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Let p_[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for |q| < 1. The function p_[1,r;t](n) is the generalisation of the two-colour partition function p_[1,r;−1](n). In this paper, the authors prove some new congruences modulo odd prime ℓ by taking r = 5, 7, 11 and 13, and non-integral rational values of t.

Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.

In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.

The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.

The purpose of this paper is to show a comparative study of different direction-of-arrival (DOA) estimation techniques, namely, multiple signal classification (MUSIC) algorithm, delay-and-sum (DAS) beamforming, support vector regression (SVR), multivariate linear regression (MLR) and multivariate curvilinear regression (MCR).

The relative delay between the microphone signals is the key attribute for the implementation of any of these techniques. The machine-learning models SVR, MLR and MCR have been trained using correlation coefficient as the feature set. However, MUSIC uses noise subspace of the covariance-matrix of the signals recorded with the microphone, whereas DAS uses the constructive and destructive interference of the microphone signals.

Variations in root mean square angular error (RMSAE) values are plotted using different DOA estimation techniques at different signal-to-noise-ratio (SNR) values as 10, 14, 18, 22 and 26dB. The RMSAE curve for DAS seems to be smooth as compared to PR1, PR2 and RR but it shows a relatively higher RMSAE at higher SNR. As compared to (DAS, PR1, PR2 and RR), SVR has the lowest RMSAE such that the graph is more suppressed towards the bottom.

DAS has a smooth curve but has higher RMSAE at higher SNR values. All the techniques show a higher RMSAE at the end-fire, i.e. angles near 90°, but comparatively, MUSIC has the lowest RMSAE near the end-fire, supporting the claim that MUSIC outperforms all other algorithms considered.

This study examines the performance between operational variables for small and medium-sized businesses (SMEs) within the context of interorganizational relationships. Specifically, it investigates the role of information quality and continuous quality improvement and the varying importance that SMEs place on each of these constructs. The sample consists of 134 vendors of a large university in the southwestern region of the United States.The results indicate that there is a positive relationship between information quality and continuous quality improvement with performance in SMEs. Implications for both research and practice, as well as ideas for future research, are discussed.