An interesting result of Ivanov implies that a non-aspherical relative presentation that defines a torsion-free group would provide a potential counterexample to the Kaplansky zero-divisor conjecture. In this point of view, we prove the asphericity of the length-6 relative presentation H, x : xh 1 xh 2 xh 3 xh 4 xh 5 xh 6 , provided that each coefficient is torsion free.
Abstract. For an even integer m at least 4 and any positive integer t, it is shown that the complete equipartite graph K km(2t) can be decomposed into edge-disjoint gregarious m-cycles for any positive integer k under the condition satisfying< k. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.
We prove that equations xm1 h1 xm2 h2 ⋯ xmk hk over torsion-free groups are solvable when k ≤ 4. In the conclusion, we assert that the Levin question is equivalent to solving certain equations with exponent sum zero over torsion-free groups.
The management of type 2 diabetes mellitus (T2DM) is generally not only focused on pharmacological therapy. Medical nutrition therapy is often forgotten by patients for several reasons, such as difficulty determining the right nutritional pattern for themselves, regulating their daily nutritional patterns, or even not heeding nutritional diet recommendations given by doctors. Management of nutritional therapy is one of the important efforts that can be made by diabetic patients to prevent an increase in the complexity of the disease. Setting a diet with proper nutrition will help patients manage a healthy diet. The development of Smart Plate Health to Eat is a technological innovation that helps patients and users know the type of food, weight, and nutrients contained in certain foods. This study involved 50 types of food with a total of 30,800 foods using the YOLOv5s algorithm, where the identification, measurement of weight, and nutrition of food were investigated using a Chenbo load cell weight sensor (1 kg), an HX711 weight weighing A/D module pressure sensor, and an IMX219-160 camera module (waveshare). The results of this study showed good identification accuracy in the analysis of four types of food: rice (58%), braised quail eggs in soy sauce (60%), spicy beef soup (62%), and dried radish (31%), with accuracy for weight and nutrition (100%).
Trust in information and communication technology devices is an important factor, considering the role of technology in carrying out supporting tasks in everyday human activities. The level of trust in technology will influence its application and adoption. Recognizing the importance of trust in technology, researchers in this study will examine trust components for the development of a type 2 diabetes mobile application. The results of this study resulted in three major focuses, namely the application design (consisting of architecture), UI design, and evaluation of trust factors of the application: functionality, ease of use, usefulness, security and privacy, and cost. This analysis of trust components will be useful for the application or adoption by users of a type 2 diabetes mellitus mobile application so that users will trust the application both in terms of functionality and the generated information.
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