Diagonal Elements Research Articles

Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs.

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.

Amount of quantum coherence needed for measurement incompatibility

A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specialising to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimisation. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an N-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving "genuinely incoherent operations" used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.

Composite Sequential Network With POA Attention for PolSAR Image Analysis

The scattering response of polarimetric synthetic aperture radar (PolSAR) data is strongly target orientation-dependent. Formulating the polarimetric matrix as sequential data by rotating the polarimetric matrix along the radar line of sight would provide rich information about land-cover properties. In this work, we propose a composite sequential network (CSN) with polarization orientation angle (POA) attention to model the polarimetric coherency matrix sequence and explore target scattering orientation diversity features. Three major factors strengthen the proposed method for PolSAR image analysis. First, CSN improves the feature comprehensiveness by extending the interpretation mode of PolSAR data from spatial polarization to spatial polarization orientation. In this way, CSN could describe polarimetric response dynamics at different orientations. Second, a two-stream composite network with both real- and complex-valued convolutional long short-term memory (ConvLSTM) network is proposed to process the diagonal and off-diagonal elements of the coherency matrix sequence, respectively. Compared to existing real-/complex-valued networks, the CSN explores the significant phase information of the off-diagonal elements by operations in the complex domain. Meanwhile, CSN prevents padding 0 meaninglessly in the imaginary part of the real-valued diagonal elements. Third, during the sequential modeling of the polarimetric matrix, a POA attention mechanism is proposed. Equipped with POA-sensitive decomposition loss, the CSN attends to substantial POA range derived by targets' physical scattering mechanism and learns features closely related to the scattering mechanism. Extensive experiments and analysis on land-cover classification demonstrate the proposed method's robustness and excellence.

L-optimal designs for a trigonometric Fourier regression model with no intercept

This paper is devoted to the problem of constructing L-optimal designs for a trigonometric Fourier regression model with no intercept. The paper considers diagonal matrices L with a combination of zeros and ones on the main diagonal. It is shown that in the case when L = I (i. e., when the unit matrix is chosen as the matrix L), the L-optimal design coincides with the D-optimal one. In the more general case (when some diagonal elements are equal to zero), it is shown that the dimension of the problem can be reduced if the optimal design is symmetric. The obtained results are illustrated by the example of the problem of constructing two L-optimal designs for the trigonometric model of order 12, which is reduced to the problem of constructing designs for models of order 3 and 4 correspondingly.

Operator form of the generalized optical theorem for wave problems

The operator form of the generalized optical theorem (OT) obtained earlier for the scalar wave equation is extended to the case of electromagnetic radiation, as well as other wave equations. It is shown that in the transition from the operator to the usual OT, instead of the "forward" scattering amplitude, the diagonal matrix element of the T-scattering operator corresponding to the incident wave appears. The transitions to known forms of OT following from operator OT as special cases are also illustrated. Keywords: energy conservation, generalized optical theorem, observations in the near and far zones, radiation losses.

Операторная форма обобщенной оптической теоремы для волновых задач

The operator form of the generalized optical theorem (OT) obtained earlier for the scalar wave equation is extended to the case of electromagnetic radiation, as well as other wave equations. It is shown that in the transition from the operator to the usual OT, instead of the "forward" scattering amplitude, the diagonal matrix element of the T-scattering operator corresponding to the incident wave appears. The transitions to known forms of OT following from operator OT as special cases are also illustrated.

Spectral response of a microresonator containing a double quantum dot modified by Coulomb interaction of localized electrons

A theoretical model of a semiconductor nanostructure consisting of a single-mode microresonator containing two quantum dots is considered. It is shown that the Coulomb interaction between electrons localized in the quantum dots modifies a spectral response of the system to an external laser field. The possibility of its use for detecting an elementary charge in the third (optically inactive) quantum dot is discussed. The influence of both diagonal (Stark effect) and non-diagonal (Foerster effect) Coulomb matrix elements of the Hamiltonian on the detection accuracy is studied. The dependences of a measuring contrast on the parameters of the resonator and the quantum dots are calculated. The existence of such structural configurations for which the contrast retains an optimal value even at large distances to the measured dot is established. Keywords: quantum dots, microresonators, nanophotonics, semiconductors, laser, measurement

Спектральный отклик микрорезонатора с двумя квантовыми точками, обусловленный взаимодействием между локализованными электронами

A theoretical model of a semiconductor nanostructure consisting of a single-mode microresonator containing two quantum dots is considered. It is shown that the Coulomb interaction between electrons localized in the quantum dots modifies a spectral response of the system to an external laser field. The possibility of its use for detecting an elementary charge in the third (optically inactive) quantum dot is discussed. The influence of both diagonal (Stark effect) and non-diagonal (Förster effect) Coulomb matrix elements of the Hamiltonian on the detection accuracy is studied. The dependences of a measuring contrast on the parameters of the resonator and the quantum dots are calculated. The existence of such structural configurations for which the contrast retains an optimal value even at large distances to the measured dot is established.

Dual-Band Four-Antenna Module Covering N78/N79 Based on PIFA for 5G Terminals

To satisfy the requirement of the sub-6 GHz bands coverage and the 4 × 4 multiple-input--multiple-output (MIMO) specification for fifth-generation (5G) era, a dual-band four-antenna module covering partial 5G bands N78 (3.4–3.6 GHz) and N79 (4.8–4.9 GHz) is proposed for 5G terminal applications. Based on a quarter-circle-shaped dual-mode slotted planar inverted-F antenna (PIFA), the two target bands are covered by the fundamental TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> mode and a hybrid higher-order mode combined by quasi-TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> and quasi-TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0,1/2</sub> modes. The four-antenna module is composed of four such PIFA elements that are arranged in a sequentially rotated layout. It presents a circular shape with a diameter of 39.4 mm and is with a low profile of 1.2 mm. The measured results show that the reflection coefficients of the four elements basically cover the target bands; across N78 and N79, the isolations are better than 8.5 and 17.6 dB for the neighboring elements, and 19.4 and 18.5 dB for the diagonal elements; the average total efficiencies of the four elements are between 38.3% and 39.5% for N78 and 39.3% and 42.6% for N79; all the envelope correlation coefficients are lower than 0.42.

DOORWAY-модели в обратной задаче для сложного вибронного аналога резонанса Ферми

We solve the inverse problem for the complex Fermi resonance or its vibronic analogue, and to this end we use the matrix XEXt, where E = diag({Ek}) is a diagonal matrix, Ek are the energies of the observed “conglomerate” of lines, and the intensities of these lines Ik determine the first row of the matrix X, (X1k)2 = Ik, k = 1, 2, … , n, n  3. Hamiltonian matrix of the direct model, HDIR, whose parameters are the energies of pre-diagonalized “dark” states, Ai, and the matrix elements of their coupling to the “bright” state, Bi, (i = 1, 2, … , n – 1), is obtained after the diagonalization of the XEXt block, which belongs to the “dark” states. We show that Hamiltonian matrix with the single doorway state (DW), HDW1, can be obtained from the matrices HDIR or XEXt by first step of the Householder triangularization, i.e. by similarity transformation with a reflection matrix constructed by quantities Bi or Di = (XEXt)1,i+1. For the energy of the first DW1 state, g1, and the matrix element of its coupling to the “bright” state, w1, the use of the Householder transformation gives: g1=Sigman-1i=1B2iAi/(Sigman-1j=1B2j)= Sigmank=1E3kIk/Sigmanl=1E2lIl, |w1|=(Sigman-1i=1B2i)1/2= Sigmank=1E2kIk)1/2. In similar way, using the Householder transformation, the Hamiltonians for the models with several doorway states, HDW2, HDW3,…, HDW(n-1), are successively obtained. The Hamiltonian of the DW(n-2) model is represented by a symmetric tridiagonal matrix HDW(n-1), its diagonal elements gi determine the energies of the DW1, DW2,…, DW(n-1) states, and the off-diagonal elements wi determine the corresponding coupling between them.

Fast SDP Relaxation of the Optimal Power Flow Using the Line-Wise Model for Representing Meshed Transmission Networks

In this paper, we propose a novel Semidefinite Programming (SDP) relaxation of the Optimal Power Flow (OPF) problem. The proposed formulation utilizes the Line-Wise Model (LWM) to represent meshed transmission networks. This allows the constraints of the proposed formulation to mostly depend on diagonal elements of the voltages&#x0027; Hermitian <inline-formula><tex-math notation="LaTeX">${\bm{W}}$</tex-math></inline-formula> matrix in contrast to the Bus Injection Model (BIM) where constraints heavily utilize its off-diagonal elements. Test cases with bus sizes of 3 to 9241 were considered and chordal sparsity was exploited for them. Obtained results show that the proposed SDP-LW OPF formulation manages to provide solutions of similar or better quality for most test cases that belong to the Typical and Congested (TYP and API) Operating conditions. Furthermore, the proposed SDP-LW OPF formulation manages to reduce the solver&#x0027;s computational time for most of large-scale test cases with reductions up to 80.298&#x0025;. Results analysis shows that reductions in the solver&#x0027;s computational time upon using the proposed SDP-LW OPF formulation are affected by its ability to significantly reduce constraints with off-diagonal elements of the <inline-formula><tex-math notation="LaTeX">${\bm{W}}$</tex-math></inline-formula> matrix without drastically increasing constraints with diagonal elements of the <inline-formula><tex-math notation="LaTeX">${\bm{W}}$</tex-math></inline-formula> matrix. Furthermore, the percentage of large sized cliques is found to affect the obtained reductions through its influence over the number of needed linking constraints for relating the elements of the <inline-formula><tex-math notation="LaTeX">${\bm{W}}$</tex-math></inline-formula> matrices of decomposed cliques.

DOORWAY models in the inverse problem for a complex vibronic analogue of the fermi resonance

We solve the inverse problem for the complex Fermi resonance or its vibronic analogue, and to this end we use the matrix XEXt, where E=diag(\Ek\) is a diagonal matrix, Ek are the energies of the observed &amp;quot;conglomerate&amp;quot; of lines, and the intensities of these lines Ik determine the first row of the matrix X, (X1k)2=Ik k=1,2,...,n,n≥3. Hamiltonian matrix of the direct model, HDIR, whose parameters are the energies of pre-diagonalized &amp;quot;dark&amp;quot; states, Ai, and the matrix elements of their coupling to the &amp;quot;bright&amp;quot; state, Bi, (i=1,2,...,n-1), is obtained after the diagonalization of the XEXt block, which belongs to the &amp;quot;dark&amp;quot; states. We show that Hamiltonian matrix with the single doorway state (DW), HDW1, can be obtained from the matrices HDIR or XEXt by first step of the Householder triangularization, i.e. by similarity transformation with a reflection matrix constructed by quantities Bi or Di=(XEXt)1,i+1. For the energy of the first DW1 state, g1, and the matrix element of its coupling to the &amp;quot;bright&amp;quot; state, w1, the use of the Householder transformation gives: g1=Sigman-1i=1B2iAi/(Sigman-1j=1B2j)= Sigmank=1E3kIk/Sigmanl=1E2lIl, |w1|=(Sigman-1i=1B2i)1/2= Sigmank=1E2kIk)1/2. In similar way, using the Householder transformation, the Hamiltonians for the models with several doorway states, HDW2,HDW3,...,HDW(n-1), are successively obtained. The Hamiltonian of the DW(n-2) model is represented by a symmetric tridiagonal matrix HDW(n-1), its diagonal elements gi determine the energies of the DW1-,DW2-,...,DW(n-1) states, and the off-diagonal elements wi determine the corresponding coupling between them. Keywords: vibronic coupling, complex vibronic analogue of the Fermi resonance, inverse problem, Householder transformation, doorway models.

Design and Testbed Implementation of Multiuser CFOs Estimation for MIMO SC-FDMA System

In this paper, we propose and implement blind multiuser carrier frequency offsets (CFOs) estimation for multi-input multi-output (MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system using orthogonal propagator method (OPM) over a noisy frequency-selective channel. The performance of typical OPM is limited at low signal-to-noise ratio (SNR) due to its noise-free signal model. The additive white Gaussian noise mainly impacts the diagonal elements of the data covariance matrix (DCM) of the received signal. First, the proposed fractional CFOs estimator minimizes the noise effect by reconstructing the denoised diagonal elements of the DCM for the received signal through cubic Hermite interpolation. Therefore, we use modified OPM to estimate multiple CFOs for MIMO SC-FDMA systems. Second, we have used an iterative method based on the first-order Taylor series approximation of the CFO vector to avoid peak ambiguity and reduce the number of iterations required in the grid search. The mean square error of the proposed CFO estimator considerably improves compared with the existing methods at a low SNR regime. The bit error rate performance of the proposed method for MIMO SC-FDMA is also compared with the existing methods. Finally, the proposed estimator is validated by implementing it on radio frequency hardware testbed over an indoor propagation environment.

Spin alignment measurement of vector mesons produced in high energy collisions

This paper covers the recent experimental development on spin alignment measurements of [Formula: see text] and [Formula: see text] vector mesons in heavy-ion and [Formula: see text] collisions at RHIC and LHC energies. Measurements in [Formula: see text] collisions at LEP energies are also discussed. Spin alignment of vector mesons is studied by measuring the second diagonal element [Formula: see text] of spin density matrix. The spin density matrix element [Formula: see text] is obtained by measuring the angular distribution of vector meson decay daughter with respect to the quantization axis in vector meson rest frame. Measured [Formula: see text] values for vector mesons are found to be larger than [Formula: see text] at high momentum in [Formula: see text] collisions at LEP energies, suggesting the preferential production of vector meson with helicity zero state from the fragmentation process. The [Formula: see text] values are found to be smaller than [Formula: see text] ([Formula: see text] implies no spin alignment) for [Formula: see text] and [Formula: see text] vector mesons at low transverse momentum in Pb–Pb collisions at [Formula: see text] TeV. These observations are qualitatively consistent with the expectation from models which attribute the spin alignment effect due to polarization of quarks in the presence of large initial angular momentum in noncentral heavy-ion collisions and its subsequent hadronization by the process of recombination. No significant spin alignment effect is observed for [Formula: see text] [Formula: see text] in mid-central Pb–Pb collisions and for vector mesons in [Formula: see text] collisions. However, the preliminary results of [Formula: see text] for [Formula: see text] mesons are larger than [Formula: see text] at intermediate [Formula: see text] in Au–Au collisions at RHIC energies and can be attributed to the presence of [Formula: see text] meson field. Although there is evidence of spin alignment effect of vector mesons in heavy-ion collisions but the measured effect is surprisingly larger in context of hyperon polarization. Therefore, these results will trigger further theoretical study.

Experimental studies of the seismic behavior of EKBFs subjected to lateral loading

In this paper an experimental study on the behavior of a new and practical technique of lateral bracing for steel frame construction for two levels of performances, is presented and discussed. Eccentrically Knee Bracing (EKB) technique, as it is called in this paper, is made up of four structural elements, the knee element, the diagonal brace element, the link element and the column elements. The knee and link elements are a fuse-like element that dissipates energy by the formation of plastic hinges, when the building is subjected to moderate and severe lateral loads, respectively. The diagonal brace element, on the other hand, provides the required level of lateral stiffness and remains in the elastic range at all time. In large earthquakes, both of them contribute in dissipating energy. Two half-scale EKB were tested using the SAC loading protocol and an innovative loading protocol. The general test arrangement, specimen details, and most relevant results such the stiffness, shear strength, cumulative dissipated energy and other major seismic parameters in the EKB are explained. Using experimental and analytical models, the energy dissipation characteristics of the EKBs and an EBF are presented. Reasonable agreement with the experimental results is observed.

Reorientation-effect measurement of the 〈21+∥Ê2∥21+〉 matrix element in Ar36

The spectroscopic quadrupole moment of the first excited 21+ state, QS(21+), at 1.970 MeV in Ar36 was determined at energies well below the Coulomb barrier—where nuclear interference effects are negligible—using the Pt194(Ar36,Ar*36)Pt*194 Coulomb-excitation reaction at 134.2 MeV. Particle-gamma coincidence data were collected using the AFRODITE array—composed of eight high-purity germanium clover detectors—and an upstream double-sided silicon detector at iThemba LABS. A large diagonal matrix element of 〈21+∥E2̂∥21+〉=0.163(42) eb was determined, which yields a more accurate value of QS(21+)=+0.12(3) eb as compared with previous work, QS(21+)=+0.11(6) eb, in agreement with modern beyond mean-field and large-scale shell-model calculations. This value is consistent with the ratio of electric quadrupole moments found for other A=4n self-conjugate nuclei extracted from the reorientation effect and the rotor model, which are surprisingly equivalent to those observed in good rotors in the mass A≈160–180 region.Received 22 September 2021Accepted 28 November 2021DOI:https://doi.org/10.1103/PhysRevC.104.L061305©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsCollective modelsElectromagnetic transitionsHydrodynamic modelsNuclear structure & decaysPhotonuclear reactionsShell modelSpectroscopic factors & electromagnetic momentsProperties20 ≤ A ≤ 38TechniquesRadiation detectorsNuclear Physics

Accounting for light source angular distribution in backscattering Mueller matrix interpretation using double-planar small-angle scattering trajectory approximation

We extend the double-planar small-angle scattering trajectory approximation to account for the influence of the light source angular distribution on the polarization patterns of lidar backscattering returns from highly forward-peaked scattering medium. We formulate the lidar Mueller matrix return by introducing the azimuthal angle of emitting light relative to the meridian plane of receiving direction. The derived formulas have exactly the same forms as that for the vertical pencil-like light source. The essential difference is that the azimuthal angle of the emitting light can adjust the linear relation between the normalized Mueller matrix and single backscattering phase matrix as the dihedral angle between the outgoing and return forward scattering plane does too. The emitting azimuth effect can be significantly stronger than the effect of the dihedral angle of the two forward scattering planes when the receiving directions are within the cone of divergence. It can make the normalized elements of the Mueller matrix being zeros except those diagonal elements describing the linear and circular polarization degrees.

Eigenvalue problems for a class of infinite complex symmetric tridiagonal matrices with related three-term recurrence relation

We consider the eigenvalue problem of a class of infinite complex symmetric tridiagonal matrices whose diagonal and off-diagonal elements diverge in modulus, and which have a compact inverse. We regard the matrix as a linear operator mapping a maximal domain in Hilbert space ℓ2 into ℓ2. This paper aims to extend the work of Ikebe et al. on a class of eigenvalue problems and for which asymptotic error estimates have been obtained. In this paper we focus on the following points: (1) considering what class of zero-finding problems of three-term recurrence relations can be reformulated as eigenvalue problems of the class of infinite tridiagonal matrices stated above; (2) determining a class of matrices for which obtaining good approximate eigenvalues is guaranteed by using those of truncated principal sub-matrices; and (3) determining a class of matrices that permits us the asymptotic error estimates computed as in (2).

Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson model below the localization transition. We show that they display eigenstate thermalization for normalized observables. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of the diagonal and the off-diagonal matrix elements is $2$, as predicted by the random matrix theory. We study distributions of matrix elements of observables and establish that they need not be Gaussian. We identify the class of observables for which the distributions are Gaussian.

Impact the shear connector properties on the behavior of steel–concrete-steel sandwich beams

This paper describes the behavior of steel–concrete-steel sandwich beams with new configuration of shear connector. Five sandwich beams composed of a normal concrete core that was filled between a pair of 4 mm steel skin plates were prepared and tested under three-point loading up to failure. The truss shear connectors were formed from vertical and diagonal elements with different diameters of 10, 12 and 16 mm and different spacing of 100, 200, and 250 mm. All beams had a cross section of 100 × 200 mm, with a total length of 1200 mm. Results indicated that ultimate load capacity increased by about approximately 32 and 43 % with the increase of shear connectors diameter by 20 and 60%, respectively. In addition, raising the spacing of the shear connectors by 100% led to a reduction in the ultimate load capacity by approximately 31 and 68%, respectively. The test results also confirmed that when the shear connectors diameter was increased from 10 to 12 and 16 mm, the ductility index, service stiffness and flexural toughness improved by approximately 23 and 155 %, 17 and 34 % and 26 and 382 %, respectively.