To describe time-dependent finite-dimensional mechanical systems, their generalized space-time is modeled as a Galilean manifold. On this basis, we present geometric theory that unifies Lagrangian and Hamiltonian mechanics. Moreover, general definition of force given, such the capable treating nonpotential forces acting on system. Within theory, elaborate interconne...

In this note the equivalence among Well-ordering Principle, Principle of Finite Induction and certain natural conditions concerning set integers is discussed, thereby clarifying facts encountered in literature.

An active device is an electron device, such as a transistor, capable of delivering power amplification by converting dc bias power into time varying signal power. It delivers a greater energy to its load than if the device were absent. The charge control framework [1-3] presents a unified understanding of the operation of all electron devices and simplifies the comparison of the several active...

Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most properties of frames and tight frames...

As a consequence of identifying the principle described in the title, we prove that for any uncountable cardinal λ, if there is a λ-free Whitehead group of cardinality λ which is not free, then there are many “nice” Whitehead groups of cardinality λ which are not free.

if in multiple offences deserving legal punishment (ḥadd) the perpetrated offences are similar, the punishments interfere and the person is sentenced to one legal punishment. this judgment is disputable from two perspectives. firstly, it is against the principle of non-interference of causes and effects. secondly, it is against the principle of justice and causes disturbance in public security ...