Metric Regularity of the Sum of Multifunctions and Applications

In this work, we use the theory of error bounds to study metric regularity of the sum of two multifunctions, as well as some important properties of variational systems. We use an approach based on the metric regularity of epigraphical multifunctions. Our results subsume some recent results by Durea and Strugariu.Comment: Submitted to JOTA 37 page

(26.55 %, or 23.69 %)-Limiting Highest Efficiencies, obtained respectively in nn+(pp+) − pp(nn) Crystalline (XX ≡ CdTe, or CdSe)- Junction Solar Cells, Due to the Effects of Impurity Size, Temperature, Heavy Doping, and Photovoltaic Conversion

 In the n+(p+)−p(n) crystalline (X≡ CdTe or CdSe)-junction solar cells at 300K, due to the effects of impurity size, temperature, heavy doping, and photovoltaic conversion, we show that, with an increasing donor (acceptor)-radius rd(a), both the relative dielectric constant and photovoltaic conversion factor decrease, and the intrinsic band gap (IBG) increases, according to the increase in photovoltaic efficiency, as observed in Tables 1-5, being in good accordance with an important result obtained by Shockley and Queisser (1961), stating that for an increasing IBG the photovoltaic efficiency increases. Further, for highest values of rd(a), the limiting highest efficiencies are found to be given in Tables 4, 6, as: 26.55 %, and 23.69 %, obtained in such n+(p+)−p(n) crystalline (CdTe, or CdSe)-junction solar cells at the open circuit voltage Voc=0.82 V, and 0.89 V, respectively, and at T=300 K. Furthermore, from the well-known Carnot-efficiency theorem, as given in Eq. (46), being obtained from the second principle of the thermodynamics, and from the above results of limiting highest efficiencies, the corresponding highest hot reservoir temperatures, TH=408.4 K, and 393.1 K, respectively. Thus, as noted above, ηmax. and TH both increase with an increasing IBG, for each (X≡ CdTe, or CdSe)- crystal at T=300 K≡TC.&nbsp

11.97% (12.12%)-Limiting Highest Efficiencies Obtained Respectively in nn+(pp+) − pp(nn) Crystalline GaSb Junction Solar Cells at T=300K, Due to the Effects of Impurity Size, Temperature, Heavy Doping, and Photovoltaic Conversion

In the n+(p+)−p(n) crystalline GaSb-junction solar cells at 300K, due to the effects of impurity size, temperature, heavy doping, and photovoltaic conversion, we show that, with an increasing donor (acceptor)-radius rd(a), both the relative dielectric constant and photovoltaic conversion factor decrease, and the intrinsic band gap increases, according to the increase in photovoltaic efficiency, as observed in Tables 1, 2 and 3, being in good accordance with an important result obtained by Shockley and Queisser (1961), with the use of the second law of thermodynamics, stating that for an increasing intrinsic band gap the photovoltaic efficiency increases. Further, for highest values of rd(a), the limiting highest efficiencies are found to be given in Tables 2 and 3, as: 11.97 % (12.12 %), obtained in such n+(p+)−p(n) crystalline GaSb-junction solar cells at 300 K, respectively.&nbsp

13.05% (14.82 %) – Limiting Highest Efficiencies Obtained Respectively in n+(p+)-p(n) Crystalline Ge-Junction Solar Cells at T=300 K, Due to the Effects of Impurity Size, Temperature, Heavy Doping, and Photovoltaic Conversion

In the n+(p+)−p(n) crystalline Ge-junction solar cells at 300K, due to the effects of impurity size, temperature, heavy doping, and photovoltaic conversion, we show that, with an increasing donor (acceptor)-radius rd(a), both the relative dielectric constant and photovoltaic conversion factor decrease, and the intrinsic band gap (IBG) increases, according to the increase in photovoltaic efficiency, as observed in Tables 1, 2 and 3, being in good accordance with an important result obtained by Shockley and Queisser (1961), with the use of the second law of thermodynamics, stating that for an increasing IBG the photovoltaic efficiency increases. Further, for highest values of rd(a), the limiting highest efficiencies are found to be given in Tables 2 and 3, as: 13.05 % (14.82 %), obtained in such n+(p+)−p(n) crystalline Ge-junction solar cells at 300 K, respectively. Then, from the well-known Carnot-efficiency theorem, as given in Eq. (47), being obtained by the second principle of thermodynamics, and from those limiting highest efficiencies, the corresponding highest hot reservoir temperatures, TH, are found to be given by: 345.04 K (352.20 K), respectively. In other words, TH also increases with an increasing IBG, being a new result.&nbsp

(43.82 %, or 44.05 %)-Limiting Highest Efficiencies, Obtained Respectively in nn+(pp+) − pp(nn) Crystalline CdS-Junction Solar Cells at T=300 K, Due to the Effects of Impurity Size, Temperature, Heavy Doping, and Photovoltaic Conversion

In the n+(p+)-p(n) crystalline (SdS) junction solar cells at 300K, due to the effects of impurity size, temperature, heavy doping, and photovoltaic conversion, we show that, with an increasing donor (acceptor)-radius rd(a) both the relative dielectric constant and photovoltaic conversion factor decrease, and the intrinsic band gap (IBG) increases, according to the increase in photovoltaic efficiency n, as observed in Tables 1-3. This is found to be in good accordance with an important result obtained by Shockley and Queisser (1961), stating that, for a fixed fraction of the total radiative recombination (=1) and for an increasing IBG (0<IBG(eV) ≤1.1), n increases and its maximum value is equal to 30 % at IBG=1.1eV.  Further, for highest values of rd(a) the limiting highest efficiencies are found to be given in Tables 2 and 3, as: 43.82 %, and 44.05 %, obtained in such n+(p+)-p(n) crystalline CdS-junction solar cells at T=300 K, with a large value of IBG (2.395 eV ≤IBG≤ 2.462eV, as seen in Table 1) and at the open circuit voltage Voc=2.7V. Furthermore, from the well-known Carnot-efficiency theorem, as given in Eq. (46), being obtained from the second principle of thermodynamics, and from the above results of limiting highest efficiencies, the corresponding highest hot reservoir temperatures, TH =534K and 536 K, respectively. Thus, as noted above, both nmax and TH increase with an increasing IBG, and at T=300 K=TC