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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.

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.

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

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.

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.

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]

We prove that for each odd integer d ≥ 3 there are infinitely many number fields K of degree d such that each generator α of K has Mahler measure greater than or equal to d-d|ΔK|d+1/d(2d-2), where ΔK is the discriminant of the field K. This, combined with an earlier result of Vaaler and Widmer for composite d, answers negatively a question of Ruppert raised in 1998 about 'small' algebraic generators for every d ≥ 3. We also show that for each d ≥ 2 and any ε > 0, there exist infinitely many number fields K of degree d such that every algebraic integer generator α of K has Mahler measure greater than (1 - ε|ΔK|1/d. On the other hand, every such field K contains an algebraic integer generator α with Mahler measure smaller that |ΔK|1/d. This generalizes the corresponding bounds recently established by Eldredge and Petersen for d = 3. [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. [ABSTRACT FROM AUTHOR]

If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

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.

Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F , whose components satisfy the same relations. [ABSTRACT FROM AUTHOR]

State-owned enterprises (BUMN) are business entities that are not only responsible for profit creation but also as a source of state revenue. This study aims to detect the financial health of BUMN using Financial Discriminant Models, namely the Springate and Taffler Models. The analysis was carried out on the BUMN financial reports for the 2014-2018 period of 16 companies with 80 financial reports being analyzed. The results of this study show that by using the Springate Model, it is known that 2017 is the best year, no BUMN is experiencing financial distress. 2018 was the worst year with 12 BUMNs declared financial distress and only 4 companies categorized as healthy. The results of the analysis with the Taffler Model show that in 2014 all BUMNs were categorized as healthy and only 1 company was declared to have financial distress.

This study aims to examine online learning effects regarding self-efficacy, generalized anxiety, and fear of COVID-19 on three distinct online learning satisfaction levels (low, moderate, and high) among university students. A cross-sectional survey was utilized for data collection between June 2020 and August 2020 to assess students' online self-efficacy, general anxiety, fear of COVID-19, and online learning satisfaction. The descriptive data analysis demonstrated a fundamental understanding of the gathered data results. Meanwhile, discriminant data analysis was employed to explore different online learning satisfaction levels following various study factors. The correlational analysis implied online learning self-efficacy to be significantly and positively associated with online learning satisfaction while general anxiety and fear of COVID-19 were significantly and negatively related to online learning satisfaction. The discriminant analysis revealed the emergence of three online learning satisfaction levels from online self-efficacy, general anxiety, and fear of COVID-19. This study theoretically justified the essentiality of online learning self-efficacy towards online learning satisfaction. High online learning satisfaction levels occurred with high online self-efficacy, moderate general anxiety, and low fear of COVID-19. Two discriminant functions (academic engagement and fear) were subsequently evolved. Academic engagement corresponded to online self-efficacy and general anxiety while fear was associated with COVID-19. In this vein, online learning self-efficacy and moderate general anxiety led to high online learning satisfaction. The fear of COVID-19 also required alleviation towards online learning satisfaction. For example, academicians and policymakers needed to focus on developing online self-efficacy and reducing the fear of COVID-19 for high online learning satisfaction.

If K is the splitting field of the polynomial f(x) = x4 + px² + p and p is a rational prime of the form 4+n², we give appropriate generators of K to obtain the explicit factorization of the ideal qOK, where q is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals. [ABSTRACT FROM AUTHOR]

Background and Aim: The authentication of honey is important to protect industry and consumers from such adulterated honey. However, until now, there has been no guarantee of honey's authenticity, especially in Indonesia. The classification of honey is based on the bee species (spp.) that produces it. The study used honey from sting bee Apis spp. and stingless bee Tetragonula spp. based on the fact that the content off honey produced between them has differences. Authenticating honey with currently available rapid detection methods, such as 13C nuclear magnetic resonance analysis, is costly. This study aimed to develop an inexpensive, fast, precise, and accurate classification method for authenticating honey. Materials and Methods: In this study, we use attenuated total reflectance Fourier-transform infrared (ATR-FTIR) spectroscopy with wavelengths ranging between 550 and 4000 cm-1 as an alternative analysis method, which is relatively less expensive. The spectra of authentic and fake honey samples were obtained using ATR-FTIR and plotted using chemometric discriminant analysis. The authentic honey samples were acquired from a local Indonesian breeder of honey bees, while the fake honey samples were made from a mixture of water, sugar, sodium bicarbonate, and authentic honey. Data were collected using Thermo Scientific's OMNIC FTIR software and processed using Thermo Scientific's TQ Analyst software. Results: Our method effectively classified the honey as authentic or fraudulent based on the FTIR spectra. To authenticate the honey, we formed two classes: Real honey and fake honey. The wavelengths that can best differentiate between these two classes correspond to four regions: 1600-1700 cm-1; 1175-1540 cm-1; 940-1175 cm-1; and 700-940 cm-1. Similarly, for classification purpose, we formed two classes: Apis spp. and Tetragonula spp. The wavelength region that can best classify the samples as belonging to the Apis spp. or Tetragonula spp. class is explicitly within the range of 1600-1700 cm-1. Conclusion: This study successfully demonstrated a method to rapidly and accurately classify and authenticate honey. ATR-FTIR is a useful tool to test the authenticity of honey.

We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the "apparent contour" of a single projection to the projective plane. We deal with the case of tangent developables and of general projections to P 3 of rational normal scrolls. In the first case, we use the fact that every such surface is the projection of the tangent developable of a rational normal curve, while in the second we start by reconstructing the rational normal scroll. In both instances we then reconstruct the correct projection to P 3 of these surfaces by exploiting the information contained in the singularities of the apparent contour. [ABSTRACT FROM AUTHOR]

We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several polynomial equations and one inequation in the coefficients, by using repeated parametric gcd's. In this paper, we give a novel condition which is not based on repeated gcd's. Furthermore, it is shown that the number of polynomials in the condition is optimal and the degree of polynomials is smaller than that in the previous condition based on repeated gcd's. [ABSTRACT FROM AUTHOR]

Let K be a number field. We investigate the indices I(K) and i(K) of K introduced respectively by Dedekind and Gunji-McQuillan. Let n be a positif integer, we then prove that for any prime p < n, there exists K a number field of degree n over Q such that p divide i(K). This result is an analogue to Bauer's one for i(K). We compute I(K) and i(K) for cubic fields and infinite families of simplest number fields of degree less than 7. We solve questions and disprove the conjecture stated in [1 ]. [ABSTRACT FROM AUTHOR]

Population variations in the dengue vector mosquito, Aedes aegypti (Linneaus) was examined using landmark based Geometric Morphometric methods of the left and right wings for both sexes from among three locations in the city of Cagayan de Oro, Philippines. Relative Warp Analysis (RWA) was conducted on both wings based on shape scores for the detection of variations within and between the three populations. Canonical variate analysis (CVA) of the relative warp scores yielded Wilk's lambda that were very near zero and Pillai trace that were at or near values of 1 indicating that wing shape scores among the three populations of mosquito had means that were different from each other. Discriminant analysis have shown the three Aedes aegypti populations differ significantly (>70% correct classification) based on the male's left and right wings and the females' right wing. The rural population was also correctly classified based on the right wings of both sexes. What is interesting in the results is that all three populations were not correctly classified based on the female's left wing. These indicate that the wings of the rural male and all the female populations of Aedes aegypti were asymmetrical in shapes which may be due to genetic, developmental, or as a result of environmental processes and are "probably normally adaptive". These findings strongly demonstrate strong infraspecific variations in wing structures of Aedes aegypti at different areas of Cagayan de Oro City.

Let n > 1 be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form ℚ ( x 2 − 2 y n ) whose ideal class group has an element of order n. This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups. [ABSTRACT FROM AUTHOR]

Background: Literature on the validity of outcome measurement in lymphedema and lipedema is very sparse. This study aimed to examine the convergent, divergent and discriminant validity of a set of 5 instruments in both conditions.Methods: Cross-sectional outcome was measured by the generic Short Form 36 (SF-36), the lymphedema-specific Freiburg Quality of Life Assessment for lymphatic disorders, Short Version (FLQA-lk), the knee-specific Knee Outcome Survey Activities of Daily Living Scale (KOS-ADL), the Symptom Checklist-90-revised (SCL-90R), and the Six-Minute Walk Test (6 MWT). Construct convergent/divergent validity was quantified by bivariate correlations and multivariate factor analysis, and discriminant validity by standardized mean differences (SMDs).Results: Health was consistently better in lymphedema (n = 107) than in lipedema (n = 96). The highest construct convergence was found for physical health between the SF-36 and KOS-ADL (bivariate correlations up to 0.78, factor loads up to 0.85, explained variance up to 56.8%). The second most important factor was mental health (bivariate correlations up to 0.79, factor loads up to 0.86, explained variance up to 13.3%). Discriminant validity was greatest for the FLQA-lk Physical complaints (adjusted SMD = 0.93) followed by the SF-36 Bodily pain (adjusted SMD = 0.83), KOS-ADL Function (adjusted SMD = 0.47) and SF-36 Vitality (adjusted SMD = 0.39).Conclusions: All five instruments have specific strengths and can be implemented according to the scope and aim of the outcome examination. A minimum measurement set should comprise: the SF-36 Bodily pain, SF-36 Vitality, FLQA-lk Physical complaints, FLQA-lk Social life, FLQA-lk Emotional well-being, FLQA-lk Health state, KOS-ADL Symptoms, KOS-ADL Function, and the SCL-90R Interpersonal sensitivity. [ABSTRACT FROM AUTHOR]

In this paper, we show that if a vector bundle of rank n 1 on projective ðn 1Þspace is very ample and if its top Chern class is greater than one, then the discriminant locus of the vector bundle, the locus of singular sections of the vector bundle, is an irreducible hypersurface and that the degree of the hypersurface can be expressed as a function of invariants of the vector bundle. As applications, we study the eigendiscriminant locus (the locus of tensors whose eigenschemes are singular) and the discriminant locus of the generic graded matrix (the locus of singular determinantal schemes). [ABSTRACT FROM AUTHOR]

We determine the 166104 extremal monomials of the discriminant of a quaternary cubic form. These are in bijection with D-equivalence classes of regular triangulations of the 3-dilated tetrahedron. We describe how to compute these triangulations and their D-equivalence classes in order to arrive at our main result. The computation poses several challenges, such as dealing with the sheer number of triangulations effectively, as well as devising a suitably fast algorithm for computation of a D-equivalence class. [ABSTRACT FROM AUTHOR]

We compute and study two determinantal representations of the discriminant of a cubic quaternary form. The first representation is the Chow form of the 2-uple embedding of ℙ³ and is computed as the Pfaffian of the Chow form of a rank 2 Ulrich bundle on this Veronese variety. We then consider the determinantal representation described by Nanson. We investigate the geometric nature of cubic surfaces whose discriminant matrices satisfy certain rank conditions. As a special case of interest, we use certain minors of this matrix to suggest equations vanishing on the locus of k-nodal cubic surfaces. [ABSTRACT FROM AUTHOR]

This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special ‘external’ devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision that should be recommended for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher’s discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a rich fine-grained structure with many clusters and corresponding peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. On the basis of these theorems, the multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including the correlation transformation, supervised Principal Component Analysis (PCA), semi-supervised PCA, transfer component analysis, and new domain adaptation PCA.

A new determinantal representation for the implicit equation of offsets to conics and quadrics is derived. It is simple, free of extraneous components and provides a very compact expanded form, these representations being very useful when dealing with geometric queries about offsets such as point positioning or solving intersection purposes. It is based on several classical results in “A Treatise on the Analytic Geometry of Three Dimensions” by G. Salmon for offsets to non-degenerate conics and central quadrics.

Recently, Otake and Shaska have given a formula for the discrim- inant of quadrinomials of the form f(x) = xn + t(x² + ax + b). In their concluding remarks, they ask if a formula can be found for the discriminant of f(x) = xn + tg(x) when n > deg(g) = 3. Assuming that f(x) = xn + tg(x) is irreducible, and under certain restrictions on a polynomial related to g(x), in this article we give a formula for the discriminant of f(x), regardless of deg(g) ≥ 1. We then use our discriminant formula to generate some new in- finite families of monogenic polynomials f(x) = xn + tg(x) with n > deg(g), when g(x) is monic and deg(g) ∊ {2; 3; 4}. [ABSTRACT FROM AUTHOR]

Let (K, |·|) be a local field. In this paper we define an invariant analogous to the discriminant over K for certain transcendental elements over K. [ABSTRACT FROM AUTHOR]

We determine all degree 7 number fields where the absolute value of the discriminant is ≤ 2 ⋅ 10 8. To accomplish this large-scale computation, we distributed the computation over many servers on the internet through the BOINC network. [ABSTRACT FROM AUTHOR]

Background and Aim: The authentication of honey is important to protect industry and consumers from such adulterated honey. However, until now, there has been no guarantee of honey's authenticity, especially in Indonesia. The classification of honey is based on the bee species (spp.) that produces it. The study used honey from sting bee Apis spp. and stingless bee Tetragonula spp. based on the fact that the content off honey produced between them has differences. Authenticating honey with currently available rapid detection methods, such as 13C nuclear magnetic resonance analysis, is costly. This study aimed to develop an inexpensive, fast, precise, and accurate classification method for authenticating honey. Materials and Methods: In this study, we use attenuated total reflectance Fourier-transform infrared (ATR-FTIR) spectroscopy with wavelengths ranging between 550 and 4000 cm-1 as an alternative analysis method, which is relatively less expensive. The spectra of authentic and fake honey samples were obtained using ATR-FTIR and plotted using chemometric discriminant analysis. The authentic honey samples were acquired from a local Indonesian breeder of honey bees, while the fake honey samples were made from a mixture of water, sugar, sodium bicarbonate, and authentic honey. Data were collected using Thermo Scientific's OMNIC FTIR software and processed using Thermo Scientific's TQ Analyst software. Results: Our method effectively classified the honey as authentic or fraudulent based on the FTIR spectra. To authenticate the honey, we formed two classes: Real honey and fake honey. The wavelengths that can best differentiate between these two classes correspond to four regions: 1600-1700 cm-1; 1175-1540 cm-1; 940-1175 cm-1; and 700-940 cm-1. Similarly, for classification purpose, we formed two classes: Apis spp. and Tetragonula spp. The wavelength region that can best classify the samples as belonging to the Apis spp. or Tetragonula spp. class is explicitly within the range of 1600-1700 cm-1. Conclusion: This study successfully demonstrated a method to rapidly and accurately classify and authenticate honey. ATR-FTIR is a useful tool to test the authenticity of honey. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we develop a general theory of quasi-orthogonal polynomials. We first derive three-term recurrence relation and second-order differential equations for quasi-orthogonal polynomials. We also give an expression for their discriminants in terms of the recursion coefficients of the corresponding orthogonal polynomials. In addition, we investigate an electrostatic equilibrium problem where the equilibrium position of movable charges is attained at the zeros of the quasi-orthogonal polynomials. The examples of the Freud weight w (x) = e − x 4 + 2 t x 2 and the Jacobi weight w (x) = (1 − x) α (1 + x) β are discussed in some detail. Finally, we consider the nonlinear orthogonality preserving transformation and related matrix problem. [ABSTRACT FROM AUTHOR]

In [9] and [10], Filip Najman examined the torsion of elliptic curves over the number fields ℚ(−1) and ℚ(−3). In this paper, we study the torsion structures of elliptic curves over the real quadratic number fields ℚ(2) and ℚ(5), which have the smallest discriminants among all real quadratic fields ℚ(d) with d ≢ 1 mod 4 and d ≡ 1 mod 4 respectively. [ABSTRACT FROM AUTHOR]

We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because arbitrary systems split into reduced irreducible ones upon monomial changes of variables. In particular, our result proves the multivariate version of the Abel–Ruffini theorem: the classification of general systems of equations solvable by radicals reduces to the classification of lattice polytopes of mixed volume 4 (which we prove to be finite in every dimension). We also notice that the monodromy of every general system of equations is either symmetric or imprimitive. The proof is based on a new result of independent importance regarding dual defectiveness of systems of equations: the discriminant of a reduced irreducible square system of general polynomial equations is a hypersurface unless the system is linear up to a monomial change of variables. [ABSTRACT FROM AUTHOR]

Computing the intersection curves of two quadrics (QSIC) is a fundamental problem in computer aided design system, where the topology analysis of the QSIC is an essential task to realize the robust computation. In this paper, a new method is proposed to classify the topology of the QSIC in three dimensional projective space by using a set of discriminants associated with the two quadrics. The new topology classification method presents explicit representations and can be applied even when the coefficients of the two quadrics contain symbols. Some examples are provided to illustrate the usage of the new classification method. • A new method is presented to classify the topology of the intersection curves of two quadrics. • The classification is determined by a set of discriminants to provide explicit representations. • The new method can be applied even when the coefficients of the two quadrics contain symbols. [ABSTRACT FROM AUTHOR]