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In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.

Transmission of high volume of data in a restricted wireless sensor network (WSN) has come up as a challenge due to high-energy consumption and larger bandwidth requirement. To address the issues of high-energy consumption and efficient data transmission adaptive block compressive sensing (ABCS) is one of the optimum solution. ABCS framework is well capable to adapt the sampling rate depending on the block’s features information that offers higher sampling rate for less compressible blocks and lower sampling rate for more compressible blocks In this paper, we have proposed a novel fuzzy rule based adaptive compressive sensing approach by leveraging the saliency and the edge features of the image making the sampling rate selection completely automatic. Adaptivity of the block sampling ratio has been decided based on the fuzzy logic system (FLS) by considering two important features i.e., edge and saliency information. The proposed framework is experimented on standard dataset, Kodak data set, CCTV images and the Set5 data set images. It achieved an average PSNR of 34.26 and 33.2 and an average SSIM of 0.87 and 0.865 for standard images and CCTV images respectively. Again for high resolution Kodak data set and Set 5 dataset images, it achieved an average PSNR of 32.95 and 31.72 and SSIM of 0.832 and 0.8 respectively. The experiments and the result analysis show that proposed method is efficacious than the state of the art methods in both subjective and objective evaluation metrics.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s  integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.