The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

There is a case about a system comprising two queues of M/M(a)/1/K with a due date with FCFS service policy in each queue. Using the methods of simulation and mathematical analysis, the solution diagrams were illustrated for the fixed due date Ɵ=1 second at the phase of due date up to the commencement of the service, limited capacity K₁=5 and K₂=4, for both scenarios of different service management rate resulted. For the analytical solution, first, a SAN model from the system was created in the Mobius tool. For simulation, a java discrete systems simulation code was used. Adjustment of the initial values, selection of the scenarios for service rate, the number of the consumers in the simulation, etc. were all carried out in the simulation code.

As we approach the 135th anniversary of the automobile, two industry trends, automation and digitalization, are rapidly revolutionizing the thus far, relatively unchanged automotive user experience. This paper describes the development of the Valeo MyMobius user interface concept. The goal of this project was to explore how to achieve an intuitive driving experience as the automotive industry undergoes transition from primarily analog to primarily digital interfaces and from physical buttons to multimodal interactions. To achieve the perception of intuitiveness, designers must understand their users, find and reduce physical and cognitive friction points, and bridge knowledge gaps with interface designs that facilitate discovery and learnability. The Valeo MyMobius concept featured steering wheel touch displays that supported quick, frequent menu selections using swiping gestures (common in smartphone interactions) and reinforcing icons (to facilitate learnability). Learning algorithms personalized the experience by tailoring suggestions, while more complex interactions were handled with a conversational voice assistant, which also served as a driving copilot, capable of contextually suggesting when Advanced Driving Assistance System (ADAS) features such as ACC could be utilized. The visual design aesthetic embodied Kenya Hara’s design philosophy of “Emptiness,” reducing visual clutter and creating spaces that are ready to receive inspiration and information. Altogether, the Valeo MyMobius concept demonstrated an attainable future where the perception of intuitiveness can be achieved with today’s technologies.

The part of this article dealing with topological insulators and topological superconductors was first written about two years ago - the ideas in the part about the topological universe originated six years ago or more. It’s rather strange that I never put the two parts together in writing before. My belief in unification is unshakeable - I’ve been convinced for years that the universe must be composed of topology. Since Earth is part of the cosmos, entanglement means it must have topological materials. The reverse is also true: topological materials on Earth are well known to science - so in a unification, space and time inevitably possess topological composition. Topological materials (topological insulators, topological superconductors) can be less mystifying if they’re related to the paradigm-shifting deterministic view of quantum mechanics which is described in the universal topology (the “rubber-sheet geometry” of the cosmos): see my previous submission “Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories" at https://www.preprints.org/manuscript/202105.0239/v1 (the first section of this present article is a quick summary of the relevant parts).

According to Swiss-American Doctor of Sciences and Agricultural Engineer Jean-Pierre Jost, "plants communicate with each other by the quality of light emitted by their leaves or by means of stress hormones and other volatile chemicals. They also make use of cocktails of chemicals, pheromones, shape and colors to attract pollinators whereas other signals repel unwanted organisms. Insects are able to decode such messages and respond accordingly. Plants are apparently also communicating by sounds and electric signals." (1) How do plants do these things? Of course, it's easy to imagine it's all purely mechanical. But at the risk of sounding like a mysticism fanatic, I wonder if plants' activities are part of a spectrum of consciousness that pervades the entire universe. This spectrum would result from everything in the universe having the BITS or BInary digiTS of electronics as their ultimate composition. As explained in this hypothesis, something I call vector-tensor-scalar geometry is essential to my hypothesis. VTS geometry produces the particles of chemicals and pheromones, and refers to communication via electric signals when it speaks of electromagnetic-gravitational interaction. There's another consequence if everything in the universe is ultimately composed of electronic BITS and the cosmos is a spectrum of consciousness/artificial intelligence. It's impossible for an absence of consciousness to exist, either after death or before conception.