జర్నల్ ఆఫ్ జెనరలైజ్డ్ లై థియరీ అండ్ అప్లికేషన్స్

This study addresses the numerical solution of a nonlocal boundary-value issue for a two-dimensional pseudoparabolic equation that arises in a variety of physical events. For the solution of this problem, a three-layer alternating direction implicit approach is examined. Peaceman-ADI Rachford's approach for the 2D parabolic equation is generalised in this method. The suggested method's stability is demonstrated in the specific norm. To demonstrate its stability, we study the algebraic eigenvalue problem using nonsymmetric matrices.

Since it was first proposed in 2018, researchers have paid attention to the concept of verifiable delay functions. Verifiable delay has numerous applications in blockchain research, including: computational timestamping, public random beacons, blockchains that use fewer resources and data replication proofs This paper provides an overview of the various types of verifiable delay functions as well as an introduction to the concept of verifiable delay functions. First, weak verifiable delay functions, incremental verifiable delay functions, decodable verifiable delay functions and trapdoor verifiable delay functions are introduced, along with their descriptions and characteristics. Two security assumptions are typically used to construct verifiable delay functions: structural assumption or algebraic assumption. On the basis of cryptography theory, the security assumptions of two distinct verifiable delay functions are then described. Second, a super-singular isogeny-based post-quantum verifiable delay function is presented. The paper concludes by providing a synopsis of the blockchain-related uses of verifiable delay functions.