Optimal spectral bandwidth for long memory

For long range dependent time series with a spectral singularity at frequency zero, a theory for optimal bandwidth choice in non-parametric analysis ofthe singularity was developed by Robinson (1991b). The optimal bandwidths are described and compared with those in case of analysis of a smooth spectrum. They are also analysed in case of fractional ARIMA models and calculated as a function of the self similarity parameter in some special cases. Feasible data dependent approximations to the optimal bandwidth are discussed

Closed description of arbitrariness in resolving quantum master equation

In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.Comment: 13 pages, v2: Section 2 extended, misprint corrected, references added, formula on page 7 corrected, new formula (4.30) and a phrase on it inserted, v3: misprints in formulas (2.12), (4.23), (4.36)-(4.39) corrected, v4: formulae (A.8), (A.11), (A.12) added, v5:published versio

Representation of a gauge field via intrinsic "BRST" operator

We show that there exists a representation of a matrix valued gauge field via intrinsic "BRST" operator assigned to matrix valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang - Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.Comment: 15 pages, no figures, Section 6 extended with (6.14), (6.15); v3: Section 7 added, minor corrections; v4: Section 4, minor corrections; v5: formula (4.11) modifie