Complex Roots Research Articles

Students’ Experience, Self-Confidence, and Perception Toward Endodontic Learning: National Survey Among Malaysian Dental Schools

Objective: This study aimed to evaluate the first endodontic case experiences, self-confidence levels, and perceptions toward endodontic learning of final-year undergraduate students. Methods: An online questionnaire was emailed to 270 final-year dental students at 10 Malaysian dental schools. The questionnaire consists of 29 questions on students’ experience, self-confidence, and perception toward endodontic learning. Results: The response rate was 74.4%. The most frequently treated case was tooth diagnosed as nonvital associated with periapical periodontitis. Most of the students perceived working length determination as the most difficult stage and reported having low confidence in locating canal orifices in multirooted teeth and achieving satisfactory obturation. Overall, the students were satisfied with the endodontic knowledge taught by their respective faculties. Conclusion: Endodontic teaching in Malaysian dental schools was perceived as satisfactory by most dental students. Although endodontic treatment is perceived as difficult, students demonstrated high confidence in carrying out this treatment. However, they had limited ability in treating the complex root canal system.

Automated Segmentation of Dental CBCT Image Using an Improved U-Net Network

In the field of clinical dental medicine, Cone Beam Computed Tomography (CBCT) is a useful tool for the measurement of various dimensions related to the oral cavity, including height and thickness. This provides invaluable guidance and reference for risk assessment in orthodontic treatment, selection of treatment plans and implant treatment. However, segmentation of the teeth region from CBCT images is a daunting task due to complex root morphology and indistinct boundaries between the root and the alveolar bone. Manual annotation of the teeth area is resource-intensive, and deep learning-based segmentation methods are susceptible to noise, reducing their efficiency. To tackle these complexities, a multi-filter attention module is proposed in this paper, which effectively minimizes the noise in CBCT images through utilization of multiple filters and self-attention techniques. Additionally, an Improved U-Net model is proposed, where the original convolution block in the U-Net is replaced with a Double ConvNeXt block to yield better network performance. Experimentally, the proposed Improved U-Net method showed remarkable progress as it achieved a Dice Similarity Coefficient of 86.95% in oral CBCT image segmentation, surpassing existing models and affirming the effectiveness and advancedness of the proposed model and method.

Reconstructing Neurath's Ship: A Case Study in Reevaluating Equity in a Program of Assessment.

Inequity in assessment has been described as a "wicked problem"-an issue with complex roots, inherent tensions, and unclear solutions. To address inequity, health professions educators must critically examine their implicit understandings of truth and knowledge (i.e., their epistemologies) with regard to educational assessment before jumping to solutions. The authors use the analogy of a ship (program of assessment) sailing on different seas (epistemologies) to describe their journey in seeking to improve equity in assessment. Should the education community repair the ship of assessment while sailing or should the ship be scrapped and built anew? The authors share a case study of a well-developed internal medicine residency program of assessment and describe efforts to evaluate and enable equity using various epistemological lenses. They first used a postpositivist lens to evaluate if the systems and strategies aligned with best practices, but found they did not capture important nuances of what equitable assessment entails. Next, they used a constructivist approach to improve stakeholder engagement, but found they still failed to question the inequitable assumptions inherent to their systems and strategies. Finally, they describe a shift to critical epistemologies, seeking to understand who experiences inequity and harm to dismantle inequitable systems and create better ones. The authors describe how each unique sea promoted different adaptations to their ship, and challenge programs to sail through new epistemological waters as a starting point for making their own ships more equitable.

ANALYSIS OF ROOT CANAL CHARACTERISTICS OF MAXILLARY INCISORS WITH CONE BEAM COMPUTED TOMOGRAPHY

Pulpitis is a common oral disease that greatly affects the health as well as the quality of life of patients. Which if left untreated or poorly treated can lead to inflammation of apical tissues [3]. Root canal treatment (endodontic treatment) aimed at eliminating bacteria, preserving and restoring mechanical function of teeth. Root canal treatment takes time, instrument and depends on doctor's skills and clinical experience. It is clear that the additional information provided by CBCT may increase and/or improve diagnostic accuracy and confidence in decision-making as well as have an impact of treatment planning. More clinical studies are required to assess the long-term impact of CBCT on the outcomes of endodontic treatment [10]. In Vietnam, cone beam computed tomography (CBCT) is a new technology in the field of endodontics with multiple advantageous features such as establishing 3D images of the root canal system with a low dose of X rays, providing more information, true spatial relationships, and image data can be sectioned. Hence, CBCT is highly beneficial and has high value in the field of endodontics, especially in cases of teeth with complex root canal systems. With the desire to apply science and technology into clinical pratice, we carry out this study: "Analysis of root canal characteristics of maxillary incisors with cone beam computed tomography” with the 2 aims:
 
 To evaluate the number of root canals in maxillary incisors.
 To analyze curvature and morphology of the root canal system in maxillary incisors.

Multiple facets of cutting-edge mycorrhizal research: 11th International Conference on Mycorrhiza (ICOM 11), Beijing, China, August 2022: 11th International Conference on Mycorrhiza (ICOM 11), Beijing, China, 1-5 August 2022.

Multiple facets of cutting-edge mycorrhizal research: 11th International Conference on Mycorrhiza (ICOM 11), Beijing, China, August 2022: 11th International Conference on Mycorrhiza (ICOM 11), Beijing, China, 1-5 August 2022.

Lateral root branching: evolutionary innovations and mechanistic divergence in land plants.

The root system architecture in plants is a result of multiple evolutionary innovations over time in response to changing environmental cues. Dichotomy and endogenous lateral branching in the roots evolved in lycophytes lineage but extant seed plants use lateral branching instead. This has led to the development of complex and adaptive root systems, with lateral roots playing a key role in this process exhibiting conserved and divergent features in different plant species. The study of lateral root branching in diverse plant species can shed light on the orderly yet distinct nature of postembryonic organogenesis in plants. This insight provides an overview of the diversity in lateral root (LR) development in various plant species during the evolution of root system in plants.

Rayleigh waves in nonlocal generalized thermoelastic media

PurposeThe purpose of this article is to investigate the propagation characteristics (such as particle motion, attenuation and phase velocity) of a Rayleigh wave in a nonlocal generalized thermoelastic media.Design/methodology/approachThe bulk waves are represented with Helmholtz potentials. The stress-free insulated and isothermal plane surfaces are taken into account. Rayleigh wave dispersion relation has been established and is found to be complex. Due to the presence of radicals, the dispersion equation is continuously computed as a complicated irrational expression. The dispersion equation is then converted into a polynomial equation that can be solved numerically for precise complex roots. The extra zeros in this polynomial equation are eliminated to yield the dispersion equation’s roots. These routes are then filtered for inhomogeneous wave propagation that decays with depth. To perform numerical computations, MATLAB software is used.FindingsIn this medium, only one mode of Rayleigh wave exists at both isothermal and insulated boundaries. The thermal factors of nonlocal generalized thermoelastic materials significantly influence the particle motion, attenuation and phase velocity of the Rayleigh wave.Originality/valueNumerical examples are taken to examine how the thermal characteristics of materials affect the existing Rayleigh wave’s propagation characteristics. Graphical analysis is used to evaluate the behavior of particle motion (such as elliptical) both inside and at the isothermal (or insulated) flat surface of the medium under consideration.

On the Practicality of the Analytical Solutions for all Third- and Fourth-Degree Algebraic Equations with Real Coefficients

In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that satisfies the following two conditions at the same time: (1) Its discriminant is identical to the discriminant of the general quartic equation. (2) It has at least one positive real root whenever the general quartic equation is non-biquadratic. This unique special form of the resolvent cubic is defined here as the “Standard Form of the Resolvent Cubic”, which becomes relevant since it allows us to reveal the relationship between the nature of the roots of the general quartic equation and the nature of the roots of all the forms of the resolvent cubic. Finally, this new analysis is the basis for designing and programming efficient algorithms that analytically solve all algebraic equations of the fourth and lower degree with real coefficients, always avoiding the application of complex arithmetic operations, even when these equations have non-real complex roots.

Albedo effects in the ER3BP with an oblate primary, a triaxial secondary and a potential due to belt

We have examined the effects of Albedo in the Elliptic Restricted Three-Body Problem (ER3BP) with an oblate primary, a triaxial secondary, and potential due to belt for the Earth–Moon system. We have found that as the perturbed parameters increases, the possible boundary regions of the primary come closer to one other, allowing particles to travel from one region to the next freely and possibly merge the permissible regions. Our study has revealed that the formation of triangular libration points depends on the Albedo effects, semi-major axis, the Eccentricity of the orbits, triaxiality, and the potential due to the belt. As the parameters mentioned above increase, the triangular positions {L}_{4} and {L}_{5} move towards the center of origin in cases 1, 2, 3, and 4 and away from the center of the origin in cases 5, 6, and 7. Considering the range of a stable and unstable libration point for the problem under study given as 0<mu <{mu }_{c} for stable libration points and {mu }_{c}leqmu le frac{1}{2} for unstable libration points, our study has established that the triangular libration points are respectively stable and unstable for cases 1, 2, and 6 and cases 3, 4, 5, and 7. Our study has also revealed that each set of values has at least one characteristic complex root with a positive real part. Hence, the triangular libration points for the Earth–Moon system are unstable in the sense of Lyapunov. The Earth–Moon system's Poincare Surface of Section (PSS) has demonstrated that a slight change in the initial conditions, the semi-major axis, and the Eccentricity of the orbits have affected the system's behavior dramatically. Further, it is seen that a chaotic dynamical behavior of the system results into either regular or irregular orbits.

Role of the Anterior Cruciate Ligament, Anterolateral Complex, and Lateral Meniscus Posterior Root in Anterolateral Rotatory Knee Instability: A Biomechanical Study

Background: Injuries to the anterior cruciate ligament (ACL), Kaplan fibers (KFs), anterolateral capsule/ligament (C/ALL), and lateral meniscus posterior root (LMPR) have been separately linked to anterolateral instability. Purpose: To investigate the contributions of the ACL, KFs, C/ALL, and LMPR to knee stability and to measure instabilities resulting from their injury. Study Design: Controlled laboratory study. Methods: Ten fresh-frozen human knees were tested robotically to determine restraints of knee laxity at 0° to 90° of flexion. An 88-N anterior-posterior force (anterior and posterior tibial translation), 5-N·m internal-external rotation, and 8-N·m valgus-varus torque were imposed and intact kinematics recorded. The kinematics were replayed after sequentially cutting the structures (order varied) to calculate their contributions to stability. Another 10 knees were tested in a kinematics rig with optical tracking to measure instabilities after sequentially cutting the structures across 0° to 100° of flexion. One- and 2-way repeated-measures analyses of variance with Bonferroni correction were used to find significance (P < .05) for the robotic and kinematics tests. Results: The ACL was the primary restraint for anterior tibial translation; other structures were insignificant (<10% contribution). The KFs and C/ALL resisted internal rotation, reaching 44% ± 23% (mean ± SD; P < .01) and 14% ± 13% (P < .05) at 90°. The LMPR resisted valgus but not internal rotation. Anterior tibial translation increased after ACL transection (P < .001) and after cutting the lateral structures from 70° to 100° (P < .05). Pivot-shift loading increased anterolateral rotational instability after ACL transection from 0° to 40° (P < .05) and further after cutting the lateral structures from 0° to 100° (P < .01). Conclusion: The anterolateral complex acts as a functional unit to provide rotatory stability. The ACL is the primary stabilizer for anterior tibial translation. The KFs are the most important internal rotation restraint >30° of flexion. Combined KFs + C/ALL injury substantially increased anterolateral rotational instability while isolated injury of either did not. LMPR deficiency did not cause significant instability with the ACL intact. Clinical Relevance: This study is a comprehensive biomechanical sectioning investigation of the knee stability contributions of the ACL, anterolateral complex, and LMPR and the instability after their transection. The ACL is significant in controlling internal rotation only in extension. In flexion, the KFs are dominant, synergistic with the C/ALL. LMPR tear has an insignificant effect with the ACL intact.

On the index divisors and monogenity of number fields defined by x 5 + ax 3 + b

The main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz[24] for any quintic number field K generated by a complex root α of a monic irreducible trinomial F(x) = x 5 + ax 3 + b ∈ ℤ [x]. Namely we calculate the index of the field K. In particular, if the index is not trivial, then K is not mongenic. Finally, we illustrate our results by some computational examples.

Investigation of Morphological Variations of Canal and Root of First Mandibular Molar in Tomographic Images Computer with Cone Beam in Patients of Arak City

Introduction: Being the first teeth to erupt, first molars have the most complex root system and canal morphology and are among the most susceptible teeth to decay and destruction. The aim of this study is to determine the frequency of morphological variations of the canal and root of the mandibular first molar in cbct images so that appropriate treatment can be performed with a better understanding of the anatomy of the root and canal of the molar tooth.Materials &amp; Methods: In this descriptive cross-sectional study, the morphological variation of the mandibular first molar canal and root was investigated in 170 cbct radiology image samples. In this study, the age and gender of the individual, the number of roots and canals of the mandibular first molar, the morphology of the canal in each root, the presence of the midmesial canal and the presence of the distolingual root were also investigated. In the end, frequency and percentage indicators were used to analyze data and chi-square test was used to compare frequencies.Results: The average age of the subjects studied was 39.2 years. The subjects included 86 women and 84 men. The most seen sample was a molar tooth with two roots and three canals. In terms of canal morphology in the mesial root, the most common canal morphology was type 4 and then type 2. In terms of canal morphology in the distal root, the most common canal morphology was type 1. In the studied samples, midmesial canal was not found in 99.4% of cases and distolingual root was not found in 94.7% of cases.Conclusion: Two-rooted and three-channel molar without midmesial canal and without distolingual root was the most common case found in this study. The most common canal morphology in the mesial root was type 4 and the most common canal morphology in the distal root was type 1.

IMPACT OF THE PASSIVE/ACTIVE ULTRASONIC ACTIVATION ON THE ENDODONTIC IRRIGANTS EFFECTIVENESS - A REVIEW

Introduction: various irrigation devices and chemical solutions are being developed and improved nowadays for better penetration deep into the complex root canal system. Activation of irrigating solutions enhances the solution effectiveness. Evidence in the literature suggests that ultrasonic irrigation is much more effective in this respect than syringe irrigation alone. Passive ultrasonic irrigation (PUI) and/or ultrasonically activated irrigation (UAI): nowadays, the two terms, PUI and UAI, are interchangeable in the literature and represent the same technique. Literature data have shown that combining ultrasonically activated NaOCl with EDTA results in significantly greater removal of the smear layer. Conclusion: the use of ultrasonic activation of the irrigating solution after root canal preparation significantly improves the removal of debris from hard-to-reach areas such as isthmuses, lateral canals and the apical delta.

The collinear equilibrium points in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary

The study investigates the collinear positions and stability in the elliptic restricted synchronous three-body problem under an oblate primary and a dipole secondary for Luhman 16 and HD188753 systems. Our study has established four collinear equilibrium points (L1,2,3,6) which are greatly affected by the parameters under review. The collinear position L1 move away and closer as the parameters increase and decrease respectively. For the collinear positions L2andL3, we witnessed a uniform space movement away from the origin in the negative direction while L6 seems to be moving closer to the origin from the negative part of the origin. We observed changes in the movements of the collinear positions (L1,2,3,6) as a result of the half distance between the mass dipoles and the oblateness of the primary for the problem under review. The movements away and closer to the origin from collinear positions do not change the status of the collinear points as they remain unstable and unchanged. It is also found that as the half distance between mass dipoles and oblateness of the primary increase, the region of stability of the collinear positions decreases for the aforementioned binary systems. The collinear equilibrium point (L3) is stable for the characteristic roots (λ1,2) for Luhman 16 system. This is evidenced by at least one characteristic root, a positive real part and a complex root. The stability of collinear points in most cases are unstable for the stated binary systems in Lyapunov.

Accuracy verification of dental cone-beam computed tomography of mandibular incisor root canals and assessment of its morphology and aging-related changes.

The root canal morphology undergoes aging-related changes, and relevant quantitative analyses have not yet been reported. We compared the cone beam computed tomography (CBCT) and micro-computed tomography (micro-CT) scans of extracted mandibular incisors to check the accuracy of morphological measurements. Thereafter, the root canal morphology and aging-related changes in the mandibular incisors of Japanese individuals were assessed using CBCT. Six extracted teeth were fixed in a phantom head and imaged using CBCT and micro-CT. The correlation between the findings of the two imaging modalities was examined. Further, CBCT reconstructed images of the mandibular incisors of 81 individuals were observed. Age-related changes of the root canals were compared between participants aged <30 years and those aged ≥30 years. The CBCT and micro-CT findings regarding the root canals of the extracted teeth coincided in 94.4% of the cases. Mandibular incisors exhibiting two root canals in either cross-section accounted for 9.9% of central incisors and 12.4% of lateral incisors. Mandibular central incisors with two root canals were observed in two (6.3%) individuals aged <30 years and six (12.2%) aged ≥30 years. Mandibular lateral incisors with two root canals were observed in one (3.1%) individual aged <30 years and nine (18.4%) aged ≥30 years. CBCT allows accurate evaluation of complex root canal morphologies and is useful for endodontic preoperative assessment. Mandibular incisors have more frequent occurrence of two root canals with aging.

APPLICATION OF MAPLE PROGRAM AND MATLAB CODE ON THE STABILITY ANALYSIS OF AN EXPLICIT FOURTH-STAGE SECOND-ORDER RUNGE-KUTTA METHOD

The essence of this paper is to analyze the stability of a derived explicit fourth-stage second-order Runge-Kutta methodusing MAPLE PROGRAM and MATLAB CODE. The property of stability is essential and necessary requirement for anynumerical method to be termed reliable. The analysis revealed that the method is absolutely stable. The test equation was applied on the method and a polynomial equation was generated. The MAPLE program was used to resolve thepolynomial equation resulting to sets of real and complex roots. The MATLAB code was used to plot the stability curvewhich shows the region of absolute stability. Hence, the whole analysis revealed that the method is not just stable, but itis absolutely stable.

Cone-Bean Computed Tomography and Light Microscopic Examination of Human Extracted Molars - An in Vitro Study

Introduction: For appropriate root canal therapy, understanding the anatomical and morphological aspects of the endodontic area is critical. Therefore, the study and analysis of images is an important step in the assessment and current clinical treatment of endodontic problems. Furthermore, microscopic-assisted endodontic therapy, particularly for multirooted teeth, is becoming more common in contemporary endodontic clinical practice. The aim of this in vitro study was to examine the distinct types of isthmuses using a light microscope and Cone-Beam Computed Tomography (CBCT). Method: Fifty-five extracted human molars were used for this study. CBCT was used to realize the study. After the CBCT analysis, all teeth were inspected under a light microscope, and the results were compared with those of the CBCT examination. Results: The results from the CBCT at the coronary third of the root canals were as follows: Types I, II, III, IV, and V isthmuses were found in 50.9%, 16.4%, 1.8%, 7.3%, and 23.6% of all samples, respectively. For the middle third, we found Types I, II, III, IV, and V isthmuses in 40.0%, 23.6%, 1.8%, 16.4%, and 18.2% of the samples, respectively. For the apical third, we found Types I, II, III, IV, and V isthmuses in 60.0%, 29.1%, 5.5%, 1.8%, and 3.6% of all samples, respectively. The results obtained from the microscopic examination were similar to those from the CBCT study. There is no confirmed statistically significant difference between the examination methods (p = 0.07). Conclusion: Three-dimensional examinations have a significant role among the methods for diagnosing and detecting an isthmus in the complex root canal system, especially in the apical part.

Comparison of obturation quality in natural and replica teeth root-filled using different sealers and techniques

ObjectivesThis study aims to assess the obturation efficacy of sealers placed with different techniques using microcomputed tomography (µCT) and assess the influence of µCT testing parameters on the obturation data obtained.Materials and methodsIncisors and mesial roots of lower molars with standardized root length were scanned using µCT, and one tooth of each type was 3D printed in acrylic. Two obturation techniques (warm vertical and single cone) and 4 sealer types (AH Plus, BioRoot RCS, Totalfill BC, and Bio-C Sealers) were assessed following storage in Hank’s balanced salt solution for 3 and 6 months by assessing gap and void volume percentages on both natural and replica incisor and molar roots. The storage solution was analysed to assess calcium ion leaching. The influence of temperature, tooth positioning, and moisture content of the teeth while µCT scanning was also investigated.ResultsThe obturation quality in the incisor group was the same using both natural teeth and replicas (p > 0.05). No changes in void volume were identified when comparing the same sealer using different obturation techniques. The premixed sealers used in single-cone obturation exhibited high void volume in the 3D printed replicas in the long term. The temperature, positioning, and moisture content of the teeth did not affect the outcome of µCT testing.ConclusionsBioRoot RCS, Totalfill BC, and Bio-C Sealers are suitable for obturation of both complex and simple root canal systems using different obturation techniques with BioRoot RCS exhibiting the highest calcium ion release. 3D printed acrylic teeth can be used to assess the obturation quality in uncomplicated root canal systems. µCT parameters had no significant effect on the µCT measurement.Clinical relevanceThe single-cone obturation technique with hydraulic sealer is a simple technique that can be used for obturation of all root canal systems.

Multi-lump wave patterns of KPI via integer partitions

The connection between the theory of integer partitions and a class of nonsingular rational solutions of the Kadomtsev–Petviashvili (KP) I equation referred to as multi-lumps is investigated. It is shown that specific partitions of a given positive integer N lead to multi-lump solutions that exhibit distinctive surface wave patterns. The pattern formations are described by the complex roots of special polynomials such as the Yablonskii–Vorob’ev, Okamoto and generalized Okamoto polynomials arising in the study of rational solutions of Painlevé II and IV equations. Stationary KPI multi-lumps which correspond to rational solutions of the Boussinesq equation are also discussed.

Cubic root-locus format for structures with a local viscous damping device

The tuning and efficiency of a local viscous damper on a flexible structure is described via an approximate representation of the characteristic equation in the form of a cubic polynomial. Increasing the viscosity to the limit of locking of the device typically leads to an increased modal resonance frequency, but may lead to a decrease. A cubic approximation is developed covering both cases in which the effect of the non-resonant modes is represented by an equivalent stiffness or inertia term, respectively. The magnitude of the stiffness or inertia parameter is determined by the change in resonance frequency following from locking of the device, and thus the cubic root-locus curve is determined by only two parameters: the original undamped resonance frequency, and the frequency after locking. The length parameter along the curve is given by a suitably scaled non-dimensional damping parameter. It is demonstrated that when introducing the geometric mean of the unlocked and locked frequencies the complex root locus curve for increasing damping parameter consists of inverse points with respect to a circle with the geometric mean frequency as radius, and furthermore the inverse points correspond to reciprocal values of the normalized damping parameter. The explicit results of optimal damper tuning and the resulting structural damping enable direct design based solely on the three parameters, that can typically be extracted from a standard finite element analysis of the structure. Two examples demonstrate the accuracy of the cubic format, and clarify the reason for decrease of the modal frequency by damping for certain cases.