A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstra...A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.展开更多
Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. A...Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. Applications to partial differential equations including that of elliptic, parabolic and hyperbolic type are investigated. Moreover, partial differential equations of higher order with real and complex coefficients and with variable coefficients with or without boundary conditions are considered.展开更多
Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the rev...Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the reversed Dickson polynomials Dn,k(1,x)over finite fields in the case of n=mp* with 0<m<p-1.In particular,we provide some precise characterizations for Dn,k(1,x)being permutation polynomials over finite fields with characteristic p when n=2p^(s),or n=3p^(s),or n=4p^(s).展开更多
Switched-capacitor converters can deliver better performance,power density,and switch utilization compared to inductor-based power converters,but they suffer from current spikes during switching due to capacitor charg...Switched-capacitor converters can deliver better performance,power density,and switch utilization compared to inductor-based power converters,but they suffer from current spikes during switching due to capacitor charge redistribution.This can be solved by methods such as split-phase control,which was developed to address charge redistribution in Dickson SC converters by controlling the charging and discharging of the circuit‟s flying capacitors,such that the equivalent branch voltages line up when the circuit switches states.However,split-phase control is most effective at compensating for charge redistribution when all the circuit‟s flying capacitors are matched in capacitance value.Differences between the capacitance values of the circuit flying capacitors may result in split-phase control not being able to fully compensate for charge redistribution,due to the different charge/discharge rates of the flying capacitors.The work presented in this paper provides an in-depth analysis of the sensitivity of the split-phase Dickson converter to mismatches in flying capacitor values,as well as discussions regarding the design considerations and prototype test results of a split-phase Dickson converter for high-current loads.展开更多
This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almos...This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.展开更多
文摘A class of meta-invariant operators over Cayley-Dickson algebra is studied. Their spectral theory is investigated. More- over, theorems about spectra of generalized unitary operators and their semigroups are demonstrated.
文摘Multidimensional noncommutative Laplace transforms over octonions are studied. Theorems about direct and inverse transforms and other properties of the Laplace transforms over the Cayley-Dickson algebras are proved. Applications to partial differential equations including that of elliptic, parabolic and hyperbolic type are investigated. Moreover, partial differential equations of higher order with real and complex coefficients and with variable coefficients with or without boundary conditions are considered.
基金supported by National Natural Science Foundation of China(No.12226335)by China's Central Government Funds for Guiding Local Scientific and Technological Development(No.2021ZYD0013).
文摘Let p be an odd prime,and n,k be nonnegative integers.Let Dn,k(1,x)be the reversed Dickson polynomial of the(k+1)-th kind.In this paper,by using Hermite's criterion,we study the permutational properties of the reversed Dickson polynomials Dn,k(1,x)over finite fields in the case of n=mp* with 0<m<p-1.In particular,we provide some precise characterizations for Dn,k(1,x)being permutation polynomials over finite fields with characteristic p when n=2p^(s),or n=3p^(s),or n=4p^(s).
文摘Switched-capacitor converters can deliver better performance,power density,and switch utilization compared to inductor-based power converters,but they suffer from current spikes during switching due to capacitor charge redistribution.This can be solved by methods such as split-phase control,which was developed to address charge redistribution in Dickson SC converters by controlling the charging and discharging of the circuit‟s flying capacitors,such that the equivalent branch voltages line up when the circuit switches states.However,split-phase control is most effective at compensating for charge redistribution when all the circuit‟s flying capacitors are matched in capacitance value.Differences between the capacitance values of the circuit flying capacitors may result in split-phase control not being able to fully compensate for charge redistribution,due to the different charge/discharge rates of the flying capacitors.The work presented in this paper provides an in-depth analysis of the sensitivity of the split-phase Dickson converter to mismatches in flying capacitor values,as well as discussions regarding the design considerations and prototype test results of a split-phase Dickson converter for high-current loads.
基金supported by the National Basic Research Program of China under Grant No.2011CB302400
文摘This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.
