The Modified Information Criterion (MIC) is an Akaike-like criterion which allows performance control by means of a simple a priori defined parameter, the upper-bound on the error of the first kind (false alarm probability). The criterion MIC is for example used to estimate the order of Auto-Regressive (AR) processes. The criterion can only be used to test pairs of composite hypotheses; in an A...

Let Gk be defined as = \(\left\langle {a,b;{{a}^{{ - 1}}}ba {{b}^{k}}} \right\rangle \), where k ≠ 0. It is known that if p a prime number then residually finite p-group iff p|k – 1. also and q are primes not dividing 1, < π {p, q} π-group (k, q) p|q 1 the order of in multiplicative group field ℤq p-number. This paper examines question two-element sets numbers satisfy conditions last criterion....

We present several asymptotic analyses for quantities associated with the Riemann and Hurwitz zeta functions. We first determine the leading asymptotic behavior of the Stieltjes constants γk(a). These constants appear in the regular part of the Laurent expansion of the Hurwitz zeta function. We then use asymptotic results for the Laguerre polynomials Ln to investigate a certain sum Sγ(n) involv...

Let G be an abelian group, and F a downward directed family of subsets of G. In [6], I. Protasov and E. Zelenyuk describe the finest group topology T on G under which F converges to 0; in particular, their description yields a criterion for T to be Hausdorff. They then show that if F is the filter of cofinite subsets of a countable subset X ⊆ G (the Fréchet filter on X), there is a simpler crit...

His basic criterion for disconjugacy turned out to be 1 0 is continuous and fal/P= °°, then the substitution t — fll/p transforms the first equation into one where p = l and the new f-interval is infinite. Thus this more general case reduces to Nehari's and again the criterion is 1 <X(o). However part of the whole picture seems to be lost by this transformation. If Ial...

For a sequence {Tn} of continuous linear operators on a separable Fréchet space X, we discuss necessary conditions and sufficient conditions for {Tn} to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect ...

Diagnosis The criterion for the diagnostic confirmation of myocarditis defined by 2013 European and Brazilian Myocarditis Guidelines is identification myocardial inflammation endomyocardial biopsy (EMB)., This criterion, used solely without option classifying clinical suspicion, does not mirror practice in real world, where only a minority patients specialized centers are referred investigation...

Two decades ago, Gribov pointed out a possible mechanism of colour confinement in Coulomb gauge or Landau gauge QCD via infrared divergence of the Faddeev-Popov ghost propagator. At nearly the same time, Kugo and Ojima proposed a criterion for the absence of coloured massless asymptoptic states in Landau gauge QCD using the BRST symmetry. We study the confinement signal in the gluon propagator,...

A criterion for the stability of control systems which contain an arbitrary jinik number oj memoryless nonlinearities is considered. The criterion is such that the degree oj stability may be specijied, and such that for the case when the absolute stability of a control system having one memoryless nonlinearity is considered, it reduces to the original Popov criterion. Introduction The formulati...