Traditional ligand-field theory has to be improved by taking into account both pure electronic contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy).By means of improved li...Traditional ligand-field theory has to be improved by taking into account both pure electronic contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy).By means of improved ligand-field theory,the R line,t_2^(32)T_1 and t_2^(32)T_2 lines,t_2~2(~3T_1)e^4T_2,t_2~2(~3T_1)e^4T_1 and t_2e^2(~4A_2)~4T_1 bands,g factors of t_2~3 ~4A_2 and t_2^(32)E,four strain-induced level-splittings and R-line thermal shift of MgO:V^(2+) have been calculated.The results are in very good agreement with the experimental data.It is found that for MgO:V^(2+),the contributions due to electron- phonon interaction (EPI) come from the first-order term;the contributions from the second-order and higher terms are insignificant.In thermal shift of R line of MgO:V^(2+),the temperature-dependent contribution due to EPI is dominant. The results obtained in this work may be used in theoretical calculations of other effects of EPI.展开更多
Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and...Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.展开更多
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holde...In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.展开更多
The conventional methodology for designing QC-LDPC decoders is applied for fixed configurations used in wireless communication standards, and the supported largest expansion factor Z (the parallelism of the layered de...The conventional methodology for designing QC-LDPC decoders is applied for fixed configurations used in wireless communication standards, and the supported largest expansion factor Z (the parallelism of the layered decoding) is a fixed number. In this paper, we study the circular-shifting network for decoding LDPC codes with arbitrary Z factor, especially for decoding large Z (Z P) codes, where P is the decoder parallelism. By buffering the P-length slices from the memory, and assembling the shifted slices in a fixed routine, the P-parallelism shift network can process Z-parallelism circular-shifting tasks. The implementation results show that the proposed network for arbitrary sized data shifting consumes only one times of additional resource cost compared to the traditional solution for only maximum P sized data shifting, and achieves significant saving on area and routing complexity.展开更多
文摘Traditional ligand-field theory has to be improved by taking into account both pure electronic contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy).By means of improved ligand-field theory,the R line,t_2^(32)T_1 and t_2^(32)T_2 lines,t_2~2(~3T_1)e^4T_2,t_2~2(~3T_1)e^4T_1 and t_2e^2(~4A_2)~4T_1 bands,g factors of t_2~3 ~4A_2 and t_2^(32)E,four strain-induced level-splittings and R-line thermal shift of MgO:V^(2+) have been calculated.The results are in very good agreement with the experimental data.It is found that for MgO:V^(2+),the contributions due to electron- phonon interaction (EPI) come from the first-order term;the contributions from the second-order and higher terms are insignificant.In thermal shift of R line of MgO:V^(2+),the temperature-dependent contribution due to EPI is dominant. The results obtained in this work may be used in theoretical calculations of other effects of EPI.
文摘Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.
文摘In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
文摘The conventional methodology for designing QC-LDPC decoders is applied for fixed configurations used in wireless communication standards, and the supported largest expansion factor Z (the parallelism of the layered decoding) is a fixed number. In this paper, we study the circular-shifting network for decoding LDPC codes with arbitrary Z factor, especially for decoding large Z (Z P) codes, where P is the decoder parallelism. By buffering the P-length slices from the memory, and assembling the shifted slices in a fixed routine, the P-parallelism shift network can process Z-parallelism circular-shifting tasks. The implementation results show that the proposed network for arbitrary sized data shifting consumes only one times of additional resource cost compared to the traditional solution for only maximum P sized data shifting, and achieves significant saving on area and routing complexity.
