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We generalize the global construction of code loops introduced by Nagy, which is based on the connection between Moufang loops and groups with triality. This follows from the construction of a nilpotent group G_n of class 3 with triality and 2n generators, based on embeddings of G_n into direct products of copies of G_3. In the finite case, where G_n is a group such that |G_n| = 2^4n+m with n ≥ 3 and m = 3 n 2 + 2 n 3, we prove that the corresponding Moufang loop is the free loop F_n with n generators in the variety generated by code loops. The result depends on a construction similar to that of G_n, namely, embedding F_n into direct products of copies of F_3, the free code loop associated with G_3.
A ring R (not necessary associative) is normal with respect to involution σ if xx^σ=x^σx for every x from R. We construct some class of diassociative loops, named Q-loops, with normal loop rings. By definition a loop L is a Q-loop if every two generated subloop of L is a subgroup of some group H⊆ L isomorphic to quaternion group Q_8 .
A design method is proposed for the working components of low-power rotary milling snowplows. By correcting the initial parameters, this method may be adapted for snowplows of medium and high power. An algorithm is presented for calculating the basic parameters of the working components.
Local area networks are widely used in modern organizations for data transmission and user interaction. The growth and development of information and communication technologies lead to the need for careful design and evaluation of the quality of functioning of local area networks before implementing new solutions. The prevalent methods employed for the calculation of bandwidth and packet delay are frequently insufficient to encompass the true operational state of a network. Such insufficiency arises from their reliance on simplifying assumptions pertaining to the nature of network load and traffic. Designing and optimizing such networks is a difficult task, especially under conditions of limited resources and increasing demands on information processing speed. This article illustrates the feasibility of employing simulation modeling techniques for the investigation of local computer networks, encompassing the assessment of their efficacy and the refinement of their architecture. A simulation model of a local computer network has been built. The settings of the main elements of the simulated process are described. Tests are conducted with the constructed model with different queue capacities and server loads. Based on the results of the tests, the parameters and characteristics of the network are clarified, conclusions on optimizing its operation and improving its functioning are noted. In particular, it was found that the network under consideration has problems with queuing. The queue size is a controllable parameter, and its optimal value can be selected experimentally using a simulation model. It is noted that improving network performance, namely reducing the percentage of lost requests, can be achieved by optimizing the queue size. The materials presented in the article serve as a basis for evaluating local computer network functionality during design and modernization, and are also relevant to the development of foundational educational programs.
BACKGROUND: The problem of determining the minimum force required for the soil excavation process remains relevant. However, this force is consumed in moving soil volumes that are not well studied at present. Previous studies have primarily focused on the compacted core of the soil, while the rest of the involved soil has been poorly examined. AIM: Determination of the contours of moving soil mass would make it possible to identify the moving mass itself and to incorporate it into a mathematical model, enabling the selection of optimal force for the excavation process. METHODS: A special test rig with a transparent screen for observing the soil to determine the contours was built. A steel plate was used as the stamp. The plate motion with the displaced soil was recorded on video. An analysis of the video recording was conducted after the test. To identify the moving mass, several frames were extracted from the recorded footage and were used for compilation of a new video. The mobility of a point in the soil was assessed by changes in its shade. RESULTS: As a result, 20 contours were obtained for each type of soil. Abnormal results, identified through statistical analysis, were excluded. Areas and visual locations of the contours of moving mass were determined for dry loam, wet loam, and wet clay. CONCLUSION: Thus, the contours of the moving mass of dry loam, wet loam, and wet clay were studied.
