Swanson was partially motivated by the analogous question for “Frobenius powers”, which has important applications to the theory of tight closure (the so-called “localization problem;” see [HH, Section 4]). Suppose now that R has prime characteristic p > 0 and q is a power of p. The Frobenius power I [q] of an ideal I is the ideal generated by all the qth powers of the elements (equivalently, t...

ABS’I’RA(’.T. In this paper, we study initial value problems for couph’d second order delay" differcntial equations with variable coefficients. By means of the application of the method of st,ps al the method of Frobenius, the exact solution of the problem is constrcted. Then, in a toain, a fitite analytic solution with error bounds is provided. C, iven an admissible error t, we give the number...

Quantum systems in which the position and momentum take values in the ring Zd and which are described with d-dimensional Hilbert space, are considered. When d is the power of a prime, the position and momentum take values in the Galois field GF (p), the position-momentum phase space is a finite geometry and the corresponding ‘Galois quantum systems’ have stronger properties. The study of these ...

in this research the chaocity of precipitation time series in daily, weekly and monthly scales in the pole-kohneh and ghourbaghestan stations located in qarah-soo watershed is investigated. in order to reassure about the absence of stochastic behavior of the time series, method of surrogate data is applied. thereafter, the aperiodicity of the time series is investigated using power spectrum ana...

Introduction Let G be a simply connected and connected semisimple group over an algebraically closed field k of characteristic p > 0. T ⊂ G is a maximal torus and R is the root system relative to T . X(T ) is the weight lattice. Let B ⊃ T be a Borel subgroup corresponding to the negative roots R− = R. Denote by Gr the r-th Frobenius kernel of G. The socle and radical structures of the cohomolog...

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...