Area Of Triangle Research Articles

Ultrasound-guided ablation for T1N0M0 papillary thyroid carcinoma adjacent and non-adjacent danger triangle area: a retrospective comparative study

Objectives To compare the safety and efficacy of ultrasound-guided radiofrequency ablation (RFA) in the treatment of T1N0M0 papillary thyroid carcinoma (PTC) with adjacent and non-adjacent danger triangle area (DTA). Materials and methods This retrospective study involved collecting clinical data of all T1N0M0 PTC patients who underwent RFA between January 2018 and December 2020 at the hospital. A total of 211 patients were enrolled in the study (mean age 43.25 ± 12.30 years, male-to-female ratio = 1:3). Among them, 91 had adjacent DTA involvement, while 120 had non-adjacent DTA involvement. Comparisons were made between the two groups patients regarding tumor volume changes, technical success rates, tumor disappearance, disease progression, complications. Results In both groups, the technical success rate was 100%, with a median follow-up period of 30 months. The rates of complete tumor disappearance were 78% (71/91) and 74.2% (89/120) for the adjacent and non-adjacent DTA(p = .517). Disease progression rates were 2.2% (2/91) and 1.7% (2/120) (p > .99), Complication rates were 3.3%(3/91) in the adjacent DTA group and 1.7% (2/120) in the non-adjacent DTA group (p = .654). At 6th month after ablation, the volume reduction rate (VRR) in the non-adjacent DTA group (42.3%) was higher than in the adjacent DTA group (37.3%) (p = .002). However, no significant differences were observed in VRR between the two groups at 1, 3, 12, 18, 24, 30, and 36 months (p > .05). Conclusion In the treatment of T1N0M0 PTC, the complication rates and short-term efficacy of RFA in adjacent to the DTA did not differ from those of non-adjacent DTA.

Mullan's triangle or anteromedial triangle of the middle cranial fossa: a cadaveric study with its surgical importance.

Surgical approaches to the cavernous sinus (CS) and middle cranial fossa (MCF) can be challenging, particularly for young neurosurgeons. The anteromedial (Mullan's) triangle is a triangle by the side of the CS and constitutes part of the floor of the MCF. The contents include the sphenoid sinus, superior ophthalmic vein, and sixth cranial nerve. The literature contains very little research that has precisely defined and measured the anteromedial triangle while considering anatomical variances minimally. The present study was conducted on the skulls of 25 adult human cadavers which were dissected to expose the anteromedial (Mullan's) triangle on both sides. After precisely defining the triangle on each side, measurements of the three borders were taken, and using Heron's formula, the area of each triangle was calculated. On average, the length of the medial border was 12.5 (+ 3.1mm); the length of the lateral border was 9.9 (+ 3.1mm); the length of the base was 10.75 (+ 2.4mm) and the area of the anteromedial triangle was 43.9 (+ 15.06mm2). Precise anatomical knowledge of the Mullan's triangle enables the treatment of disorders in often deformed anatomy or difficult-to-access structures. That is the reason it is important to gain a thorough understanding of the surgical anatomy and to adopt a safe procedure.

Integrating remote sensing and geophysical data for mapping potential gold mineralization localities at Abu Marawat area, central Eastern Desert, Egypt

Abu Marawat area in the Central Eastern Desert of Egypt is a very promising mineralization district located in the Golden Triangle area. The current study provides an integrated approach from multisource datasets including; remote sensing, airborne geophysical spectrometry and magnetic data supported by field studies and spectroscopic analyses for delineating potential mineralization localities. Several remote sensing techniques were adopted including; Band Ratios, Relative Band Depth, Mineralogical Indices, Spectral Angle Mapper, and Constrained Energy Minimization. These techniques showed that the alteration mineral assemblage is mainly, kaolinite, sericite, and iron oxides, with less abundant chlorite, epidote, and carbonates. In addition, the radiometry data were processed to map the localities with the highest possibility of potassic alteration abundance by integrating the potassium distribution, K/eTh ratio, and the F-parameter maps. The surface and subsurface linear structural features were also mapped using Digital Elevation Model (DEM) and aeromagnetic data, respectively. The surface linear structures were found exhibiting E-W and NE-SW trends, while, the subsurface structures showed dominant NW–SE trend. All the depicted fault trends match well with the local and regional geological and tectonic setting of the study area suggesting structural control on the mineralization in this area. Integration between the results obtained from both the remote sensing and the geophysical data was conducted by a GIS weighted overlay model. The obtained mineralization potentiality map highlights eight potential localities for mineralization. The accuracy of the adopted methodology was demonstrated through fieldwork and spectral analyses; several alteration indicators were observed, including quartz veins, iron oxides, kaolinite, malachite, montmorillonite, chlorite, talc, and sericite alteration indicator minerals. The adopted remote sensing-geophysical approach showed being very effective for mapping the hydrothermal gold-related alteration zones, and is recommended for other similar investigations.

Mitogenomic recognition of incognito lineages in the mud spiny lobster Panulirus polyphagus (Herbst, 1793): A tale of unique genetic structuring and diversification

This study provides the first documentation of three deep conspecific lineages within Panulirus polyphagus in the Indian Ocean, bridging the gap in genetic research. Comparative mitogenomics between lineages (L) at both species and family levels, evolutionary relationships and heterogeneity of sequence divergence within Decapoda, and divergence time estimation were performed. The characterized mitogenomes ranged from 15,685–15,705 bp in size and exhibited a typical pancrustacean pattern. Among the three lineages, L1 predominated the Bay of Bengal, L2 the Arabian Sea, and L2.a, a less common lineage genetically closer to L2, was restricted to the latter region. A minor lineage L1.a, was observed in the Coral Triangle area. All PCGs displayed evidence of purifying selection across species and family levels. The largest genetic distance (K2P) between lineages was 9 %, notably between L1.a and L2.a. The phylogenetic tree subdivided the Achelates into Palinuridae and Scyllaridae, and the topology demonstrated a distinct pattern of lineage diversification within P. polyphagus. AliGROOVE analysis revealed no discernible divergence in Decapoda. The diversification of P. polyphagus appears to have occurred during Miocene, with further diversification in Pliocene. Furthermore, genetic stocks and population connectivity recognized here will provide valuable insight for spatial management planning of this dwindling resource.

Unveiling the governing role of ‘remodeling triangle area’ in soft-hard tissue interface equilibrium for metal implants advancement

Metal implants holds significant promise for diverse fixed prostheses. However, their long-term reliability and broader application are hindered by challenges related to the disequilibrium at the soft-hard tissue interface. By using anti-inflammatory (PDA/IL4) and pro-inflammatory (PDA/LPS/IFNγ) coatings to modulate distinct immune characteristics, we discovered a dynamic bioactive structure at the soft-hard tissue interface around metal implant, which we have named the 'Remodeling Triangle Area' (RTA). We further demonstrate that the RTA can be influenced by the PDA/IL4 coating to favor a phenotype that enhances both innate and adaptive immunity. This leads to stronger epithelial adhesion, the formation of dense connective tissue via IGF1 secretion, and a more balanced soft-hard tissue interface through the OPG/RANKL axis. Conversely, the PDA/LPS/IFNγ coating shifts the RTA towards a phenotype that activates the innate immune response. This results in a less cohesive tissue structure and bone resorption, characterized by reduced IGF1 secretion and an imbalanced OPG/RANKL axis. Over all, our study introduces the novel concept termed the 'Remodeling Triangle Area' (RTA), an immune-rich anatomical region located at the nexus of the implant interface, epithelial, connective, and bone tissue, which becomes highly interactive post-implantation to modulate the soft-hard tissue interface equilibrium. We believe that an RTA-centric, immunomodulatory approach has the potential to revolutionize the design of next-generation metal implants, providing unparalleled soft-hard tissue interface equilibrium properties.

Evaluation of Interdental Papilla Regeneration Using Injectable Hyaluronic Acid: A Clinical Study.

This study aimed to assess the efficacy of hyaluronic acid (HA) gel injections in deficient papillae and record the effects for four weeks. Fifteen deficient class 1 papilla sites according to Nordland and Tarnow classification were included. After scaling and root planing, 0.5 ml HA gel was injected into the papillae. Measurements of black triangle height (BTH) and black triangle area (BTA) from the contact point to the most coronal level of the visible papilla tip weredone on the clinical photographs using ImageJ software at baseline, one week, and four weeks postoperatively, and a comparison was made. Descriptive data were examined using the mean and standard deviation (SD). Paired t-test was used for intragroup comparisons, with p-values <0.05 considered significant. All the data analysis was done using SPSS software version 25.0. There was a mean decrease in the BTA from baseline (0.54 mm2), one week (0.13 mm2), to four weeks (0.26 mm2) with a slight loss of papilla volume from the first week to the fourthweek, and this decrease in area was statistically significant. A mean decrease in the BTH throughout the follow-ups from baseline (1.36 mm) to the first week (0.30 mm) to the fourth week (0.73) was recorded with a slight loss of papilla volume from the first week to the fourthweek, and this decrease in height was also statistically significant (p < 0.05). However, the decrease in the BTA and BTH recorded was more from baseline to the first week as compared to baseline to the fourth week postoperatively. HA gel is an effective treatment for minimally invasive papilla augmentation, particularly in class I Nordland and Tarnow papilla deficits.

Ultrasound-guided percutaneous radiofrequency ablation versus surgery for solitary T1N0M0 papillary thyroid carcinoma in the danger triangle.

To compare the safety and efficiency of ultrasound-guided percutaneous radiofrequency ablation (RFA) and surgical resection (SR) for thyroid papillary carcinoma (PTC) in the danger triangle area. The clinical data of 298 patients who underwent either percutaneous RFA or SR for PTC in the thyroid danger triangle at our hospital between January 2018 and April 2020 were retrospectively analyzed. Propensity score matching is employed to regulate for confounding factors. All patients undergoing ablation were treated using a strategy that combined sufficient paratracheal fluid isolation with a low-power, short electrode. Disease progression was analyzed in patients with T1N0M0 PTC (T1a and T1b) employed in Kaplan‒Meier curves. Treatment parameters and the rates of local recurrence, distant metastasis, and complications are recorded and compared. Of 182 eligible patients who were included, 91 were in the RFA (age 44.84 ± 13.19; 71 females; 77 T1a) and 91 were in the SR (age 47.36 ± 11.05; 68 females; 69 T1a). The average treatment time, length of hospital stays, blood loss volume, and scar length are substantially less in the RFA than in the SR. Major complications as well as postoperative permanent recurrent laryngeal nerve injury and postoperative transient parathyroid dysfunction occurred only in the SR, with a substantial distinction between the two groups (p < 0.05). There is no substantial distinction in the disease progression between RFA and SR treatment of T1N0M0 PTC. RFA is as effective as surgery for PTC in the danger triangle area in the short term, with faster recovery and fewer complications. Radiofrequency ablation has a clinical efficacy comparable to surgery in the treatment of papillary thyroid carcinoma in the danger triangle area in the short term with the advantages of faster recovery and fewer complications when compared with surgery. Use of radiofrequency ablation (RFA) in the thyroid danger triangle is still controversial. RFA and surgery groups showed no difference in disease progressions, and no major complications occurred with RFA. Radiofrequency ablation offers a new option for papillary thyroid carcinoma patients in the danger triangle.

Key Industrial Sectors In The Sulampua Area As A Result Of Nusantara Capital City Development

This study aims to determine the sectors that need to be developed in the non-golden triangle area of the SULAMPUA region as a result of the Nusantara Capital City (NCC) development. Descriptive research is being conducted utilizing secondary data from Statistics Indonesia’s 2016 IRIO (Inter-Regional Input-Output) table. The IRIO model is used in data analysis for 20 secondary sub-sectors. The SULAMPUA region comprises 10 provinces, with the Golden Triangle region comprising South Sulawesi, Central Sulawesi, and West Sulawesi. The study results show that to take advantage of opportunities for the development of NCC, several key industries need to be developed for non-golden triangle areas, namely the food industry (I-13), non-metallic mineral goods industry (I-21); other processing industries, machinery and equipment repair and installation services (I-27); and the wood industry, goods from wood and cork, and woven goods from bamboo, rattan, and the like (I-17). Maluku, Papua, and West Papua provinces have relatively little opportunity to develop the industrial sector and benefit from moving NCC. Because the sectors connected directly or indirectly and the key sectors of these three provinces are capital-intensive industries, MSMEs have more significant barriers to entry. This research can be a reference for local governments in exploring potential industrial sectors to be developed to achieve NCC development opportunities.

Learning Trajectories for the Learning Area of Triangles and Quadrilaterals

Students encounter difficulties in solving areas of triangles and quadrilaterals due to a lack of conceptual understanding of the topic. The researchers have developed the following activities and the hypothetical learning trajectory (HLT) through the design research approach focusing on developing activities for students to learn the concepts properly. Reallotment or reshaping has been the primary idea for the activities. The designed activities in 2 cycles have been trialled out, improved, and implemented for 7-grade students in a classroom. Students’ understanding and development of this study will be further discussed in this paper.

Triangle area model (TAM) for predicting germination: An approach to enhance hydrothermal time model applications

A thorough examination of assumptions in hydrothermal time models revealed areas for enhancing model performance. We introduce the Triangle Area Model (TAM), which uses the area of right-angled triangles to calculate hydrothermal time for predicting population germination fractions (g). TAM is characterized by its depiction of triangles, considering insightful parameters such as the distance of germination temperature (T) to the base (Tb), optimal (To), and ceiling (Tc) temperatures, the range of Tc – To, To – Tb, and the germination water potential (Ψ), i.e. mean base water potential (Ψb(g)), along with potential g that may occur with T and Ψ combinations within Tc – Tb when Ψ > Ψb(g). Applied to germination data from Ambrosia psilostachya L., Cynanchum acutum L., and Bidens pilosa L., TAM achieves an RMSE of 0.03 for A. psilostachya and C. acutum, and 0.05 for B. pilosa. Moreover, TAM demonstrates an R2 of 0.96, 0.97, and 0.98 for the respective species. TAM significantly outperforms earlier models through a comparison with varying T and Ψ. TAM determined Tb for A. psilostachya, C. acutum, and B. pilosa as 0.19, 14.57, and 5.76 °C; To as 25.1, 39.9, and 29.8 °C; and Tc as 46.7, 53, and 41°C, for the respective species. It also estimates Ψb(g) as -1.48 for A. psilostachya, -0.98 for C. acutum, and -0.97 for B. pilosa. The TAM approach deepens our understanding of temperature-moisture processes influencing plant survival, colonization, and habitat expansion for these three invasive alien species. Furthermore, it can be more widely applied for estimating TT and HTT across different growth stages, enhancing the prediction accuracy of plant phenological development.

ON THE QUESTION OF THE COEXISTENCE OF NICKEL AND COBALT SPINEL

For the development of composite materials based on alumina and high-alumina cements using resource-saving technology when replacing the original raw materials with substandard raw materials and chemical wastes, there is a need for a physical and chemical substantiation of the coexistence of newly formed phases in the composition of the binder, which necessitated the study of the subsolidus structure of the system. The paper presents the results of calculations characterising the elements of the subsolidus structure of the CoO - NiO - Al2O3 system. The results of the study revealed the predominance of solid-phase exchange reactions and determined the structure of the CoO - NiO - Al2O3 system in the subsolidus region. It was found that the sub-solidus structure of the system is simple and consists of three elementary triangles. The analysis of the area of the elementary triangles and the low degree of asymmetry indicate that there are no significant risks of deviation from the specified phase composition of the synthesised materials due to the preparatory technological stages, and no special measures are required during the synthesis of materials to ensure the accuracy of the dosage of the starting ingredients. Based on the results of the calculations, the most thermodynamically stable compound in the studied system (aluminocobalt spinel) was identified, and the maximum probability of its existence was determined. Aluminium-nickel spinel has a lower probability of existence because it does not coexist with CoO and is not represented in the elementary triangle with the maximum area. Aluminium-nickel spinel has a lower probability of existence, and the least likely is the identification of Al2O3 in the composition of heterophase combinations. Based on the results of the study, the geometric-topological and statistical characteristics of the subsolidus structure of the system were analysed, which are important for the accuracy of predicting phase combinations in the synthesis of new heterogeneous composite materials.

Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr.

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.

Retrolabyrinthine approach to the lateral skull base: The value of preoperative temporal bone CT analysis

PurposeThe most used neurosurgical approach to reach cerebellar-pontine angle is the retrosigmoid route. This article describes the presigmoid approach which requires excellent knowledge of the labyrinthine block together with quantitative analysis of temporal bone CT. MethodsCT-based quantitative measurements were obtained in patients undergoing vestibular neurectomy with a presigmoid approach. Eighteen patients were enrolled, and five measures were taken: Trautmann’s area, the petro-clival angle, presigmoid dura length and its angle. The relationship between these measurements and hospitalization days, operating times, and complications was explored. ResultsThe posterior semicircilar canal (PSC)-sigmoid sinus (SS) distance, presigmoid dura- internal auditory canal (IAC)-PSC angle, and duration of surgery are predictors of complications. Specifically, a PSC-sigmoid sinus distance <11 mm, a dura presig-IAC-PSC angle <14 are associated with the highest risk of complications. ConclusionPreoperative temporal bone CT scan can guide the surgeon through the narrowest areas of the surgical approach. Trautmann’s triangle area and petro-clival angle reduction are challenging and can be faced with combined microscopic-endoscopic technique, and with optics angulation-rotation. The retrolabyrinthine approach can enable hearing preservation and minimal cerebellar retraction.

Confidentially Compare Rational Numbers under the Malicious Model

&lt;p&gt;Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires&amp;rsquo; problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao&amp;rsquo;s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires&amp;rsquo; problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.&lt;/p&gt; &lt;p&gt;&amp;nbsp;&lt;/p&gt;

Research on resilience assessment method of train control on-board system

To address the problem of difficult performance assessment of train control on-board system after recovery from failures, we have proposed a resilience assessment methodology that uses reliability as an indicator of system resilience. Since the system failures are time-dependent, we adopted the Discrete Time Bayesian Network method to obtain the system's reliability before and after failure. Subsequently, we used an exponential recovery model to quantify the system's performance curve during the recovery phase, and finally utilized the resilient triangle area method to quantify its resilience size. Analyzing the CTCS3-300T train control on-board system, we found that the resilience of the system with cold standby redundancy design and hot standby redundancy design were 89.44 % and 87.34 %, respectively, indicating a slight decrease in system performance after recovery from failures compared to pre-failure levels. At that time, it was necessary to adjust operational plans based on actual conditions to avoid greater impact on the railway network. This paper realizes performance resilience of train control on-board system after failure recovery, which can be applied to similar systems and provide theoretical references for realizing intelligent maintenance of the high-speed train.

Learning Obstacles of Junior High School Students on the Concept of Triangle

Geometry is one of the important topics in school mathematics. Many people solve daily life problems using geometry, including the concept of triangles. However, many students still have obstacles in learning the concept of triangles. This study aims to analyze students’ learning obstacles on the concept of triangle. A qualitative research along with a case study was conducted on 45 students of 9th grade, studying at one of the junior high schools in Majalengka, West Java, Indonesia. The data were collected using triangulation which included document analysis, test, and interview. The results showed that students experienced several types of learning obstacles, including students facing issues in incomplete or inadequate presentation of triangle material (didactical obstacle); their inability to use the triangle concept in the context of non-routine questions (epistemological obstacle); and their inability to follow the learning demands about the definition of triangle, the types of triangles, and the area of triangle (ontogenic obstacle), so that it is indicated that students have problems in understanding the concept of triangle. The results of this study can be used as a reference for developing a more optimal didactical design. Keywords: junior high school, learning obstacles, triangle

LEADERSHIP STYLES PREVAILING IN PRIMARY SCHOOLS IN THE TRIANGLE AREA IN THE PALESTINIAN INTERIOR, AND THEIR RELATIONSHIP TO THE ORGANIZATIONAL CLIMATE FROM THE TEACHERS' POINT OF VIEW

This study aimed to identify the leadership patterns prevailing among primary school principals in the Triangle area in the Palestinian interior, and their relationship to the organizational climate from the teachers' point of view, and the descriptive approach was used, as it is more suitable for such studies. The study relied on the questionnaire in data collection, a questionnaire was used to measure leadership styles (democratic style, autocratic style) dictatorship and the transmitter pattern) among primary school principals, and a questionnaire to measure the areas of organizational climate communication and communication, working conditions, organizational and administrative structure) among teachers. The study population consisted of all primary school teachers in the Triangle area in the Palestinian interior, numbering (2760) teachers, and the study sample consisted of (386) teachers. The results showed that the prevailing leadership style among primary school principals, in the triangle area in the Palestinian interior is the democratic pattern, and it came at a high level, and the results also showed that there were no statistically significant differences due to the variables of gender and experience, the results also showed that the organizational climate came to a high degree, as well as The results showed a positive correlation between the democratic leadership style and the organizational climate, as it was found that the more the level of democratic leadership style prevails, the more positive the organizational climate becomes , and the results showed a negative correlation between the autocratic leadership style (dictatorship) and the organizational climate

Habitat suitability model of future coral reef region in the Halmahera Waters under the projection of environmental pressures from future climate change and coastal pollution

The coral reef region of the Halmahera waters situated within the tropical area of the coral triangle, covers approximately 193,126 km2, with coral reef habitats occupying roughly 958.47 km2. The coral reefs in Halmahera waters are essential for ecosystem services and local fisheries. However, they are at risk from climate change and coastal pollution. This study aimed to develop habitat suitability models for coral reefs in the Halmahera waters under future climate change scenarios. MaxEnt modeling was employed to project suitability for the coral Acropora spp. using occurrence data. Suitability projections were made for 2050 under IPCC RCP 2.6, 6.0, and 8.5 scenarios, assuming no measures are taken to mitigate coastal water pollution. Environmental factors considered in the modeling included temperature, salinity, current velocity, pH, sunlight penetration, and chlorophyll levels. Results demonstrated a significant decline in habitat suitability, with an 85% loss of highly suitable areas under RCP 2.6 – 8.5 compared to current conditions (741 km2). Chlorophyll levels, a marker of coastal pollution, were predicted to be the most influential factor, followed by temperature and salinity. The findings highlight the need to reduce global carbon emissions and implement conservation measures to mitigate coastal water pollution in preserving coral reef habitats.

The geometrical and physical interpretation of fractional order derivatives for a general class of functions

The aim of this article is to find a geometric and physical interpretation of fractional order derivatives for a general class of functions defined over a bounded or unbounded domain. We show theoretically and geometrically that the absolute value of the fractional derivative value of a function is inversely proportional to the area of the triangle. Further, we prove geometrically that the fractional derivatives are inversely proportional to the classical integration in some sense. The established results are verified numerically for non‐monotonic, trigonometric, and power functions. Further, this article establishes a significant connection between the area of the projected fence and the area of triangles. As the area of triangles decreases, the area of the projected fence increases, and vice versa. We calculate the turning points of the fractional derivative values of different functions with respect to order , including non‐monotonic, trigonometric, and power functions. In particular, we demonstrate that for the power function , with being a positive real number, the value is a turning point when . However, for , the turning point shifts to the left of point and shifts to the right of point for We discuss the physical interpretation of fractional order derivatives in terms of fractional divergence. We present some applications of fractional tangent lines in the field of numerical analysis.

Anthropometric Study Via Digital X-Rays of the Obturator Foramen in Surgical Treatment of Urine Incontinence in the South-Western Adult Female Population of Iran

Background: The trans-obturator tape (TOT) procedure is an efficient treatment option that provides support for the urethra in cases of stress urinary incontinence (SUI). Objectives: This research aimed to ascertain the accuracy of anthropometric parameters of the female pubic arch and the obturator foramen (OF) and their application in clinical anatomy. Methods: In this cross-sectional observational research conducted from October 2021 to September 2022, the morphometric characteristics of the pubic arch and the OF were measured on digital pelvic radiographs of 500 adult women from southwestern Iran. They were grouped into three age categories, namely, 18 - 34, 35 - 50, and more than 50 years old, and compared within and between the groups. Results: Significant differences were observed in computed parameter indices of the OF and pubic arch based on age. Parameters such as inter-obturator foramina distance, pubic symphysis length, pubic ramus width, and length increased significantly with age (P ≤ 0.05). Additionally, as women's ages increased, their subpubic angle decreased significantly (P = 0.001). However, other parameters, such as the OF area and the anterior urogenital triangle area, did not show a significant increase with age (P ≥ 0.05). These findings indicate that anatomical pelvic measurements change significantly with age in women. Conclusions: The present study revealed a wide range of variant bony pelvic anatomy in southwestern Iranian adult women, distinct from norms in other groups. Our findings could be utilized in surgical approaches and the production of trans-obturator kits by companies.