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Journal articles on the topic 'The discriminant equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Smart, N. P. "Solving a quartic discriminant form equation." Publicationes Mathematicae Debrecen 43, no. 1-2 (1993): 29–39. http://dx.doi.org/10.5486/pmd.1993.1183.

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2

Chávez-Pichardo, Mauricio, Miguel A. Martínez-Cruz, Alfredo Trejo-Martínez, Ana Beatriz Vega-Cruz, and Tanya Arenas-Resendiz. "On the Practicality of the Analytical Solutions for all Third- and Fourth-Degree Algebraic Equations with Real Coefficients." Mathematics 11, no. 6 (2023): 1447. http://dx.doi.org/10.3390/math11061447.

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In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that satisfies the following two conditions at the same time: (1) Its discriminant is identical to the discriminant of the general quartic equation. (2) It has at least one positive real root whenever the general quartic equation is non-biquadratic. This unique special form of the resolvent cubic is defined here as the “Standard Form of the Resolven

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3

Salas Salas, Alvaro Humberto, Jairo Ernesto Castillo Hernández, and Lorenzo Julio Martínez Hernández. "The Duffing Oscillator Equation and Its Applications in Physics." Mathematical Problems in Engineering 2021 (November 30, 2021): 1–13. http://dx.doi.org/10.1155/2021/9994967.

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In this paper, we solve the Duffing equation for given initial conditions. We introduce the concept of the discriminant for the Duffing equation and we solve it in three cases depending on sign of the discriminant. We also show the way the Duffing equation is applied in soliton theory.

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4

Zhao, Haiqing, and Yuzhao Zhou. "A New Discriminant Method for the Stability of Fourth-Order Differential Equation." Journal of Physics: Conference Series 2660, no. 1 (2023): 012031. http://dx.doi.org/10.1088/1742-6596/2660/1/012031.

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Abstract The stability of nonlinear differential equations has been widely studied based on various methods. In this paper, we transform a class of fourth-order differential equations into a perturbation system and study the stability and asymptotic stability of zero solutions. By utilizing Lyapunov’s second method, we give sufficient conditions for zero-solution stability and asymptotic stability and provide the construction method of the zero-solution asymptotically stable Lyapunov function of such fourth-order differential equations. In addition, this paper removes the requirement of negati

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5

Shawi, Zahraa A. "Bifurcation Solutions of Fourth Order Non-linear Differential Equation Using a Local Method of Lyapunov –Schmidt." BASRA JOURNAL OF SCIENCE 39, no. 2 (2021): 221–33. http://dx.doi.org/10.29072/basjs.202124.

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In this paper, the bifurcation solutions of the boundary condition problem has been studied by using the local method from Lyapunov-Schmidt. We reduce the bifurcation equation and make it in the form of Operator equation. In addition, the finite dimensional reduction theorem for the bifurcation equation is given by the nonlinear system of fourth order equations. We investigate the analysis system of the bifurcation equation, we also find the Discriminant set of corresponding to the nonlinear differential equation by using (Maple 2016) program. The classification of the equilibrium points of th

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6

Brindza, B., J. H. Evertse, and K. Györy. "Bounds for the solutions of some diophantine equations in terms of discriminants." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 1 (1991): 8–26. http://dx.doi.org/10.1017/s1446788700033267.

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AbstractSeveral effective upper bounds are known for the solutions of Thue equations, Thue-Mahler equations and superelliptic equations. One of the basic parameters occurring in these bounds is the height of the polynomial involved in the equation. In the present paper it is shown that better (and, in certain important particular cases, best possible) upper bounds can be obtained in terms of the height, if one takes into consideration also the discriminant of the polynomial.

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Ляшков, А., A. Lyashkov, К. Панчук, K. Panchuk, Л. Варепо, and L. Varepo. "Four-Dimensional Space’s Hypersurface Mapping Singularity." Geometry & Graphics 5, no. 3 (2017): 3–10. http://dx.doi.org/10.12737/article_59bfa3078af4c1.45321238.

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Investigation of singularity related to a mapping by the orthogonal projection in a four-dimensional space of a hypersurface given by parametric equations is presented in this paper. On this investigation’s basis have been proposed in a united way three approaches to the hypersurface’s discriminant determination. Thus, have been defined conditions which the investigated hypersurface’s discriminant set and criminant are satisfied. Have been obtained dependencies settling the relationship between parameters of the hypersurface at its discriminant points. They are used to determine the singularit

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8

Nagase, Goro. "Using the Discriminant for Problems Involving Extrema." Mathematics Teacher 79, no. 2 (1986): 145–46. http://dx.doi.org/10.5951/mt.79.2.0145.

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Various methods for solving problems involving maxima and minima without calculus have been elegantly presented by Niven (1981). However, the method of using the discriminant of a quadratic equation is not emphasized in that book. The discriminant plays an important role in many areas of algebra, precalculus, calculus, analysis, and even statistics.

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9

Panzeri, Anna, Gianluca Castelnuovo, and Andrea Spoto. "Assessing Discriminant Validity through Structural Equation Modeling: The Case of Eating Compulsivity." Nutrients 16, no. 4 (2024): 550. http://dx.doi.org/10.3390/nu16040550.

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Food addiction (FA) and disordered eating behaviors related to obesity are gaining attention in clinical and research fields. The modified Yale Food Addiction Scale 2.0 (mYFAS2.0) is the gold standard questionnaire to measure FA, while another tool is the Measure of Eating Compulsivity 10 (MEC10). Discriminant validity is present when two measures of similar but distinct constructs show a correlation that is low enough for the factors to be regarded as distinct. However, the discriminant validity of these measures has never been tested. Through a cross-sectional study design, 717 inpatients (f

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10

Chávez-Pichardo, Mauricio, Miguel A. Martínez-Cruz, Alfredo Trejo-Martínez, Daniel Martínez-Carbajal, and Tanya Arenas-Resendiz. "A Complete Review of the General Quartic Equation with Real Coefficients and Multiple Roots." Mathematics 10, no. 14 (2022): 2377. http://dx.doi.org/10.3390/math10142377.

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This paper presents a general analysis of all the quartic equations with real coefficients and multiple roots; this analysis revealed some unknown formulae to solve each kind of these equations and some precisions about the relation between these ones and the Resolvent Cubic; for example, it is well-known that any quartic equation has multiple roots whenever its Resolvent Cubic also has multiple roots; however, this analysis reveals that any non-biquadratic quartic equation and its Resolvent Cubic always have the same number of multiple roots; additionally, the four roots of any quartic equati

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11

Jiří, Klaška. "Quartic Polynomials with a Given Discriminant." Mathematica Slovaca 72, no. 1 (2022): 35–50. http://dx.doi.org/10.1515/ms-2022-0003.

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Abstract Let 0 ≠ D ∈ ℤ and let QD be the set of all monic quartic polynomials x 4 + ax 3 + bx 2 + cx + d ∈ ℤ[x] with the discriminant equal to D. In this paper we will devise a method for determining the set QD . Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell’s equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculations on a computer.

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12

Liu, Jingjing, and Huili Wei. "Solving the exact solution to the modified Zakharov-Kuznetsov equation by using the trial equation method." Journal of Physics: Conference Series 3021, no. 1 (2025): 012071. https://doi.org/10.1088/1742-6596/3021/1/012071.

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Abstract The exact solution of the nonlinear development equation can describe the actual physical phenomenon more accurately, so it is particularly important to study the exact solution of the nonlinear development equation. In this paper, we use the trial equation method and the polynomial complete discriminant system to find modified Zakharov-Kuznetsov equation exact solutions. We will discuss 9 cases in total and ultimately arrive at 18 solutions.

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13

Lin, Yu Rong, and Qiang Wang. "Direct Orthogonal Neighborhood Preserving Discriminant Analysis." Advanced Materials Research 179-180 (January 2011): 1254–59. http://dx.doi.org/10.4028/www.scientific.net/amr.179-180.1254.

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Several orthogonal feature extraction algorithms based on local preserving projection have recently been proposed. However, these methods don’t address the singularity problem in the high dimensional feature space,which means that the eigen-equation of orthogonal feature extraction algorithms cannot be solved directly. In this paper, we present a new method called Direct Orthogonal Neighborhood Preserving Discriminant Analysis (DONPDA), which is able to extract all the orthogonal discriminant vectors simultaneously in the high-dimensional feature space and does not suffer the singularity probl

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14

Simões, Eunice N., Ana L. Novais Carvalho, and Sergio L. Schmidt. "The Role of Visual and Auditory Stimuli in Continuous Performance Tests: Differential Effects on Children With ADHD." Journal of Attention Disorders 25, no. 1 (2018): 53–62. http://dx.doi.org/10.1177/1087054718769149.

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Objective: Continuous performance tests (CPTs) usually utilize visual stimuli. A previous investigation showed that inattention is partially independent of modality, but response inhibition is modality-specific. Here we aimed to compare performance on visual and auditory CPTs in ADHD and in healthy controls. Method: The sample consisted of 160 elementary and high school students (43 ADHD, 117 controls). For each sensory modality, five variables were extracted: commission errors (CEs) and omission errors (OEs), reaction time (RT), variability of reaction time (VRT), and coefficient of variabili

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15

Самсонов, Владимир, Vladimir Samsonov, Юлий Перельман, et al. "METHOD FOR ASTHMA PREDICTION IN PATIENTS WITH POLYPOUS RHINOSINUSITIS." Bulletin physiology and pathology of respiration 1, no. 70 (2018): 38–41. http://dx.doi.org/10.12737/article_5c1265588a8194.05879815.

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The method for prediction of asthma in patients with polypous rhinosinusitis was developed. It consists of determination of the average mass molecules (AMM, optical density units), measurement of exhaled and inhaled air temperature (T exh, ºC), and (T inh, ºC), and determination of the temperature difference (ΔT, ºC) between the inhaled and exhaled air temperatures and with the help of the discriminant equation: D = +5.028 × T exh - 0.405×ΔT - 8.910 × AMM, where the discriminant function (D) boundary value is 152.16. At D greater than or equal to the discriminant function boundary value, the a

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16

Chávez-Pichardo, Mauricio, José Daniel López-Barrientos, and Saúl Perea-Flores. "Scrutinizing the General Conic Equation." Mathematics 13, no. 9 (2025): 1428. https://doi.org/10.3390/math13091428.

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We present a general formula that transforms any conic of the form Ax2+Bxy+Cy2+Dx+Ey+F=0, with B≠0, into A′(x′)2+C′(y′)2+D′x′+E′y′+F=0, without requiring the rotation angle θ. This directly eliminates the cross term xy, simplifying the rotated conics analysis. As consequences, we obtain new formulae that remove both rotations and translations, a novel proof of the discriminant criterion, improved expressions for eccentricity, and a detailed taxonomy of all loci described by the general conic equation.

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17

Park, Young Joo, and Ho Shin Ryu. "A Study on the Differentiation of Women with Perimenstrual Symptom Severity and Perimenstrual Distress Patterns." Korean Journal of Women Health Nursing 4, no. 1 (1998): 93–104. http://dx.doi.org/10.4069/kjwhn.1998.4.1.93.

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The purpose of this study was to describe perimenstrual symptom severity levels and perimenstrual distress patterns of women. The study performed the discriminant analysis in which included seven factors : age, pariety, social support, menstrual socialization(mother's symptom, sister's symptom, and menstrual effect), attitude of sex role and depression. The subjects were 283 women that they were not pregnant or lactating, had at least one period in past three months, would understand the purpose of study and willingly accepted the participation. The data analysis was done by pc-SAS program aft

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18

Liu, Xin, and Ying Guo. "Feasibility Study on Color Grading of Blue Iolite Based on GemDialogue Color Comparison Charts." Applied Sciences 13, no. 11 (2023): 6475. http://dx.doi.org/10.3390/app13116475.

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To explore the feasibility of applying the GemDialogue color comparison charts to the color grading of blue iolite, the color of the charts was quantified by the integrating sphere handheld spectroscopy in this paper, and the screened data were classified into a total of 9 categories using the elbow rule and K-Means clustering analysis. Using Fisher’s discriminant to perform discriminant analysis on the 9 categories that have been classified, the discriminant function equation was established separately to verify the accuracy of this classification. Finally, the color parameters of iolite samp

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19

de Souza, Ana Cláudia, Neusa Maria Costa Alexandre, and Edinêis de Brito Guirardello. "Validation of the Brazilian Version of the Job Satisfaction Survey Using Confirmatory Factor Analysis." Journal of Nursing Measurement 25, no. 1 (2017): 46E—65E. http://dx.doi.org/10.1891/1061-3749.25.1.46.

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Background and Purpose: The purpose of this study was to evaluate the validity of the Brazilian version of the Job Satisfaction Survey (JSS) using confirmatory factor analysis supported by structural equation modeling in a sample of Brazilian nursing workers. Methods: Data from 360 nursing workers were analyzed. Confirmatory factor analysis used partial least squares structural equation modeling (PLS-SEM). Results: The results showed that the Brazilian version of the JSS presented better adjustment to the model after the removal of four items from the scale. According to confirmatory factor an

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20

McKeon, Jennifer M. Medina, Craig R. Denegar, and Jay Hertel. "Sex Differences and Discriminative Value of Lower Extremity Alignments and Kinematics during Two Functional Tasks." Journal of Applied Biomechanics 26, no. 3 (2010): 295–304. http://dx.doi.org/10.1123/jab.26.3.295.

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The purpose of this study was to formulate a predictive equation to discriminate males from females using static and dynamic lower extremity (LE) alignments. Twenty-four healthy adults volunteered to participate. Three-dimensional motion analysis was used to assess the kinematics of the right hip and knee during two functional tasks. Six measures of static LE alignment were also performed. Statistical comparisons were made between males and females for all variables. Static and dynamic variables that were significantly different by sex were entered into separate discriminant analyses for each

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21

Sosin, I., M. Ovcharenko, L. Pinsk, et al. "Integrated forecasting and prevention pseudoabsentative syndrome in the remission period of opioid dependence." Fundamental and applied researches in practice of leading scientific schools 30, no. 6 (2018): 23–29. http://dx.doi.org/10.33531/farplss.2018.6.03.

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Patent in Ukraine "A method for predicting pseudoabsentative syndrome in the remission period in patients with opioid dependence" (Patent of Ukraine 67150), which includes diagnostic clinical and psychopathological integrated screening, the innovative essence of which is that in addition, according to ultrasound diagnosis, detect the liver, carry out quantification the evaluation of the risk factors of relapse, compare the obtained mathematical indicators (predictive factors - digital constants, determined by statistical methods) using the system two discriminant equations, and if the absolute

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22

Poulakis, D., and P. G. Walsh. "On the Diophantine equation x2-dy4=1 with prime discriminant II." Colloquium Mathematicum 105, no. 1 (2006): 51–55. http://dx.doi.org/10.4064/cm105-1-6.

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23

Nakata, Mitsusada. "On the factorization of the discriminant of a classical modular equation." Acta Arithmetica 178, no. 1 (2017): 77–85. http://dx.doi.org/10.4064/aa8538-8-2016.

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24

Pankrashkin, Konstantin. "A remark on the discriminant of Hill’s equation and Herglotz functions." Archiv der Mathematik 102, no. 2 (2014): 155–63. http://dx.doi.org/10.1007/s00013-014-0612-x.

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25

Blickle, Gerhard. "Assessing Convergent and Discriminant Validity of the Influence Behavior Questionnaire." Psychological Reports 82, no. 3 (1998): 923–29. http://dx.doi.org/10.2466/pr0.1998.82.3.923.

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The purpose was to study convergent and discriminant validity of the 1997 Influence Behavior Questionnaire (short version) used to assess lateral attempts at influence. 479 German employees participated in a multitrait-multimethod study with nine trait measures (Rational Persuasion, Inspirational Appeal, Consultation, Ingratiation, Exchange, Personal Appeal, Coalition, Legitimating, Pressure) and two methods (self- and peer-ratings). Data, analyzed with incomplete structural equation models, supported scales' convergent but not discriminant validity of the influence scales.

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Ota, Hideki, and Toshihiro Hanazato. "Study on Reconstruction of Condominium in the Metropolitan Area Using Real Estate Data." International Journal of Real Estate Studies 17, no. 2 (2023): 102–15. http://dx.doi.org/10.11113/intrest.v17n2.317.

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In Japan, there is concern about the impact of the growing stock of older condominiums on the buildings themselves and the surrounding environment, and immediate action is needed. While in other countries, repair, elimination, and retirement of aged condominiums are the mainstream methods, in Japan, reconstruction is sometimes used. This study proposes a new decision criterion using discriminant analysis to address the problem of the difficulty and long time required to build consensus for rebuilding older condominiums. Discriminant analysis used building attributes and other variables to diff

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Zhang, Wei-Guo, Xing-Qian Ling, Xiang Li, and Shao-Wei Li. "The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms." Complexity 2019 (June 20, 2019): 1–17. http://dx.doi.org/10.1155/2019/4209275.

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In this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthermore, on the basis of the two bell-shaped solitary wave solutions of the equation, the explicit expressions of the orbital stability discriminants are deduced to give the orbitally stable and instable intervals for the two solitary waves as the wave velocity changing. Moreover, the influence caused

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28

Rohmani, Afiana. "Sexual Dimorphism of the first Lumbar vertebra in the Malaysian Population." Indonesian Journal of Legal and Forensic Sciences (IJLFS) 12, no. 1 (2022): 37. http://dx.doi.org/10.24843/ijlfs.2022.v12.i01.p05.

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Sex determination is one of the main steps in the identification of human skeletal remains. The vertebrae are weight-bearing structures in the human body that may provide variety of information from an individual. The aim of this study is to assess the sexual dimorphism of the first lumbar (L1) vertebrae using three-dimensional (3D) computed tomography (CT) imaging to develop population-specific equations for sex identification in the Malay population. Thirteen linear measurements of the first lumbar (L1) vertebrae were taken from 50 males and 50 females’ patients in the Radiology Department o

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Bronski, Jared C., Vera Mikyoung Hur, and Robert Marangell. "Floquet theory and stability analysis for Hamiltonian PDEs." Nonlinearity 37, no. 12 (2024): 125010. http://dx.doi.org/10.1088/1361-6544/ad8698.

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Abstract We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third order), the nonlinear Schrödinger and Boussinesq equations (fourth order), and the Kawahara equation (fifth order). Our analysis reveals that the characteristic polynomial of the monodromy matrix inherits symmetry from the underlying PDE, enabling us to determine the essential spectrum along the imaginary axis and bifurcations of the spectrum away from

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30

Schmidt, Frank L., and In-Sue Oh. "Can Synthetic Validity Methods Achieve Discriminant Validity?" Industrial and Organizational Psychology 3, no. 3 (2010): 344–50. http://dx.doi.org/10.1017/s1754942600002510.

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Our focus is on the difficulties that synthetic validity encounters in attempting to achieve discriminant validity and the implications of these difficulties. Johnson et al. (2010) acknowledge the potential problems involved in attaining discriminant validity in synthetic validity. For example, they report that Peterson et al. (2001), Johnson (2007), and other synthetic validity studies report failure to achieve discriminant validity. What this failure means is that a synthetic validity equation developed to predict validity for Job A does as well in predicting validity for Jobs B, C, D, and s

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Supriyanto, Supriyanto, Dewi Anggraini, Fahmi Sulaiman, Elserra Siemin Ciamas, and Yeni Rachmawati. "Paket Program, Indeks Prestasi Kumulatif, Umur dan Domisili sebagai Faktor Pembeda Prestasi Akademik Mahasiswa." JUPIIS: JURNAL PENDIDIKAN ILMU-ILMU SOSIAL 13, no. 1 (2021): 224. http://dx.doi.org/10.24114/jupiis.v13i1.23735.

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One measure of success in teaching and learning in tertiary institutions is academic achievement. Through student academic achievement, it will increase the enthusiasm of prospective students in determining the tertiary institution of their choice. This research is aimed to determine the differentiating factors of student academic achievement, with the independent variables, namely Program Package, Grade Point Average (GPA), Age and Domicile. The research conducted included classifying students into two groups based on student academic achievement, so the analysis method used was Discriminant

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32

Hardy, Kenneth, and Kenneth S. Williams. "The squareroot of an ambiguous form in the principal genus." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (1993): 145–50. http://dx.doi.org/10.1017/s0013091500005952.

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Gu, Musong, Chen Peng, and Zhao Li. "Traveling wave solution of (3+1)-dimensional negative-order KdV-Calogero-Bogoyavlenskii-Schiff equation." AIMS Mathematics 9, no. 3 (2024): 6699–708. http://dx.doi.org/10.3934/math.2024326.

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<abstract><p>We explored the (3+1)-dimensional negative-order Korteweg-de Vries-alogero-Bogoyavlenskii-Schiff (KdV-CBS) equation, which develops the classical Korteweg-de Vries (KdV) equation and extends the contents of nonlinear partial differential equations. A traveling wave transformation is employed to transform the partial differential equation into a system of ordinary differential equations linked with a cubic polynomial. Utilizing the complete discriminant system for polynomial method, the roots of the cubic polynomial were classified. Through this approach, a series of ex

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Duan, Jun-Sheng, and Yun-Yun Zhang. "Discriminant and Root Trajectories of Characteristic Equation of Fractional Vibration Equation and Their Effects on Solution Components." Fractal and Fractional 6, no. 9 (2022): 514. http://dx.doi.org/10.3390/fractalfract6090514.

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The impulsive response of the fractional vibration equation z′′(t)+bDtαz(t)+cz(t)=F(t), b>0,c>0,0≤α≤2, is investigated by using the complex path-integral formula of the inverse Laplace transform. Similar to the integer-order case, the roots of the characteristic equation s2+bsα+c=0 must be considered. It is proved that for any b>0, c>0 and α∈(0,1)∪(1,2), the characteristic equation always has a pair of conjugated simple complex roots with a negative real part on the principal Riemann surface. Particular attention is paid to the problem as to how the couple conjugated complex roots

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Kardomateas, George A., and Catherine N. Phan. "Three-dimensional elasticity solution for sandwich beams/wide plates with orthotropic phases: The negative discriminant case." Journal of Sandwich Structures & Materials 13, no. 6 (2011): 641–61. http://dx.doi.org/10.1177/1099636211419127.

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In an earlier paper, Pagano (1969) [Pagano NJ. Exact solutions for composite laminates in cylindrical bending. J Compos. Mater. 1969; 3: 398–411] presented the three-dimensional elasticity solution for orthotropic beams (applicable also to sandwich beams) for the cases of: (1) a phase with positive discriminant of the qudratic characteristic equation, which is formed from the orthotropic material constants and further restricted to positive real roots and (2) an isotropic phase, which results in a zero discriminant. The roots in this case are all real, unequal, and positive (positive discrimin

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Hsu, Hsien-Yuan, Tze-Li Hsu, KoFan Lee, and Lori Wolff. "Evaluating the Construct Validity of Ryff’s Scales of Psychological Well-Being Using Exploratory Structural Equation Modeling." Journal of Psychoeducational Assessment 35, no. 6 (2016): 633–38. http://dx.doi.org/10.1177/0734282916652756.

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The purpose of this study was to evaluate the construct validity of Ryff’s Scales of Psychological Well-Being (SPWB) using exploratory structural equation modeling (ESEM). The data were drawn from the national survey of Midlife in the United States conducted during 1994 and 1995. Measurement models assuming different number of factors (1-6 factors) and considering the effect of negatively wording items were specified and compared to determine optimal number of underlying factors. The discriminant validity was assessed following Farrell’s suggestions. The results showed the discriminant validit

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Abuteen, Eman. "Solving Fractional Riccati Differential Equation with Caputo-Fabrizio Fractional Derivative." European Journal of Pure and Applied Mathematics 17, no. 1 (2024): 372–84. http://dx.doi.org/10.29020/nybg.ejpam.v17i1.5013.

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This article offers an analytical solution for the fractional Riccati differential equation in three distinct cases. These cases are determined by the discriminant and the analytical solution based on the properties of the Caputo-Fabrizio fractional derivative and integral. Several examples were tested using this analytical solution. It is noteworthy that various methods have yielded related results as indicated in the literature.

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Kundu, Arjun, Dhwani Patel, and Dharmesh Silajiya. "Cephalometric Analysis for Gender Determination Using Maxillary Sinus Index in Population of Gujrat, India." INTERNATIONAL JOURNAL OF ETHICS, TRAUMA & VICTIMOLOGY 7, no. 02 (2022): 6–9. http://dx.doi.org/10.18099/ijetv.v7i02.2.

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Introduction: Humans are sexually dimorphic. Identification of remnants of skeletal and decomposing parts of humans is one of the most difficult skills in forensic medicine. Forensic anthropologists can receive whole or fragmented skeletal remains. But the unique thing is that the maxillary sinus is intact within the skull, so maxillary sinus radiography is being used to identify remains and determine gender. Materials and Method: A total of 51 adult digital lateral cephalometric radiographs (20 males and 31 females) were included in the study. The maxillary sinus analysis was performed by mea

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Radomir, Lăcrămioara, and Ovidiu I. Moisescu. "Discriminant validity of the customer-based corporate reputation scale: some causes for concern." Journal of Product & Brand Management 29, no. 4 (2019): 457–69. http://dx.doi.org/10.1108/jpbm-11-2018-2115.

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Purpose This study aims to reexamine the discriminant validity of the customer-based corporate reputation (CBR) scale in both its original and short forms. Design/methodology/approach The authors used data from end-use customers in two countries and two service industries. Results obtained in partial least squares structural equation modeling for the heterotrait–monotrait (HTMT)-based inference test and the Fornell and Larcker criterion were compared to make judgements about the empirical distinctiveness of the CBR scale’s five dimensions. Findings This study’s findings demonstrate that the CB

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Lee, Jun Hwa, Kyung‐Hee Kim, Ji‐Won Park, et al. "Low‐mass‐ion discriminant equation: A new concept for colorectal cancer screening." International Journal of Cancer 134, no. 8 (2013): 1844–53. http://dx.doi.org/10.1002/ijc.28517.

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Canales, Muna T., Terri Blackwell, Areef Ishani, et al. "Renal Function and Death in Older Women: Which eGFR Formula Should We Use?" International Journal of Nephrology 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/8216878.

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Background. The Berlin Initiative Study (BIS) eGFR equations were developed specifically for aged populations, but their predictive validity compared to standard formulae is unknown in older women.Methods. In a prospective study of 1289 community-dwelling older women (mean age 79.5 years), we compared the performance of the BIS1 SCr-based equation to the CKD-EPIcrand the BIS2 SCr- and Scysc-based equation to the CKD-EPIcr,cyscto predict cardiovascular and all-cause mortality.Results. Prevalence of specific eGFR category (i.e., ≥75, 60–74, 45–59, and <45) according to eGFR equation was 12.3%

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VILLA-SALVADOR, GABRIEL. "AN ELEMENTARY PROOF OF THE CONDUCTOR-DISCRIMINANT FORMULA." International Journal of Number Theory 06, no. 05 (2010): 1191–97. http://dx.doi.org/10.1142/s1793042110003459.

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For a finite abelian extension K/ℚ, the conductor-discriminant formula establishes that the absolute value of the discriminant of K is equal to the product of the conductors of the elements of the group of Dirichlet characters associated to K. The simplest proof uses the functional equation for the Dedekind zeta function of K and its expression as the product of the L-series attached to the various Dirichlet characters associated to K. In this paper, we present an elementary proof of this formula considering first K contained in a cyclotomic number field of pn-roots of unity, where p is a prim

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Hanif Abdullah, Mohd, Hafizan Juahir, Fathurahman Lananan, et al. "Pattern Recognition of Melaleuca cajuputi Powell Essential Oils Fingerprint in Terengganu, Malaysia Using Chemometric Approach." International Journal of Engineering & Technology 7, no. 3.14 (2018): 132. http://dx.doi.org/10.14419/ijet.v7i3.14.16873.

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Cajuputi essential oil is extracted from the leaves of Melaleuca cajuputi Powell. This study is performed to spatially classify the variation of Melaleuca cajuputi essential oil fingerprint based on different sampling location using chemometric technique along Terengganu coastal area. Discriminant Analysis (DA) successfully discriminate 10 fingerprint of essential oil into three different groups with three significant peaks in FTIR analysis. Hierarchical agglomerative cluster analysis (HACA) successfully grouped the 10 sampling stations into three groups (cluster A, B and C).Classification cri

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Duke, William. "Integral and rational representations of forms." Journal of Experimental Mathematics 1, no. 1 (2025): 23–35. https://doi.org/10.56994/jxm.001.001.002.

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Criteria are given for the integral representation of a binary quartic form by certain integral ternary quadratic forms and its rational representation by some discriminant forms. These conditions depend on integral or rational solutions of a Weierstrass equation associated to the forms.

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Hassan, Al-Zaid, B. Brindza, and Á. Pintér. "On Positive Integer Solutions of the Equation xy + yz + xz = n." Canadian Mathematical Bulletin 39, no. 2 (1996): 199–202. http://dx.doi.org/10.4153/cmb-1996-024-5.

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AbstractAs it had been recognized by Liouville, Hermite, Mordell and others, the number of non-negative integer solutions of the equation in the title is strongly related to the class number of quadratic forms with discriminant —n. The purpose of this note is to point out a deeper relation which makes it possible to derive a reasonable upper bound for the number of solutions.

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Couppoussamy, Rajkumar, M. Jonathan Daniel, Srinivasan Subramanian Vasudevan, and Jimsha Vanathan Kumaran. "Gender Determination from Digital Lateral Cephalogram for an Adolescent and Adult Cohort from a Pondicherry Population – A Cross-Sectional Study." Journal of Indian Academy of Oral Medicine and Radiology 36, no. 2 (2024): 164–68. https://doi.org/10.4103/jiaomr.jiaomr_155_23.

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Abstract Background: Identifying sex from a skull is a test for a forensic odontologist. There are research done to determine sex based on cranial values. The aim of the present research is to assess the role of facial skeletal traits in digital lateral cephalogram to determine gender. Objectives: To derive a discriminant function equation to determine gender for an adolescent and adult cohort. Methods and Material: From the archive of the Institution, 98 digital lateral cephalograms of 52 males and 46 females with an age range from 13 to 55 years were retrieved to measure 12 facial skeletal v

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Wysocka, Joanna, Agata I. Cieślik, and Dariusz P. Danel. "Sex estimation using measurements of the proximal femur in a historical population from Poland." Anthropological Review 86, no. 1 (2023): 37–49. http://dx.doi.org/10.18778/1898-6773.86.1.04.

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Sex estimation is one of the most important components in assessing the biological profile of an individual. In an archaeological context, the pelvis, which is the most dimorphic part of the skeleton, is often poorly preserved, which can cause an inability to use morphological sex estimation methods. Therefore, alternative methods are required in such cases. Because the utility of the metric methods based on the femur measurement has been confirmed, and the bone is usually available for examination due to its good preservation, developing methods using the landmarks of the femur could have imp

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Pyasetska, S. I., N. P. Grebenyuk, and S. V. Savchuk. "THE CONSTRUCTION OF THE LINEAR DISCRIMINANT ANALYSIS FUNCTION AND ITS EVALUATION TO DETERMINE EXTREME METEOROLOGICAL PHENOMENA (ICE DEPOSITS) IN UKRAINE." Hydrology, hydrochemistry and hydroecology, no. 1 (56) (2020): 82–94. http://dx.doi.org/10.17721/2306-5680.2020.1.9.

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o predict the possibility of ice deposits on the territory of Ukraine in the winter season, an analogous approach is proposed using the construction of the equations of the linear discriminant function. For this, the correlation coefficients between 13 meteorological values (per day) at the start dates of ice deposits at all stations of Ukraine were calculated. Significant correlation coefficients were determined between individual meteorological variables, such as average air temperature, maximum, minimum average air humidity, average wind speed, and atmospheric pressure at sea level. It is t

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Thalib, Najdah, Hotnida Nainggolan, Fuad Gagarin Siregar, and Gegga Firyant Firdaus. "The Influence of Social Impact, and Product Quality on Sustainable Business Growth in the Textile Industry in Bandung." West Science Journal Economic and Entrepreneurship 1, no. 06 (2023): 115–23. http://dx.doi.org/10.58812/wsjee.v1i06.456.

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Within the framework of Bandung's textile industry, this study explores the intricate relationships that exist between social effect, product quality, and sustainable economic success. The survey included a sample of 150 companies with a range of product specializations and sizes. Using partial least squares structural equation modeling, measurement model assessment, discriminant validity analysis, and structural model analysis were carried out (PLS-SEM). Product quality, social impact, and sustainable business growth were found to be significantly positively correlated. The results also confi

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Cao, Damin, Cheng Li, and Fajiang He. "Exact solutions to the space-time fraction Whitham–Broer–Kaup equation." Modern Physics Letters B 34, no. 16 (2020): 2050178. http://dx.doi.org/10.1142/s021798492050178x.

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The objective work of this paper is to transform the nonlinear space-time fraction Whitham–Broer–Kaup equation into ordinary differential equation by using the conformal fractional derivative, and find the exact solutions through the complete polynomial discriminant system. At the same time, we build the appropriate solution for the identified parameters to show the existence of the solution. In addition, we provide the 3D and 2D graphics to show that the solutions are real and effective.

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