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Reliability is an important performance measure of navigation systems and this is particularly true in Global Navigation Satellite Systems (GNSS). GNSS positioning techniques can achieve centimetre-level accuracy which is promising in navigation applications, but can suffer from the risk of failure in ambiguity resolution. Success rate is used to measure the reliability of ambiguity resolution and is also critical in integrity monitoring, but it is not always easy to calculate. Alternatively, success rate bounds serve as more practical ways to assess the ambiguity resolution reliability. Meanwhile, a transformation procedure called decorrelation has been widely used to accelerate ambiguity estimations. In this study, the methodologies of bounding integer estimation success rates and the effect of decorrelation on these success rate bounds are examined based on simulation. Numerical results indicate decorrelation can make most success rate bounds tighter, but some bounds are invariant or have their performance degraded after decorrelation. This study gives a better understanding of success rate bounds and helps to incorporate decorrelation procedures in success rate bounding calculations.
The Wielandt subgroup of a group
, denoted by
, is the intersection of the normalisers of all subnormal subgroups of
. The terms of the Wielandt series of
are defined, inductively, by putting
. In this paper, we investigate the relations between the
-length of a
-soluble finite group and the Wielandt series of its Sylow
-subgroups. Some recent results are improved.
-length of a finite
-soluble group is an important invariant parameter. The well-known Hall–Higman
-length theorem states that the
-length of a
-soluble group is bounded above by the nilpotent class of its Sylow
-subgroups. In this paper, we improve this result by giving a better estimation on the
-length of a
-soluble group in terms of other invariant parameters of its Sylow
A subgroup H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G=HT and H∩T≤Hse. In this note, we study the influence of the weakly s-permutably embedded property of subgroups on the structure of G, and obtain the following theorem. Let ℱ be a saturated formation containing 𝒰, the class of all supersolvable groups, and G a group with E as a normal subgroup of G such that G/E∈ℱ. Suppose that P has a subgroup D such that 1<∣D∣<∣P∣ and all subgroups H of P with order ∣H∣=∣D∣ are s-permutably embedded in G. Also, when p=2 and ∣D∣=2 , we suppose that each cyclic subgroup of P of order four is weakly s-permutably embedded in G. Then G∈ℱ.
Let ℨ be a complete set of Sylow subgroups of a finite group G; that is to say for each prime p dividing the order of G, ℨ contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be ℨ-permutable in G if H permutes with every member of ℨ. In this paper we characterise the structure of finite groups G with the assumption that (1) all the subgroups of Gp ∈ ℨ are ℨ-permutable in G, for all prime p ∈ π(G), or (2) all the subgroups of Gp ∩ F*(G) are ℨ-permutable in G, for all Gp ∈ ℨ and p ∈ π(G), where F*(G) is the generalised Fitting subgroup of G.
The purpose of this paper is to study the influence of $c$-supplemented minimal subgroups on the $p$-nilpotency of finite groups. We obtain ‘iff' and ‘localized' versions of theorems of Itô and Buckley on nilpotence, $p$-nilpotence and supersolvability.
The purpose of this paper is to give some necessary and sufficient conditions for p-nilpotent groups. We extend some results, including the well-known theorems of Burnside and Frobenius as well as some very recent theorems. We also apply our results to determine the structure of some finite groups in terms of formation theory.
The main purpose of this paper is to generalise a supersolvability theorem of O. U. Kramer to a saturated formation containing the class of supersolvable groups. As applications, we generalise some results recently obtained by some scholars.
A subgroup H of a
group G is said to be c-supplemented inG
if there exists a subgroup K of G such thatHK=G
and H \cap K is contained in Core_G (H).
We follow Hall's ideas to characterize the structure of the finite groups in which every subgroup is
c-supplemented. Properties of c-supplemented subgroups are also applied to determine
the structure of some finite groups.
A finite dinilpotent group G is one that can be written as the product of two finite nilpotent groups, A and B say. A finite dinilpotent group is always soluble. If A is abelian and B is metabelian, with |A| and|B| coprime, we show that a bound on the derived length given by Kazarin can be improved. We show that G has derived length at most 3 unless G contains a section with a well defined structure: in particular if G is of odd order, G has derived length at most 3.
A subgroup H is called c-normal in a group G if there exists a normal subgroup N of G such that HN = G and H∩N ≤ HG, where HG =: Core(H) = ∩g∈GHg is the maximal normal subgroup of G which is contained in H. We use a result on primitive groups and the c-normality of maximal subgroups of a finite group G to obtain results about the influence of the set of maximal subgroups on the structure of G.
Artificial Neural Network (ANN), as a potential powerful classifier, was explored to assist psychiatric diagnosis of the Composite International Diagnostic Interview (CIDI).
Both Back-Propagation (BP) and Kohonen networks were developed to fit psychiatric diagnosis and programmed (using 60 cases) to classify neurosis, schizophrenia and normal people. The programmed networks were cross-tested using another 222 cases. All subjects were randomly selected from two mental hospitals in Beijing.
Compared to ICD-10 diagnosis by psychiatrists, the overall kappa of BP network was 0.94 and that of Kohonen was 0.88 (both P < 0.01). In classifying patients who were difficult to diagnose, the kappa of BP was 0.69 (P < 0.01). ANN-assisted CIDI was compared with expert system assisted CIDI (kappa=0.72–0.76); ANN was more powerful than a traditional expert system.
ANN might be used to improve psychiatric diagnosis.
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