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							<ml:real>10</ml:real>
							<ml:real>-8</ml:real>
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								<ml:apply>
									<ml:mult/>
									<ml:apply>
										<ml:mult/>
										<ml:apply>
											<ml:mult/>
											<ml:apply>
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												<ml:real>1</ml:real>
												<ml:real>2</ml:real>
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											<ml:id xml:space="preserve">μ0</ml:id>
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						<b>
							<inlineAttr line-through="false">Note: in what follows, frequency has units of MHz (i.e. multiplier M has been chosen)</inlineAttr>
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						<ml:real>50.156541336816794</ml:real>
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										<ml:id xml:space="preserve">f</ml:id>
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							<ml:id xml:space="preserve">f</ml:id>
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								<ml:id xml:space="preserve">f</ml:id>
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						<ml:real>83.8</ml:real>
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							<ml:real>10</ml:real>
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						<inlineAttr line-through="false">length of coaxial probe</inlineAttr>
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					<ml:id xml:space="preserve">n</ml:id>
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						<ml:sequence>
							<ml:real font="0">1</ml:real>
							<ml:real>2</ml:real>
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						<ml:real>6</ml:real>
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			<math optimize="false" disable-calc="false">
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								<ml:pow/>
								<ml:real>10</ml:real>
								<ml:real>-6</ml:real>
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						<ml:apply>
							<ml:mult/>
							<ml:apply>
								<ml:mult/>
								<ml:real>2</ml:real>
								<ml:id xml:space="preserve">L</ml:id>
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								<ml:sqrt/>
								<ml:id xml:space="preserve">εr</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">f0</ml:id>
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						<ml:real>1249.3219326044293</ml:real>
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			<text use-page-width="false" push-down="false" lock-width="true">
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					<f family="Times New Roman" charset="0" size="10">
						<inlineAttr line-through="false">Fundamental resonant frequency</inlineAttr>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
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						<inlineAttr line-through="false">based on actual length</inlineAttr>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">g1</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:id xml:space="preserve">g2</ml:id>
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			<math optimize="false" disable-calc="false">
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							<ml:id xml:space="preserve">n</ml:id>
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							<ml:apply>
								<ml:mult/>
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								<ml:id xml:space="preserve">π</ml:id>
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							<ml:id xml:space="preserve">g1</ml:id>
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						<ml:apply>
							<ml:mult/>
							<ml:real>2</ml:real>
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								<ml:pow/>
								<ml:real>0.0549</ml:real>
								<ml:real>2</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:id xml:space="preserve">Qo</ml:id>
						<ml:real>1</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>597.61983136608978</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:id xml:space="preserve">Qo</ml:id>
						<ml:real>2</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1195.2396627321796</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
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						<ml:real>5</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2988.0991568304489</ml:real>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Times New Roman" charset="0" size="10">
						<inlineAttr line-through="false">Unloaded</inlineAttr>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Times New Roman" charset="0" size="10">
						<inlineAttr line-through="false">quality factor</inlineAttr>
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				<p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">
					<f family="Times New Roman" charset="0" size="10">
						<inlineAttr line-through="false">of each mode</inlineAttr>
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			<math optimize="false" disable-calc="false">
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						<ml:real>3</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>1792.8594940982691</ml:real>
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			<math optimize="false" disable-calc="false">
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						<ml:real>4</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>2390.4793254643591</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:apply>
						<ml:id xml:space="preserve">Qo</ml:id>
						<ml:real>6</ml:real>
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					<result xmlns="http://schemas.mathsoft.com/math30">
						<ml:real>3585.7189881965382</ml:real>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
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							<ml:id xml:space="preserve">f</ml:id>
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									<ml:id xml:space="preserve">f0</ml:id>
								</ml:apply>
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							<ml:apply>
								<ml:id xml:space="preserve">Qo</ml:id>
								<ml:real>1</ml:real>
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						<ml:id xml:space="preserve">f0</ml:id>
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							<ml:id xml:space="preserve">f</ml:id>
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							<ml:apply>
								<ml:id xml:space="preserve">Qo</ml:id>
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							</ml:apply>
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						<ml:id xml:space="preserve">f0</ml:id>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
					<ml:function>
						<ml:id xml:space="preserve">S21_0</ml:id>
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							<ml:id xml:space="preserve">f</ml:id>
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					<ml:apply>
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							<ml:real>2</ml:real>
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								<ml:sqrt/>
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									<ml:id xml:space="preserve">g1</ml:id>
									<ml:id xml:space="preserve">g2</ml:id>
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						</ml:apply>
						<ml:apply>
							<ml:plus/>
							<ml:apply>
								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:real font="0">1</ml:real>
									<ml:id xml:space="preserve">g1</ml:id>
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								<ml:id xml:space="preserve">g2</ml:id>
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							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">j</ml:id>
									<ml:real>2</ml:real>
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								<ml:apply>
									<ml:id xml:space="preserve">F0</ml:id>
									<ml:id xml:space="preserve">f</ml:id>
								</ml:apply>
							</ml:apply>
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			<math optimize="false" disable-calc="false">
				<ml:define xmlns:ml="http://schemas.mathsoft.com/math30">
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							<ml:real>2</ml:real>
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								<ml:sqrt/>
								<ml:apply>
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									<ml:id xml:space="preserve">g2</ml:id>
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						<ml:apply>
							<ml:plus/>
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								<ml:plus/>
								<ml:apply>
									<ml:plus/>
									<ml:real font="0">1</ml:real>
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								<ml:id xml:space="preserve">g2</ml:id>
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							<ml:apply>
								<ml:mult/>
								<ml:apply>
									<ml:mult/>
									<ml:id xml:space="preserve">j</ml:id>
									<ml:real>2</ml:real>
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								<ml:apply>
									<ml:id xml:space="preserve" subscript="alt">F0</ml:id>
									<ml:sequence>
										<ml:id xml:space="preserve">f</ml:id>
										<ml:id xml:space="preserve">n</ml:id>
									</ml:sequence>
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						<inlineAttr line-through="false">power absorption coefficients</inlineAttr>
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						<inlineAttr line-through="false">The following graphs show reflected power as a function of permittivity of sample. The final graphs show the curve fitting used to obtain resonator parameters.</inlineAttr>
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