iosr-Jm   Volume-18 ~ Issue-4 ~ Jul. – Aug. 2022

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Abstract: An amazing digital multimedia revolution was marked at the end of the 20th century. In this revolution, images are extremely important to communicate in the present era of multimedia. In this world of hasty evolution of exchanging digital data as well as images, data protection is essential to protect data from the unauthorized parities. With the broad use of digital images of various fields, it is important to preserve the confidentiality of image's data from any party without authorization access. In this paper, encryption and decryption process is based on key which is generated randomly which is applied on Rubik's Cube Algorithm.

Key Words: Rubik cub,Scrambled image,image encryption-decryption, key generation

[1]. Chen, L., Yin, H., Yuan, L., Machado, J. T., Wu, R., &Alam, Z. (2021). Double color image encryption based on fractional order discrete improved Henon map and Rubik's cube transform. Signal Processing: Image Communication, 97, 116363.
[2]. Chepuri, S. (2017). An RGB image encryption using RSA algorithm. International Journal of Current Trends in Engineering & Research (IJCTER), 3(3), 1-7.
[3]. Devi. S. R, Rajarajeswari.V, Thenmozhi. K, RengarajanAmirtharajan and PraveenkumarP.(2018). Henon and LFSR assisted key based encryption. International Journal of Pure and Applied Mathematics, 119(16), 455-460.
[4]. Mousavi, M., &Sadeghiyan, B. (2021). A new image encryption scheme with Feistel like structure using chaotic S-box and Rubik cube based P-box. Multimedia Tools and Applications, 80(9), 13157-13177.
[5]. Zhao, J., Zhang, T., Jiang, J., Fang, T., & Ma, H. (2022). Color Image Encryption Scheme Based On Alternate Quantum Walk and Controlled Rubik's Cube.

Abstract: To Find the Principal Value of an Inverse Trigonometric Functions using a Unit Circle, and analysing the domain and range of Inverse Trigonometric Functions.

[1]. https://courses.lumenlearning.com/boundless-algebra/chapter/trigonometric-functions-and-the-unit-circle/
[2]. https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:inverse-trig/v/inverse-trig-functions-arcsin
[3]. https://www.ck12.org/na/inverse-trigonometric-functions-and-principal-value-branch-1/lesson/Inverse-Trigonometric-Functions-xii-maths/.

Abstract: In recent years, security concerns have grown tremendously, necessitating extremely secure picture transmission. Image encryption based on chaos is gaining popularity as a more safe and stable method of securing images than previous encryption methods.. As a result, new chaotic dynamical systems with more advanced characteristics and models are being developed for this purpose. To investigate and analyze their complexity, they are subjected to various chaos detection techniques. This study looks at the frequency and effectiveness of chaos experiments performed on 18 discrete chaotic systems. As a result, three key facts must be understood. The emerging system must first be carefully analyzed using a suitable chaos detection method. Second, a system's chaotic and quasi regions must be represented in their complete. Third, the chaos's strength must be considered. These studies are essential for developing a highly secure nonlinear key for an attack-resistant encryption scheme.

Keywords –-; chaotic Maps; Chaos detection Algorithms; image encryption based on chaos.

[1]. Dhall S, Pal SK, Sharma K (2017) Cryptanalysis of image encryption based on a new 1D chaotic Signal processing, PII S0165–1684(17)30434–6, https://doi.org/10.1016/j.sigpro.2017.12.021
[2]. Liu Y, Zhang LY, Wang J, Zhang Y, Wong K-w (2016) Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure. Nonlinear Dynamics 84(4):2241–2250
[3]. Zhang Y, Xiao D, Wen W, Nan H (2014) Cryptanalysis of image scrambling based on chaotic sequences and vigen'ere cipher. Nonlinear Dynamics 78(1):235–240
[4]. Zhu Z-l, Zhang W,Wong K-w et al (2011) A chaos-based symmetric image encryption scheme using a bitlevel permutation. Inf Sci 181(6):1171–1186
[5]. Fu C, Meng W-h, Zhan Y-f et al (2013) An efficient and secure medical image protection scheme based on chaotic maps. Comput Biol Med 43(8):1000–1010

Abstract: Every emerging country's economy relies heavily on stock market trade and India is one among the world's most active electronic stock market dealers. The stochastic modellingis extremely successfully employed in predicting the stock market behaviour, and it has become a high field of research because of its tremendous importance for every profitable industry and stockholders to take out his confident decisions.This study deals with developing and analysing stochastic models using the Markov Chains approach to forecast the stock price in the stock market. Real-time data of the daily closing share price is obtained from the historical price of NSE (National Stock Exchange) for Nifty banks to conduct a detailed and exploratory data analysis. Daily closing price differences are divided into two categories: increase and decrease. If the closing price on day t+1 is higher than the closing price on day t,....

Keywords: Markov Processes,Transition Probability matrix, Steady-state probabilities, Stock Market Assessment, Finance Growth Studies

[1]. Neenwi, S., Asagba, P. O., and Kabari, L. G. (2013). Predicting the Nigerian stock market using artificial neural network.
EuropeanJournal of Computer Science and Information,1(1), 30-39.
[2]. Abdulsalam, S. O; Adewole, K. S. and Jimoh, R. G. (2011), "Stock Trend Prediction using egression: A Data Mining Approach," ARPN Journal of Systems and Software, 1(4): 154-157.
[3]. Ariyo, A. A., Adewumi, A. O., and Ayo, C. K. (2014, March). Stock price prediction using the ARIMA model. In 2014 UKSim-AMSS 16th International Conference on Computer Modelling and Simulation. IEEE 106-112.
[4]. Renjith, K.S., and Patrick, M. (2021). FII Flows in Indian Capital Market and Volatility, Asian Journal of Economic and Finance 3(3):305318.
[5]. Ibiwoye, A. and Adeleke, I. A. (2008). Is insurance Nigeria‟s next capital market "honey pot‟? An investigation using daily stock data. African Journal of Business Management, 2(9), 157–164.

Abstract: In this paper, Author's extent the two warehouses inventory models for non-instantaneous deteriorating items by considering shortages under progressive trade credit policy. In this paper we derived some cost functions for several realistic cases sub cases and scenarios based on the non-instantaneous deterioration and the trade credit period have been formulated as non-linear constrained optimization problem along with the solution procedure. Impact of shortages are observed and to illustrate the robustness of the model, a comprehensive sensitivity analysis has been performed on the optimal case, which is obtained by solving the hypothetical numerical examples with the help of proposed algorithm using Mathematica..

Keywords: Inventory theory, non-instantaneous deterioration, Progressive trade credit, two-ware house, Shortages.

[1]. Ghare, P.M. and Schrader, G.F. (1963). A model for exponential decaying inventory, Journal of Industrial Engineering, Vol. 14,
238-243.
[2]. Haley, C.W. and Higgins, H.C. (1973). Inventory policy and trade credit financing, Manage. Sci., Vol. 20, 464–471.
[3]. Aggrawal, S.P. and Jaggi, C.K. (1995). Ordering policies of deteriorating items under permissible delay in payments, Journal of
Operational Research Society, Vol. 46, 658-662.
[4]. Wee, H.M. (1995). A deterministic lot size inventory model for deteriorating items with shortages and a declining market,
Computers and Operations Research, Vol. 22 (3), 345–356.
[5]. Ouyang, L. Y., Wu, K. S., and Yang, C. T. (2006). A study on an inventory model for non-instantaneous deteriorating items with
permissible delay in payments. Computers and Industrial Engineering, Vol. 51, No. 4, 637-651.

Abstract:Statistical analysis is usually done on data sets that contain precise information. However, data obtained may not be precise always. Thismay be due to vagueness in the process of measurement itself or due to the values being expressed in linguistic terms. Data that are not precise are referred to as imprecise data or fuzzy data. Developing statistical measures for imprecise data has been pursued by researchers during the past decade. However, the methodologies adopted involve operations on fuzzy numbers through α-cut approach, thereby making the process difficult. Liu (2007) developed a mathematical theory for studying the behavior of fuzzy phenomena known as "Credibility Theory".........

Keywords: Credibility theory, credibility distribution, fuzzy number, expectation, variance, percentiles

[1]. J.D. Gibbons, S.Chakraborti, Non Parametric Statistical Inference, 5th Ed. Chapman and Hall: 2010.
[2]. L.A.Zadeh, Fuzzy Sets. Inform. Control. 1965; 8(3): 338–353p.
[3]. R. Kruse, K.D.Meyer, Statistics with Vague Data, Riedel, Dordrecht, 1987.
[4]. R.Viertl, Statistical Methods for Fuzzy Data, John Wiley and Sons Ltd., UK, 2011.
[5]. C.Carlsson, R.Fuller, On Possibilistic Mean Value and Variance of Fuzzy Numbers. Fuzzy Set Syst. 2001; 122: 315–326p.