This paper presents a novel approach for the generation of periodic waveforms in digital form using Field Programmable Gate Array (FPGA) and orthogonal functions. The orthogonal function consists of a set of Rademacher–Walsh Functions, and utilizing these functions, virtually any periodic waveform can be synthesized. Recent technological advancements in FPGA and availability of sophisticated di...

Submodular functions arewell-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions, which we call weakly submodular functions. Our extension is somewhat unusual in that it includes some (mildly) supermodular functions. We show that several natura...

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions and proves that several fam...

It is the objective of this paper to introduce a new class of generalizations of continuous functions via λ-open sets called weakly λcontinuous functions. Moreover, we study some of its fundamental properties. It turns out that weak λ-continuity is weaker than λ-continuity [1]. AMS Mathematics Subject Classification (2000): 54C10, 54D10