 springs alternates according to what is dictated by the corresponding quasiperiodic pattern, i.e. $l_j \in \{l_p,l_q\}$. The bulk spectrum of cases (c) and (d) reveals the effect of the distribution of the elastic supports in the low frequency range. Since the beam itself is continuous without heterogeneous distribution of parameters, it is expected that the high frequency range associated to short wavelength  will be less affected  by the stiffness of the supports. This behavior can be visualized in fig.~\ref{fig12}(c) and (d) where passbands are closer each other in the high frequency range.
\begin{table}
	\input{tab02.tex}
	\caption{Example 3: Properties of Timoshenko beams in fig.~\ref{fig12}}
	\label{Table_Properties_TIBeam}	
\end{table}

The Timoshenko beam model provides a glimpse into the range of possible bulk spectra as a function of the different parameters. Our motivation is still to find closed forms that allow predicting the general behavior of the Sturmian systems along the range $0 \leq \alpha \leq 1$, without the numerical computation of the dispersion relation for each $\alpha$, something that is computationally expensive, specially if $4 \times 4$ transfer matrices are involved. 



\section{Conclusions}


In this paper we study the dynamic properties of heterogeneous elastic structured media with quasiperiodic pattern.  Sturmian words have been originally defined in the context of information theory. Quasiperiodic patterns based on Sturmian words have been applied in theoretical physics such as condensed matter or quantum mechanics, but to the best of our knowledge, they have not been applied to the generation of mechanical systems such as elastic waveguides. Consider any real number in the interval [0,1] given as a continued fraction, we can construct a word or sequence from a binary alphabet, giving rise to so-called Sturmian sequence. The methodology proposed in this paper takes such a string consisting of two symbols and transforms it into a quasi-periodic sequence consisting of two different values of one single parameter from the mechanical system. Dynamical properties and dispersion relations of Sturmian mechanical systems have been analytically determined using the transfer matrix method. This method also allows to justify self-similarity of the bulk spectrum. These properties have been validated and visualized along three numerical examples covering a  spring-mass lattice and two continuous systems: a rod and a beam. In the first case, the spring constants have been used as the quasiperiodic parameter. In the case of the rod, the sectional stiffness is changed according to the Sturmian pattern and in the beam case four different mechanical variables to be distributed quasiperiodically are considered separately: sectional stiffness, mass, spring supports rigidity and distances between springs. In all cases, the complete bulk spectrum of admitted states or frequencies of the system have been obtained and the results derived from the theoretical analysis validated. 









Bragg Gaming Group, a global gaming technology supplier, has made a commercial agreement with Novibet for its subsidiary ORYX, an iGaming content and solutions provider.
Bragg’s ORYX Boosts Presence in Greece with Novibet
Just weeks after receiving a B2C supplier license, Bragg Gaming Group has strengthened its foothold in Greece. Its ORYX Gaming content going live with Novibet, one of the largest operators in the country. Through its subsidiary, ORYX Gaming, Bragg delivers exclusive casino games with its in-house remote games server (RGS) and ORYX Hub distribution platform.
With this collaboration, ORYX will expand its reach in Greece after the supplier secured a license and already formed partnerships with several local brands. Novibet aims to provide an entertaining, immersive experience and ORYX can guarantee such an offering.
Bragg and Novibet’s Partnership Could Be Destined for Success
Bragg is a fast-growing global gaming technology group that owns B2B companies in the iGaming industry. Established in 2018, Bragg has created a strong foothold in key markets across Europe, LatAm, and North America. In May, Bragg announced its acquisition of Spin Games, a Nevada-based B2B gaming technology and content provider with licenses in key regulated US markets. The definitive merger is valued at $30 million.
Bragg recently appointed Chris Looney as its CCO. When commenting on the new partnership deal between Bragg and Novibet, he said that the company has what it takes to run in Greece and this collaboration with Novibet is essential because it would distribute ORYX’s content to one of the biggest brands in the country.
Since 2010, Novibet offers online sports wagering and casino games in key markets like Greece and the UK. With its constantly growing customer base and cutting-edge content, Novibet is an established gaming company with operations across Europe. The company has licenses from HGC, ADM, MGA and the UKGC. Its offering is constantly evolving to meet players’ demands and exceed expectations.
Novibet Casino Manager Fotini Matthaiou said that ORYX has a portfolio of great titles and players in Greece will appreciate them.
Novibet Will Distribute Oryx Content across Italy and the UK
After its successful integration, Novibet customers will access ORYX’s premium content offering of hit titles. Under the deal, Novibet is to distribute provider’s content across the Italian and the UK markets. Later this year, ORYX expects to receive a UKGC license and have its first titles certified for Italy.
Looney said that, by strengthening its position in Greece, the deal would also provide an opportunity for ORYX in the future to expand in other regulated markets.
As part of its expansion strategy, Bragg has also announced that it plans to enter regulated markets in Europe, North America and other parts of the world in the future.
Matthaiou said that Novibet is thrilled to have ORYX on board when expanding its portfolio and looks forward to a fruitful collaboration.A National Research Council committee is conducting a study on how well greenhouse gas emissions can be measured for treaty monitoring and verification. The committee’s analysis suggests that NASA’s Orbiting Carbon Observatory (OCO), which failed on launch in February 2009, would have provided proof of concept for spaceborne technologies to monitor greenhouse gas emissions, as well as baseline emissions data. This letter focuses on the capabilities of an OCO and currently deployed satellites that measure atmospheric carbon dioxide (CO2) and their potential role in monitoring and verifying a greenhouse gas treaty.
There is a niche gaming market that likes to take their simulation gaming to extremes. Turtle Beach is taking advantage of that opportunity with their VelocityOne Flight System for Xbox Series X and PC. The VelocityOne Flight System includes two components, with a third optional accessory. First there is the VelocityOne Flight System Universal Control System, which includes a yoke a throttle. Then there is the VelocityOne Rudder. And finally, the optional component is the upcoming VelocityOne Stand that allows you to install the various components into one handy, portable cockpit. The combined set up is designed to give aspiring pilots the most realistic experience for Microsoft’s Flight Simulator.
Turtle Beach was generous enough to send us a VelocityOne Rudder for review purposes. Unfortunately, we were unable to give it a proper test. In order to use the VelocityOne Rudder on the Xbox Series X, you need the VelocityOne Flight Universal Control System. The rudder on its own is completely useless with the Xbox Series X – so keep this in mind if your intention is to game on your Xbox.
The VelocityOne Rudder is compatible, on it’s own, on PC, by simply plugging it into the PC USB port. Unfortunately, in order to play Microsoft Flight Simulator on PC, you’ll need to use the PC Xbox app – and for many folks, myself included, that app just won’t work. Despite my efforts to reach out to Xbox support to get the PC Xbox app/PC Game Pass working on my PC, my requests were ignored.
With this all said, the extent of my impressions is limited to what I was able to unbox and observe.
The first thing of note is just how hefty the VelocityOne Rudder is. It weighs over ten pounds and feels extremely sturdy. Despite its heft, I noticed it would shift quite a bit when I would put my feet on the pedals. It’s clear to me that for optimal performance, folks will want to buy the VelocityOne Stand, which should add enough weight to prevent it from shifting around too much.
The VelocityOne Rudder offers the ability to adjust the pedals in two distinct ways. The first is adjusting it for larger aircraft or light aircraft – defined by either using the full pedal or removing the heel portion of the pedal. The second way is adjusting the pedal width, which from what I can tell is likely more for comfort purposes.
So, why would you need a VelocityOne Rudder? I’m glad you asked. The rudder, in this case, provides gamers with three different movement options. The first, and most significant, is adjusting the planes yaw – in flight – by sliding the pedals. The second and third options involve the braking while the plane is taxiing. Toe brakes to slow the plane and differential braking for tight turns while taxiing.
The VelocityOne Rudder is an impressive piece of hardware. It feels well-designed and sturdy. It probably would have benefited from a bit more weight to prevent accidental sliding, but I imagine the most ambitious aspiring pilots