Integer Solutions of Integral Inequalities and <svg style="vertical-align:-0.0pt;width:21.7125px;" id="M1" height="14.7625" version="1.1" viewBox="0 0 21.7125 14.7625" width="21.7125" xmlns="http://www.w3.org/2000/svg">
			<g transform="matrix(1.25,0,0,-1.25,0,14.7625)">
				<g transform="translate(72,-60.19)">
					<text transform="matrix(1,0,0,-1,-71.95,60.24)">
						<tspan style="font-size: 17.93px; " x="0" y="0">𝐻</tspan>
					</text>
				</g>
			</g>
		</svg>-Invariant
Jacobian Poisson Structures

<table>An example of the polytope <svg height="14.925" id="M485" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 20.4375 14.925" width="20.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.925)">
<g transform="translate(72,-60.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝒫</tspan>
</text>
<text transform="matrix(1,0,0,-1,-60.57,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
</text>
</g>
</g>
</svg> in the case <svg height="10.6875" id="M486" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 33.700001 10.6875" width="33.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">2</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in Mathematical Physics

fig3

Figure 3

Figure 3: Integer Solutions of Integral Inequalities and <svg style="vertical-align:-0.0pt;width:21.7125px;" id="M1" height="14.7625" version="1.1" viewBox="0 0 21.7125 14.7625" width="21.7125" xmlns="http://www.w3.org/2000/svg">
			<g transform="matrix(1.25,0,0,-1.25,0,14.7625)">
				<g transform="translate(72,-60.19)">
					<text transform="matrix(1,0,0,-1,-71.95,60.24)">
						<tspan style="font-size: 17.93px; " x="0" y="0">𝐻</tspan>
					</text>
				</g>
			</g>
		</svg>-Invariant
Jacobian Poisson Structures 

Advances in Mathematical Physics

Integer Solutions of Integral Inequalities and 𝐻 -Invariant Jacobian Poisson Structures

Figure 3

Integer Solutions of Integral Inequalities and -Invariant Jacobian Poisson Structures