Triangular Approximation Research Articles

Novel photopeak-independent correction method for internal activity calculation of 99mTc: a simulation study.

This paper presents a new method for correcting the contribution of scattered radiation to the measurement of 99mTc internal activity in nuclear medicine patients using gamma cameras. So, this study aims to derive scattering correction factors by Monte Carlo simulation for anterior and posterior count rates (${I}_{\mathrm{A}}$ and ${I}_{\mathrm{P}}$) in the conjugate view method, enabling more precise estimation of activity A(t) compared to traditional trapezoidal and triangular approximations. The new approach eliminates the need to use photopeak for determining the fraction of scattered photons. Our results showed differences of <3% with respect to the real activity and 11% for the trapezoidal and triangular approaches.

Neutrino emission in cold neutron stars: Bremsstrahlung and modified urca rates reexamined

Neutrino emission in cold neutron stars is dominated by the modified urca (murca) process and nucleon-nucleon bremsstrahlung. The standard emission rates were provided by Friman and Maxwell in 1979, effectively based on a chiral Lagrangian framework with pion and rho meson exchange, supplemented by Landau parameters to describe short-range interactions. We reevaluate these rates withinthe same framework, correcting several errors and removingunnecessary simplifications, notably the triangular approximation — where the Fermi momenta of protons and leptons negligible compared to that of neutrons — in MURCA, and quantify their importance.The impact of rho meson exchange, previously argued to cancel with interference effects, is actually quite relevant. Altogether, the cooling rates are reduced by as much as a factor 2. We provide comprehensive analytical formulas encompassing all contributions, designed for straightforward numerical implementation. Our results are particularly relevant for studies of physics beyond the standard model, where the emission of new particles — such as axions — is typically computed within the same framework we adopt here.

On detection of BaO molecular lines in sunspot spectrum

ContextSpectral lines of diatomic molecules are perfect tools for studying the structure of sunspots and their temperature layers and magnetic sensitive absorption features, which are typically higher than in atomic lines. The integrated intensities of a few bands in the rotational structure of the astrophysically significant A1Σ+−X1Σ+and A′1Π−X1Σ+ systems of barium monoxide (BaO) have been measured experimentally using band spectra. An analysis of the prominent lines of (0, 0; 1, 1; 2, 2) bands of A1Σ+−X1Σ+transition and (0, 0; 1, 1; 2, 2) bands of A′1Π−X1Σ+transition with those of sunspot umbral spectrum. The effective rotational temperatures of the A′1Π−X1Σ+transition of BaO in the sunspot umbral spectrum are found to be in the range of 1600 K to 3200 K. AimsAn analysis of BaO prominent rotational molecular lines of A1Σ+−X1Σ+and A′1Π−X1Σ+transition with those of sunspot umbral spectral lines. To find the significant values of radiative transition parameters, vibrational temperature and the effective rotational temperature of the molecule in celestial objects. MethodsCalibrated the rotational structure of molecular band heads and lines for and A1Σ+−X1Σ+and A′1Π−X1Σ+ransitions in laboratory spectrum using most precise Hartmann's technique. High resolution FTS sunspot umbral spectra from NSO/Kitt Peak were used to detect rotational molecular lines due to the A′1Π−X1Σ+transition of the BaO molecule using the method of line coincidence. The effective rotational temperature was derived from the variation of equivalent width (W) with rotational quantum number (J) of spectrally well resolved rotational lines of a band in umbral spectrum. The triangular profile approximation method was used to estimate the equivalent width of the well resolved spectral lines. ResultsThe effective rotational temperatures of the A′1Π−X1Σ+transition of BaO in the sunspot umbral spectrum are found to be in the range of 1600 K to 3200 K. It is compared with other results with a view to obtaining useful physical parameters. This is an evidence to ascertain the possible presence of BaO molecule in solar spectrum in different layers. ConclusionsUnblended rotational lines due to the band of BaO, provide a good range of temperatures for the study of absorbing layers in umbral spectra. The A′1Π−X1Σ+transition of BaO molecular lines is found to be very sensitive to effective temperature. Radiative transition parameters data of these lines, in contrast to intensity measurements, provide us with more direct and detailed information to study the coolest parts of sunspot umbrae.

Failure analysis of unidirectional CFRP composites with the coupled effects of initial fibre waviness and voids under longitudinal compression

This research delves into the failure mechanisms exhibited by unidirectional Carbon Fiber Reinforced Polymer (CFRP) composites under longitudinal compression, while considering the interplay of three types of manufacturing-induced defects: initial waviness of fibres, void volume fraction, and void size. The study employs 3D high-fidelity intact representative volume element (RVE) models, incorporating the initial waviness of fibres and voids based on Micro-CT imaging. A novel algorithm is proposed to generate more accurate 3D void shapes, departing from conventional circular or triangular approximations. The results highlight the substantial influence of the initial waviness angle on the reduction of predicted compressive stiffness and strength. The volume and size of voids play a significant role in determining damage initiation within the composites. The failure mechanisms of the composite under the coupled effects of initial waviness of fibres and voids are discussed, exhibiting reasonable agreement with experimental observations.

Assessment of Anteroposterior Diameter and Interpedicular Distance in the Approximation of Cervical Spinal Canal Area.

Rationale and objectives This study seeks to generate a model based on two linear measurements, anteroposterior (AP) diameter and interpedicular (IPD) distance, to approximate the cervical central canal (CCC) area in a non-pathologic patient population by employing area calculations of shapes such as ellipse, rectangle, and triangle. Secondarily, this study aims to generate second-order approximations (SOAs), using the aforementioned shape approximations, to increase the utility of this linear measurement-based model. Methods The authors reviewed medical and radiographic records of patients aged 18-35 who received computed tomography (CT) imaging of the cervical spine to collect AP diameter, IPD distance, and area of the CCC from C2-3 to C6-7. Subsequently, shape approximations were calculated for each patient at all cervical spine levels. Lastly, SOAs were generated by combining optimal ratios of shape approximations to improve the statistical reliability of approximations. Results The ellipse shows the closest approximation to manual measurements of the individual shape approximations. Percent error analysis demonstrated the superiority of the ellipse, followed by the rectangle, and lastly the triangular approximation. The highest correlation of approximations was observed at C6-7. All individual shape approximations demonstrated statistical differences from manual measurements. SOAs combining ellipse and rectangle measurements demonstrated superior accuracy and were not statistically different from manual measurements. Conclusion Individual shape approximations based on AP diameter and IPD distance show some value as a model for the assessment of the CCC area. SOAs demonstrated greater utility than individual shape approximations and show promise as a linear measurement-based tool to assess the CCC area.

Modelling and Optimization of Machined Surface Topography in Ball-End Milling Process.

In order to optimize machined surface topography, this paper presents a novel algorithm for simulating the surface topography and predicting the surface roughness of a ball-end milling process. First, a discrete workpiece model was developed using the Z-map method, and the swept surface of a cutter edge was represented using triangular approximation. The workpiece surface was updated (i.e., material removal process) using the intersection between the vertical reference line and the triangular facet under a cutting judgement. Second, the proposed algorithm was verified by comparing the simulated 3D surface topography as well as 2D surface profile and average roughness (Sa) with experimental measurements. Then, numerical simulation examples planed by the Box-Behnken design methods were carried out to investigate the Sa in the ball-end milling operation. The correlations of Sa and cutting parameters were represented by a response surface reduced quadratic model based on the ANOVA results. Finally, the feed per tooth, radial depth of cut, and tilt and lead angles were optimized for improving the machining efficiency under the Sa constraints. This study presents an effective method for simulating surface topography and predicting the Sa to optimize the cutting parameters during ball-end milling process.

A fuzzy computing approach to aggregate expert opinions using parabolic and exparabolic approximation procedures for solving multi-criteria group decision-making problems

AbstractTriangular fuzzy numbers (TFNs) are widely used for selection problems to determine expert opinions using linguistic expressions. Some aggregation procedures are developed to determine expert opinions more accurately. However, there is a need for a simple and more useful procedure to solve the selection problems more suitably. For this purpose, our study offers a triangular, exparabolic, and parabolic area calculation-based approximation approach for TFNs to aggregate the possible hedges (very and more or less) for TFNs. Hence, this aggregation procedure provides a tuning opportunity for classical TFN expressions to capture possible tuning processes to reflect the hesitancies of experts. The technique for order preferences by similarity to ideal solution (TOPSIS) method is applied in the two studies from extant literature, and suitable alternatives are determined as a result of the ranking process. Finally, a comparative analysis is presented to illustrate the efficiency of the proposed procedure. The conventional TOPSIS model’s ranking scores are very close for exemplified examples (i.e., 0.5308, 0.4510, 0.4550 and 0.5304, 0.4626, 0.4940), but the proposed model’s result has fluctuated for the same examples (i.e., 0.346, 0,669, 0,567 and 0.208, 0.991, 0.148). So, the main advantage of the proposed aggregation procedure is the alternative ranking scores separation capability analyzed with their linguistic diversification.

Life settlement pricing with fuzzy parameters

Existing literature asserts that the growth of life settlement (LS) markets, where they exist, is hampered by limited policyholder participation and suggests that to foster this growth appropriate pricing of LS transactions is crucial. The pricing of LSs relies on quantifying two key variables: the insured's mortality multiplier and the internal rate of return (IRR). However, the available information on these parameters is often scarce and vague. To address this issue, this article proposes a novel framework that models these variables using triangular fuzzy numbers (TFNs). This modelling approach aligns with how mortality multiplier and IRR data are typically provided in insurance markets and has the advantage of offering a natural interpretation for practitioners. When both the mortality multiplier and the IRR are represented as TFNs, the resulting LS price becomes a FN that no longer retains the triangular shape. Therefore, the paper introduces three alternative triangular approximations to simplify computations and enhance interpretation of the price. Additionally, six criteria are proposed to evaluate the effectiveness of each approximation method. These criteria go beyond the typical approach of assessing the approximation quality to the FN itself. They also consider the usability and comprehensibility for financial analysts with no prior knowledge of FNs. In summary, the framework presented in this paper represents a significant advancement in LS pricing. By incorporating TFNs, offering several triangular approximations and proposing goodness criteria of them, it addresses the challenges posed by limited and vague data, while also considering the practical needs of industry practitioners.

Convexification approaches for regional route guidance and demand management with generalized MFDs

Traffic congestion is one of the main concerns in big cities with many adverse socioeconomic effects. A promising solution is to simultaneously regulate the admission of vehicles (i.e., demand management) and redistribute traffic flows within the network (i.e., route guidance). In this work, we integrate demand management with route guidance within a Model Predictive Control framework using regional traffic dynamics with generalized Macroscopic Fundamental Diagram (MFD) shapes. Dealing with generalized MFD shapes is challenging due to the resulting nonlinear and non-convex optimization formulation. To tackle this challenge, we develop two real-time solution approaches: (i) a successive convexification approach that constructs convex bounding sets for all nonlinear terms, and (ii) a linear approximation approach that solves the problem using triangular macroscopic fundamental diagram approximations. The proposed approaches offer a trade-off between execution speed and solution quality, as the linear approximation approach runs faster while the successive convexification approach yields better quality and accuracy solutions. Macroscopic simulation results illustrate the efficiency of the successive convexification and linear approximation approaches yielding an optimality gap of less than 3.5% and 10% in all considered cases, respectively. Furthermore, both approaches outperform a state-of-practice nonlinear solver in terms of solution quality and execution time. Finally, substantial gains are also obtained regarding travel time and traffic flow efficiency in a realistic microsimulation environment.

A Generalized Raman Scattering Model for Real-Time SNR Estimation of Multi-Band Systems

We investigate the impact of stimulated Raman scattering (SRS) in multi-band transmissions. We first derive and test against numerical results an extended Christodoulides-Zirngibl (ECZ) SRS model based on a triangular approximation of the Raman gain. Then, we exploit the ECZ SRS model in the context of the Gaussian noise (GN) model. We generalize some known closed-form expressions of the self- and cross-phase modulation variances, as well as the amplified spontaneous emission noise variance, over multi-band systems of bandwidth wider than the SRS bandwidth, i.e., beyond the C+L band. Finally, the proposed theoretical model is used to estimate the performance of multi-band systems in terms of signal-to-noise ratio (SNR) and achievable information rate (AIR).

The Best Approximation of Generalized Fuzzy Numbers Based on Scaled Metric

The ongoing study has been vehemently allocated to propound an ameliorated α‐weighted generalized approximation of an arbitrary fuzzy number. This method sets out to lessen the distance between the original fuzzy set and its approximation. In an effort to elaborate the study, formulas are designed for computing the ameliorated approximation by using a multitude of examples. The numerical samples will be exemplified to illuminate the improvement of the nearest triangular approximation (Abbasbandy et al., Triangular approximation of fuzzy numbers using α‐weighted valuations, Soft Computing, 2019). A variety of features of the ameliorated approximation are then proved.

Existence of inner addition and inner multiplication on Set of Triangular numbers and some inherent properties of Triangular numbers

The set Ptof real parameters for a fuzzy number belonging to a general family of all important parameters are calculated such that a triangular fuzzy number with the same value of the parameter exists for every specified flozzy number. We suggest a method for computing a triangular fuzzy number closest to p/Pt, and review the identity features, scale and translation invariance, additivity and consistency of the approximation operator obtained. Examples of recent findings in this topic and implementation of a flush-number retaining the value for the near triangular approximation. In this paper, we are revisits the topic of TRIANGULAR NUMBERS with new perspective direction to generate them to all integers and proved some of their inherent properties. Also we are defined two types of binary operations inner addition and inner multiplication are satisfied by triangular numbers, which are represented in below.According these binary operations, we are proven is almost Semi Ring under inner addition and inner multiplication. Also we are finding the relation between Triangular numbers with Pascal triangles. And we are proven some of their Inherent Properties.

Triangular approximation of intuitionistic fuzzy numbers on multi-criteria decision making problem

Most of the engineering applications depend on incomplete and imprecise information which are represented by nonlinear mathematical functions for defining membership and nonmembership functions in intuitionistic fuzzy setup. Shuyang Li and Hongxing Li have studied the approximation of conventional intuitionistic fuzzy numbers in which the membership function is bounded and nonmembership function is unbounded in nature. The concepts of intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs) have bounded membership function and bounded nonmembership function. As the generalization of both IFSs and IVIFSs, the notion of intuitionistic fuzzy numbers of new type with bounded membership function and bounded nonmembership function has been introduced by Lakshmana et al. In this paper, the procedure for weighted triangular approximation of intuitionistic fuzzy number of new type is provided with some suitable illustrations. Moreover, some useful properties of the triangular approximation on intuitionistic fuzzy numbers have also been discussed.

Profile imitation algorithm research for the cam contour

In this paper, the characteristics and simulation accuracy of different simulation algorithms are studied for the cam profile. The triangular square approximation is improved, and a high-precision simulation algorithm is proposed. The improved simulation algorithm has achieved good results in practical applications. Comparative analysis using examples: comparing the accuracy of the three approximation methods of spline interpolation, unconstrained best square approximation, and best square approximation with first-order boundary. It is concluded that the optimal triangular square approximation of the first-order boundary can more accurately reflect the law of periodic motion, and is suitable for the state approximation and characteristics of periodic motion.

A two-dimensional finite element recursion relation for the transport equation using nine-diagonal solvers

A Galerkin-based finite element recursion relation is used to solve the heat transport equation in two-dimensions. The finite element method (FEM) is a powerful technique that is commonly used for solving complex engineering problems. However, the implementation of the FEM in multi-dimensional problems can be computationally expensive. A finite element recursion algorithm based on bilinear triangular, bilinear quadrilateral and quadratic Lagrangian approximations are employed to discretize the 2-D advection-diffusion equation. This algorithm is an extension of the 1-D Chapeau (linear element) technique, which employed a tridiagonal recursion expression common to the classical central finite-difference approach. The global matrix is nine-diagonal (for 2-D) and is solved using a modified strongly implicit procedure and a left-to-right sweep method.

Far field radiation properties of gaseous modelled wind-blown pool fires: An experimental investigation and simplified geometrical analysis

This paper presents an experimental study on the far-field radiation properties of modelled gaseous pool fires in cross winds, which have not been previously discussed in the literature. Bench scale experiments were conducted to quantify the evolution of radiation emission of pool fires using square porous burners (stainless-steel boxes filled with quartz sand) of different sizes (8, 10, 15 and 20 cm), employing propane as the fuel. The radiation heat flux as well as the radiation fraction were measured by a single-point method. For all pool fires employed, it was found that the radiation heat flux, as well as the radiation fraction, declined with increasing wind speed from ~0.5 m/s up to ~5 m/s. Based on an assumed triangular geometric approximation of flame projection area of wind-blown pool fires, a simplified correlation related to the flame surface area exposed to the radiometer was proposed to interpret the changing radiation fraction of pool fires of different sizes and heat release rates (HRR) in cross winds. The proposed function correlates the experimental data well under relative strong wind conditions (Fr > 1). This work provides new basic data revealing the radiation evolution behaviour of gaseous pool fires with respect to wind speed.

Microporous networks of NiMn2O4 as a potent cathode material for electric field emission

The electric field-induced sterling electron emission of NiMn2O4 microporous networks synthesized via the sol-gel auto combustion route was investigated. Some primary characterization techniques such as x-ray diffraction, Fourier-transform infrared spectroscopy, and Raman spectroscopy were performed to confirm the pure crystallinity and metal oxide (Ni–O and Cr–O) stretching vibrations and also to provide a molecular fingerprint of the NiMn2O4 porous network. The distinct field emission (FE) properties of the NiMn2O4 microporous network was observed which was correlated with an electric field induced electron tunneling F–N (Fowler–Nordheim) model from a nearly planner conducting emitter surface with triangular potential-energy barrier approximation. A low turn-on field of 4.15 V µm−1 and threshold field of 5.25 V µm−1 were detected to draw emission current densities of 1 µA cm−2 and 10 µA cm−2 respectively. The local work function (Φ) of 5.509 eV for the NiMn2O4 porous network was computed using density functional theory (DFT) and it exhibits an impressive field enhancement factor (β) of 3381 with good FE current stability. These results demonstrate the potential application of this material for future vacuum micro/nanoelectronics and FE panel display applications.

Local-Adaptive Image Alignment Based on Triangular Facet Approximation.

Accurate and efficient image alignment is the core problem in the research of panoramic stitching nowadays. This paper proposes a local-adaptive image alignment method based on triangular facet approximation, which directly manipulates the matching data in the camera coordinates, and therefore rises superior to the imaging model of cameras. A more robust planar transformation model is proposed and extended to be local-adaptive via combining it with two weighting strategies. By approximating the scene as a combination of adjacent triangular facets, the planar and spherical triangulation strategies are introduced to more efficiently align normal and fisheye images respectively. The efficiency of the proposed method are verified through the comparative experiments on several challenging cases both qualitatively and quantitatively.

Relationship of aortic excess pressure obtained using pressure-only reservoir pressure analysis to directly measured aortic flow in humans

Objectives: A reservoir pressure model describing left ventricular-large artery interaction has been proposed as a useful heuristic model providing insight into the propagation of the central blood pressure as well as providing clinical prognostic information. A pressure-only approach to calculation of reservoir pressure waves has been proposed but this assumes that the resultant excess pressure is proportional to the volume flow rate out of the left ventricle; this has not been tested in humans.Approach: We use non-invasively acquired central pressure and flow data obtained in the 2nd Australian National Blood Pressure Study to test this assumption and to investigate the use of flow approximations based on excess pressure or an assumed triangular flow pattern in calculation of forward and backwards waves in the aortic root.Main results: Results from 821 subjects showed close association between the shape of measured flow patterns and calculated excess pressure, with mean coefficient of determination R2 = 0.931 ± 0.046(SD). For directly measured versus triangular flow approximation R2 was 0.918 ± 0.057. Comparison of the peak amplitudes of forwards (Pf) and backwards (Pb) going pressure waves resulted in significant correlation between Pfmax and Pbmax using both measured flow and the triangular flow approximation (0.83 and 0.79 respectively) and using excess pressure as a flow approximation (Pfmax 0.86 and Pbmax 0.77). All associations for peak pressures and integrals were high with R-values between 0.70 and 0.95.Significance: Pressure-only reservoir wave analysis appears to conform to the inherent assumptions underpinning the mathematical approach employed: this provides support for use of reservoir analysis as a non-invasive method to describe potentially important features and functions of ventriculo-vascular interaction without the requirement for flow measurement.

Pricing European Options with Triangular Fuzzy Parameters: Assessing Alternative Triangular Approximations in the Spanish Stock Option Market

The aim of this paper is contributing from a practical and empirical perspective to option pricing under fuzziness. When we evaluate Black–Scholes option pricing formula with triangular fuzzy numbers, we obtain a non-triangular price that may be slightly difficult to use in practical applications. We improve the applicability of the fuzzy version of that formula by proposing and testing three triangular approximations when the subjacent asset price, its volatility and free interest rate are triangular fuzzy numbers. To check the goodness of these approximations, we firstly evaluate their closeness to the actual values of fuzzy Black and Scholes model. We find that the quality of those approximations depends on options maturity and moneyness grade and if we are pricing call or put options. We also assess the capability of those approximating methods to reflect satisfactorily real market prices and obtain good results. To develop all empirical applications, we use a sample of options on IBEX35 traded in the Spanish derivatives market on 3/1/2017.