An explicit form of the joint distribution of an arbitrary fixed triple of events from a finite family in a Bernoulli scheme with parameters (n, p) is obtained. The relationship between the parameter n and the maximum value of each of the derived joint distributions is established under the condition p = 2–1. The value of the parameter p that ensures the maximum of these joint distributions is determined. An example of estimating the randomness of the placement of zeros and ones in specific (0,1)-sequences is presented. An example of determining the uniqueness threshold of a system of linear random Boolean equations over a special set of (0,1)-vectors is also given.
We consider single-channel blind separation of two PSK signals with unknown parameters. This problem is particularly important for communication systems where two signals occupy the same frequency band. It is shown that the blind separation problem can be reduced to a multi-class classification problem, which can be solved using modern machine learning methods. A four-layer neural network is proposed to solve this problem. The effectiveness of this method has been verified using BPSK and QPSK signals under various amplitude ratios and noise levels. It is also shown that in the absence of one of the signals, the proposed separation method effectively demodulates the present signal.
We formulate a fuzzy two-stage continuous–discrete optimal set partitioning problem, which generalizes, on the one hand, the classical finite-dimensional transportation problem to the case where production volumes at given locations are unknown in advance and are determined as the solution to the corresponding fuzzy continuous problem of optimal partitioning of a set of consumers (suppliers of a continuously distributed resource) into fuzzy subsets (the service areas of these points), and, on the other hand, discrete two-stage production–transportation problems for the case of a continuously distributed resource. Theorems regarding the conditions for the existence and form of the optimal solution to the formulated problem are proved. A method for solving it is developed based on the synthesis of the theory of optimal set partitioning and fuzzy set theory.
The convergence of a stochastic optimal control problem with Markov switches in an averaging scheme is analyzed. A combination of the standard Wiener process and a uniformly ergodic Markov process is considered, allowing us to describe the system’s evolution under the influence of diffusion noise and random mode switches. The ergodic properties of the fast process and the conditions for the regularity of the coefficients are presented, which guarantee stable behavior of the system on average. The convergence in probability of the trajectories of the original system to the solutions of the marginal averaged system is proved (through Lp-estimates). The obtained results enable the solution of stochastic optimization and optimal control problems.
To improve the positioning accuracy and management efficiency of laboratory equipment, this study proposes an efficient positioning management system based on an improved Bat Algorithm (BA) and Radio Frequency Identification (RFID) technology. Findings demonstrate that the improved BA converges after 120 iterations, with its accuracy and recall approaching 0.982 and 0.956. In the efficient positioning management system for laboratory equipment, its positioning accuracy is superior to the comparative system, while its response time is only 0.031 s. This research can avoid equipment idleness or overuse, thereby optimizing the allocation and utilization efficiency of laboratory resources.
