Abstract. In this paper, the author established the general solution and generalized Ulam-Hyers-Rassias stability of n-dimensional additive functional equationin generalized 2-normed space.

This work presents the implementation of trainable Artificial Neural Network (ANN) chip, which can be trained to implement certain functions. Usually training of neural networks is done off-line using software tools in the computer system. The neural networks trained off-line are fixed and lack the flexibility of getting trained during usage. In order to overcome this disadvantage, training algorithm can implemented on-chip with the neural network. In this work back propagation algorithm is implemented in its gradient descent form, to train the neural network to function as basic digital gates and also for image compression. The working of back propagation algorithm to train ANN for basic gates and image compression is verified with intensive MATLAB simulations. In order to implement the hardware, verilog coding is done for ANN and training algorithm. The functionality of the verilog RTL is verified by simulations using ModelSim XE III 6.2c simulator tool. The verilog code is synthesized using Xilinx ISE 10

Abstract. In the current work, we define and find the general solution of the decic functional equation g(x + 5y) − 10g(x + 4y) + 45g(x + 3y) − 120g(x + 2y)where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.

Electrocardiograms (ECG) are extensively used for the diagnosis of cardiac arrhythmias. This paper investigates the use of machine learning classification algorithms for ECG analysis and arrhythmia detection. This is a crucial component of a conventional electronic health system, and it frequently necessitates ECG signal reduction for long-term data storage and remote transmission. Signal processing methods must be used to extract the function of the morphological properties of the ECG signal changing with time, which is difficult to discern in the typical visual depiction of the ECG signal. In biomedical research, signal processing and data analysis are commonly employed methodologies. This work proposes the use of an ECG arrhythmia classification method based on Fast Fourier Transform (FFT) for feature extraction and an improved AlexNet classifier to distinguish the difference between four types of arrhythmia conditions that were collected from records. The Convolutional Neural Network (CNN) algorithm’s results are compared to those of other algorithms, and the simulation results prove that the proposed technique is more effective for various parameters. The final results of the proposed system show that its ability to find deviations is 20% better than that of traditional systems.

In this paper, the authors established the solution in vector space and Intuitionistic Fuzzy stability of n-dimensional quadratic functional equation

Abstract. In this paper, the authors obtain the generalized Ulam -Hyers stability of a 2 -variable AC -mixed type functional equationin Felbin's type spaces using fixed point method.Mathematics Subject Classification: 39B52, 32B72, 32B82

In this paper, the authors obtain the general solution and generalized Ulam -Hyers stability of n dimensional additive quadratic functional equationin Banach spaces using direct and fixed point methods. We also investigate the stability of the above equation in Banach algebra using direct and fixed point approach.

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