Normal forms for Hopf-Zero singularities with nonconservative nonlinear part

In this paper we are concerned with the simplest normal form computation of a family of Hopf-zero vector fields without a first integral. This family of vector fields are the classical normal forms of a larger family of vector fields with Hopf-Zero singularity. Indeed, these are defined such that this family would be a Lie subalgebra for the space of all classical normal form vector fields with Hopf-Zero singularity. The simplest normal forms and simplest orbital normal forms of this family with non-zero quadratic part are computed. We also obtain the simplest parametric normal form of any non-degenerate perturbation of this family within the Lie subalgebra. The symmetry group of the simplest normal forms are also discussed. This is a part of our results in decomposing the normal forms of Hopf-Zero singular systems into systems with a first integral and nonconservative systems

Electrochemical corrosion assessment of RaCe and Mtwo rotary nickle-titanium instruments after clinical use and sterilization

Aim: The aim of the present study was to electrochemically evaluate corrosion resistance of RaCe and Mtwo files after repeated sterilization and preparation procedures. Study Design: A total of 450 rotary files were used. In the working groups, 72 files from each file type were distributed into 4 groups. RaCe and Mtwo files were used to prepare one root canal of the mesial root of extracted human mandibular first molars. The procedure was repeated to prepare 2 to 8 canals. The following irrigation solutions were used: group 1, RaCe files with 2.5% NaOCl; group 2, RaCe files with normal saline; group 3, Mtwo files with 2.5% NaOCl; and group 4, Mtwo files with normal saline in the manner described. In autoclave groups, 72 files from each file type were evenly distributed into 2 groups. Files were used for a cycle of sterilization without the use of files for root canal preparation. Nine new unused files from each file type were used as controls. Then the instruments were sent for corrosion assessment. Mann-Whitney U and Wilcoxon tests were used for independent and dependent groups, respectively. Results: Statistical analysis indicated that there were significant differences in corrosion resistance of files associated with working and autoclave groups between RaCe and Mtwo file types (p<0.001). Conclusions: Corrosion resistance of #25, #30, and #35 Mtwo files is significantly higher than that in RaCe files with similar sizes. © Medicina Oral

Volume-preserving normal forms of Hopf-zero singularity

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any non-degenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified R\"{o}ssler and generalized Kuramoto--Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple

Dexmedetomidine in Neurocritical Care

Early and appropriate management of brain insults has significantly reduced patient morbidity and mortality. Neuromonitoring, neuroprotection and secondary brain injury prevention are the essential principals of brain injury management. In this literature review we have elaborated the neuroprotective role of dexmedetomidine (DEX), predominantly in different animal models of brain insults and reports in patients cared in a neurocritical care setting. &nbsp;We undertook an electronic literature search of articles published in English prior to July 2019. This search resulted in inclusion of 59 studies from medical databanks such as PubMed, Scopus, EMBSCO, CINAHL, ISC and the Cochrane Library. The keywords used were brain, α2 agonist, neurocritical care and dexmedetomidine. DEX may have a neuroprotective effect in a broad spectrum of brain pathologies such as traumatic brain injury (TBI), subarachnoid hemorrhage (SAH), ischemic stroke, intracerebral hemorrhage (ICH), and cerebral hypoxia. However, its neuroprotective role in status epilepticus (SE) is less clear. Further animal and human studies are needed before we could consider DEX as a neuroprotective agent in this patient population. Due to its favorable properties outlined in this review, DEX could be considered a favorable sedative agent in the neurocritical care settings

In vitro comparison of apical microleakage following canal obturation with lateral and thermoplasticized gutta-percha compaction techniques

The purpose of this study was to compare apical microleakage following canal obturation with lateral and thermoplasticized gutta-percha compaction techniques. Ninety extracted single-rooted maxillary teeth were used in this study. Seventy teeth were randomly divided into two groups: One group was obturated by lateral compaction technique and the other was obturated by Obtura II (thermoplasticized gutta-percha compaction technique); 5 teeth were positive controls (without obturation) and 5 teeth were negative controls (with obturation) in each group. The specimens were placed in India ink for 48 h and then divided into two halves. The amount of dye penetration was observed under a stereomicroscope at ×16 magnification and 0.1 mm accuracy. In this study, there was apical leakage in the two experimental groups but the amount of microleakage was not significant. According to the results of independent samples test, there was no significant difference between the two experimental groups.Key words: Apical seal, gutta-percha, lateral compaction, microleakage, Obtura II

Comprehensive assessment of irrigation water requirements in Iran

A national web-based simulation portal was developed to estimate the irrigation water requirements at plain scale in Iran. The National Water Portal (NWP) consists of four national databases (climatic, soil, crop, and spatial data), a lumped water balance model, and a graphical user interface (GUI). The irrigation water requirements in standard conditions were estimated based on the dual crop coefficient approach presented by FAO 56. Net irrigation requirements (NIR) and gross irrigation requirements (GIR) were calculated for 125 different crops cultivated in the 609 plains in Iran. Results were aggregated at both political and hydrological scales. The statistical comparison between the estimated NIR and reported values in the literature reviews indicates a correlation coefficient of 75% with root mean square error (RMSE) of less than 280 m3 ha−1. Results showed that sugar cane has the highest NIR value (18318 m3 ha−1) among the studied crops, and sugar beet has the second highest NIR value (5100–11896 m3 ha−1). The aggregated amount of NIR and GIR for the entire country was calculated as 47 and 105 billion cubic meters (BCM), respectively. Results indicate that 3.772 million cubic meter (MCM) of water can be saved by applying 15% water stress. By increasing the irrigation efficiency to 65% without considering any water stress, 3.482 MCM of water can be saved