In this study, different drying conditions were investigated on quality and thermodynamic properties of almond kernel. Experiments were performed using a convection dryer with ultrasound pretreatment in 40, 50, 60, and 70 °C air temperature, 1 m/s air velocity, and duration of ultrasonic pre‐treatment of 0 min (for control sample), 10, 20, and 40 min. The drying kinetic of the almond kernel was estimated by 15 mathematical models. Furthermore, Artificial Neural Networks (ANNs) and Adaptive Neuro‐Fuzzy Inference Systems (ANFIS) were applied to fit the experimental data on the thin layer drying. The lowest and highest values of the effective moisture diffusivity (Deff) was 1.81 × 10−9 and 9.70 × 10−9 m2/s, respectively. Activation energy (Ea) of the samples was obtained between 26.35 and 36.44 kJ/mol. The highest and lowest values of specific energy consumption (SEC) were calculated 561.72 and 169.88 kW hr/kg, respectively. Maximum (13.14%) and the minimum (7.1%) values of shrinkage were achieved at air temperatures of 70 and 40 °C, respectively. The color changing of dried samples was obtained between 9.14 and 17.96. Furthermore, results revealed that the ANFIS model had the high ability to predict the moisture ratio (R2 = 0.9998 and MSE = 0.0003) during drying. As a result, ANFIS model has the highest ability to evaluate all output as compared with other models and ANNs method. Practical applications Algorithms are modern methods that have been successfully applied to solve the various problems and modeling in engineering and science. Drying is one of the oldest procedures to preserve the food quality. Reduction of moisture content to a certain value can be caused to decay and minimize the microbiological activity and deteriorating chemical reactions in agricultural products, respectively. Determination of almond drying process under convective with ultrasound pre‐treatment dryer in terms of desirable thermal properties (effective moisture diffusivity and energy consumption) provides the high‐quality products. Furthermore, this research can be able to provide a technical basis for almond drying and the related equipment designing.

In this paper we establish the general solution of the functional equationand investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

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In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.