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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 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]

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]

New expressions for the off-shell solutions of the Manning-Rosen potential are derived and make certain useful checks on their limiting behaviours to examine the correctness of our constructed expressions. The off-shell Jost function and the half-shell T-matrix thus obtained are found in order. [ABSTRACT FROM AUTHOR]

Based on the method of continued boundary conditions, two algorithms for the numerical solution of the problem of plane wave diffraction by a Janus sphere in the form of a permeable sphere partially covered by an absolutely soft or an absolutely rigid spherical screen have been developed. The calculation results obtained for the scattered field intensity using the proposed methods have been compared with results obtained by the T-matrix method. The accuracy of the fulfillment of the optical theorem and residual of the boundary condition in the case of the Dirichlet and Neumann conditions on the screen has been tested. The angular dependences of the scattered field intensity for different opening angles of the reflecting screen were constructed. [ABSTRACT FROM AUTHOR]

Classifying mental disorder is a big issue in psychology in recent years. This article focuses on offering a relation between decision tree and encoding of fMRI that can simplify the analysis of different mental disorders and has a high ROC over 0.9. Here we encode fMRI information to the power-law distribution with integer elements by the graph theory in which the network is characterized by degrees that measure the number of effective links exceeding the threshold of Pearson correlation among voxels. When the degrees are ranked from low to high, the network equation can be fit by the power-law distribution. Here we use the mentally disordered SHR and WKY rats as samples and employ decision tree from chi2 algorithm to classify different states of mental disorder. This method not only provides the decision tree and encoding, but also enables the construction of a transformation matrix that is capable of connecting different metal disorders. Although the latter attempt is still in its fancy, it may have a contribution to unraveling the mystery of psychological processes. [ABSTRACT FROM AUTHOR]

We theoretically investigate quantum conductance across a point contact between two strongly-interacting ultracold Fermi gases. We evaluate the tunneling current, taking into account pairing fluctuations in the Fermi gases within the framework of a combined strong-coupling T-matrix approximation with the Schwinger-Keldysh non-equilibrium formalism. We show that quasi-particle conductance is gradually suppressed, as one passes through the BCS–BEC crossover region from the weak-coupling side. On the other hand, with increasing the strength of a pairing interaction, the fluctuation-pair conductance is found to remarkably increase in the crossover region, which is followed by the suppression in the strong-coupling regime. [ABSTRACT FROM AUTHOR]

We revisit the information on the two lightest a 0 resonances and S-wave π η scattering that can be extracted from photon–photon scattering experiments. For this purpose we construct a model for the S-wave photon–photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic T-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV. We perform a combined fit of the γ γ → π η and γ γ → K S K S high statistics experimental data from the Belle collaboration. Minimisation of the χ 2 is found to have two distinct solutions with approximately equal χ 2 . One of these exhibits a light and narrow excited a 0 resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the J = 0 and J = 2 resonance effects which is likely to be unphysical. In both solutions the a 0 (980) resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be m - i Γ / 2 = 1000. 7 - 0.7 + 12.9 - i 36. 6 - 2.6 + 12.7 MeV. The solutions are also compared to experimental data in the kinematical region of the decay η → π 0 γ γ . In this region an isospin violating contribution associated with π + π - rescattering must be added for which we provide a dispersive evaluation. [ABSTRACT FROM AUTHOR]

In this paper, a multi-band metal-insulator-metal (MIM) perfect absorber with refractive index sensing capability has been investigated in near-infrared region. The proposed structure has been studied for biomedical applications such as detection of solution of glucose in water, diagnosis of different stages of malaria infection, bacillus bacteria and cancer cells. The MIM configuration improves the sensing parameters of the biosensor due to the good interaction with the analyte. The high sensitivity and figure of merit of 2000 nm/RIU and 100 RIU−1 have been achieved, respectively. Also, the Ag-air grating in the suggested plasmonic sensor helps the localized surface plasmons excitation and makes the structure sensitive to the incident lightwave polarization. Therefore, the presented biosensor behaves like a polarization switch with the high extinction ratio and fast response time of 25.15 dB and 100 fs, respectively. The methods of equivalent circuit model and transmission matrix have been utilized to verify the simulation results, as a new challenge in near-infrared region. The new idea of multi-application plasmonic devices, the feasibility of fabrication for the presented structure and utilizing mentioned analytical methods in near-infrared region could pave the way for the future of plasmonic structures. [ABSTRACT FROM AUTHOR]

The finite-element method (FEM) is increasingly used as a numerical tool to support experimental and theoretical studies of the optical properties of nanoparticles, in contexts such as surface-enhanced spectroscopy, molecular plasmonics, metamaterials, and optical trapping. Here, we investigate the validity of such calculations, focusing in particular on numerically challenging cases involving strong optical (plasmon) resonances and solutions with large electric field gradients and intensities. These are exemplified by elongated metallic nanoparticles and two closely spaced metallic spheres (dimer), where highly localized regions of intense electric field enhancements occur at the tip or in the gap, so-called electromagnetic hot-spots. We assess the accuracy of the FEM solutions by comparing the result to exact analytic solutions based on the T-matrix method for an elongated particle and generalized Mie theory for a dimer. Particular attention is given to the electromagnetic properties that have seldom been studied in this context, notably near-field properties such as surface-field enhancement factors and far-field radiation profiles. We also demonstrate explicitly how the accuracy of the FEM predictions can be inferred from the solution of two problems with different mesh and bounding box parameters. Such a numerical check is crucial in practice as no exact solutions are in general available to compare with. While we chose the commercial software COMSOL to illustrate our results, the methods and conclusions are equally applicable to other FEM implementations. We provide for convenience full details of how to set up these calculations in COMSOL, which we hope will allow readers to easily reproduce them and seamlessly adapt them to their modeling needs. We expect this work will cement the FEM as a reliable method for routine calculation of electromagnetic scattering by nanoparticles. [ABSTRACT FROM AUTHOR]

Aircraft panel automatic drilling and riveting system is the key equipment to realize aircraft panel assembly with high efficiency and quality. In practical application, automatic drilling and riveting system should bear cyclic riveting force with large load, which means such systems must have enough stiffness to deal with this situation. The stiffness of each components in automatic drilling and riveting system reflects as the end stiffness finally; in the meanwhile, end stiffness and riveting ability of the system will be affected when the posture of the system changes. According to this situation, stiffness matrixes related to mechanics characteristic of motion axes, transmission parts, inner-side working head, and outer-side working head of automatic horizontal dual-machine cooperative drilling and riveting system are established, in which the Jacobi matrix method, point transformation matrix method, and finite element analysis are applied. Finally, the static end stiffness model is proposed based on multi-body small deflection theory. The end stiffness model has been validated through experimental measurement, and the stiffness relationship of dual-machine tool system was obtained, which applied important data for structure optimization and control system design. [ABSTRACT FROM AUTHOR]

This paper presents an efficient structural design optimization strategy that combines the reduced basis method (RBM) with the equivalent static load (ESL). In dynamic response optimization using ESL, the computation of a static system optimization is repeatedly executed under multiple static loads. In this process, we propose parametrizing the static system and employing the RBM with global proper orthogonal decomposition (POD). In general, the snapshots for the sampling procedure under multiple loads increase proportionally to the number of loads, which results in an inefficient computational procedure. Thus, we propose taking snapshots with a proper orthogonal mode (POM) of the multiple loads rather than for the multiple loads themselves. The number of snapshots then decreases, and the original system can be efficiently reduced. We directly employ the framework of the proposed RBM with the POM of multiple loads to ESL-based design optimization, and the results indicate that the proposed method is more efficient than conventional ESL-based optimization as well as a full order model. Various numerical examples, including comparisons of relative errors and the dynamic response optimizations, support the strength of the proposed strategy. [ABSTRACT FROM AUTHOR]

Aims: To compare optic disc perfusion, radial peripapillary capillaries (RPC) and macular vascular density, between normal subjects and subjects with obstructive sleep apnea syndrome (OSAS) using spectral-domain OCT angiography (OCTA).Methods: Sixteen eyes of patients with mild OSAS, 17 eyes with moderate OSAS, 20 eyes with severe OSAS on polygraphy and 28 controls were evaluated with OCTA RT XR Avanti (AngioVue software, Optovue Inc., Fremont, CA). Optic nerve head (ONH), RPC and macular vessel density were measured. Clinical data, visual field parameters, and Spectral Domain OCT evaluation (retinal nerve fiber layer (RNFL) thickness and ganglion cell complex (GCC) thickness) were recorded for all patients.Results: ONH vascular flow (p = 0,396), RPC vascular density (automatized data “whole” p = 0,913, “peripapillary” p = 0,539, and segmented analysis with a topographic grid) and macular vascular density (foveal p = 0,484, parafoveal p = 0,491) were not significantly different between the four groups. FDT-Matrix™ and Humphrey 24/2 mean deviation were significantly lower in eyes with severe OSAS and were correlated to the apnea-hypopnea index. Retinal nerve fiber layer (RNFL) thickness, Cup/Disc ratio, rim area, and ganglion cell complex (GCC) were not significantly modified.Conclusions: OCTA did not detect reduced ONH, RPC, neither macular blood vessel density in eyes with OSAS. The precise mechanisms that link OSAS with optic nerve pathologies remain unclear: our study was not able to demonstrate a vascular impact by OCTA examination. [ABSTRACT FROM AUTHOR]

We propose a solution for the modal controllability problem for linear autonomous differential systems of neutral type with commensurate delays in two classes of differentialdifference controllers. [ABSTRACT FROM AUTHOR]

We study the light scattering properties of moderately large dust aggregates ( $0.8~\upmu \mbox{m} \lesssim R \lesssim 2.0~\upmu \mbox{m}$ ) with a wide variation of porosity ( $\mathcal{P}$ ) from 0.57 to 0.98. The computations are performed using the Superposition T-matrix code with BAM2 cluster ( $\mathcal{P} \sim 0.57\mbox{--}0.64$ ), BAM1 cluster ( $\mathcal{P} \sim 0.74$ ), BA or BPCA cluster ( $\mathcal{P} \sim 0.85\mbox{--}0.87$ ) and BCCA cluster ( $\mathcal{P} \sim 0.98$ ). The simulations are executed at two wavelengths $0.45~\upmu \mbox{m}$ and $0.65~\upmu \mbox{m}$ with highly absorbing particles (organic refractory) as well as with low absorbing particles (amorphous silicates) to understand the photopolarimetric behavior (phase function, polarization, and color) of dust aggregates. The effect of aggregate size parameter ( $X$ ) on the light scattering properties of aggregates (BA and BAM2) having different porosities is explored in this study. We find that the positive polarization maximum ( $P_{\max}$ ), the amplitude of the negative polarization ( $P_{\min}$ ) and phase function at the exact backscattering direction ( $S_{11}(180^{\circ })$ ) are correlated with the porosity of aggregates. Compact aggregates show deeper negative polarization as compared to porous aggregates when the characteristic radius ( $R$ ) of the aggregates are considered to be the same. Further lower porosity aggregates show higher $S_{11}(180^{\circ })$ and vice versa. When $\mathcal{P}$ is increased in a range from 0.64 to 0.98, both ${S}_{11}(180^{\circ })$ and $P_{\min}$ decrease linearly, whereas $P_{\max}$ increases linearly. We also find that the porosity of the aggregates plays a crucial role in determining the polarimetric color for high absorbing organic refractories. The compact clusters (BAM1 and BAM2) show the negative polarimetric color whereas BA clusters show almost positive polarimetric color at all values of scattering angle. We have also made some comparisons of our simulated results with PROGRA experimental results. [ABSTRACT FROM AUTHOR]

We consider the state feedback stabilization problem for a linear time-varying system. Attention is mainly paid to the reduction of the system to canonical form; to this end, we suggest an algorithm for constructing the transformation matrix. This algorithm is based on the solution of a hybrid system and, in contrast to the classical approach, does not require the multiple differentiability of the system parameters. [ABSTRACT FROM AUTHOR]

A class of 4-band symmetric biorthogonal wavelet bases has been constructed, in which any wavelet system the high-pass filters can be determined by exchanging position and changing the sign of the two low-pass filters. Thus, the least restrictive conditions are needed for forming a wavelet so that the free degrees can be reversed for application requirement. Some concrete examples with high vanishing moments are also given, the properties of the transformation matrix are studied and the optimal model is constructed. These wavelets can process the boundary conveniently, and they lead to highly efficient computations in applications. [ABSTRACT FROM AUTHOR]

We study the light scattering properties of aggregate particles in a wide range of complex refractive indices ( $m = n + i k$ , where $1.4 \le n \le 2.0$ , $0.001 \le k \le1.0$ ) and wavelengths ( $0.45 \le \lambda\le1.25 \mbox{ }\upmu \mbox{m}$ ) to investigate the correlation among different parameters e.g., the positive polarization maximum ( $P_{\mathrm{max}}$ ), the amplitude of the negative polarization ( $P_{\mathrm{min}}$ ), geometric albedo ( $A$ ), $(n,k)$ and $\lambda$ . Numerical computations are performed by the Superposition T-matrix code with Ballistic Cluster-Cluster Aggregate (BCCA) particles of 128 monomers and Ballistic Aggregates (BA) particles of 512 monomers, where monomer's radius of aggregates is considered to be 0.1 μm. At a fixed value of $k$ , $P_{\mathrm{max}}$ and $n$ are correlated via a quadratic regression equation and this nature is observed at all wavelengths. Further, $P_{\mathrm{max}}$ and $k$ are found to be related via a polynomial regression equation when $n$ is taken to be fixed. The degree of the equation depends on the wavelength, higher the wavelength lower is the degree. We find that $A$ and $P_{\mathrm{max}}$ are correlated via a cubic regression at $\lambda= 0.45\mbox{ }\upmu \mbox{m}$ whereas this correlation is quadratic at higher wavelengths. We notice that $|P_{\mathrm{min}}|$ increases with the decrease of $P_{\mathrm{max}}$ and a strong linear correlation between them is observed when $n$ is fixed at some value and $k$ is changed from higher to lower value. Further, at a fix value of $k$ , $P_{\mathrm{min}}$ and $P_{\mathrm{max}}$ can be fitted well via a quartic regression equation when $n$ is changed from higher to lower value. We also find that $P_{\mathrm{max}}$ increases with $\lambda$ and they are correlated via a quartic regression. [ABSTRACT FROM AUTHOR]

We investigate thermodynamic properties and effects of quantum fluctuations in the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover region of a superfluid Fermi gas in the low-temperature limit. Including strong-coupling corrections within the framework of an extended T-matrix approximation, we numerically compute the isothermal compressibility $$\chi _n$$ . While quantum fluctuation effects on $$\chi _n$$ in the strong-coupling BEC regime are explained by the quantum depletion due to a repulsive interaction between tightly bound molecules, effects of self-energy shift on the Fermi chemical potential are found to enhance $$\chi _n$$ in the weak-coupling BCS region. We also show that the calculated $$\chi _n$$ agrees well with the recent experiment on a $$^6$$ Li Fermi gas done from the weak-coupling region to the unitarity limit. Our result would be useful for the study of many-body quantum corrections in the BCS-BEC crossover region of a strongly interacting Fermi superfluid. [ABSTRACT FROM AUTHOR]

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal phase. In the three-dimensional case, it has been shown that the so-called pseudogap phenomena can be well described by a (non-self-consistent) T-matrix approximation (TMA). In the two-dimensional case, while this strong-coupling theory can explain the pseudogap phenomenon in the strong-coupling regime, it unphysically gives large pseudogap size in the crossover region, as well as in the weak-coupling regime. We show that this difficulty can be overcome when one improves TMA to include higher-order pairing fluctuations within the framework of a self-consistent T-matrix approximation (SCTMA). The essence of this improvement is also explained. Since the observation of the BKT transition has recently been reported in a two-dimensional $$^6\hbox {Li}$$ Fermi gas, our results would be useful for the study of strong-coupling physics associated with this quasi-long-range order. [ABSTRACT FROM AUTHOR]

We theoretically investigate the normal state properties of a Bose-Fermi mixture with a strong attractive interaction between Fermi and Bose atoms. We extend the ordinary T-matrix approximation (TMA) with respect to Bose-Fermi pairing fluctuations, to include the Hugenholtz-Pines' relation for all Bose Green's functions appearing in TMA self-energy diagrams. This extension is shown to be essentially important to correctly describe the physical properties of the Bose-Fermi mixture, especially near the Bose-Einstein condensation instability. Using this improved TMA, we clarify how the formation of composite fermions affects Bose and Fermi single-particle excitation spectra, over the entire interaction strength. [ABSTRACT FROM AUTHOR]

We theoretically investigate the shear viscosity $$\eta $$ , as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover region. We also evaluate $$\eta / s$$ , to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity $$\eta $$ is remarkably suppressed near the superfluid phase transition temperature $$T_{\mathrm{c}}$$ , due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe $$\eta $$ . We also show that $$\eta / s$$ decreases with increasing the interaction strength, to become very close to the KSS bound, $$\hbar /4\pi k_{\mathrm{B}}$$ , on the BEC side. [ABSTRACT FROM AUTHOR]

We introduce transformation matrix connecting sets of the displaced states with different displacement amplitudes. Arbitrary pure one-mode state can be represented in new basis of the displaced number (Fock) states ( $$\alpha $$ -representation) by multiplying the transposed transformation matrix on a column vector of initial state. Analytical expressions of the $$\alpha $$ -representation of superposition of vacuum and single photon and two-mode squeezed vacuum are obtained. On the basis of the developed mathematical formalism, we consider the mechanism of interaction between qubits which is based on their displaced properties. Superposed coherent states deterministically displace target state on equal modulo but opposite on sign values. Registration of the single photon in auxiliary mode (probabilistic operation) results in constructive interference and gives birth to entangled hybrid state corresponding to outcome of elementary quantum gates. The method requires minimal number of resource and works in realistic scenario. [ABSTRACT FROM AUTHOR]

We consider companion matrices of size 2 × 2 with general complex spectra satisfying a root condition with respect to the closed complex unit circle or the closed complex left half plane. For both cases, smooth and naturally conditioned basis transformations are constructed such that the resulting, transformed matrix is contracting or dissipative, respectively, with respect to the ℓ -norm. [ABSTRACT FROM AUTHOR]

In protein structure prediction, a considerable number of models are usually produced by either the Template-Based Method (TBM) or the ab initio prediction. The purpose of this study is to find the critical parameter in assessing the quality of the predicted models. A non-redundant template library was developed and 138 target sequences were modeled. The target sequences were all distant from the proteins in the template library and were aligned with template library proteins on the basis of the transformation matrix. The quality of each model was first assessed with QMEAN and its six parameters, which are C_β interaction energy (C_beta), all-atom pairwise energy (PE), solvation energy (SE), torsion angle energy (TAE), secondary structure agreement (SSA), and solvent accessibility agreement (SAE). Finally, the alignment score (score) was also used to assess the quality of model. Hence, a total of eight parameters ( i.e., QMEAN, C_beta, PE, SE, TAE, SSA, SAE, score) were independently used to assess the quality of each model. The results indicate that SSA is the best parameter to estimate the quality of the model. [ABSTRACT FROM AUTHOR]

To determine the error compensation for cutting forces with a machine tool, this paper proposes a comprehensive error compensation method that determines an equivalent cutting force. The loading system that applies this equivalent cutting force was designed to load a constant force that imitates the actual cutting force of a machine tool. The equivalent cutting force, when applied to the working table of the machine tool, induces an error that can be directly measured by a laser interferometer. Moreover, a stable measurement environment suitable for laser interferometer is configured. A comprehensive error compensation model of a three-axis computer numerical control (CNC) machine tool was developed using multi-body systems theory and homogeneous transformation matrices. Solutions for the error compensation model and parametric equation were automatically found using MATLAB, based on this model. The effectiveness of this compensation method has been confirmed by machining experiments. The experimental results show that this comprehensive error compensation of the equivalent cutting force can greatly improve machining accuracy. [ABSTRACT FROM AUTHOR]

In this paper we study semigroups defined either by means of weak inverses modulo Green's relation $$\mathcal{{H}}$$ , or by means of the set of completely regular elements. Basic properties of E-inversive semigroups are analyzed, and semigroups whose completely regular elements form a subsemigroup or a rectangular band modulo $$\mathcal{{H}}$$ are considered. We obtain results that generalize the corresponding results for E-semigroups or semigroups whose idempotents form a rectangular band, and also new results for E-inversive semigroups. [ABSTRACT FROM AUTHOR]

Let $$X_{n}=\{1,2,\ldots ,n\}$$ and let $${\mathcal {S}}_{n}$$ and $${\mathcal {I}}_{n}$$ be the symmetric group and symmetric inverse semigroup on $$X_{n}$$ respectively. In this paper, we show that the semigroup $${\mathcal {SI}}_{n}={\mathcal {I}}_{n}{\setminus } {\mathcal {S}}_{n}$$ , of all strictly partial one-to-one maps on $$X_{n}$$ , is generated by quasi-idempotent elements (non-idempotent elements $$\alpha $$ satisfying $$\alpha ^{4}=\alpha ^{2}$$ ). Also, we give the least upper bound for the minimum length factorisation of each $$\alpha \in {\mathcal {SI}}_{n}$$ into a product of quasi-idempotents. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a method for enhancing the nonlinear optical properties in silica glass by using metallic nanoparticles. First, the T-matrix method is developed to calculate the effective dielectric constant for the compound of silica glass and metallic nanoparticles, both of which possess nonlinear dielectric constants. In the second step, the Maxwell-Garnett theory is exploited to replace the spherical nanoparticles with cylindrical and ellipsoidal ones, facilitating the calculation of the third-order nonlinear effective susceptibility for a degenerate four-wave mixing case. The results are followed by numerical computations for silver, copper and gold nanoparticles. It is shown, graphically, that the maximum and minimum of the real part of the reflection coefficient for nanoparticles of silver occurs in smaller wavelengths compared to that of copper and gold. Further, it is found that spherical nanoparticles exhibit greater figure-of-merit compared to those with cylindrical or ellipsoidal geometries. [ABSTRACT FROM AUTHOR]

We investigate strong-coupling properties of a two-dimensional ultracold Fermi gas in the normal state. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate the distribution function $$n({\varvec{Q}})$$ of Cooper pairs in terms of the center of mass momentum $${\varvec{Q}}$$ . In the strong-coupling regime, $$n({\varvec{Q}}=0)$$ is shown to exhibit a remarkable increase with decreasing the temperature in the low temperature region, which agrees well with the recent experiment on a two-dimensional $$^6$$ Li Fermi gas (Ries et al. in Phys Rev Lett 114:230401, ). Our result indicates that the observed remarkable increase of the number of Cooper pairs with zero center of mass momentum can be explained without assuming the Berezinskii-Kosterlitz-Thouless (BKT) transition, when one properly includes pairing fluctuations that are enhanced by the low-dimensionality of the system. Since the BKT transition is a crucial topic in two-dimensional Fermi systems, our results would be useful for the study toward the realization of this quasi-long-range order in an ultracold Fermi gas. [ABSTRACT FROM AUTHOR]

The method of wave function expansion is adopted to study the three dimensional scattering of a plane progressive harmonic acoustic wave incident upon an arbitrarily thick-walled helically filament-wound composite cylindrical shell submerged in and filled with compressible ideal fluids. An approximate laminate model in the context of the so-called state-space formulation is employed for the construction of T-matrix solution to solve for the unknown modal scattering coefficients. Considering the nonaxisymmetric wave propagation phenomenon in anisotropic cylindrical components and following the resonance scattering theory which determines the resonance and background scattering fields, the stimulated resonance frequencies of the shell are isolated and classified due to their fundamental mode of excitation, overtone and style of propagation along the cylindrical axis (i.e., clockwise or anticlockwise propagation around the shell) and are identified as the helically circumnavigating waves. [ABSTRACT FROM AUTHOR]

The position of a magnetic target can be obtained through magnetic anomaly which is measured by a magnetic sensor. Comparing with vector magnetic sensor, the measurement value of the scalar magnetic sensor is almost not influenced by its orientation in measurement coordinate axes. Therefore, scalar magnetic sensors can be easily assembled into an array. Based on analysis of the total scalar magnetic anomaly measured by scalar magnetometer, we present an efficient method for tracking a magnetic target using scalar magnetometer array. In this method, we separate the position information and magnetic moment information of magnetic target by matrix transformation. Then, we can obtain the position of the magnetic target in real time by a scalar magnetometer array and a particle swarm optimization algorithm. In addition, the magnetic moment of the target can be estimated when the target's position had been calculated. The simulation shows that the position of the target can be calculated accurately and the relative error of the position is <5 %. The calculated magnetic moment of the target is close to the theoretical value. In addition, execution time of each calculation is <1 s. Thus, the position of the magnetic target can be obtained in real-time through this method. [ABSTRACT FROM AUTHOR]

The Ensemble Transform (ET) method has been shown to be useful in providing guidance for adaptive observation deployment. It predicts forecast error variance reduction for each possible deployment using its corresponding transformation matrix in an ensemble subspace. In this paper, a new ET-based sensitivity (ETS) method, which calculates the gradient of forecast error variance reduction in terms of analysis error variance reduction, is proposed to specify regions for possible adaptive observations. ETS is a first order approximation of the ET; it requires just one calculation of a transformation matrix, increasing computational efficiency (60%-80% reduction in computational cost). An explicit mathematical formulation of the ETS gradient is derived and described. Both the ET and ETS methods are applied to the Hurricane Irene (2011) case and a heavy rainfall case for comparison. The numerical results imply that the sensitive areas estimated by the ETS and ET are similar. However, ETS is much more efficient, particularly when the resolution is higher and the number of ensemble members is larger. [ABSTRACT FROM AUTHOR]

We have examined the properties of the T matrix in the Rayleigh approximation (i.e., in the electrostatic problem) for axisymmetric particles using an analog of the extended boundary condition method (EBCM). The T matrix can be constructed by two methods. In the first method, the field inside of the particle is initially determined and then the 'scattered' field is found. In terms of the second approach, the problem is formulated straight for the scattered field. Theoretically, the two schemes are equivalent. Based on the refined analysis of a vast amount of numerical calculations for Chebyshev particles and pseudospheroids, it has been shown that, taking into account the influence of calculation errors, the second approach is much more efficient than the first one for determining the scattered field and the T matrix taking into account its symmetric character. Numerical investigations of the range of applicability of the EBCM have unambiguously confirmed theoretical inferences. Namely, the T matrix can be constructed by the EBCM only if there exists a nonempty intersection of analytical continuations of the expansions of the scattered and internal fields in terms of spherical functions. In other words, the radii of convergence of these expansions should satisfy the condition R < R, which depends only on the particle shape. [ABSTRACT FROM AUTHOR]

Schoenflies point groups are presented in terms of spatial partitions and Laue classes based on abstract groups. A much simpler system using only a minimal set of generators for three dimensional groups is then presented in the same form. This simplified treatment allows group operations of a given Laue class to be correlated to a greatly simplified Mulliken-style notation for irreducible representations of that class. Transformation matrix representations of point groups in the simplified style can then be manipulated according to their position in the class or to their sub-groups in very clear procedures. Simple rules can replace the large numbers of tables necessary in the Schoenflies approach. Some applications of the method are described. [ABSTRACT FROM AUTHOR]

This paper introduces a type of modified generalized projective synchronization with complex transformation matrix (CMGPS) for fractional-order complex chaos and real chaos with the same dimension and different structures. The transformation matrix in this type of chaos synchronization is a non-diagonal square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, necessary and sufficient criteria are established to guarantee CMGPS for the fractional-order complex chaos and fractional-order real chaos, and for two fractional-order complex chaotic systems, respectively. Numerical examples are provided to illustrate the feasibility and effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

The study of plasmon-induced electromagnetic fields is a very interesting topic for basic research and photonic applications. The plasmon properties depend on many factors, such as composition, size, shape and arrangement of nanoparticles. In this paper, we propose an experimental and theoretical study on the optical properties of gold nanoparticles deposited by pulsed laser ablation and investigated by near-field optical microscopy (SNOM) in a transmission far-field collection scheme. The electromagnetic field properties have been simulated by an exact theoretical analysis based on the multipolar expansion of the fields and on T-matrix approach. The theoretical model almost accurately reproduces the experimental data and makes us confident that the used method is suitable to describe more complex system of metal nanoparticles. [ABSTRACT FROM AUTHOR]

A new solution to relative motion on elliptical orbits is presented, based on a novel transformation from the reference state vector to the relative state vector. The relative orbit is constructed assuming that the anomaly, and not the time, is the invariant element throughout the transformation. This concept arises naturally from the variational form of anomaly-explicit formulations. In particular, this paper explores the capabilities of a formulation developed by Peláez et al. (Celest Mech Dyn Astron. 97, 131-150, ), called Dromo. This formulation exploits the advantages of the ideal reference frames and quaternionic descriptions of the orbital plane. The linear variational form of the equations of motion in Dromo is developed herein, and the resulting transformation matrix is presented. When applied to the reference state vector, this linear transformation provides the relative state vector at any step. The invariance in the anomaly implies a certain time delay in the results. Physical times for leader and follower do not coincide after the transformation. To recover the sense of the solution an additional correction is applied a posteriori to cancel this intrinsic time delay. The performance of the new transformation is compared against previous solutions to the problem through a set of numerical examples. Important error reductions in determining the relative orbit are observed in these tests. [ABSTRACT FROM AUTHOR]

We present a practical entanglement classification scheme for pure state in form of $$2\times L\times M\times N$$ under the stochastic local operation and classical communication (SLOCC), where every inequivalent class of the entangled quantum states may be sorted out according to its standard form and the corresponding transformation matrix. This provides a practical method for determining the interconverting matrix between two SLOCC equivalent entangled states, and classification examples for some $$2\times 4\times M\times N$$ systems are also presented. [ABSTRACT FROM AUTHOR]

We consider matrix structures in the quantum N-body problem that generalize the Faddeev components for resolvents, T-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of T-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators. [ABSTRACT FROM AUTHOR]

The discrete W transform (DWT) is widely used in digital signal processing. This paper proposes a novel approach to compute DWT via computation of the first-order moments without multiplications. A scalable and efficient systolic array is designed to implement this approach. Compared with the other existing methods, the proposed algorithms are simpler and more applicable. [ABSTRACT FROM AUTHOR]