Understanding trigonometry relational system is a school mathemat-ics demanding topic. The angle, the unit circle and trigonometric functions are its foundational notions. Trigonometric contents mean-ing their understanding involve these three concepts re-lationships. This research aims to deepen in pre-service teachers’ about function when converting notions between two repre-sentation systems...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

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the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

Abstract Funding Acknowledgements Type of funding sources: None. Background Dynamic substrate changes play a key role in facilitating conduction delay and re-entry ventricular tachycardia (VT) circuits. Extrastimuli pacing can unmask functional channels demonstrated by dynamic delay, which may the VT circuit. We have previously developed sense protocol mapping, using short coupled single extras...

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally,...

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.