The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis world in Pythagorean manner. unifies foundations mathematics (Peano and set theory), physics (quantum mechanics information), philosophical transcendentalism (Husserl’s phenomenology) into formal theory mathematical structure literally following Husserl’s tracе “philosophy rigorous science”. In pathway to ...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations o...

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

A group G is called bounded if every conjugation-invariant norm on has finite diameter. We introduce various strengthenings of this property and investigate them in several classes groups including semisimple Lie groups, arithmetic linear algebraic groups. provide applications to Hamiltonian dynamics.

In a real situation, digital filters are usually implemented via the two’s complement arithmetic because subtraction can be implemented easily via addition. However, the two’s complement arithmetic involves a periodic discontinuous nonlinear function, and the dynamics of digital filters could be very complicated even when no input signal is applied. Limit cycle and chaotic behaviors could occur...