tailored for computing the polarimetric variables. The National Weather Service's radar operates in this band; hence the library is pertinent to those studying hail in the USA. The library contains several axis ratios and a range of hail sizes from 5 mm to 100 mm. Moreover, hailstone surface roughness is expressed as a percentage of the equatorial diameter. Our computational electromagnetic approach to modeling hailstones is compared with typically employed simpler methods. The polarimetric variables calculated using our models can be compared to observations. Furthermore, we illustrate the potency of the CEM approach to hydrometeors with extreme axis ratios for which simpler methods (i.e., the T-matrix) fail. [ABSTRACT FROM AUTHOR]

The extended quasiparticle picture is adapted to non-Fermi systems by suggesting a Padé approximation which interpolates between the known small scattering-rate expansion and the deviation from the Fermi energy. The first two energy-weighted sum rules are shown to be fulfilled independent of the interpolating function for any selfenergy. For various models of one-dimensional Fermions scattering with impurities the quality of the Padé approximation for the spectral function is demonstrated and the reduced density matrix or momentum distribution is reproduced not possessing a jump at the Fermi energy. Though the two-fold expansion is necessary to realize the spectral function and reduced density, the extended quasiparticle approximation itself is sufficient for the description of transport properties due to cancellation of divergent terms under integration. The T-matrix approximation leads to the delay time as the time two particles spend in a correlated state. This contributes to the reduced density matrix and to an additional part in the conductivity which is presented at zero and finite temperatures. Besides a localization at certain impurity concentrations, the conductivity shows a maximum at small temperatures interpreted as onset of superconducting behaviour triggered by impurities. The Tan contact reveals the same universal behaviour as known from electron–electron scattering. [ABSTRACT FROM AUTHOR]

This paper studies the control problem of continuous interval type 2 fuzzy singular fractional-order systems with order 0 < α < 1. A dynamic output feedback control strategy is proposed to solve it. The advantages of our approach with respect to the existing results are threefold. First, the control design allows mismatched membership functions between the controller and the plant, thus enhancing its universality. Second, some specific assumptions on the system matrix are removed, hence improving the generality of our approach. Third, for ease of calculation of the controller gains, the equivalent transformation method and the linear matrix inequality technique are adopted, instead of iterative algorithms or singular value decomposition technique. The simulation results are given to show the effectiveness and the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the temperature dependence of defect modes of several one-dimensional superconducting-dielectrics photonic crystals was studied implementing the matrix transformation method. The thermo-optical effect and the thermal expansion effect were considered for a closer look (to obtain more accurate results). The studied photonic crystals contained SiO2 (L), Bi4Ge3O12 (H), MoSe2 (M) dielectrics, and the YBa2Cu3O7 (S) superconductor. Our results indicated that among the considered photonic crystals, the (HLM)NS(MLH)NL structure had the most temperature sensitivity, which could be applied as a low-temperature sensor and a tunable filter. The thickness of the layers was assumed in the nano-meter range. In order to validate our method, we compared our simulation result with an available experimental data in the literature. [ABSTRACT FROM AUTHOR]

The closed-form analytical expressions for the off-shell solutions for Hulthén-distorted Yamaguchi potential are derived to deal with the charged hadron systems. To construct these solutions, the particular integrals of the non-homogeneous Schrödinger equations are utilised in conjunction with the interacting Green’s functions. The Jost functions thus obtained, both on- and off-shell, are exploited to find the half-off-shell T-matrix. The off-shell Jost function exists but off-shell Jost solution for the said potential has not yet been discussed in the literature. The merits of the T-matrix are examined through some model calculations. Exploiting the expressions for on- and half-shell transition matrices, the s-wave elastic and inelastic scattering cross-sections are also estimated. Our results for the proton–proton and proton–oxygen systems are in close agreement with other calculations. [ABSTRACT FROM AUTHOR]

In this work, exact analytical expressions for regular solution and on-shell Jost function are calculated for nuclear Hulthén plus atomic Hulthén potential by imposing the same range approximation to both nuclear and atomic potentials. In this context, the regular solution is utilised to find expressions for the off-shell Jost function and half-shell T-matrix. The half-off-shell T-matrix and the elastic scattering phase shifts for the nucleon–nucleon and nucleus–nucleus systems are computed. Our results are found to be in good agreement with the standard data. [ABSTRACT FROM AUTHOR]

Typically, an 8 × 8 substitution box (S-box) is a square matrix of order 16 designed over Galois field GF(28) having binary field F2 algebra. A 24 by 24 S-box over GF(224) is not effective as it covers a large computer memory. The finite commutative chain ring is primarily an algebra over F2. In this work, we take the benefit and establish a new scheme of 24-by-24-replacement-matrix (Customarily known as an S-box (the only non-linear component of block ciphers)) design over commutative chain ring of the form F 2 u < u 24 > . The designed S-box shows high confusion ability than any customarily S-boxes. To gauge this effect, various digital astronomical RGB images are encrypted and compared with some existing S-box based encrypted images. In the planed ciphering scheme, firstly, we extract different layers of a color astronomical image and then concatenate the layers to form a 256 × 256 matrix having each entry of 24-bits. Thus, a novel method of RGB image ciphering scheme is functionalized that use 24 binary bits instead of 8 bits. Diffusion is attained by applying the linear permutation P = (i × 32) mod 257 and finally, an operation of bitwise Exclusive-or is performed. Results of analysis guarantees that the suggested encryption scheme approach to the peak values and may replace many S-box based image encryption techniques. [ABSTRACT FROM AUTHOR]

New analytical expressions for the off-shell wave functions and T-matrix with the Manning–Rosen potential are constructed in terms of generalised hypergeometric functions. The off-shell T-matrices are computed for the neutron–proton and neutron–deuteron systems. The limiting behaviours of our expression for the off-shell T-matrix are verified and found correct. [ABSTRACT FROM AUTHOR]

We discuss an alternative scheme for including effective range corrections in pionless effective field theory. The standard approach treats range terms as perturbative insertions in the T-matrix. In a finite volume this scheme can lead to singular behavior close to the unperturbed energies. We consider an alternative scheme that resums the effective range but expands the spurious pole of the T-matrix created by this resummation. We test this alternative expansion for several model potentials and observe good convergence. [ABSTRACT FROM AUTHOR]

Amplitudes of the form γ ∗ (q 2) → γ P 1 P 2 appear as sub-processes in the computation of the muon g - 2 . We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at q 2 = m ϕ 2 . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low's soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of P 1 P 2 = π η , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from γ γ scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the I = 1 scalar form factors and to the a 0 (980) resonance complex pole are presented. [ABSTRACT FROM AUTHOR]

When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linear regression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer's rule and matrix and propose the Cramer's rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation. [ABSTRACT FROM AUTHOR]

Exact analytical expressions of the Fredholm determinants for the Hulthén-modified separable nonlocal potential with regular, irregular, and physical boundary conditions are constructed in terms of the generalized hypergeometric functions. Exploiting the regular solution, the off-shell Jost function and half-shell T-matrix are obtained in maximal reduced form. The T-matrix and the elastic scattering phase shifts for the nucleon-nucleus and nucleus-nucleus systems are computed. Good agreement with standard data in phase shift results is obtained. [ABSTRACT FROM AUTHOR]