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It is a classical result that there are 12 (irreducible) rational cubic curves through 8 generic points in P C 2 , but little is known about the non-generic cases. The space of 8-point configurations is partitioned into strata depending on combinatorial objects we call quatroids, a higher-order version of representable matroids. We compute all 779,777 quatroids on eight distinct points in the plane, which produces a full description of the stratification. For each stratum, we generate several invariants, including the number of rational cubics through a generic configuration. As a byproduct of our investigation, we obtain a collection of results regarding the base loci of pencils of cubics and positive certificates for non-rationality. [ABSTRACT FROM AUTHOR]

A study of the boundaries of the working space of a three-link planar manipulator, specified by analytical equations, is carried out. A new geometric interpretation of these samples is proposed. On its basis, it is established that outer space consists of two-parameter volumes of eccentric and concentric circles. When transforming such environments into four-dimensional space, two types of hypersurfaces are obtained, which represent a geometric model of the manipulator's workspace. The discriminants of these hypersurfaces on the hyperplane are two two-dimensional surfaces. Both an analytical description of these surfaces and their computer models are obtained. As a result, it is established that the boundaries of the working space on the plane of the mechanism are the discriminants of such surfaces. To confirm the reliability of the results obtained, as an example, an inverse kinematics problem is solved on discriminant surfaces — the values of generalized coordinates at the boundary points of the manipulator’s workspace are determined for their given Cartesian coordinates.

Parkinson's disease is related to nervous system disorders in human beings. In this paper, the status of Parkinson's disease has been predicted based on the analysis of features of two Parkinson's disease symptoms: Dysphonia and Dysarthria. The Dysphonia symptom has been measured by analyzing the features extracted from the vocal sounds of a patient. The Dysarthria symptom of Parkinson's disease has been analyzed by the features extracted from the speech signals of a patient. Hence, two different prediction models have been built for deriving the status of Parkinson's disease. The derivation of these prediction systems is based on statistical and discriminant feature analysis. The statistical-based feature analysis is carried out using descriptive and inferential analysis. In contrast, the enteric, deviation, and correlation-based information between the features are utilized for descriptive analysis. The inferential analysis has been performed using hypothetical testing of the distribution of features. The descriptive and inferential feature analyses are used to derive effective features for the Parkinson's disease problem based on the Dysphonia and Dysarthria symptoms. In the discriminant feature analysis, the feature sets undergo deriving discriminant features. The best-selected features are used to build a prediction model for detecting Parkinson's disease problems in a patient. Extensive experimentation has been carried out using a Dysphonia dataset containing 195 samples. Each sample has 23 features. One dataset for Dysarthria symptoms contains 756 observations, with each observation having 754 features. The best prediction models that have been obtained correspond to these datasets, and 93.50% is obtained for Dysphonia and 87.63% for Dysarthria symptoms databases, respectively. The performance of the proposed system has been compared with some existing methods concerning each employed dataset, showing the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper concerns a classical subject regarding the structural properties of abelian number fields. The primitive elements, integral bases, conductors and discriminants are important for studying abelian number fields, and this paper emphasizes that they are closely related to the associated Dirichlet characters. Then by evaluating the Gauss sums, we can give explicit forms of abelian fields of small degree. [ABSTRACT FROM AUTHOR]

The discriminant of a number field is an important invariant measuring its size and ramification behavior. We will first recall classical results by Minkowski, Odlyzko, Serre, and Golod and Šafarevič about discriminants. We then discuss the relevance of number fields with small root discriminants to cryptography. [ABSTRACT FROM AUTHOR]

Let K = ℚ(ϑ) be an algebraic number field with ϑ satisfying a monic irreducible polynomial f (x) of degree n over ℚ. The polynomial f (x) is said to be monogenic if {1,ϑ,..., ϑn-1} is an integral basis of K. Deciding whether or not a monic irreducible polynomial is monogenic is an important problem in algebraic number theory. In an attempt to answer this problem for a certain family of polynomials, Jones ['A brief note on some infinite families of monogenic polynomials', Bull. Aust. Math. Soc. 100 (2019), 239-244] conjectured that if n ≥ 3, 1 ≤ m ≤ n - 1, gcd(n, mB) = 1 and A is a prime number, then the polynomial xn + A(Bx + 1)m ∈ ℤ[x] is monogenic if and only if nn + (-1)n+mBn(n - m)n-mmm A is square-free. We prove that this conjecture is true. [ABSTRACT FROM AUTHOR]

In [11], Hausel introduced a commutative algebra — the multiplicity algebra — associated to a fixed point of the C ∗ -action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the discriminant of this family, providing a new viewpoint on the moduli space of stable bundles. The discriminant in our examples demonstrates that as the bundle varies, we obtain a continuous variation in the isomorphism class of the algebra. [ABSTRACT FROM AUTHOR]

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equalities and one inequality in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is also known that discriminants can be obtained by using repeated parametric gcd's. The resulting discriminants are usually nested determinants, i.e., determinants of matrices whose entries are determinants, and so on. In this paper, we give a new type of discriminants which are not based on repeated gcd's. The new discriminants are simpler in the sense that they are non-nested determinants and have smaller maximum degrees. [ABSTRACT FROM AUTHOR]

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 variables using DIMAXIS-3 software. Discriminant function analysis was used to analyze the data. Results: On initial discriminant function analysis, Ramus height (RH), lower facial height, mandibular length, and anterior cranial base (SN length) were found to be better predictors. On subsequent stepwise discriminant function analysis, RH only appeared to detect the gender with utmost accuracy when all 12 variables were included in the analysis. Conclusions: RH is the better predictor of gender of all the parameters taken in this study on a Pondicherry population.

Let F be a field of characteristic 0, and let f (x) = x 8 + a x 6 + b x 4 + a x 2 + 1 ∈ F [ x ] be irreducible with Galois group Gal (f) . We extend results in the literature to give a complete and elementary classification of Gal (f) , identified as a transitive subgroup of S8 up to conjugacy. The approach involves testing whether a small number of elements in F are perfect squares. As an application, we give one-parameter families of polynomials for each of the six possible Galois groups. [ABSTRACT FROM AUTHOR]

In this article, we extend the classical framework for computing discriminants of special quasi-orthogonal polynomials from Schur's resultant formula, and establish a framework for computing discriminants of a sufficiently broader class of polynomials from the resultant formulas that are proven by Ulas and Turaj. More precisely, we derive a formula for the discriminant of a sequence { r A , n + c r A , n - 1 } of polynomials. Here, c is an element of a field K and { r A , n } is a sequence of polynomials satisfying a certain recurrence relation. There are several works computing the discriminants of given polynomials. For example, Kaneko–Niiho and Mahlburg–Ono independently proved the formula for the discriminants of certain hypergeometric polynomials that are related to j-invariants of supersingular elliptic curves. Sawa–Uchida proved the formula for the discriminants of quasi-Jacobi polynomials and applied it to prove the nonexistence of certain rational quadrature formulas. Our main theorem presents a uniform way to prove a vast generalization of the above formulas for the discriminants. [ABSTRACT FROM AUTHOR]

The problem of classifying elliptic curves over $\mathbb Q$ with a given discriminant has received much attention. The analogous problem for genus $2$ curves has only been tackled when the absolute discriminant is a power of $2$. In this article, we classify genus $2$ curves C defined over ${\mathbb Q}$ with at least two rational Weierstrass points and whose absolute discriminant is an odd prime. In fact, we show that such a curve C must be isomorphic to a specialization of one of finitely many $1$ -parameter families of genus $2$ curves. In particular, we provide genus $2$ analogues to Neumann–Setzer families of elliptic curves over the rationals. [ABSTRACT FROM AUTHOR]

We point out that there is an error in the proof of Theorem 1.1 in [The discriminant of compositum of algebraic number fields, Int. J. Number Theory 15 (2019) 353–360]. We also prove that the result of this theorem holds with an additional hypothesis. However, it is an open problem whether the result of the theorem is true in general or not. [ABSTRACT FROM AUTHOR]

Let $K_n=\mathbb{Q}(\alpha_n)$ be a family of algebraic number fields where $\alpha_n\in \mathbb{C}$ is a root of the n th exponential Taylor polynomial $\frac{x^n}{n!}+ \frac{x^{n-1}}{(n-1)!}+ \cdots +\frac{x^2}{2!}+\frac{x}{1!}+1$ , $n\in \mathbb{N}$. In this paper, we give a formula for the exact power of any prime p dividing the discriminant of Kn in terms of the p -adic expansion of n. An explicit p -integral basis of Kn is also given for each prime p. These p -integral bases quickly lead to the construction of an integral basis of Kn. [ABSTRACT FROM AUTHOR]

Let f(x) = x8 + ax4 + b be an irreducible polynomial with rational coefficients and Galois group Gal(f). We extend previous results to give an elementary classification of Gal(f), identified as a transitive subgroup of S8 up to conjugacy. We show Gal(f) is one of 12 possibilities and can be determined by considering the squareness of at most 11 rational numbers; each number is an expression involving a and b. We give several applications of our results. [ABSTRACT FROM AUTHOR]

Objective: Valid estimates of premorbid cognitive functioning (PMIQ) are crucial for the assessment of older adults at risk for Alzheimer's disease. We investigated the relationship between the NIH Toolbox-Cognition Battery's (NIHTB-CB) Oral Reading Recognition (ORR) subtest and Wechsler Test of Adult Reading scores (WTAR, convergent validity). We also compared ORR to NIHTB-CB Flanker scores, where null relationships were expected (discriminant validity). Methods: The WTAR and NIHTB-CB were administered to 130 cognitively normal (CN) and 113 participants with mild cognitive impairment (MCI). Participants were community-dwelling, older Black and White adults, ages 55–88 years. Data analysis used uncorrected standard scores and Bayesian bivariate correlations. Supplemental materials include intraclass correlations. Results: ORR and WTAR scores were strongly positively associated, while ORR and Flanker scores were unrelated. This pattern held when restricting analyses to the two cognitive status groups, the two racial groups, and the four race-by-diagnosis subgroups. Conclusion: The findings demonstrate convergent and discriminant validity and support NIHTB-CB ORR scores as valid estimates of scores on a PMIQ measure in older Black and White adults with and without MCI. [ABSTRACT FROM AUTHOR]

Sex estimation models are specific to populations and cannot be generalized due to genetic and environmental variabilities. This retrospective cross-sectional study, conducted between January and September 2023 at the Tamale Teaching Hospital, included 119 (50.9 %) females and 115 (49.1 %) males aged 23–82 years. Measurements, including manubrium length (M), manubrium width (MW), sternal body length (B), combined manubrium and sternal body lengths (CL), corpus sterni width at first sternebrae (CSWS1), and corpus sterni width at third sternebrae (CSWS3), were obtained from Computerized Tomographic (CT) images of the sternum using DICOM Viewer, accurate to 0.1 cm. Subsequently, sternal area (SA) and sternal index (SI) were calculated. Univariable and stepwise multivariable discriminant function analysis (DFA) and logistic regression (LR) models were developed using a training sample (70 %), and cross-validation was performed on a holdout sample (30 %). Results showed that the linear measurements, excluding M, and sternal area were higher in males than females (P50 % in females (P

Abstract Background The Minimal Eating Observation Form – Version II (MEOF-II) is a brief and easy to use screening tool for eating difficulties, that is psychometrically robust. The aim of this study was to explore convergent (measuring similar constructs) and discriminant (measuring somewhat different constructs) validity of the MEOF-II to other validated dysphagia specific, activity and participation related instruments. Methods In this cross-sectional study, participants (n = 100, mean age 72, n = 42 women), diagnosed with either chronic pulmonary disease, Parkinson´s disease, Multiple Sclerosis, or stroke were recruited from rehabilitation centres. Patient-reported outcomes and clinical-rated assessments, capturing eating ability in general and swallowing in specific, included: The Dysphagia Handicap Index (DHI), the 4-question test (4QT), the Minimal Eating Observation Form – II, the Volume – Viscosity Swallow Test (V-VST), Flexible Endoscopic Evaluation of Swallowing (FEES) documented according to the Penetration-Aspiration Scale (PAS). Type of oral intake was documented using the Functional Oral Intake Scale (FOIS). Activities in daily living was assessed with Barthel index (BI). Spearman’s correlation coefficient was used to analyze associations. The MEOF-II total score was hypothesised to have moderate correlations (r ≥ 0.3) with the other assessments, besides with PAS and FOIS (weak correlations, r

On the Waring's problem for matrices over a commutative ring, there are some trace conditions provided for matrices eligibly expressed as sums of kth powers with $ k\in \{2,3,4,5,6,7,8\} $ k ∈ { 2 , 3 , 4 , 5 , 6 , 7 , 8 } in the literature. In this paper, we provide similar conditions for matrices written as sums of kth powers with $ k\in \{9,10,11,12,13,14,15,16\} $ k ∈ { 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 }. [ABSTRACT FROM AUTHOR]

In this paper, rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalized Laguerre polynomials, which are the main subject of this paper, and the other in terms of the generalized Umemura polynomials. Both the generalized Laguerre polynomials and the generalized Umemura polynomials can be expressed as Wronskians of Laguerre polynomials specified in terms of specific families of partitions. The properties of the generalized Laguerre polynomials are determined and various differential‐difference and discrete equations found. The rational solutions of the fifth Painlevé equation, the associated σ‐equation, and the symmetric fifth Painlevé system are expressed in terms of generalized Laguerre polynomials. Nonuniqueness of the solutions in special cases is established and some applications are considered. In the second part of the paper, the structure of the roots of the polynomials are investigated for all values of the parameters. Interesting transitions between root structures through coalescences at the origin are discovered, with the allowed behaviors controlled by hook data associated with the partition. The discriminants of the generalized Laguerre polynomials are found and also shown to be expressible in terms of partition data. Explicit expressions for the coefficients of a general Wronskian Laguerre polynomial defined in terms of a single partition are given. [ABSTRACT FROM AUTHOR]

A sign pattern matrix is a matrix whose entries are from the set { + , − , 0 }. For a sign pattern matrix A , the qualitative class of A , denoted Q (A) , is the set of all real matrices whose entries have signs given by the corresponding entries of A. An n × n sign pattern matrix A requires all distinct eigenvalues if every real matrix in Q (A) has n distinct eigenvalues. Li and Harris (2002) [13] characterized the 2 × 2 and 3 × 3 irreducible sign pattern matrices that require all distinct eigenvalues, and established some useful general results on n × n sign patterns that require all distinct eigenvalues. In this paper, we characterize 4 × 4 irreducible sign patterns that require four distinct eigenvalues. This is done by characterizing 4 × 4 irreducible sign patterns that require four distinct real eigenvalues, that require four distinct nonreal real eigenvalues, or that require two distinct real eigenvalues and a pair of conjugate nonreal eigenvalues. The last case turns out to be much more involved. Some interesting open problems are presented. Three important tools that are used in the paper are the following: the discriminant of a polynomial; the fact that if a square sign pattern matrix A requires all distinct eigenvalues then A requires a fixed number of real eigenvalues; and the known result that if A is a " k -cycle" sign pattern then for each B ∈ Q (A) , the k nonzero eigenvalues of B are evenly distributed on a circle in the complex plane centered at the origin. [ABSTRACT FROM AUTHOR]

In this work, we establish formulas for the prime decompositions of resultant and discriminant of the ring class polynomial associated with Thompson series for Fricke group Γ 0 (p) + for p prime and imaginary quadratic field, and as a consequence, validate a conjecture of Chen and Yui on the upper bound of prime factors of such resultants and discriminants. All associated numerical conjectures of Chen and Yui are verified using the Magma code for our formulas written by Chao Qin. [ABSTRACT FROM AUTHOR]

Let O (3) denote the group of orthogonal 3 × 3 real matrices, and M the 5-dimensional real vector space of all 3 × 3 real symmetric matrices with trace zero. Let λ 1 (A) ≤ λ 2 (A) ≤ λ 3 (A) be the eigenvalues of A ∈ M and Ξ - = { A ∈ M ∣ λ 1 (A) = λ 2 (A) } . M is an inner product space with the inner product ⟨ A , B ⟩ = trace (A B) . Let G 3 (M) be the set of all 3-dimensional subspaces of M , a 6-dimensional Grassman manifold. O (3) acts on M on the left by conjugation via inner product preserving linear isomorphisms, which map any 3-dimensional subspace into another 3-dimensional subspace; thus G 3 (M) also has a left action of O (3) . G 3 (M) becomes a category, an action groupoid, with morphisms (V , M , W) ∈ G 3 (M) × O (3) × G 3 (M) , where W = M V M T . Composition of morphisms is (V 1 , N , V 2) ∘ (V 0 , M , V 1) = (V 0 , N M , V 2) . Let C be a category whose objects (V, S) consist of a real inner product space V and S ⊂ V , and whose arrows (V , S) → (W , T) consist of f : V → W , an inner product preserving real linear mapping such that f (S) ⊂ T . We have the functor V ↓ (V , M , W) W G 3 (M) ⟶ F - (V , Ξ - ∩ V) ↓ F - (M) (W , Ξ - ∩ W) C where F - (M) : V → W : A ↦ M A M T . Suppose further that S 3 denotes the group of permutations of { 1 , 2 , 3 } , and ρ : S 3 → O (3) denotes a group homomorphism which is isomorphic as a group representation to the natural representation of S 3 on R 3 (which permutes the coordinates). Let Obj (L S) denote the set of all V ∈ G 3 (M) whose isotropy subgroup contains S = ρ (S 3) as a subgroup. This paper completely describes the full subcategory L S of G 3 (M) with object set Obj (L S) , as well as the details of the above functor restricted to L S . Thus all the members V ∈ Obj (L S) are determined, as well as the smooth manifold structure on Obj (L S) ; it is embedded as a one-dimensional submanifold of G 3 (M) . The isotropy subgroups of all V ∈ Obj (L S) are computed and all pairs V , W ∈ Obj (L S) which are isomorphic via some M ∈ O (3) are determined. The sets Ξ - ∩ V are all determined, and the functorial mappings on morphism sets are computed. However, L S is not a Lie groupoid. The image of Obj (L S) under the functor π 1 F - is the collection of fibres of the smooth manifold ∐ V ∈ Obj (L S) V , which is the total space of the canonical vector bundle over the base manifold Obj (L S) . The bifurcation points of the family of subsets Ξ - ∩ V as V ranges over Obj (L S) (within this total space) are seen to be the points of Obj (L S) with infinite isotropy subgroups. We also show how this mathematical problem arises naturally from a problem in mathematical chemistry. Hence certain features of numerical calculations of energy eigenvalue intersection patterns of the simple chemical system H3 are rationalized through linearization about the triple intersection point. [ABSTRACT FROM AUTHOR]

Objective. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important imaging modality for breast cancer diagnosis. Intratumoral heterogeneity causes a major challenge in the interpretation of breast DCE-MRI. Previous studies have introduced decomposition methods on DCE-MRI to reveal intratumoral heterogeneity by analyzing distinct dynamic patterns within each tumor. However, these methods estimated the dynamic patterns and their corresponding component coefficients in an unsupervised manner, without considering any clinically relevant information. Approach. To decipher molecular subtype-related dynamic patterns, we propose a weakly supervised nonnegative matrix factorization method (WSNMF), which is able to decompose the pixel kinetics of DCE-MRI with image-level subtype labels. The WSNMF is developed based on a discriminant nonnegative matrix factorization (NMF) to utilize coarse-grained subtype information, in which between- and within-class scatters are defined on the mean vector of component coefficients over all pixels in each tumor, rather than directly on the vector of component coefficients of each pixel. Main results. Experiments demonstrated that the dynamic patterns identified by WSNMF had superior performance in distinguishing between luminal A and the other subtype tumors. The classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). WSNMF yielded better classification performance (AUC = 0.822) than other heterogeneity analysis methods, including two partitioning-based methods (KPC with AUC = 0.697 and TTP with AUC = 0.760) and two unsupervised decomposition-based methods (PCA with AUC = 0.774 and NMF with AUC = 0.797). Significance. Our method adds a valuable new perspective into DCE-MRI decomposition-based heterogeneity analysis by taking advantage of intrinsic tumor characteristics to improve the diagnosis of breast cancer. [ABSTRACT FROM AUTHOR]

We study the discriminants of the minimal polynomials $\mathcal {P}_n$ of the Ramanujan $t_n$ class invariants, which are defined for positive $n\equiv 11\pmod {24}$. We show that $\Delta (\mathcal {P}_n)$ divides $\Delta (H_n)$ , where $H_n$ is the ring class polynomial, with quotient a perfect square and determine the sign of $\Delta (\mathcal {P}_n)$ based on the ideal class group structure of the order of discriminant $-n$. We also show that the discriminant of the number field generated by $j({(-1+\sqrt {-n})}/{2})$ , where j is the j -invariant, divides $\Delta (\mathcal {P}_n)$. Moreover, using Ye's computation of $\log|\Delta(H_n)|$ ['Revisiting the Gross–Zagier discriminant formula', Math. Nachr. 293 (2020), 1801–1826], we show that 3 never divides $\Delta(H_n)$ , and thus $\Delta(\mathcal{P}_n)$ , for all squarefree $n\equiv11\pmod{24}$. [ABSTRACT FROM AUTHOR]

As key players in innovation and entrepreneurial ecosystems, Higher Education Institutions (HEI) assume a position as catalysts in creating and disseminating knowledge with repercussions in the societal, economic, political and innovation environments. In this scenario, HEI are facing the need to balance the performance of their traditional missions—teaching and research—with the pursuit of entrepreneurial performance. This brings awareness of the need to pay particular attention to HEI entrepreneurial performance (HEIEP) and how to measure it. Based on HEInnovate, a self‐assessment tool resulting from a joint effort of the European Community and the OECD, this study aims to explore the benefits of university entrepreneurial metrics, analysing HEIEP as a discriminant function of the HEInnovate dimensions complemented with a qualitative approach using Fuzzy Set Qualitative Comparative Analysis (fsQCA). The analysis provides valuable details, presenting recipes based on the HEInnovate dimensions or combinations of dimensions to achieve a mission legitimation. This research brings awareness to the use of the HEInnovate scale, where it is possible to highlight the importance of the digital transformation and capability dimension to entrepreneurial performance (EP) and university mission legitimation. [ABSTRACT FROM AUTHOR]

Copyright of Mediterranean Journal of Sport Science (MJSS) is the property of Mediterranean Journal of Sport Science (MJSS) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we count the number N 3 tor (X) of 3-dimensional algebraic tori over Q whose Artin conductor is bounded above by X. We prove that N 3 tor (X) ≪ ε X 1 + log ⁡ 2 + ε log ⁡ log ⁡ X , and this upper bound can be improved to N 3 tor (X) ≪ X (log ⁡ X) 4 log ⁡ log ⁡ X under the Cohen-Lenstra heuristics for p = 3. We also prove that for 67 out of 72 conjugacy classes of finite nontrivial subgroups of GL 3 (Z) , Malle's conjecture for tori over Q holds up to a bounded power of log ⁡ X under the Cohen-Lenstra heuristics for p = 3 and Malle's conjecture for quartic A 4 -fields. [ABSTRACT FROM AUTHOR]

Urea is naturally present in milk, yet urea is added intentionally to increase milk's nitrogen content and shelf life. In this study, a total of 50 Ultra heat treatment (UHT) milk samples were spiked with known urea concentrations (0–5 w/v%). Attenuated total reflectance–Fourier transform infrared (ATR-FTIR) spectroscopy with principal component analysis (PCA), discriminant analysis (DA), and multiple linear regression (MLR) were used for the discrimination and quantification of urea. The PCA was built using 387 variables with higher FL > 0.75 from the first PCA with cumulative variability (90.036%). Subsequently, the DA model was built using the same variables from PCA and demonstrated the good distinction between unadulterated and adulterated milk, with a correct classification rate of 98% for cross-validation. The MLR model used 48 variables with p-value < 0.05 from the DA model and gave R2 values greater than 0.90, with RMSE and MSE below 1 for cross-validation and prediction. The DA and MLR models were then validated externally using a test dataset, which shows 100% correct classification, and the t-test result (p > 0.05) indicated that the MLR could determine the percentage of urea in UHT milk within the permission limit (70 mg/mL). In short, the wavenumbers 1626.63, 1601.98, and 1585.5534 cm−1 are suitable as fingerprint regions for detecting urea in UHT milk. [ABSTRACT FROM AUTHOR]

Background and Aim: The multivariate discriminant (MVD) analysis was a successful statistical tool with a discriminatory capacity for tracing sheep breeds based on meat characteristics. Thus, this study aimed to identify three Saudi sheep breeds based on the physical and histochemical aspects of meat using MVD analysis. Materials and Methods: Eight male lambs from each breed, Najdi, Neami, and Harri, were selected randomly at 90 days of age and allocated into three groups for breeding in a completely randomized design. The feeding and rearing management were similar for an experimental period of 90 days. The experimental diet consisted of a concentrated mixture with identical amounts of calories and nitrogen. Fifty-one meat characteristics were measured in the preliminary MVD, representing hot and cold carcass weight, meat cuts and quality measures, body component weights, fat deposit weights, and histochemical characteristics. Results: Out of the total meat characteristics measured, only 19 characteristics had significant discriminant power. The most powerful characteristics were temperature, empty intestinal weight, pH24, external carcass length, heart weight, and L1, based on partial R-square and Wilks' lambda values. The phenotypic associations between the characteristics had strong associations. The obtained principal components efficiently classified the eight individuals of each breed into distinct groups using robust discriminant characteristics. Conclusion: This method allowed us to determine the breed of sheep carcasses and cuts by considering the physical characteristics of the meat. Therefore, butchers and consumers should use scientific techniques for assigning carcasses and meat to their sheep breed after slaughtering.

This paper first defines a bi-parameter ellipse and then place it together with the rectangular hyperbola xy = N to study their intersections. The study reveals several new properties of the intersections that are merely dependent on the two parameters that determine the ellipse. It is also shown that the new properties are available for studying integers and are helpful to develop new method to factorizing integers. Mathematical reasoning is presented in detail for each conclusion and each conclusion is demonstrated with Geogebra software. [ABSTRACT FROM AUTHOR]

Let K = ℚ () be an algebraic number field with a root of an irreducible trinomial f (x) = x 5 + a x + b belonging to ℤ [ x ]. In this paper, we compute the highest power of each prime p dividing the discriminant of K in terms of powers of p dividing a , b and the discriminant of f (x) besides explicitly constructing a p -integral basis of K. These p -integral bases lead to the construction of an integral basis of K which is illustrated with examples. [ABSTRACT FROM AUTHOR]

Background: Nerve Conduction Velocities (NCVs) measures electrical changes and speed in the nerve. Objectives of this study were: to compare mean velocities, to find rank of importance of different velocities and to frame equation to classify severely acute malnourished (SAM) children with normal children. Material & Methods: Present case- control study was conducted on 50 SAM children and 50 normal children aged 6 months to 59 months. Independent t test and Discriminant analysis was performed. Standardized discriminant coefficient, canonical correlation and Wilks’ Lambda was calculated and p value was judges at 5% level of significance. Results: NCVs were observed significantly lower among the cases as compared with the controls. Sural Sensory Nerve Velocity holds first position followed by Sensory Nerve Velocity. So, in final discriminant model 3 variables i.e., Sural Sensory Nerve Velocity; Median Sensory Nerve Velocity; Tibial Motor Nerve Velocity were used and 42.1 % of the total variance in the discriminant scores not explained by differences among the groups by the three-variable model. Model is able to classify 82.5% cases correctly. Conclusion: Sural Sensory Nerve Velocity; Median Sensory Nerve Velocity; Tibial Motor Nerve Velocity were found as most important nerve conduction velocities with a good classification ability.

We consider discriminant Δ n of a general polynomial of degree n and Newton polytope N for the discriminant, and prove that Newton polytopes with truncations of Δ n with respect to faces N are the Minkowski sums of Newton polytopes for the discriminants of the polynomials of lower degrees. [ABSTRACT FROM AUTHOR]

Copyright of Global Journal of Economics & Business is the property of Refaad for Studies, Research & Development and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we study the discriminant of a hypersurface in a weighted projective space with isolated singularities. We define the discriminant of a hypersurface in ℙ (q 0 , q 1 , 1 , ... , 1) with gcd (q 0 , q 1) = 1 , and show that it satisfies a smoothness criterion over any commutative ring. A smooth hypersurface of degree 6 in the weighted projective three-fold ℙ (3 , 2 , 1 , 1) is a del Pezzo surface of degree 1. We show that the determinant of the Galois action on the E 8 -lattice arising from its exceptional curves can be computed via the square roots of the discriminant. [ABSTRACT FROM AUTHOR]

In this note, we introduce an idea of deriving some inequalities, using the discriminants of polynomials. This gives another proof of the famous Hölder's inequality. [ABSTRACT FROM AUTHOR]

The article presents a classification methodology of regional development in Romania (41 counties and Bucharest) using a set of data registered in 2019 by the National Institute of Statistics. Several indicators cover information related to the population (the migration, permanent residence, and education), local investments, private turnover, and investments in water supply and sewerage systems, including waste management. After applying the statistical tests, the separation of the counties was done in three classes, the delimitation indicating a high percentage of 59.5% of regions that have low values of the selected indicators. These regions require major investments that will lead to rising living standards, and the emergence of new jobs, driving down the average age of the population. 21.4% of the regions present an average level of the analyzed indicators while only 19% registered the highest values of the parameters, indicating urban agglomerations and a high level of industrial development.

A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial equations admits two or more positive roots. Much recent work has focused on analyzing multistationarity regions of biologically significant reaction networks and determining whether such regions are connected; indeed, a better understanding of the topology and geometry of such regions may help elucidate how robust multistationarity is to perturbations. Here we focus on the multistationarity regions of small networks, those with few species and few reactions. For two families of such networks – those with one species and up to three reactions, and those with two species and up to two reactions – we prove that the resulting multistationarity regions are connected. We also give an example of a network with one species and six reactions for which the multistationarity region is disconnected. Our proofs rely on the formula for the discriminant of a trinomial, a classification of small multistationary networks, and a recent result of Feliu and Telek that partially generalizes Descartes' rule of signs. [ABSTRACT FROM AUTHOR]