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The triangular-type Ising nanowire is constructed on the Bethe lattice (BL) by using the core-shell structure consisting of spin-3/2 atoms as the core and spin-1/2 atoms as the triangular shell. Each triangular plaquette of spins forms a nanoparticle which is connected to upper and lower plaquettes symmetrically. The additions of the plaquettes continue indefinitely until the thermodynamic limit to construct the nanowire. The inter- and intra-bilinear interaction parameters (J) are assumed to be positive or negative to simulate the ferromagnetic (FM) or antiferromagnetic (AFM) interactions, respectively. The crystal field for spin-3/2 and external magnetic field for all sites are also included into the model. After obtaining the formulation of the model in terms of exact recursion relations (ERRs), the thermal variations of magnetizations are studied in detail to obtain the phase diagrams. It is found that the model leads to different types of FM and AFM regions with various forms of phase transitions. It is also interesting that the model presents random or oscillatory magnetization behavior regions for the appropriate values of our system parameters. [ABSTRACT FROM AUTHOR]

This work investigates the effectiveness of a shape-memory alloy (SMA) in controlling the instabilities of triangular composite plates under supersonic flow. Lagoudas' quadratic polynomial hardening theory models the SMA effect. First-order piston theory was used for the aerodynamic modeling, and the reference-temperature method was used for modeling the thermal heating. The buckling and post-buckling behaviors were studied for different boundary conditions with four different layups. In addition, buckling and post-buckling of the composite plate, with and without shape memory alloy wire, has been studied. The effect of SMA wire on aeroelastic instabilities is accurately studied. The embedded SMA wire significantly increased the stability region (postpone divergence and flutter velocities) and buckling temperature. Also, the time responses of the triangular composite plate are determined at different Mach numbers, showing that by increasing the Mach number, the SMA wire can control or decrease the vibration amplitudes. [ABSTRACT FROM AUTHOR]

This work investigates the effect of two wall roughness types, triangular and circular, on convection and radiation heat transfer in a small space. The ANSYS Fluent is used to do thermal and dynamic modeling; the left wall is warmer than the right one. The upper and lower walls are adiabatic. The Nusselt numbers are compared in all cases and for two Rayleigh values, which change based on the cavity's characteristic length. The results show temperature contours and Nusselt curves. It was observed that the roughness had a strong effect on the air's thermal behavior inside the cavity, where the Nusselt decreased in both roughness cases, especially at small heights. However, the largest decrease is in the triangular case and for angles less than 90°. For 72°, Nusselt is 13.32 and 6% less than smooth and circular cases respectively. [ABSTRACT FROM AUTHOR]

Sacroiliac joint (SIJ) fusion, to treat back pain caused by SIJ dysfunction, can employ open or minimally invasive surgery (MIS) techniques and either cylindrical (screw-shaped) or triangular (wedge-shaped) implants. Fusion nonunion sometimes explains recurrent SIJ pain following fusion and occasionally requires hardware revision. MIS revision minimizes patient pain, infection, and disability, but due to the triangular implant size and form factor, implant removal can present challenges for MIS access during the explantation and achieving good bony purchase for reinstrumentation. Here, we report a prone single-position lateral MIS/posterior mini-open procedure for triangular-implant SIJ fusion revision. The patient is a 72-year-old female who underwent right SIJ fusion for lower back and leg pain sustained after a fall 2 years prior but experienced recurrent pain over the subsequent 2 years, with imaging findings of right SIJ peri-hardware lucencies and diagnostic injections confirming persistent right-sided sacroiliitis. The patient underwent hardware removal using the lateral MIS incision with table-mounted tubular access and image-guided navigation to maintain exposure, plus simultaneous reinstrumentation using a navigated S2-alar-iliac screw and iliac bolt construct with connecting rod through the posterior mini-open incision made for the navigation reference frame spinous process clamp. The use of navigation and MIS access can significantly decrease the complexity of lateral hardware removal, and mini-open navigated screw-and-rod constructs offer reinstrumentation options accessible to surgeons unfamiliar with specialized posterior SIJ systems. [ABSTRACT FROM AUTHOR]

In this paper, photonic generation of arbitrary shape radio-frequency (RF) waveforms like triangular, square and fullwave rectifier types are demonstrated based on a dual-parallel Mach–Zehnder modulator (DP-MZM) driven by a single sinusoidal RF signal. In the proposed technique, one of the sub-MZM (MZM-2) has no driven signal, while other the sub-MZMs (MZM-1) of the DP-MZM is driven by the sinusoidal RF signal. The powers of even and odd-order sidebands are separately controlled by proper adjustment of modulation index through modulating the bias of the MZM-1. An RF signal with controllable harmonics are generated, after detecting the modulated signal by a photodetector. Thus, by separately modulating its harmonics a desired RF waveform is generated. The proposed method is theoretically analysed followed by experimental validation. [ABSTRACT FROM AUTHOR]

We identify the class of real square invertible matrices A for which the signs of the diagonal entries of A-1 match those of A, and begin their study. We say such matrices have the inverse diagonal property (IDP). This class includes many important classes: the positive definite matrices, the M-matrices, the totally positive matrices and some variants, the P-matrices, the diagonally dominant and H-matrices and their inverse classes, as well as triangular matrices. This class is closed under any real invertible diagonal multiplication on either the right or the left. So questions about this class can be reduced to the case of positive diagonal entries. Other basic properties are given. One theme is what conditions need be added to the IDP to insure membership in a familiar class. For example, the positive definite matrices are characterized as certain IDP matrices with special conditions on certain particular principal minors. The tridiagonal case is highlighted. Certain specially simple conditions on such matrices are mentioned that ensure them to be P-matrices, positive definite matrices or M-matrices. We also note that recent results about the invertibility of weakly diagonally dominant matrices are used. Examples are given throughout the paper. [ABSTRACT FROM AUTHOR]

The research was done for analyze understand mathematical concepts of students on the material of triangular and quadrangular in terms of the characteristics of the student's way of thinking. This type of research is descriptive qualitative. The subjects in this study were students of class VII F and VII G of SMP Negeri 3 Muntilan. Subject selection procedure using purposive sampling. Data collection techniques use tests of mathematical concept comprehension ability, questionnaires of characteristics of ways of thinking, interviews, and documentation. The results showed that (1) the characteristics of concrete sequential thinking with Ability to understand high-category mathematical concepts can meet all indicators of understanding mathematical concepts, in the medium category it can meet 5 indicators and the low category only meet 3 indicators; (2) characteristics of abstract sequential thinking with the ability to understand mathematical concepts in the high category can meet 6 indicators, in the medium category it can only meet 5 indicators, and in the low category only meet 4 indicators; (3) the characteristics of concrete random thinking with the ability to understand mathematical concepts in the high category can meet 6 indicators, in the medium category it can only meet 5 indicators, and in the low category it can only meet 3 indicators; (4) characteristics of abstract random thinking with high ability to understand mathematical concepts can meet 6 indicators, in the medium category it can only meet 4 indicators and in the low category only meet 3 indicators.

The labyrinth side weir structure is an optimal solution to regulate and divert excess flows across rivers, and irrigation and drainage channels when the opening length of the side weir is limited. Changing the geometry of the side weir is considered one way to improve its efficiency. The present study investigates the hydraulic effects of stepped labyrinth side weirs to increase their discharge capacity. To estimate the outflow over symmetrical stepped labyrinth side weir, the discharge coefficient needs to be determined. Normal triangular labyrinth side weir in one cycle mode has been modified by increasing the crest path using different steps. A total of 417 experiments were conducted on normal and stepped side weirs for various weir opening lengths, weir heights, internal head angles, and hydraulic conditions. The results were analyzed and compared. It was found that efficiency improved, and the discharge coefficient increased as the number of the steps decreased. Furthermore, the water surface profile becomes more uniform with decreasing number of steps. A lower number of steps, smaller head angle, and high weir length produce a higher discharge coefficient by approximately 15%–35% compared to a normal triangular labyrinth side weir; in addition, the Knope length decreases by approximately 40%–70% for the same effective length. Additionally, a reliable equation to estimate the discharge coefficient of the stepped labyrinth side weir was presented. The results of this study can be used to design side weirs with high hydraulic performance when the weir-included angle selected is small or there is a lack of space. [ABSTRACT FROM AUTHOR]

A roughness of the absorber plate can improve the efficiency of a solar air heater. To boost the efficiency of triangle solar air heaters, this research presents the results of a comparison study between with and without rib roughness on absorber plates. Both use black paint with graphene nanoparticles infused into it, coating an absorber plate. Both numerical and experimental methods have been used to examine the impact of surface roughness on friction factors and heat transport properties. ANSYS 14.5 software module and RNG turbulence, k-€ model is used to conduct a three-dimensional simulation and solve the governing equations in the turbulent situation. Based on experimental data, it has been established that smooth plates are more efficient in converting heat into useful work than rough ones, on average, by a factor of 4.82 and 4.46, respectively. The length of the duct in the solar air heater mitigates the temperature gradient seen in the simulation result. The roughness of V-shaped ribs has a far larger effect on the heat transfer and friction factor properties than do variations in relative roughness pitch (P/e) and Reynolds number (Re). Experimental observations supported by modeling and simulation confirms that triangular duct absorber surface roughness provides improved outcome.

Purpose: The aim of our retrospective study is to analyze how spinopelvic dissociations (SPDs) were treated in a single center trying to better understand how to improve surgical and non-surgical options. Methods: Twenty patients of a single center surgically treated for SPDs between 2013 and 2021 were retrospectively included in this study. Three surgical techniques have been used: modified triangular stabilization, triangular stabilization and double iliac screws stabilization. Follow-up was assessed for up to 11.6 ± 9.9 months through ODI, MRS, NRS, IIEF or FSFI, a CT scan and whole spine X-ray examination. Results: Twenty patients were admitted to our ER for traumatic spinopelvic dissociation. Surgical treatment for spinopelvic dissociation has been performed on average 11.5 ± 6.7 days after the trauma event. Eighteen fractures were C3 type and two C2 types. Neurological examination showed nerve root injury (N2) in 5 patients, incomplete spinal cord injury (N3) in 4 patients and cauda equina syndrome in two patients (N4). In case of neurologic deficits, routinary nerve decompression was performed. Three different surgical techniques have been used: 8 triangular fixations (Group 1), 6 modified triangular stabilization (Group 2) and 6 double iliac screws triangular fixation (Group 3). Conclusion: In patients with post-traumatic neurological deficit, decompression surgery and fracture reduction seem to be associated with clinical improvement; however, sexual disorders seem to be less responsive to the treatment. Some open stabilization techniques, such as the double iliac screw, could help in restoring the sagittal balance in case of severe deformities. [ABSTRACT FROM AUTHOR]

Flood is number one Indonesian natural disaster in the last 10 years and its occurrence at Manokwari is frequently reported. Biophysical condition is playing a key role in carrying capacity of this catchment area. This study is to determine biophysical characteristics of Wosi Watershed to manage and mitigate flooding in Manokwari. Spatial analysis and field observation methods were used to collect the data. Biophysical variables are rainfall, watershed morphometric, slope, and land used. Carrying capacity is measured using flow regime coefficient and annual flow coefficient. The results showed that the heavy rainfall (> 100 mm) throughout the ten years with 10.5 wet months at average resulting very wet tropical climate. This watershed has an area of 2,346.32 ha, its circumference of 29.95 km2 with river length of 8.38 km resulting 0.33 (triangle) and 1.027 (triangle) for Rc and Re, respectively. This morphometry is rectangular and slightly oval (triangular) formed of four rivers with drainage pattern of dendritic, which resembles the shape of a tree branch/twig. Steep slopes are dominant (58.5%), with non-forest area (62%) of the flat and steep slope for settlement (698 ha), and flat slope for mixed dry farming (707 ha). From 2016-2020, river water flow changes rapidly from low to very high to generate flooding, but the carrying capacity is sometime changeable from good to bad. Water drainage, retaining walls, replantation, early warning system, and flooding leaflets mitigation campaign, are structural and non-structural mitigation could be parallelly conducted to manage and mitigate the flooding risks in future. [ABSTRACT FROM AUTHOR]

Additive manufacturing technologies enable the production of components with lightweight cores, by means of infills with various patterns and densities. Together with reduced mass and material consumption, infill geometries must ensure that strength and stiffness conditions are fulfilled. For the proper correlation of the infill type with the loading case of the part, the mechanical behavior of the infill along all three principal axes of inertia has to be known. In this paper, the behavior in symmetric and asymmetric bending of three infill geometries, commonly used in 3D printing processes (honeycomb, grid and triangles) is analyzed. The variations of deflections as a function of force orientation are presented, showing that honeycomb and triangular structures exhibit similar behaviors along the Y and Z principal axes of inertia. Furthermore, the displacements obtained for the three types of structures are compared, in relation to the consumed volume of material. The larger displacements of the grid structure compared to the honeycomb and triangular structures are highlighted. [ABSTRACT FROM AUTHOR]

The purpose of this research is to find out a comprehensive picture of students' mathematical understanding in the online learning process, especially in the triangle and quadrilateral material. The study was conducted on 20 students in MTs. Nurul Islah Gegelang. The qualitative research method was chosen. Interactive analysis is applied to obtain in-depth information related to interpreting research findings. Data collection is done by using zoom meeting. The research data are in the form of test scores for mathematical understanding abilities, observation sheets related to the online learning process carried out and in-depth interviews to determine students' mathematical understanding abilities. The results of the study showed that, out of 20 students, only 8 students scored 30 and 12 were below. The ability of students' mathematical understanding in the online learning process was still very poor, especially in the concept of triangles and quadrilaterals. Students' understanding is still limited to memorizing properties without understanding in detail the characteristics of each flat shape. Students still have difficulty in applying formulas to triangles and quadrilaterals in solving problems.

This work defines MM-Fuzzy Cone Metric Space, as a new metric space. It also analyzes possible forms of contractive conditions and groups them accordingly to set up generalized contractive conditions for self-mappings defined over MM-fuzzy cone metric spaces. We prove the existence of fixed points of these mappings and exhibit the same through a suitable example.

Objectives. To carry out mathematical simulations of changes in time of tornado compositions in channels with projections of semicircular, triangular, square profiles for average Reynolds criteria based on multiblock computing technology with the solution of finite- volume factorized methods of the Reynolds equation and energy equations.Method. The calculations were carried out on the basis of theoretical approaches based on the solution of Reynolds equations by finite-volume factorized methods, which were closed using the simulation of Menter stresses, and the energy of a structured grid.Result. The calculations of time-dependent flow and heat transfer parameters carried out in the article showed that the excess dissipation of turbulence generation for projections of sharp profiles - square profile, triangular profile - and rounded profiles - semicircular profile, segment profile - is provided with radically different hydraulic losses: channels with protrusions of rounded profiles, for example, semicircular, have much lower hydraulic resistance coefficients than channels with protrusions with sharp profiles, for example, triangular or square, rectangular.Conclusion. In the article, mathematical simulations of time-dependent tornado compositions were performed in channels with transversal profiles in the form of a square, triangle and semicircle, which is as informative as possible in terms of studying turbulent flows and heat transfer arising under average Reynolds criteria based on computer multiblock technology when using solutions of finite-volume factorized methods (FCOM-am) Reynolds equations and energy equations. The following protrusions were considered in the article: square transversal profiles, in which tornadoes are most pronounced, and side tornadoes affect the flow in the maximum way; triangular transversal profiles, where tornadoes are not so strong, and side tornadoes affect the main flow weaker than with square protrusions; semicircular transversal profiles, in which the incoming main tornado moves along the stream with the generation of limited side tornadoes. The calculated information obtained in the article correlates to a high degree with the available experimental data, which indicates the verification of the mathematical modeling involved in the article.

In this paper, block upper triangular systems of linear difference equations are considered, in which the coefficient matrices are not assumed invertible. The relationship between the exponential dichotomy properties of such a system and its associated block diagonal system is studied. The reason it is important to study triangular systems is that any system of linear difference equations is kinematically similar to an upper triangular system. In the bounded invertible case, it is known that for equations on the intervals J = Z + or Z − , a block upper triangular system has an exponential dichotomy if and only if the associated block diagonal system has one. However, when J = Z , only the sufficiency holds. The sufficiency extends to the noninvertible case, provided the off-diagonal matrices are bounded. However, the necessity does not hold even when J = Z + or Z − . Nevertheless, if certain conditions are added, then the necessity does hold and it is also shown that these conditions are needed since it turns out that if both the triangular and diagonal systems have dichotomies, then these extra conditions must hold. [ABSTRACT FROM AUTHOR]

Flooding is a major and recurring natural disaster in Northeast Penang, Malaysia. The ability to effectively identify flood hazard areas represents an important part of flood risk analysis and management. There is a need for a structured study that incorporates stakeholders' inputs such as the multi-criteria decision-making (MCDM) model to delineate flood-prone locations to support the management and mitigation measures of flooding in this area. Previous studies have compared the analytic hierarchy process (AHP) and fuzzy AHP methods in flood hazard mapping. Therefore, this study proposes to test the predicting capability of three MCDM models in the determination of flood-prone areas: the AHP, triangular fuzzy AHP (TF-AHP), and trapezoidal fuzzy AHP (TZF-AHP) in this area. The methodology applies nine flood-causative factors (FCFs) which include drainage density, elevation, land use, slope, rainfall, flood depth, distance from rivers, lithology, and distance from inundation. The resulting flood hazard maps showed a closer similarity between the TF-AHP and TZ-AHP methods compared to the AHP method for flood hazard mapping. The sensitivity analysis indicated that the AHP was more accurate than the fuzzy AHP models based on the weight estimation. The validation results showed that 100%, 93%, and 93% of the actual flood events occurred in the 'moderate' to 'very high' flood hazard areas for the AHP, TF-AHP, and TZF-AHP, respectively. Overall results showed the accuracy of all three models in modeling flood hazard areas. Therefore, the findings can be adopted as a tool in making informed and accurate policies about flood management for effective climate mitigation decision making. [ABSTRACT FROM AUTHOR]

Consider a linear time-varying (LTV) system described by the state-space equation x = A(t)x + B(t)u(t). The main objectives of this paper include (i) determination of the analytical or closed-form solutions for the fundamental matrix X(t) and the state transition matrix (t,to) Φ of the LTV system; (ii) design of feedback control, such that the closed-loop system matrix Acl (t) = A(t)-B(t)K(t), where K(t) is a gain matrix, has desirable properties, in particular, Acl (t) being commutative and triangular; and (iii) design of observers such that the observer matrix Ao(t)=A(t)-H(t)C(t), where H(t) is the observer gain matrix, has desirable properties as in (ii), namely, Ao(t) being commutative and triangular. The commutativity and triangularization of Acl(t) and Ao(t) facilitate the analytical solutions for their fundamental and state transition matrices. Examples and simulations demonstrate the design objectives. [ABSTRACT FROM AUTHOR]

Abstract Background Recent developments in robotic technology have brought significant changes in robotic video-assisted thoracoscopic surgery (r-VATS) worldwide, particularly including the treatment in the thorax for the mediastinal, esophagus, and pulmonary lesions. Currently, there are only a few reports describing the procedural experience and outcomes with r-VATS. The objective of this study is to provide our initial experience using r-VATS at a single center, with specific attention to safety, efficacy, and procedural details. Methods We retrospectively reviewed patients who underwent a newly modified r-VATS procedure for various surgical operations at the thoracic department of our hospital, from July 2018 to January 2020. Multiport trocars were placed in the classic triangular arrangement as in conventional VATS (c-VATS) but with modifications based on the type of surgery. The peri- and postoperative outcomes such as duration of surgery, complications, and duration of hospital stay for these patients were reported. Results Overall, 142 patients underwent r-VATS for lobectomy (66), wedge resection (15), thymectomy (22), mediastinal tumor resection (30), pneumonectomy (4), transthoracic esophagectomy (1), esophageal tumor resection or esophageal diverticulum repair (2), diaphragm plication (1), and mediastinal tumor resection plus thymectomy (1). For the entire cohort, the median operative time was 110 min, and the median length of hospital stay was 5 days. Conversion to open thoracic surgery was reported only in a total of 3 (2.1%) patients of pneumonectomy (1.4%) and mediastinal tumor resection (0.70%). All our patients were managed successfully with no postoperative complications and mortality. Conclusion Our method of r-VATS was found to be safe and effective and may be applied to different surgical operations. Adequate and proper training of thoracic surgeons is immediately needed for the transition from c-VATS to r-VATS. The utility and advantages of triangular trocar configuration for r-VATS require further refinement and research before it can be routinely adopted in clinical practice. Trial registration Retrospectively registered.

Objective. Conduct mathematical modeling of tornado zone structure systems between cyclic flow turbulence stimulators with the surface arrangement of triangular and square cross-sections based on multiblock computational techniques, based on solutions of the factorialized finite- volume procedure of the Reynolds equations (closed through the Menter shear stress transport model) and energy equations (on a multiscale intersecting structured grid) at high Reynolds criteria Re=106 with an exhaustive analysis of the relevant current lines. Methods. The calculations were carried out on a mathematical foundation based on the solution of the factorized finite-volume procedure of the Reynolds equations, which are closed using the low-Reynolds Menter shear stress transport model, and the energy equations on a multiscale intersecting structured grid (factorized finite-volume procedure). Results. Mathematical simulations of the heat exchange process in straightand round horizontal pipes with turbulence stimulators with d/D=0.95...0.90 and t/D=0.25...1.00 of triangular and square transverse profiles with large Reynolds numbers (Re=106) on a foundation with multiblock computing technologies, which are based on solutions of factorized and finite-volume Reynolds equations and energy equations, were conducted. It was found that the relative intensification of heat transfer [(Nu/NuGL)|Re=106]/[(Nu/NuGL)|Re=105] in round pipes with square air turbulence stimulators for large Reynolds numbers (Re=106), which may be relevant in the channels used in heat exchangers, could be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re=105), for relatively high flow turbulence stimulators d/D=0.90 for the entire range under consideration for the parameter of the relative step between them t/D=0.25...1.00 a little more than 3%; for triangular turbulence stimulators, the crosssection profiles have similar values. For lower square turbulence stimulators with d/D=0.95, this increase in relative heat transfer for large Reynolds numbers (Re=106) compared to smaller numbers (Re=105) does not exceed 6%; for triangular cross-section turbulence stimulators, similar indicators are slightly more than 4%. Conclusion. The calculated results based on the developed model can optimize the intensification by turbulence stimulators and control the processes of heat transfer intensification. It is shown that for higher square turbulence stimulators and higher Reynolds numbers, a limited increase in the relative Nusselt criterion Nu/NuGL is accompanied by a significant increase in the relative hydro resistance due to the very significant influence of return currents, which can flow directly on the turbulence stimulator to the greater extent, the higher the Reynolds number; for triangular turbulence stimulators, the above trend persists and even deepens.

This work aims to generalize the Banach contraction theorem to M-fuzzy cone metric spaces. We construct generalized M-fuzzy cone contractive conditions for three self mappings with which they have a unique common fixed point.

This work aims to extend the idea of Banach contraction principle to intuitionistic generalized fuzzy cone metric spaces. We inherit the existing ideas to bring out new definitions in these spaces. This work extends the contractive conditions of self-mappings by having the presence of all the possible restrictions. This extension is up to the limit in a linear way it can be extended. We construct some contraction theorems for the generalized intuitionistic fuzzy cone metric spaces. We prove the existence of fixed points and their uniqueness of self-mappings under the extended contractive conditions. [ABSTRACT FROM AUTHOR]

This paper presents the torsional analysis of isotropic, orthotropic, and functionally graded material (FGM) triangular and rectangular sections. The formulation of the governing equation of the torsion problem is done using the Saint–Venant torsion theory. Classical power law has been considered for the modeling of FGM material. A meshfree technique based on various radial basis functions is used for the solution of the governing differential equation. MATLAB code is developed to solve the discretized partial differential equations. To demonstrate the effectiveness and accuracy of this technique, convergence study and numerical examples are presented by varying the various parameters. The torsional rigidity factors and shear stress factors are obtained for different new conditions. The solution presented here is validated from the analytical and numerical results along with some new results, which shows the satisfactory performance of the present method. [ABSTRACT FROM AUTHOR]

The results of computational experiments for determining the effect of a mode I surface fatigue crack cross-sectional shape in a rectangular cantilever beam on the characteristics of its free and forced bending vibrations with varying cross-sectional dimensions of the crack and its longitudinal position are presented. Finite-element models of beams with 8-node 3D finite elements were developed for carrying out investigations. Three types of a breathing crack cross-section were considered: rectangular, triangular, and trapezoidal one, with the solution of a contact problem to ensure the non-penetration of crack edges. Plots of relative change in the natural frequency of vibration, the amplitudes of the first and second harmonics and their ratios at the main, super- and subharmonic resonances versus the shape, relative area and location of the crack were obtained. It is shown that when bending vibrations of the beam with a rectangular crack, are excited along the axis Oy, there arise displacements only in the direction of driving force, while in the case of triangular and trapezoidal cracks, there arise additional displacements along the axis of minimum stiffness, Oz. It was found that the change in the natural frequency of the beam, as well as the ratio of the amplitudes of dominant harmonics during the recording of vibrations along the excitation axis at the main, super- and subharmonic resonances increase with increasing relative area of the crack cross-section. Under this condition, their largest value was characteristic of a rectangular crack, and the smallest of a triangular one. It was noted that a characteristic indicator of the asymmetric shape of the crack was the appearance of vibrations in the plane perpendicular to the excitation plane. [ABSTRACT FROM AUTHOR]

This paper shows the results of a novel research conducted with the overall aim of developing a system that can provide continuous desalination. Productivity enhancement of solar stills is regarded as the main purpose of the investigators in desalination field. This paper represents the experimental results in a new approach of paraffin + graphene oxide nanoparticles mixture. The paraffin mixture in a semicircular, triangular and rectangular absorber with paraffin + graphene oxide of 0.1, 0.3 and 0.5 mass% has been investigated. The finding indicated that for all absorbers, the use of paraffin + graphene oxide in higher mass fractions enhances daily freshwater production. The results showed that the thermal performances are greater applying graphene oxide + paraffin of 0.5 mass% with semicircular absorber compared to triangular and rectangular absorber. The achievement of the present paper can be implemented to design more efficient absorbers for solar still parts. [ABSTRACT FROM AUTHOR]

In this study, inclined broken roughness is experimentally investigated to enhance the thermohydraulic performance of solar air heaters. Current article focuses on a fuzzy-based structure as a substitution method for predicting the thermohydraulic performance. A separated fuzzy inference system for each smooth and roughened plate along with an integrated one designed for both plates was selected as the strategy of modeling. In addition, utilizing temperature and velocity features with their generality in all solar air heaters were suggested as a cutting-edge solution to dominate complexity restrictions of geometrical roughness parameters. Throughout the experiments, triangular membership functions obtained better agreement with experimental data than Gaussian functions except for the friction factor of the roughened plate in the separated method. Sugeno structure demonstrated better forecasting ability than Mamdani. Additionally, Nusselt number showed better applicability in being predicted more easily by the considered fuzzy structures rather than the friction factor. Moreover, the system constructed based on the Gaussian membership function showed higher accuracy in forecasting the roughened plate parameters. The least mean square error of the separated method for the Nusselt number and the friction factor of the smooth plate were 2.5477 × 10−04 and 8.1115 × 10−04, respectively. Furthermore, these values were equal to 2.0218 × 10−04 and 7.5150 × 10−04, for the Nusselt number and friction factor of the roughened plate, respectively. Having considered the thermohydraulic performance, the least mean square error of the separated method was equal to 8.6255 × 10-04. The obtained results approved that the fuzzy method is a significantly efficient method for anticipating the parameters of solar air heaters. [ABSTRACT FROM AUTHOR]

Additive manufacturing technologies enable the production of components with lightweight cores, by means of infills with various patterns and densities. Together with reduced mass and material consumption, infill geometries must ensure that strength and stiffness conditions are fulfilled. For the proper correlation of the infill type with the loading case of the part, the mechanical behavior of the infill along all three principal axes of inertia has to be known. In this paper, the behavior in symmetric and asymmetric bending of three infill geometries, commonly used in 3D printing processes (honeycomb, grid and triangles) is analyzed. The variations of deflections as a function of force orientation are presented, showing that honeycomb and triangular structures exhibit similar behaviors along the Y and Z principal axes of inertia. Furthermore, the displacements obtained for the three types of structures are compared, in relation to the consumed volume of material. The larger displacements of the grid structure compared to the honeycomb and triangular structures are highlighted.

In this letter, we design, analyze, simulate, fabricate, and measure the performance of reflectarrays capable of forming cosecant-squared beam shape. Due to their unique pattern and abrupt change, achieving a cosecant-squared beam is challenging. In our effort, we evaluate the efficacy of a commonly used rectangular lattice and compare it, for the first time, to a triangular lattice. Two linearly polarized reflectarrays, each with 20 λ0 diameter in size, are fabricated and tested at 20 GHz. Through statistical methods, we quantify the gain agreement between the desired cosecant-squared mask and the measured beam patterns for both rectangular and triangular lattices. We have found that the rectangular lattice conforms better to the cosecant-squared mask at the design frequency of 20 GHz with a root-mean-square error of 6.27 dB. The triangular lattice conforms less, however, it does allow for an increase in gain bandwidth of 6.2% as compared to 4.5% for the rectangular lattice. Measured and simulated patterns are in a good agreement. [ABSTRACT FROM AUTHOR]

In this work, spherical-, rod-, triangular- and hexagonal-shaped silver nanoparticles were prepared by chemical reduction method and their antibacterial efficacy against selected Gram-positive and Gram-negative bacteria had been assessed and compared. The dose-dependent antibacterial activities of prepared silver nanoparticles were observed on the batch studies of disc diffusion and MIC with various strains. Based on the excellent response of disc diffusion and MIC, further concentration-dependent killing kinetics test was conducted on K. pneumoniae with nano-silver. The killing kinetics confirmed that the death rate of K. pneumoniae was higher against spherical Ag as compared to other nanoparticles. The synthesized nano-silver was also characterized by UV–Vis absorption spectroscopy, XRD and TEM techniques to investigate the optical and structural properties. [ABSTRACT FROM AUTHOR]

Temporal triangular alopecia (TTA) is a non-cicatricial alopecia characterized by an alopecic patch, usually located in the frontotemporal region, unilateral or bilateral, with an oval or narrow triangular base and no terminal hairs on it. It can manifest at birth or develop in the first years of life. It is a rare condition and its exact etiology remains unknown. The diagnosis is based on its clinical appearance. The differential diagnosis includes alopecia areata, trichotillomania, tractional alopecia and congenital aplasia cutis. Due to its rarity, misdiagnosis and unnecessary treatments can be applied. Clinical and dermoscopic examination is sufficient in the diagnosis of the disease. A 3-year-old boy with a diagnosis of TTA is presented as a case report.

In this article, a photonic technique is proposed for generating the microwave signal of multiple shapes. Furthermore, this is modified to give a microwave signal with frequency multiplying capability, which does not require an optical filter. The proposed methodology is relied on the polarization modulator (PM), the Mach-Zehnder modulator (MZM), and the variable optical delay line (VODL), where the transmission point of PM has been selected by static phase of polarizer controller and MZM by the dc bias voltage. An RF signal of 6-GHz frequency is applied at PM to modulate the optical carrier signal. Frequency-dependent VODL has been used to provide dynamic phase shifts in the harmonics of the modulated signal. Firstly, 12-GHz full-wave rectified (FWR) and 6-GHz half-wave rectified (HWR) sinusoidal signals have been generated using PM and VODL. For the generation of FWR and HWR, respective phase shifts of −π/2 and π have been introduced by VODL. Then, a sextupled microwave signal of 36-GHz frequency has been generated which is further processed for the generation of triangular-shaped HWR of 6-GHz frequency. This has been achieved by modulating one of the split powers of PM with the help of an MZM. The generation of such multishape rectified waveforms has not been reported before. Also, the frequency sextupling capability of the proposed technique defines the multifunctionality of the system. Theoretical analysis of the considered approach has been given which is supported by simulated results and validated by the experimental results. [ABSTRACT FROM AUTHOR]

The optimization of heat and mass distribution within triangular cavities has received substantial attention in engineering research. In this study, heat and mass transfer involving Casson fluid in a closed, partially heated, porous triangular chamber has been extensively analyzed. A heated triangular impediment has been placed inside the cavity to assist us in comprehending the circumstances. The governing partial differential equations are converted into a non-dimensional form by employing appropriate similarity variables. The well-known finite element method (FEM) has been used to solve these equations and investigating the effects of various physical parameters on the flow patterns, concentration isotherms, and local Nusselt numbers, including the partial heating length, buoyancy-driven force, Casson fluid characteristics, Soret and Dufour effects, Lewis number, Rayleigh number, heat generation/absorption, and porous medium features. It has been observed that the dispersion and movement of materials inside a fluid can be indirectly impacted by changes in the Casson parameter. The length of the heated wall significantly affects how evenly the temperature is supplied. When the wall length is shorter, the temperature drops noticeably and intensely. Although the Dufour parameter is small, the thermal diffusion effect is not as significant as mass diffusion. As the Soret parameter is increased, an inverse relationship to the Dufour effect is noticed. Convective heat transfer gradually prevails in the flow as the Darcy number rises, indicating increased permeability compared to other characteristics. [ABSTRACT FROM AUTHOR]

Objectives. Mathematical modeling of heat transfer in flat channels with turbulators symmetrically located on both its sides, depending on the cross section of the turbulators.Methods. The calculation was carried out on the basis of a theoretical method based on solving the Reynolds equations factorized by the finite-volume finite-volume method, closed using the Menter shear stress transfer model, and the energy equation on multi-scale intersecting structured grids (FCOM), which was successfully tested in [23].Results. The article results of calculating the intensified heat exchange in flat channels with double turbulators of different cross sections (square, rectangular, semicircular, triangular) depending on the determining parameters were quite satisfactorily consistent with the existing experimental material, but having an indisputable advantage over the latter, since the assumptions made in their derivation cover a much wider range of defining parameters than the limitations found in the experiments (Pr=0.7÷100, Re=103÷106, h/dE =0.005÷0.2, t/h=1÷200).Conclusion. According to the results of calculations on the basis of the developed model, it is possible to optimize heat transfer intensification in flat channels with double turbulators of different cross sections, as well as control the heat transfer intensification process. As shown by the calculated data, with the intensification of heat transfer in the flat channels, symmetrical protrusions of square, rectangular and triangular cross sections, i.e. relatively sharp outlines, in the vortices up to the protrusions and behind them the production of turbulence is comparable to energy dissipation, which leads to increased hydraulic losses; for flat channels with protrusions of a semicircular cross section, i.e. relatively smooth outlines, the energy dissipation is much smaller, therefore, the hydraulic resistance in such channels is less. A detailed analysis of the structure of the vortex zones (main, angular, secondary, etc.) between periodic surface flow turbulators of square, semicircular, triangular and rectangular cross sections depending on the geometric and regime parameters of the coolant flow was carried out, the effect of the above vortex zones heat transfer and hydraulic resistance of the channel; additionally confirmed the optimality of application to abrutized turbulators, where hydraulic losses are much smaller than for sharp turbulators, which is directly or indirectly verified by existing experimental material [1—6].

A numerical study was achieved on a new design of storage solar collector. The storage collector is a triangular face and a right triangular pyramid for the volumetric shape. It is obtained by cutting a cube from one upper corner at 45o, down to the opposite hypotenuse of the base of the cube. The numerical study was carried out using the computational fluid dynamics code (ANSYS-Fluent) software with natural convection phenomenon in the pyramid enclosure. The results show that, the temperature and velocity distributions throughout the operating period were obtained. The influence of introducing an internal partition inside the triangular storage collector was investigated. Also the optimum geometry and location for this partition were obtained. The enhancement was best at y= 0.25 m whereas the height of triangular collector was 0.5 m. The hourly system performance was evaluated for all test conditions.

Background: Recent developments in robotic technology have brought significant changes in robotic video-assisted thoracoscopic surgery (r-VATS) worldwide, particularly including the treatment in the thorax for the mediastinal, esophagus, and pulmonary lesions. Currently, there are only a few reports describing the procedural experience and outcomes with r-VATS. The objective of this study is to provide our initial experience using r-VATS at a single center, with specific attention to safety, efficacy, and procedural details.Methods: We retrospectively reviewed patients who underwent a newly modified r-VATS procedure for various surgical operations at the thoracic department of our hospital, from July 2018 to January 2020. Multiport trocars were placed in the classic triangular arrangement as in conventional VATS (c-VATS) but with modifications based on the type of surgery. The peri- and postoperative outcomes such as duration of surgery, complications, and duration of hospital stay for these patients were reported.Results: Overall, 142 patients underwent r-VATS for lobectomy (66), wedge resection (15), thymectomy (22), mediastinal tumor resection (30), pneumonectomy (4), transthoracic esophagectomy (1), esophageal tumor resection or esophageal diverticulum repair (2), diaphragm plication (1), and mediastinal tumor resection plus thymectomy (1). For the entire cohort, the median operative time was 110 min, and the median length of hospital stay was 5 days. Conversion to open thoracic surgery was reported only in a total of 3 (2.1%) patients of pneumonectomy (1.4%) and mediastinal tumor resection (0.70%). All our patients were managed successfully with no postoperative complications and mortality.Conclusion: Our method of r-VATS was found to be safe and effective and may be applied to different surgical operations. Adequate and proper training of thoracic surgeons is immediately needed for the transition from c-VATS to r-VATS. The utility and advantages of triangular trocar configuration for r-VATS require further refinement and research before it can be routinely adopted in clinical practice.Trial Registration: Retrospectively registered. [ABSTRACT FROM AUTHOR]

Objectives: The main objective of this study was to assess the clinical and functional outcomes of arthroscopic TFCC repair in patients with an isolated Atzei type 1, 2 or 3 lesion or after a distal radius fracture. The secondary objective was to identify which factors could contribute to poor functional outcome. Methods: A retrospective study was conducted from November 2017 to May 2019. The inclusion criteria were patients with an Atzei type 1, 2 or 3 TFCC lesion who underwent arthroscopic repair and with a minimum of 6-month follow-up. Wrist motion, grip and pronation–supination strength were noted. QuickDASH, MMWS and PRWE scores were performed. An analysis was conducted to search for poor outcomes predictive factors (MMWS < 80). Results: Twenty-one patients were included with a mean follow-up of 26 months. Seventeen patients (80%) had an Atzei 1 lesion, one (4.8%) had an Atzei 2, and 3 (14%) had an Atzei 3. Wrist motion significantly decreased compared to contralateral. Only pronation and supination were not significant. Grip strength was 73.4% compared to the contralateral (p = 0.002). Mean PRWE was 29.14 (1.5–70.5), QuickDASH was 30.72 (2.3–70.5), and MMWS was 79.3 (35–100). In all patients with a MMWS ≥ 80, none had lunotriquetral lesions when it was the case for 5 of 9 patients with a MMWS < 80 (p = 0.006). Except a story of workplace injury, no other prognosis factor was significant. Conclusion: Patients with Atzei 1, 2 or 3 TFCC who underwent arthroscopic repair seem to have good outcomes. However, an associated lunotriquetral lesion appears to worsen the functional prognosis. [ABSTRACT FROM AUTHOR]

Background: Routine TEP technique requires three skin incisions for placement of three trocars in the midline. Otherwise, this can be done by three-port triangular technique or two-hand technique. This study reports a randomised trial of perioperative outcomes and ergonomics characteristics of this procedure using two different techniques of port insertion. Methods: N = 28 patients were randomised into two groups for triangular three-port (TTEP) versus midline three-port TEP (MTEP) hernioplasty after informed written consent in Department of Surgery, King George's Medical University UP between September 2016 and September 2017 after institutional ethical approval. Patient-related outcomes in terms of quality of life (QOL) and ergonomic evaluation of the technique were compared in double-blinded fashion. Results: Postoperative pain score at 24 h post surgery (5.1 ± 0.6; 95% CI 4.9–5.3 vs. 4.8 ± 0.4; 95% CI 4.6–4.9) differed, while hospital stay, time to return to routine work, tolerance to oral feeds and intraoperative complications occurrence (OR 2.1; 95% CI 0.2–24.3) were comparable in both groups. Time to return to office work (5.5 ± 0.5; 95% CI 5.4–5.7 vs. 4.0 ± 0.8; 95% CI 3.7–4.3) and immediate postoperative sensation of mesh and pain score were significantly higher in MTEP compared to TTEP. Ergonomic parameters including visualization of landmark score, spreading of mesh score and total surgeon satisfaction score (TTEP 8.4 ± 0.7; 95% CI 8.1–8.6 vs. MTEP 7.0 ± 0.8; 95% CI 6.7–7.3), mental effort quotient (SMEQ score: TTEP 50.6 ± 12.7; 95% CI 45.9–55.3 vs. MTEP 70.8 ± 12.6: 95% CI 66.1–75.4) and physical effort quotient (LEDQ scores in wrist, hand, arm and shoulders) were also superior in triangular technique of port placement. Conclusion: Triangular three-port TEP hernioplasty is ergonomically feasible and enables a surgeon to perform surgery safely using basic principles of laparoscopy. [ABSTRACT FROM AUTHOR]