On the extension of the mode-matching procedure for modeling a wave-bearing cavity

The present work highlights the scattering of fluid–structure coupled waves through a wave-bearing cavity in rigid waveguide. The cavity is filled with compressible fluid and comprises horizontal as well as vertical elastic boundaries. The mode-matching technique is extended by tailored-Galerkin and Galerkin procedures to incorporate the vibrational response of the vertical elastic components having different sets of edge conditions. It is found that in mode-matching tailored-Galerkin (MMTG) method, a unique general description of the displacement of vertical elastic component can deal with a variety of edge conditions, whereas the mode-matching Galerkin (MMG) technique relies upon the orthogonal basis a priori whose description varies by changing the edge conditions of vertical elastic components. Accordingly, for some sets of edge conditions the eigenvalues cannot be expressed explicitly and must be found numerically. The eigenmodes of the cavity region satisfy the generalized orthogonal conditions which ensure the point-wise convergence of MMTG and MMG approaches. Moreover, the truncated MMTG and MMG solutions reconstruct the matching conditions as well as satisfying the conserved power identity. It confirms the accuracy of performed algebra and retained solutions. From the numerical results it is found that by varying the conditions on the edges of bridging elastic components, the stopbands can be enhanced and shifted as well as broadened over the certain frequency regimes.

Fixed Point of Orthogonal F-Suzuki Contraction Mapping on O-Complete b-Metric Spaces with Applications

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

Forecasting developed and BRICS stock markets with cryptocurrencies and gold: generalized orthogonal generalized autoregressive conditional heteroskedasticity and generalized autoregressive score analysis

PurposeThe purpose of this paper is threefold. First, it models and forecasts the risk of the five leading cryptocurrencies, stock market indices (developed and BRICS) and gold returns. Second, it conducts different backtesting procedures forecasts. Third, it focuses on the hedging potential of cryptocurrencies and gold.Design/methodology/approachThe authors used the generalized autoregressive score (GAS) models to model and forecast the risk of cryptocurrencies, stock market indices and gold returns. They conduct different backtesting procedures of the 1% and 5%-value-at-risk (VaR) forecasts. They also use the generalized orthogonal generalized autoregressive conditional heteroskedasticity (GO-GARCH) model to explore the hedging potential of cryptocurrencies by estimating the dynamic conditional correlation between cryptocurrencies and gold, on the one hand, and stock markets on the other hand.FindingsWhen conducting different backtesting procedures of VaR, our finding suggests that Bitcoin has the highest VaR among cryptocurrencies and Gold and the BRICS indices returns have lower VaR compared to the developed countries. Finally, we provide evidence that the risks among developed stock markets can be hedged by Bitcoin and Gold. Bitcoin can be considered as the new Gold for these economies. Unlike Bitcoin, Gold can be considered as a hedge for Chinese and Indian investors. However, Gold and Bitcoin can be considered as diversifier assets for the other BRICS economies while Dash and Monero are diversifier assets for developed stock markets.Originality/valueThe first paper's empirical contribution lies in analyzing optimal forecast models for cryptocurrencies (other than Bitcoin) returns and risk. The second contribution consists of studying the hedging potential of five leading cryptocurrencies. To the best of our knowledge, no previous studies have investigated the role of cryptocurrencies for BRICS investors.

A New Analysis for Support Performance with Block Generalized Orthogonal Matching Pursuit

For recovering block-sparse signals with unknown block structures using compressive sensing, a block orthogonal matching pursuit- (BOMP-) like block generalized orthogonal matching pursuit (BgOMP) algorithm has been proposed recently. This paper focuses on support conditions of recovery of any K -sparse block signals incorporating BgOMP under the framework of restricted isometry property (RIP). The proposed support conditions guarantee that BgOMP can achieve accurate recovery block-sparse signals within k iterations.

Generalized Orthogonal Discrete W Transform and Its Fast Algorithm

Based on the generalized discrete Fourier transform, the generalized orthogonal discrete W transform and its fast algorithm are proposed and derived in this paper. The orthogonal discrete W transform proposed by Zhongde Wang has only four types. However, the generalized orthogonal discrete W transform proposed by us has infinite types and subsumes a family of symmetric transforms. The generalized orthogonal discrete W transform is a real-valued orthogonal transform, and the real-valued orthogonal transform of a real sequence has the advantages of simple operation and facilitated transmission and storage. The generalized orthogonal discrete W transforms provide more basis functions with new frequencies and phases and hence lead to more powerful analysis and processing tools for communication, signal processing, and numerical computing.