Affine space-time mappings have been extensively studied for systolic array design and parallelizing compilation. However, there are practical important cases that require other types of transformations. This paper considers so-called modular mappings described by linear transformations modulo a constant vector. Sufficient conditions for these mappings to be one-to-one are investigated fc~r rec...

*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contr...

The quantum modular invariant jqt(θ) of θ ∈R is defined as a discontinuous PGL2(Z)-invariant multi-valued map using the distance-to-the-nearest-integer function ‖ · ‖. For θ ∈Q it is shown that jqt(θ) =∞ and for quadratic irrationalities PARI/GP experiments suggest that jqt(θ) is a finite set. In the case of the golden mean φ, we produce explicit formulas involving weighted versions of the Roge...

The theory of modular space was initiated by Nakano [1] in connection with the theory of order spaces and was redefined and generalized byMusielak and Orlicz [2]. By defining a norm, particular Banach spaces of functions can be considered. Metric fixed theory for these Banach spaces of functions has been widely studied (see [3]). Another direction is based on considering and abstractly given fu...

Model checking by exhaustive state space enumeration is one of the most developed analysis methods for distributed event systems. Its main problem—the size of the state spaces—has been addressed by various reduction methods. Complex systems tend to consist of loosely connected modules, which may perform internal tasks in parallel. The possible interleavings of these parallel tasks easily leads ...

Space Vector Pulse Width Modulation is popular for variable frequency drives. The method has several advantages over carried based PWM and is computation intensive. The implementation of SVPWM for multilevel inverter requires special attention and at the same time consumes considerable resources. Due to faster processing power and reduced over all computational burden, FPGAs are being investiga...

In this article we develop the theory of H-Orlicz space generated by generalised Young function. Modular convergence for case vector-valued functions and norm in $$\mathcal {H}^\theta (X, \overline{\mu })$$ where X is any Banach are discussed. Relationships modular spaces