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The signal-to-interference-and-noise ratio (SINR) of a configuration is calculated as described in [11] and given as below , SINR = frac{P_{S}}{P_{phn}+P_{ip3}+P_{n}}, (19).
Details of this scheme are given as below , and a pictorial description of this scheme is given in Fig. 12. Fig. 12 Channel model of Scheme 3. Channel model for Scheme 3 at the phase associated with ({mathcal {L}}={i_{1}, ldots, i_{L}}).
It then jumps to this state with probability (q_{ij}) or remains in the current state i with probability (1 - q_{ij},) where (q_{ij}) is given as below : begin{aligned} q_{ij} = {left{ begin{array}{ll} min left( frac{ p_{ji} }{ p_{ij} }, 1 right) & text { if } p_{ij} > 0, 1 & text { if } p_{ij} = 0. end{array}right.
In terms of the reduced displacement functions appearing, the following conditions in (35) will be given as below : begin{aligned} &w^{left( k right)} left( {y,z} right) = 0 hfill & bar{C}_{12}^{left( k right)} L + bar{C}_{22}^{left( k right)},v_{,y}^{left( k right)} + bar{C}_{23}^{left( k right)},w_{,z}^{left( k right)} = 0quad {text{at}};{text{y}}, pm,{text{b}} hfill end{aligned}.
Define a sequence ((E_{k})) as follows: E_{k} = textstylebegin{cases} { (x,y) inmathbb{Rtimes R} : x^{2} + (y-1)^{2} = frac{1}{k^{4}}}, &mbox{if }k in I_{r(j)}, text{for some } j= 1,2,3,ldots, { 0,0 }, & mbox{otherwise.} end{cases} It is easy to see that the sequence ((E_{k})) is bounded because for each ((x,y) inmathbb{Rtimes R} ), the sequence ((d((x,y), E_{k}))) given as below is bounded.
The entire spectrum of solid carbonaceous materials like coals, lignite, all types of biomass material, and char to residue-derived fuels have been considered in derivation of present correlation which is given as below : HHV=0.3536FC+0.1559VM−0.0078ASH (MJ/kg) (where FC 1.0 91.5% fixed carbon, VM 0.92 90.6% volatile matter and Ash 0.12 77.7% ash content in wt% on a dry basis).
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Hence, NDT is given as shown below.
When the SI channel is modeled by Rayleigh fading connection, the throughput performance of system is given as corollary below.
In [1], Lakshmikantham et al. developed a famous impulsive differential inequality given as Theorem A below.
All of the results provided below are given as the mean and the total range.
Specific forms are given below, as part of the discussion on particular kinetics.
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The phrase "given as below " functions as an introductory phrase , signaling that specific details, explanations, or examples will be presented subsequently. Ludwig AI affirms this usage, showcasing its validity in introducing subsequent information.
Expression frequency: Uncommon
