In this paper, the experimental vibration analysis of a single cylinder air compressor based on a hypocycloid straight line mechanism (HSM) is investigated. The HSM mechanism uses planetary gears to convert rotational motion to purely linear motion. In the conventional air compressor, the slider- crank mechanism is replaced by the HSM mechanism with appropriate counterweights. The constructed s...

We present nonlinear pulse compression of a high-power SESAM-modelocked thin-disk laser (TDL) using an Ar-filled hypocycloid-core kagome hollow-core photonic crystal fiber (HC-PCF). The output of the modelocked Yb:YAG TDL with 127 W average power, a pulse repetition rate of 7 MHz, and a pulse duration of 740 fs was spectrally broadened 16-fold while propagating in a kagome HC-PCF containing 13 ...

Abstract We generalize the classical Henneberg minimal surface by giving an infinite family of complete, finitely branched, non-orientable, stable surfaces in $$\mathbb {R}^3$$ R 3 . These can be grouped into subfamilies depending on a positive in...

We present two experiments confirming that hypocycloid Kagome-type hollow-core photonic crystal fibers (HC-PCFs) are excellent candidates for beam delivery of MW peak powers and pulse compression down to the sub-50 fs regime. We demonstrate temporal pulse compression of a 1030-nm Yb:YAG thin disk laser providing 860 fs, 1.9 µJ pulses at 3.9 MHz. Using a single-pass grating pulse compressor, we ...

In this paper we introduce the celebrated Kakeya Conjecture in the original real case setting and discuss the proof of its finite field analogue. The story begins in 1917 when, with the hope of figuring out a mathematical formalization of the movement of a samurai during battle, Sochi Kakeya proposed the following problem: What is the least area in the plane required to continuously rotate a ne...

It is known [1, p.115] that the envelope of the family of pedal lines (Simson or Wallace lines) of a triangle ABC is Steiner’s deltoid, a three-cusped hypocycloid that is concentric with the nine-point circle of ABC and touches it at three points. Also known [2, p.249] is that the nine-point circle is the locus of the intersection point of two perpendicular pedal lines. This paper considers a g...