Narrow Results

Given a set P of points (clients) in the plane, a Euclidean 2-centre of P is a set of two points (facilities) in the plane such that the maximum distance from any client to its nearest facility is minimized. Geometrically, a Euclidean 2-centre of P corresponds to a cover of P by two discs of minimum radius r (the Euclidean 2-radius). Given a set of mobile clients, where each client follows a continuous trajectory in the plane with bounded velocity, the motion of the corresponding mobile Euclidean 2-centre is not necessarily continuous. Consequently, we consider strategies for defining the trajectories of a pair of mobile facilities that guarantee a fixed-degree approximation of the Euclidean 2-centre while maintaining bounded relative velocity. In an attempt to balance the conflicting goals of closeness of approximation and a low maximum relative velocity, we introduce reflection-based 2-centre functions by reflecting the position of a mobile client across the mobile Steiner centre and the mobile rectilinear 1-centre, respectively.

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

Blockchain mining pools assist in reducing computational load on individual miner nodes via distributing mining tasks. This distribution must be done in a non-redundant manner, so that each miner is able to calculate block hashes with optimum efficiency. To perform this task, a wide variety of mining optimization methods are proposed by researchers, and most of them distribute mining tasks via statistical request processing models. These models segregate mining requests into non-redundant sets, each of which will be processed by individual miners. But this division of requests follows a static procedure, and does not consider miner specific parameters for set creation, due to which overall efficiency of the underlying model is limited, which reduces its mining performance under real-time scenarios. To overcome this issue, an Incremental & Continuous Q-Learning Framework for generation of miner-specific task groups is proposed in this text. The model initially uses a Genetic Algorithm (GA) method to improve individual miner performance, and then applies Q-Learning to individual mining requests. The Reason for selecting GA model is that it assists in maintaining better speed-to-power (S2P) ratio by optimization of miner resources that are utilized during computations. While, the reason for selecting Q-Learning Model is that it is able to continuously identify miners performance, and create performance-based mining pools at a per-miner level. Due to application of Q-Learning, the model is able to assign capability specific mining tasks to individual miner nodes. Because of this capability-driven approach, the model is able to maximize efficiency of mining, while maintaining its QoS performance. The model was tested on different consensus methods including Practical Byzantine Fault Tolerance Algorithm (PBFT), Proof-of-Work (PoW), Proof-of-Stake (PoS), and Delegated PoS (DPoS), and its performance was evaluated in terms of mining delay, miner efficiency, number of redundant calculations per miner, and energy efficiency for mining nodes. It was observed that the proposed GA based Q-Learning Model was able to reduce mining delay by 4.9%, improve miners efficiency by 7.4%, reduce number of redundant computations by 3.5%, and reduce energy required for mining by 7.1% when compared with various state-of-the-art mining optimization techniques. Similar performance improvement was observed when the model was applied on different blockchain deployments, thus indicating better scalability and deployment capability for multiple application scenarios.

Theorems of Osofsky and Kato imply that a right and left self-injective one-sided perfect ring is quasi-Frobenius (= QF). The corresponding question for one-sided self-injective one or two-sided perfect rings remains open, even assuming that the ring is semiprimary. The latter version of the problem is known as Faith's Conjecture (FC). We survey results on QF rings, especially those obtained in connection with FC. We also review various results that provide partial answers to another problem of Faith: Is a right FGF ring necessarily QF? On this topic, we provide a new result, namely that if all factor rings of R are right FGF, then R is QF (Theorem 6.1). In Sec. 7 we review results concerning the question of when a D-ring is QF. Sections 8 and 9 are devoted respectively to IF rings, and to Σ-injective rings and Σ-CS rings.

Structural and parametric identification of nonlinear continuous dynamic systems with a closed cycle on a set of continuous block-oriented models with feedback is considered. The method of structural identification in the steady state based on the observation of the system's input and output variables at the input periodic influences is proposed. The solution of the parameter identification problems, which can be immediately connected with the structural identification problem, is carried out in the steady and transient states by the method of least squares. The structural and parametric identification algorithms are investigated by means of both theoretical analysis and computer modeling.