Infinite product representation of solutions of indefinite problem with a finite number of arbitrary turning points

In this paper we consider the Sturm-Liouville equation (y\u27\u27+(rho^2phi^2(x)-q(x))y=0) on a finite interval I , say I=[0,1], under the assumption that I contains a finite number of arbitrary type turning points, which are zeros of (phi) in I . According to the four types of turning points, first we obtain the asymptotic forms of the solutions of (*) and then based on Hadamard\u27s factorization theorem we use this asymptotic estimates to study the infinite product representation of solutions of such equations. Infinite product form of the solution has a basic application in studies of inverse spectral problems

Existence of a homoclinic orbit in a generalized Liénard type system

The object of this paper is to study the existence and nonexistence of an important orbit in a generalized Liénard type system. This trajectory is doubly asymptotic to an equilibrium solution, i.e., an orbit which lies in the intersection of the stable and unstable manifolds of a critical point. Such an orbit is called a homoclinic orbit

Deep Learning meets Blockchain for Automated and Secure Access Control

Access control is a critical component of computer security, governing access to system resources. However, designing policies and roles in traditional access control can be challenging and difficult to maintain in dynamic and complex systems, which is particularly problematic for organizations with numerous resources. Furthermore, traditional methods suffer from issues such as third-party involvement, inefficiency, and privacy gaps, making transparent and dynamic access control an ongoing research problem. Moreover detecting malicious activities and identifying users who are not behaving appropriately can present notable difficulties. To address these challenges, we propose DLACB, a Deep Learning Based Access Control Using Blockchain, as a solution to decentralized access control. DLACB uses blockchain to provide transparency, traceability, and reliability in various domains such as medicine, finance, and government while taking advantage of deep learning to not rely on predefined policies and eventually automate access control. With the integration of blockchain and deep learning for access control, DLACB can provide a general framework applicable to various domains, enabling transparent and reliable logging of all transactions. As all data is recorded on the blockchain, we have the capability to identify malicious activities. We store a list of malicious activities in the storage system and employ a verification algorithm to cross-reference it with the blockchain. We conduct measurements and comparisons of the smart contract processing time for the deployed access control system in contrast to traditional access control methods, determining the time overhead involved. The processing time of DLBAC demonstrates remarkable stability when exposed to increased request volumes.Comment: arXiv admin note: text overlap with arXiv:2303.1475

Infinite product representation of solutions of indefinite problem with a finite number of arbitrary turning points

In this paper we consider the Sturm-Liouville equation (y\u27\u27+(rho^2phi^2(x)-q(x))y=0) on a finite interval I , say I=[0,1], under the assumption that I contains a finite number of arbitrary type turning points, which are zeros of (phi) in I . According to the four types of turning points, first we obtain the asymptotic forms of the solutions of (*) and then based on Hadamard\u27s factorization theorem we use this asymptotic estimates to study the infinite product representation of solutions of such equations. Infinite product form of the solution has a basic application in studies of inverse spectral problems

ForensiBlock: A Provenance-Driven Blockchain Framework for Data Forensics and Auditability

Maintaining accurate provenance records is paramount in digital forensics, as they underpin evidence credibility and integrity, addressing essential aspects like accountability and reproducibility. Blockchains have several properties that can address these requirements. Previous systems utilized public blockchains, i.e., treated blockchain as a black box, and benefiting from the immutability property. However, the blockchain was accessible to everyone, giving rise to security concerns and moreover, efficient extraction of provenance faces challenges due to the enormous scale and complexity of digital data. This necessitates a tailored blockchain design for digital forensics. Our solution, Forensiblock has a novel design that automates investigation steps, ensures secure data access, traces data origins, preserves records, and expedites provenance extraction. Forensiblock incorporates Role-Based Access Control with Staged Authorization (RBAC-SA) and a distributed Merkle root for case tracking. These features support authorized resource access with an efficient retrieval of provenance records. Particularly, comparing two methods for extracting provenance records off chain storage retrieval with Merkle root verification and a brute-force search the offchain method is significantly better, especially as the blockchain size and number of cases increase. We also found that our distributed Merkle root creation slightly increases smart contract processing time but significantly improves history access. Overall, we show that Forensiblock offers secure, efficient, and reliable handling of digital forensic dataComment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Uniqueness for Inverse Sturm-Liouville Problems with a Finite Number of Transmission Conditions

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the case of classical Robin and of eigenparameter dependent boundary conditions.Comment: 15 pages; Addendum adde

Dual equation and inverse problem for an indefinite Sturm–Liouville problem with m turning points of even order

In this paper the differential equation y″ + (ρ 2 φ 2 (x) –q(x))y = 0 is considered on a finite interval I, say I = [0, 1], where q is a positive sufficiently smooth function and ρ 2 is a real parameter. Also, [0, 1] contains a finite number of zeros of φ 2 , the so called turning points, 0 < x 1 < x 2 < … < x m < 1. First we obtain the infinite product representation of the solution. The product representation, satisfies in the original equation. As a result the associated dual equation is derived and then we proceed with the solution of the inverse problem