Search

Symplectic eigenvalues are known to satisfy analogs of several classic eigenvalue inequalities. Of these is a set of weak supermajorization relations concerning symplectic eigenvalues that are weaker analogs of some majorization relations corresponding to eigenvalues. The aim of this letter is to establish necessary and sufficient conditions for the saturation of the symplectic weak supermajorization relations by majorization. [ABSTRACT FROM AUTHOR]

We establish a trace inequality of symplectic matrices via a more general trace minimization theorem. As a consequence, we derive another proof of a result in [R. Bhatia, T. Jain, On symplectic eigenvalues of positive-definite matrices, J. Math. Phys., 56 (2015),112201.]. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new version of a Schur–Horn type theorem. Meanwhile, we provide a new proof of a recent result in [Bhatia R, Jain T. A Schur-Horn theorem for symplectic eigenvalues. Linear Algebra Appl. 2020;599:133–139]. [ABSTRACT FROM AUTHOR]

In this paper, we prove that some recent Rotfel’d theorem extensions are equivalent. [ABSTRACT FROM AUTHOR]

We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number, positive semi-definite matrices,, and generalized matrix functionssuch as the determinant and permanent, etc., we have A general scheme is introduced to prove more general inequalities involvingmpositive semi-definite matrices forthat extend the results of other authors. [ABSTRACT FROM PUBLISHER]

In this paper, the broadband Green’s function with low wavenumber extraction (BBGFL) is applied to modeling of traces connecting vias in arbitrarily shaped power/ground planes of printed circuit boards (PCBs). The proposed modeling method is a hybrid technique based on mode decomposition: BBGFL is used to fast compute the vias in power/ground planes, MoM is used to calculate the impedance matrix of the traces, and a physical circuit model is then applied to combine the vias and traces in the power/ground planes. The present method is compared to the method of moments (MoM) and the commercial tool HFSS. Results show that the results of the present technique are in good agreement with MoM and HFSS on the radiated emissions from PCBs. BBGFL is several hundred times faster than HFSS in CPU time for broadband simulations. The technique provides a fast broadband solution for system-level modeling of high-speed interconnects with vias and traces in electronic design automation design and applications. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to present a better bound than the recent result given by Zhang [Linear Multilinear Algebra. 2015;63:2511–2517]. [ABSTRACT FROM AUTHOR]

In this paper, a novel termination (“match”) scheme is introduced with absorbing material for high-frequency measurements. Through the absorption of electromagnetic waves, absorbing material makes an equivalent absorbing boundary condition at the interface, which creates an equivalent termination condition. The absorbing termination can be used to facilitate on-demand match condition in high-frequency measurements. The proposed technique is particularly useful when resistive termination is difficult to implement or too expensive to apply. For example, the soldering process (soldering-on soldering-off) is time-consuming, hard to control on the precise soldering position, and easy to break the printed circuit board soldering pads. It is useful for various applications, including via crosstalk measurements in socket, package breakout via array, or other dense/fine structures. The absorbing termination method provides an innovative termination solution for RF/microwave measurements. [ABSTRACT FROM PUBLISHER]

In this paper, bond via array (BVA) wirebond is used to achieve compact vertical integration and improve the electrical performance for system in package (SiP). Two techniques are presented. In the first technique, BVA wirebonds are utilized to integrate some passive or active components vertically onto other components. This significantly reduces the horizontal footprint of the entire SiP. In terms of electrical performance, this vertical integration provides much lower parasitic inductance than conventional 2-D horizontal integration design because of shorter interconnection. For example, the proposed technology can significantly reduce power delivery network impedance compared to a conventional design. In the second technique, we propose BVA wirebond wires as an electromagnetic interference (EMI) shield between different domains within SiP. This provides a lower cost solution for EMI shielding, particularly when regions within a package need to be shielded. [ABSTRACT FROM PUBLISHER]

In this paper, we apply the broadband Green's function with low wavenumber extraction (BBGFL) to fast modeling of the radiated emissions from printed circuit boards (PCBs). We study power bus structures for electromagnetic interference/compatibility (EMI/EMC). We use the BBGFL to compute the Green's function over broadband frequencies along the boundary walls of arbitrarily shaped power/ground planes. The broadband Green's function is calculated by using modal expansions and low wavenumber extraction. Because the modal expressions are independent of frequencies, they are computed once and used for all frequencies. The radiated fields are derived from the equivalent magnetic surface currents on boundary walls using Huygen's equivalent principle. Results are illustrated up to 10 GHz and for arbitrary shaped PCB up to 5 inches in size. The accuracy and computational efficiency of the present method are compared with the method of moments (MoM) and the commercial tool HFSS. The BBGFL results are in good agreement with MoM and HFSS. The BBGFL is several hundred times faster than MoM and HFSS for broadband simulations. The significant improvement in computational efficiency makes this technique useful for electronic design automation to EMI/EMC applications. [ABSTRACT FROM PUBLISHER]

In this paper, we propose and investigate two novel applications of absorbing materials to suppress high-frequency couplings in high-speed interconnects. In the first application, absorbing materials are added to connector housing to reduce the noises caused by crosstalk and resonances. In the second application, a low-emission inductor is proposed by applying absorbing materials surrounding the body of an inductor. Full-wave simulations and measurements are performed to verify the proposed techniques. Results show absorbing materials significantly improve the performance of signal/power integrity and greatly reduce electromagnetic interference for high-speed digital system designs. [ABSTRACT FROM PUBLISHER]

A new technology is developed for the mitigation of stub effects in high-speed interconnects. This technology substantially reduces the stub effects for high-speed signaling. It dampens reflected signals on stubs, thus reducing intersymbol interference and harmful coupling, and correcting timing jitter, all typically induced by the stub’s reflected signals. This paper shows two applications for high-speed digital system designs, the mitigation of via stub effects and that of empty connector effects, respectively. However, it is notable that the present method is suitable for reflection suppression for arbitrary types of stubs to improve the signal integrity. [ABSTRACT FROM PUBLISHER]

A hybrid UV/PBTG/SMCG method is developed to accelerate the solution of NMM3D for 3-D electromagnetic wave scattering by random rough soil surfaces. It takes only 1.5 min using 16 processors on a cluster of NSF TeraGrid to compute 3-D solution of Maxwell equations of 8 by 8 square wavelengths. With the improved computational efficiency, we computed results using areas up to 32 by 32 square wavelengths. With the larger surface area, we were able to compute cases with larger rms heights up to 8 cm at SMAP radar frequency of 1.26 GHz that corresponds to kh = 2.28. New results computed include the cross-polarization. The five tests on the accuracy of results were performed: convergence with realizations, convergence with discrete samplings, convergence with sample surface sizes, energy conservation for each realization, and reciprocity for each realization. The numerical results show that for a single realization VH = HV within 0.5 dB in the backscattering direction showing that reciprocity is obeyed. Results were compared with experimental data, and both co-polarization and cross-polarization were in good agreements with experimental data. [ABSTRACT FROM PUBLISHER]

Abstract: The reverse order laws for {1,3,4}-generalized inverses of a product of two operators have been studied by Wang et al. [J. Wang, H. Zhang, G. Ji, A generalized reverse order law for the products of two operators, Journal of Shaanxi Normal University, 38 (4) (2010), 13–17]. In this paper using a block-operator matrix technique we study mixed-type reverse-order laws for {1,3,4}-generalized inverses over Hilbert spaces. [Copyright &y& Elsevier]

We extend the 3-D numerical method of Maxwell's equation (NMM3D) for rough soil surface scattering from L-band to C-, X-, and Ku-bands. We illustrate the results for copolarization, cross-polarization, and polarization ratio (HH/VV). Copolarized and cross-polarized backscattering coefficients from NMM3D are analyzed for frequency dependence, incident angle dependence, and soil moisture dependence. We also cross compare results from analytical and empirical models. The 16 $\times$ 16 squared wavelength $(\lambda^2)$ of rough surface is applied for NMM3D using 256 processors on NSF Extreme Science and Engineering Discovery Environment clusters. Polarization ratio, HH/VV, is studied to address the feature of dependence on frequency for same fields (same physical parameters for the model). HH/VV is shown useful to provide additional information to study land surface. Results from NMM3D are also validated with POLARSCAT measurement data-1. NMM3D shows good agreement with data and better performance while considering copolarization, cross-polarization, and polarization ratio (HH/VV) together. The key advancement in computation efficiency in this paper is the implementation of a physically based near-field precondition algorithm in NMM3D to accelerate parallel computation. With precondition, the computation time is faster by ten times for larger root-mean-square height. [ABSTRACT FROM PUBLISHER]

The broadband Green's function with low wavenumber extractions (BBGFL) consists of low wavenumber method of moments (MoM) solutions combined with modal expansions. BBGFL is suitable for broadband simulations because the modal functions are independent of frequencies. The modal expansion in this paper has sixth-order convergence. Using wavenumber derivatives of the surface current, it is shown that the higher order extraction requires only a single MoM impedance matrix on the left-hand side. For the same number of modes, the sixth-order convergence has significant improvement in accuracy over the \textsecond - and \textfourth-order convergence. Scattering in an arbitrary-shape waveguide is modeled by using a surface integral equation formulated with the sixth-order BBGFL. Using BBGFL, the unknowns are only on the surface of the scatterer. Results of simulations are illustrated and the results are in good agreement with those of direct MoM. [ABSTRACT FROM AUTHOR]