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Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no‐cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality‐and‐uniformity and privacy in the mutual information sense. [ABSTRACT FROM AUTHOR]

An option is a financial derivative that can help investors hedge risk or speculate by taking on more risk for more profit. Therefore, option pricing models have played an important role in supporting investors. The option price is influenced by the volatility of an underlying asset return, which is impacted by both positive and negative information. The volatility of the option price is considered an important factor for approximating option, especially in short-term option trading. In this research, a fuzzy-TGARCH model is constructed to estimate volatility, which is used to calculate an option price in the stock market with a short-term maturity date. This proposed approach is described and analyzed by comparing the numerical results with those of other methods. The data in the SET50 market are used for observation. With this data, the proposed method performs well for ITM cases when time to maturity is 20 and 30 days. [ABSTRACT FROM AUTHOR]

In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of η- demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of control conditions. We also provide a numerical example to demonstrate the applicability of the variant with some applications. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space ℓ 2 , with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader's strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples. [ABSTRACT FROM AUTHOR]

Mathematical approaches to structure model problems have a significant role in expanding our knowledge in our routine life circumstances. To put them into practice, the right formulation, method, systematic representation, and formulation are needed. The purpose of introducing soft graphs is to discretize these fundamental mathematical ideas, which are inherently continuous, and to provide new tools for applying mathematical analysis technology to real-world applications including imperfect and inexact data or uncertainty. Soft rough covering models briefly; SRC-Models), a novel theory that addresses uncertainty. In this present paper, we have introduced two new concepts Li-soft rough covering graphs (Li-SRCGs) and the concept of fixed point of such graphs. Furthermore, we looked into a some algebras that dealt with the fixed points of Li-SRCGs. Applications of the algebraic structures available in covering soft sets to soft graphs may reveal new facets of graph theory. [ABSTRACT FROM AUTHOR]

The fluid containing solid nanoparticles "nanofluid" performed more effectively compared to conventional fluids. The thermal scientists and scholars considered nanofluid in their research due to its useful applications in different thermal systems. But nanofluid still not enough for the required thermal transport properties. Therefore, the researchers tried to disperse two or more than two nanoparticles which are called hybrid and tri‐hybrid nanofluid. It was tested experimentally that these hybrid nanofluids are more efficient fluids in different cooling systems compared to nanofluid and regular fluids. The present article carried out the research about the suspension of three different kinds of nanoparticles in various shapes for advance cooling applications in industries and engineering problems. The three nanoparticles are cylindrical carbon nanotubes(CNT)$({CNT})$, spherical aluminum oxide(Al2O3)$({A{l_2}{O_3}})$, and platelet shaped(Graphene) are mixed in water flowing in a rotating disk. This advance fluid has remarkable enhancement in the heat transfer rate in comparison with regular fluid, mono nanofluid and hybrid nanofluid. In this study viscoelastic radiative ternary hybrid nanofluid is considered on a rotating disk. The solutions are obtained by using the HAM method. For physical interpretation, all the flow parameters are discussed through graphs. The impact of volume fraction on the flow and heat transfer is also evaluated and presented in graphs. From the comparison, it was declared that tri‐hybrid nanofluid has the best thermal performance compared to hybrid and mono nanofluid. Furthermore, radiation increases the temperature of the fluid, while viscoelastic parameter decreases the radial and tangential velocity. From the present study, we noticed that by considering the tri‐hybrid mixture in water, the rate of heat transfer can be enhanced up to 33.69%. Finally, the results obtained show that the tri‐hybrid nanofluid has excellent performance in the heat transfer rate. [ABSTRACT FROM AUTHOR]