Narrow Results

This paper presents a complete characterization of an edge-weighted simple graph $G_{\omega }$, whose edge ideal $I(G_{\omega })$ is integrally closed. Furthermore, it is demonstrated that if $I(G_{\omega })$ is integrally closed and $G_{\omega }$ is an edge-weighted star graph, path, or cycle, then $I(G_{\omega })$ is normal.

A PIXE (Proton Induced X-ray Emission) analysis is applied for measuring the concentration of 21 major and minor trace metal elements (in the range of Z=13-53) for normal, adenoma and carcinoma human thyroid tissues. A 2.0 MeV proton beam was employed to excite the samples. The thyroid samples were obtained from 14 patients during surgical operations, with which normal and damaged parts are concerned as an aid to understand the mechanisms of formation of thyroid cancer and as a complementary diagnostic tool. Thirty samples were measured in total. Fourteen samples of them were in pairs, i.e.14 tumor samples with 14 corresponding healthy tissue specimens taken at a distance from the tumor. The statistical analysis of the results shows the lower levels of the mean value of iron and iodine in the carcinoma tissues than those in the normal tissues; especially iodine is about one tenth of the normal value. On the contrary, the elevation of the mean value for calcium and zinc in the carcinoma tissues in comparison with the normal ones is observed, while in the adenoma tissues copper is very lower than those in the normal thyroid. The concentration of iron in the adenoma is two times of normal tissues.

Let $G$ be a finite group and $p$ a fixed prime divisor of $\left|G\right|$. We prove that if every maximal subgroup of $G$ is nilpotent, or normal, or has $p^{\prime }$-order, then (1) $G$ is solvable; (2) $G$ has a Sylow tower; (3) there exists at most one prime divisor $q\ne p$ of $\left|G\right|$ such that $G$ is neither $q$-nilpotent nor $q$-closed.

The joint predictive-posterior approach to the study of the reliability of an engineering system, under a stress-strength model, is presented in this article. This new combined approach is original, is supported by charts and graphs and can be quite useful since it allows the realistic forecasting of system reliability, with known credibility levels, ahead of real experimentation and testing results. In this article, it is concretely illustrated by several engineering applications related to a highway bridge study and a quality control problem.

Purpose: This study was conducted primarily to compare the contents and distribution of Glycosaminoglycan (GAG) in the normal and regenerated menisci, and partly to elucidate the role of GAG in the meniscus to fulfill its function. Method: A total of 60 immature rabbits, weighing 300–400 gm and aged 4 weeks, were used for the study. Total medial meniscectomy in the right knee joint was performed in all rabbits. The medial menisci of the left knee joints were used as control. After 16, 20, 24 and 28 weeks postoperatively, the amount of GAG in normal and regenerated menisci were measured. For the measurement of quantity and distribution of GAG contents, photon absorptiometry and Safranin O staining method were used. Results: (1) In 48 of the 60 medial meniscectomized knees, menisci were regenerated in various sizes with degenerative changes of joints, especially on tibial side. (2) In normal menisci, GAG was distributed at inner and middle 1/3, while GAG in regenerated menisci was diffusely found in the entire width. (3) The concentration of GAG per 1 mg of regenerated menisci were 4.36 ± 1.68, 4.58 ± 1.14, 4.65 ± 2.21, 4.60 ± 2.06 μg in each 16, 20, 24, and 28 week groups, while those of normal menisci were 9.10 ± 2.09, 9.75 ± 3.97, 11.80 ± 8.44 and 14.51 ± 8.91 μg. (4) In normal menisci, the amount of GAG was gradually increased as rabbit got older. However, there was no statistical differences of quantitative amount of GAG of regenerated menisci among the 16, 20, 24, and 28 weeks groups during the observation periods (p > 0.05). (5) There was a distinctive difference in Safranin O stainability by every 4 μg increase of GAG in both 1 mg of normal and regenerated menisci. Conclusion: This study showed the quantitative change of GAG between normal and regenerated menisci, and comparative analysis of GAG contents in the menisci by biochemical method and histological method were found to be useful tools.

In this paper, we show that G is a finite group in which every nonabelian subgroup is a TI-subgroup if and only if every nonabelian subgroup of G is normal in G.

Let $G$ be a finite group in which every non-nilpotent maximal subgroup has prime index and $p$ the largest prime divisor of $\left|G\right|$, without using the solvability of $G$ we prove that either the Sylow $p$-subgroup of $G$ is normal or $G$ has a normal $p$-complement.

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, we prove that if every non-nilpotent maximal $A$-invariant subgroup of $G$ is normal, then $G$ is $p$-nilpotent or $p$-closed for each prime divisor $p$ of $\left|G\right|$, which improves a theorem obtained by Beltr$́a$n and Shao.

Epilepsy is a common neurological disorder characterized by recurrence seizures. Alcoholism causes organic changes in the brain, resulting in seizure attacks similar to epileptic fits. Hence, it is challenging to differentiate the cause of fits as epileptic or alcoholism, which is important for deciding on the treatment in the neurology ward. The focus of this paper is to automatically differentiate epileptic, normal, and alcoholic electroencephalogram (EEG) signals. As the EEG signals are non-linear and dynamic in nature, it is difficult to tell the subtle changes in these signals with the help of linear techniques or by the naked eye. Therefore, to analyze the normal (control), epileptic, and alcoholic EEG signals, two non-linear methods, such as recurrence plots (RPs) and then recurrence quantification analysis (RQA) are adopted. Approximately 10 RQA parameters have been used to classify the EEG signals into three distinct classes, i.e., normal, epileptic, and alcoholic. Six classifiers, such as support vector machine (SVM), radial basis probabilistic neural network (RBPNN), decision tree (DT), Gaussian mixture model (GMM), k-nearest neighbor (kNN), and fuzzy Sugeno classifiers have been developed to accomplish this task. Results show that the GMM classifier outperformed the other classifiers with a classification sensitivity of 99.6%, specificity of 98.3%, and accuracy of 98.6%.

Let G be a finite group and H a subgroup of G. Recall that H is said to be a TI-subgroup of G if H^g∩ H = 1 or H for each g ∈ G. In this note, we prove that if all non-nilpotent subgroups of a finite non-nilpotent group G are TI-subgroups, then G is soluble, and all non-nilpotent subgroups of G are normal.

Let S_n denote the symmetric group of degree n with n ≥ 3, S = { c_n = (1 2 ⋯ n), $c_n^{-1}$, (1 2)} and Γ_n = Cay(S_n, S) be the Cayley graph on S_n with respect to S. In this paper, we show that Γ_n (n ≥ 13) is a normal Cayley graph, and that the full automorphism group of Γ_n is equal to Aut(Γ_n) = R(S_n) ⋊ 〈Inn(ϕ) ≅ S_n × ℤ₂, where R(S_n) is the right regular representation of S_n, ϕ = (1 2)(3 n)(4 n−1)(5 n−2) ⋯ (∊ S_n), and Inn(ϕ) is the inner isomorphism of S_n induced by ϕ.

In this paper, we introduce and study the notion of left $\phi$-essential Connes amenable for dual Banach algebras. We investigate the hereditary properties of this new concept and we give some results for $𝜃$-Lau product and module extension. For unital dual Banach algebras, we show that left $\phi$-essential Connes-amenability and left $\phi$-Connes amenability are equivalent. Finally, with various examples, we examined this concept for upper triangular matrix algebras and ${\ell }^1$-direct sum of Banach algebras.