The harmonic index of a graph G is dened as H (G) =å uuÎE(G) 2 d(u)+d (u), where d (u) denotes the degree of a vertexu in G. Let G (n; k) be the set of simple n -vertex graphs with minimum degree at leastk. In this work we consider the problem of determining the minimum value of the harmonic index and the corresponding extremal graphs among G (n; k). We solve the problem for each integerk (1 £ k £ n/2) and show the corresponding extremal graph is the complete split graph K *k, n-k. This result together with our previous result which solve the problem for each integer k (n/2 £ k £ n - 1) give a complete solution of the problem.

A digraph $D=(V,E)$ is $k$-transitive if for any directed $uv$-path of length $k$, we have $(u,v) \in E$. In this paper, we study the structure of strong $k$-transitive oriented graphs having large minimum in- or out-degree. We show that such oriented graphs are \emph{extended cycles}. As a consequence, we prove that Seymour's Second Neighborhood Conjecture (SSNC) holds for $k$-transitive oriented graphs for $k \leq 11$. Also we confirm Bermond--Thomassen Conjecture for $k$-transitive oriented graphs for $k \leq 11$. A characterization of $k$-transitive oriented graphs having a hamiltonian cycle for $k \leq 6$ is obtained immediately.

The traditional method for studying non-stationary signals is spectrogram based on the short-time Fourier transform (STFT). The well known limitation of the STFT is the inherent trade-off between time and frequency resolution. The Wigner-Ville (WV) distribution has the best time-frequency resolution, but its draw back is generating cross-terms. The matching pursuit (MP) distribution based on using the Gaussian atom is always positive, does not include crossterm, and has convenient resolution. In this paper, we have shown in addition to the known properties, the MP distribution can also remove the additive noise inherently. On the other words, we are able to remove the noise just by limiting the algorithm iterations and without paying any additional cost. Although the MP distribution based on using the Gaussian atoms is always positive and it has convenient resolution, according to the MP the time marginal and the frequency marginal will not be obtained accurately. In this paper, it has been shown that by implementing the minimum cross entropy (MCE) technique according to the MP distribution as a priory positive distribution, the new extracted distribution has the most similarity to the MP distribution and it also satisfies the correct time and frequency marginal.

The distinguishing index of a simple graph G, denoted by D ′,(G), is the least number of labels in an edge labeling of G not preserved by any non-trivial automorphism...

Aim: Achieving high quality cancer registration processes requires, a set of minimum defined data besides standardized. Determining the minimum set of data ensures that all the necessary data are collected in an integrated manner, and plays a role in the integrity of the data. The aim of this study was to determine the compatibility of data elements in laboratory information system of Hormozgan Pathology Centers with minimum Data Set (MDS) in Demographic Cancer Registration Program (PBCR). Methods: This descriptive study is a cross-sectional LIS research where data were compared in lab with the minimum data set. The data collection tool was a checklist containing 30 items in 3 sections including the general profile of the pathology lab, the pathology reports structure, and the pathological information system. Data analysis was done using descriptive statistics of SPSS20. Results: All elements of patient identity information, information provider and data related to the acceptance date of the sample and type of sample, information elements of pathologic diagnosis, and the reporting date were available in all pathology software. All pathology LIS had a section on the history of the report, but only 44% of them had a dedicated section for diagnostic codes that users did not have information about or its use. Conclusion: The LIS matching with the PBCR-specific MDS showed that all the necessary data are available in the LIS and should be reminded for their completion by the personnel of the pathology labs.

Objective: Anesthetic techniques like the Akinosi technique were introduced to surmount the problems of the conventional inferior alveolar nerve block (IANB) technique. This study aimed to compare the local anesthetic efficacy of IANB via the conventional and Akinosi techniques in patients presenting to the Maxillofacial Surgery Department of School of Dentistry, Shahid Beheshti University.Methods: This clinical trial was conducted on 80 candidates for bilateral extraction of mandibular molars. For each patient, local anesthesia was induced by IANB injection, which was done by the conventional technique in one side and by the Akinosi technique in the other side of the mouth. The allocation of technique to side was randomized. Time to anesthesia for the long buccal, lingual and inferior alveolar nerves (IAN), degree of pain during injection and tooth extraction and incidence of positive aspiration in the two techniques were evaluated and analyzed using Wilcoxon Signed Rank and Chi square tests.Results: The mean time to anesthesia for the IAN was 2.82 minutes in the conventional and 3.05 minutes for the Akinosi technique. These values were 1.47 and 1.55 minutes, respectively for the lingual nerve and 1.43 and 1.56 minutes, respectively for the long buccal nerve. Four patients in the Akinosi technique and 12 patients in the conventional technique had positive aspiration. During anesthetic injection with the Akinosi technique, 72.5% were pain free, 18.8% experienced mild, 5% experienced moderate and 3.8% experienced severe pain. These values in the conventional technique were 51.3%, 27.5%, 11.3% and 10%, respectively.Conclusion: Considering the lack of a significant difference between the success rate of conventional and Akinosi IANB techniques, Akinosi technique seems to be a suitable alternative to the conventional technique since it is less painful and has lower risk of positive aspiration.

Leaf stripe disease (LSD) of grapevine, which was previously known as esca complex disease, is one of the most important and destructive trunk diseases of grapevines. Phaeoacremonium minimum is the principle hyphomycete associated with disease. Chemical control of LSD has proven difficult, meanwhile, application of biological control agents for disease management have been promising. The aim of present study was to evaluate inhibitory potentiol of three Trichoderma species sincluding one commercial product (Trichoderma harzianum T22) and two endophytic isolates, T. longibrachiatum and T. brevicompactum, against four isolates of Pm. minimum with opposite mating type (two MAT1-1 and two MAT1-2 isolates) using dual culture, volatile and non-volatile metabolite assays. The results of this study showed that all three species of the antagonist had significant inhibitory effect on the growth of Pm. minimum, in comparison to the control. In dual culture assay, T. harzianum T22 showed the highest potential in the inhibition of the Pm. minimum growth, with 76. 53 percent growth inhibition, in comparison to the two other antagonists. In volatile metabolites assay, significant differences were observed among the antagonists in growth inhibition of the Pm. minimum. In non-volatile compounds assay, T. brevicompactum with 75. 46 percent growth inhibition of pathogen, showed the highest control potential in comparison with the other two species. Non-volatile compounds of T. longibrachiatum and T. harzianum T22 showed 46. 93 and 17. 67 percent inhibition on colony growth, respectively. Evaluation of the inhibitory effects of these antagonists on the opposite mating types of Pm. minimum showed that volatile compounds of T. longibrachiatum were more effective on MAT1-1 (48. 74% growth inhibition) compared to MAT1-2 (35. 10 growth inhibition). Overall, the results of this study reveal T. brevicompactum as an effective antagonist against Pm. minimum; hence, further evaluation of its biocontrol properties and efficacy in disease control under greenhouse and field condition remain to be studied.