‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

Comparing with fixed shaft gearbox, vibration properties of planetary gearbox are much more complicated. In a planetary gearbox, there are multiple vibration sources as several pairs of sun-planet gears and several pairs of ringplanet gears mesh simultaneously. In addition, the signal transmission path changes due to the rotation of the carrier. To facilitate fault detection of a planetary gear...

Luminaire sampling plays an important role in global illumination calculation using Monte Carlo integration. A conventional approach generates samples on the surface of the luminaire, resulting in rendered images with high variance of noise. In this paper, we present an efficient solid angle sampling technique using tunable bounding volumes for global illumination calculation. In contrast to th...

  This study aimed to design a bycatch reduction device (BRD) for shrimp beam trawl, which is manufactured by flexible materials to reduce bycatch for the gear in the South Sea of Korea. The model test was carried out to understand the shape of the gear in the water and to measure the variation of flow speed due to the BRD in a circulating water channel. Catches were compared between a shrimp b...

In recent years a clear trend has developed in the aerospace industry towards the procurement of integrated systems from major suppliers (ref. 1). In this process, Messier-Dowty became a provider of integrated landing gear systems who is responsible for supplying a certifiable landing gear system and providing all the system level performance analysis. The aircraft landing gear system retractio...

Planetary Gear Trains are extensively used for the power transmission. Large reduction in a small volume is possible with planetary gear trains. High efficiency – 95% per stage is common in planetary gear trains. For the automation of car parking systems helical gear box is used. But requirements of the gear box of these kind shall be compact in size and should have high efficiency. For these r...

We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions full cylinders, rings, sectors ring segments. The derivation is done direct integration in surface charge picture. Results are closed-form expressions elliptic integrals. All special cases treated individually, which enables computation all possible position arguments ...

In this paper, we prove the existence of nontrivial unbounded domains Ω⊂Rn+1,n≥1, bifurcating from straight cylinder B×R (where B is unit ball Rn), such that overdetermined elliptic problem{Δu+f(u)=0in Ω, u=0on ∂Ω, ∂νu=constanton has a positive bounded solution. We will result for very general class functions f:[0,+∞)→R. Roughly speaking, only ask Dirichlet problem in admits nondegenerate The p...

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is mixed elliptic–hyperbolic changes type suitable formulation boundary conditions at boundaries great importance. First, we establish existence uniqueness spiral solutions with nonzero...