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EESS
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Electrical energy supply system
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RF
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Regression function
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I ⊂ N0
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With \( i,{i}_0,{i}^{\prime },{i}_0^{\prime}\in I \) and \( i,{i}_0^{\prime}\le {i}_0,{i}^{\prime}\le {i}_0^{\prime } \)
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T ⊂ R
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With t, t′, ∆t, ∆tR, tA, tE, τ ∈ T and ∆t = t′ − t
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N ⊂ R3
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With \( {x}_i,{x}_i^{\prime },{x}_j,{x}_{n_0}\in N \), pairwise coprime
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ED(t, xi)
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Energy demand function; short form \( {E}_i^N(t) \)
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\( {E}_{\mathrm{max}}^D\left({x}_i\right) \)
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Maximum energy demand; short form \( {E}_{\max, i}^N(t) \)
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\( {f}_i^D(t) \)
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Time-dependent behavior of user i
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ES(t, xi)
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Energy supply function; short form \( {E}_i^B(t) \)
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\( {E}_{j_0}^D\frac{(t)}{E_{j_0}^S}(t) \)
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Bundled energy demand/supply of j0 microcells
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\( {E}_{\mathrm{Nat}.}^D\frac{(t)}{E_{\mathrm{Nat}.}^S}(t) \)
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Energy demand/supply function of a national macrocell
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u
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Energy density of the electromagnetic field
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S
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Poynting vector
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J
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Current density
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E
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Electric field strength
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H
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Magnetic field strength
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ρ
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Electrical charge density
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\( \frac{c_0}{c} \)
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Speed of light in vacuum/in a medium
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\( {E}_i^{ST} \)
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Stationary supply component of the ith microcell
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ci ∈ R
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Stationary state constant of the ith microcell
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\( {E}_{j_0}^{ST} \)
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Stationary supply constant of a macrocell
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PS(t, xi)
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Output power of the ith source; short form \( {P}_i^B(t) \)
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\( {P}_i^{D_{\mathrm{max}}} \)
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Maximum load (power consumption) of the ith microcell
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\( {P}_i^{S_{\mathrm{max}}} \)
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Maximum supply (power generation) of the ith microcell
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\( {\dot{P}}^S\left(t,{x}_i\right) \)
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Power dynamics of the ith microcell; short form \( {\dot{P}}_i^B(t) \)
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P(j0)
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Total power from j0 microcells
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P(k0)
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Total power from k0 current sources
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\( {\wp}_{\mathrm{macrocell}}^N \)
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Maximum load of a macrocell, analogous to power generation
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\( {\wp}_{\mathrm{Nat}.}^N \)
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Maximum load of a national macro cell, analogous to power generation
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S1, …, S5
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Structure variables, components of S∗
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S∗ ∈ R5
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Technological structure vector
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\( \varDelta {t}_{r_i} \)
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Time shift in the ith microcell due to the relativity principle
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\( \varDelta {t}_{s_i} \)
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Time shift in the ith microcell considering real sources
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\( \varDelta {t}_{j_0} \)
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Total time delay within a macrocell of j0 microcells
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J ⊂ N0
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With j, j0 ∈ J and j ≤ j0
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K ⊂ N0
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With k, k0 ∈ K and k ≤k0
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Ν ⊂ N0
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With n, n0 ∈ N and n ≤ n0
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(N, d)
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Metric space on the set N with metric d
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σ
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Electrical conductivity
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Ωu ⊂ R4
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Technological solution space with u ∈ Ωu
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\( {\varOmega}_{u_0},{\varOmega}_{u_I},{\varOmega}_{u_{II}} \)
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Subsets of the technological solution space
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LE
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Unit of length
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r
s
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Substantial risk factor
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r1, r2
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Sub-risk factors
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μ
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Failure factor
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p
i
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Failure likelihood of the ith microcell
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\( {P}_{i_0} \)
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Failure likelihood of a macrocell with i0 users
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S∗∗ ∈ R6
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Extension of the structure vector S∗ with the substantial risk factor
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S
6
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Structure variable for the substantial risk factor
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v
tv
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Availability
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v
tv, B
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Sustainability boundary; sustainable availability boundary
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\( {v}_{tv}\bullet {E}_{\mathrm{Nat}.}^D(t) \)
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National sustainability
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\( {v}_{tv,n}\bullet {E}_n^D(t) \)
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Regional sustainability in a macrocell
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v
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State vector with sustainability component
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Ω ∈ R5
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Sustainable technological solution set with
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\( {E}_{T_{\mathrm{Ref}.}}^N \)
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Annual energy demand in a reference year
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\( {\lambda}_i^{-} \)
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ith supply factor
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\( {\lambda}_{\mathrm{min}}^{-} \)
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National supply factor
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h(t)
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Distribution of annual energy demand with \( {\int}_{t_0}^{t_0+365}h(t) dt=1 \)
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g(x) ∈ [0; 1] |
Weights between \( {\lambda}_{min}^{-} \) and rs
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\( {E}_{T_{\mathrm{Ref}.}}^D \)
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Annual reference energy arbitrary initial value \( {\int}_{t_0}^{t_0+365}{E}^D(t) dt \)
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