Bipolar neutrosophic soft sets are powerful tools for modeling data under conditions of uncertainty and imprecision due to their rich parametric structure and the useful mathematical properties of the operations defined on them. In this paper, motivated by the limitations of existing decision‐making algorithms, we introduce a new numerical characteristic, the energy of a bipolar neutrosophic soft set defined using singular values, analogous to the graph energy and nuclear norm. Our goal is to develop an efficient decision‐making algorithm that successfully identifies the optimal alternative even in cases where other algorithms provide inaccurate or inconsistent results. Our research is motivated by the need for more reliable decision‐making methods in complex soft environments and the potential of the energy‐based approach to overcome the weaknesses of existing methods, which we demonstrate through a comparative analysis using concrete examples.

For some time now, researchers around the world have been examining the effects of using AI in mathematics education to provide additional support and assistance to students. One line of research focuses on helping students who wish to participate in math competitions by solving more complex mathematical problems. In addition to regular national math competitions, which allow students to progress to international mathematical Olympiads, there are competitions aimed at popularizing mathematics and developing logical thinking in students. One such competition is the international Kangaroo competition. In this paper, we analyze the performance of the AI Math Solver on the Interactive Mathematics platform in solving problems from the 2024 Kangaroo competition for students in the 3rd and 4th grades of elementary school, as well as the 7th and 8th grades of elementary school, and the 3rd and 4th grades of high school. The tasks were uploaded in the form of images (screenshots), both in Serbian and English, because in the formulation of the tasks and/or provided answers for the Kangaroo competition, images often appear. Out of a total of 84 tasks, both in Serbian and in English, it correctly solved 24, which is just under 30% success in both cases. Furthermore, some tasks solved in Serbian were not solved in English, and vice versa. Additionally, differences were found in the distribution of correct answers among tasks of different difficulty levels.

The mechanisms that limit the speed at which striated muscles relax are poorly understood. This work presents novel simulations that show that the timecourse of relaxation is accelerated by interfilamentary movement resulting from series compliance; force drops faster when myosin heads move relative to actin during relaxation. This insight was obtained by using cross-bridge distribution techniques to simulate the mechanical behavior of half-sarcomeres that were connected in series with springs of varying stiffness. (The springs mimic the combined effects of half-sarcomere hetereogeneity and muscle's series elastic component.) Half-sarcomeres that shortened by more than ~10 nm when they were activated subsequently relaxed with a biphasic profile; force initially declined slowly and approximately linearly before collapsing with a fast exponential time-course. Stretches imposed during the linear phase quickened relaxation, while shortening movements prolonged the time-course. These predictions are consistent with data from experiments performed by many other groups using single muscle fibers and isolated myofibrils. When half-sarcomeres were linked to stiff springs (so that they did not shorten appreciably during the simulations), force relaxed with a slow exponential timecourse and did not show biphasic behavior. Together, these results suggest that fast relaxation of striated muscle is an emergent property that reflects multi-scaled interactions within the muscle architecture. As muscles develop force, they store energy in series elastic structures. When the cells relax, the strain energy stretches the actin-myosin cross-bridge bonds and causes some myosin heads to detach. This adds further strain to the remaining crossbridge links and starts a positive feedback loop that quickly breaks all remaining actin-myosin bonds. Series compliance therefore allows muscle to relax quickly without needing to use large amounts of ATP to power fast crossbridge cycling.