We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.

We consider the optimal H2 model reduction for large scale multiinput multi-output systems via tangential interpolation. Specifically, we prove that for general multi-input multi-output systems, the tangential interpolationbased optimality conditions and the gramian-based optimality conditions are equivalent. Based on the tangential interpolation, a fast algorithm is proposed for the optimal H2...

When we fix one side and draw different tangential quadrilaterals having the same side lengths but different angles we observe that their incenters lie on a circle. Based on a known formula expressing the incircle radius of a tangential quadrilateral by its tangent lengths, some older results will be presented in a new light and the equation of the before mentioned circle will appear. This circ...

We study gravitational lensing by quadrupole potentials within the linearized gravity approximation and the integration over the unperturbed photon trajectory. It is well known that the quadrupole potential contribution to the deviation angle is much smaller than that of the monopole one. We show, however, that quadrupole potentials can change the photon polarization vector, but there is no con...

Sir, Ambu AuraGainTM[1] is a new single-use supraglottic airway (SGA) device available in adult size 3, 4, and 5. It is an anatomically curved SGA with integrated gastric access and can be used as a conduit for direct endotracheal intubation assisted by a flexible scope.[1] The standard recommended insertion technique is as that of intubating laryngeal mask airway (LMA),[2] i.e., keeping the ha...

Piping vibration which is mainly caused by the torsional vibration of rotary compressor can be a major noise source of air-conditioner. Especially, the tangential vibration of rotary compressor which is due to the torsional vibration is much higher than the radial vibration or the vertical vibration of compressor. A study as to how the tangential vibration of rotary compressor is related with t...

A solution is developed for the oblique impact of an elastic sphere on a half-space. The Hertzian theory of impact is used for the normal components of force and velocity, and it is assumed that the contact area comprises sticking and slipping regions, in the latter of which the coefficient of friction is constant. The mixed boundary value problem for the tangential tractions and displacements ...