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We consider stationary Schrödinger equations with indefinite potential and nonlinearity sublinear at u = 0. Using linking theorem and symmetric mountain pass theorem, existence and multiplicity results are obtained. [ABSTRACT FROM AUTHOR]

Green mould contamination causes a significant challenge to mushroom growers in Malaysia leading to reduced yields and economic losses in the widely cultivated and marketed edible grey oyster mushroom, Pleurotus pulmanorius. This study aimed to identify the causal agents of green mould contaminants and determine the critical points in the cultivation process in the farm that contribute to green mould contamination. Samples of mushroom substrate (sawdust), spawn substrate (corn), environmental sources and tools were collected at different stages of mushroom cultivation. As results, the causal agents of green mould contamination were identified as Trichoderma pleuroti , T. harzianum and T. ghanese. Prior to steam pasteurisation and after steam pasteurisation, the spawn substrate and mushroom substrate were found to be free of Trichoderma. However, Trichoderma was detected in water, air within the production house and on cleaning tools. This findings suggests that water could serve as the source of green mould introduction in mushroom farms, while cultivation practices such as watering and scratching during the harvesting cycle may contribute to adverse green mould. Understanding these critical points and causal agents provides information to mitigate the green mould contamination throughout the grey oyster mushroom cultivation process. [Display omitted] • Pleurotus mushroom cultivation in Malaysia faces contamination by green mould. • T. pleuroti is the main causal agent followed by T. harzianum and T. ghanense. • Water is the primary source followed by air inside the production house. • Watering is one of critical points in mushroom cultivation. [ABSTRACT FROM AUTHOR]

We strengthen the Weierstrass approximation theorem by proving that any real-valued continuous function on an interval I ⊂ R can be uniformly approximated by a real-valued polynomial whose only (possibly complex) critical points are contained in I . The proof uses a perturbed version of the Chebyshev polynomials and an application of the Brouwer fixed point theorem. [ABSTRACT FROM AUTHOR]

We count the number of critical points of a modular form with real Fourier coefficients in a γ-translate of the standard fundamental domain ℱ (with γ ∈SL2(ℤ)). Whereas by the valence formula the (weighted) number of zeros of this modular form in γℱ is a constant only depending on its weight, we give a closed formula for this number of critical points in terms of those zeros of the modular form lying on the boundary of ℱ, the value of γ−1(∞) and the weight. More generally, we indicate what can be said about the number of zeros of a quasimodular form. [ABSTRACT FROM AUTHOR]

Recently, the authors proved in [C. Lizana and W. Ranter, Topological obstructions for robustly transitive endomorphisms on surfaces, Adv. Math. 390 (2021), pp. 107901] that every $ C^1 $ C 1 -robustly transitive toral endomorphism displaying critical points must be homotopic to a linear endomorphism having at least one eigenvalue with modulus greater than one. Here, we exhibit some examples of $ C^1 $ C 1 -robustly transitive surface endomorphisms displaying critical points in certain homotopy classes. [ABSTRACT FROM AUTHOR]

Different biological models can be evaluated using mathematical models in both qualitative and quantitative ways. A fractional bone mineralization model involving Caputo’s fractional derivative is presented in this work. The fractional mathematical model is beneficial because of its memory carrying property. An appropriate fractional order of the derivative can be chosen that is more closely related to experimental or actual data. The dynamical system of equations for the process of bone mineralization is examined qualitatively and quantitatively in this article. A numerical simulation has been performed for the model. The model’s parameters have undergone sensitivity analysis and their effects on the model variables have been explored. By studying the mineralization patterns in bone, different diseases can be cured, and it can also be examined how the deviations from healthy mineral distributions lead to specific bone diseases. [ABSTRACT FROM AUTHOR]

Let f be a Gaussian random field on R d and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has finite moments. So far, this has been established only for moments of order lower than three. In this paper, we prove the conjecture. Precisely, we show that X has finite moment of order p, as soon as, at any given point, the Taylor polynomial of order p of f is non-degenerate. We present a simple and general approach that is not specific to critical points and we provide various applications. In particular, we show the finiteness of moments of the nodal volumes and the number of critical points of a large class of smooth, or holomorphic, Gaussian fields, including the Bargmann-Fock ensemble. [ABSTRACT FROM AUTHOR]

Abstract Accurate structure elucidation of biologically active molecules is crucial for designing and developing new drugs, as well as for analyzing their pharmacological activity. In this study, density functional theory calculations are applied to explore the electronic structure and properties of phenethylamine derivatives, including Amphetamine, Methamphetamine, and Methylene Dioxy Methamphetamine(MDMA). The investigation encompasses various aspects such as geometry optimization, vibrational analysis, electronic properties, Molecular Electrostatic Potential analysis, and local and global descriptor analysis. Additionally, the study utilizes Natural Bond Orbital analysis and Quantum Theory of Atoms in Molecules to investigate the chemical bonding and charge density distributions of these compounds. Experimental techniques such as Fourier transform infrared (FT-IR) and Raman spectroscopic analysis are employed in the range of 4000-400 $$cm^{-1}$$ c m - 1 and 4000-50 $$cm^{-1}$$ c m - 1 , respectively. Theoretical vibrational analysis with Potential Energy Distribution(PED) assignments is conducted, and the resulting frequencies are compared to experimental spectral data, revealing good agreement. By correlating various structural parameters with the pharmacological activity of each derivative, computational structure elucidation aids in understanding the unique actions of phenethylamine derivatives. The obtained results offer a comprehensive understanding of the molecular behavior and properties of these drugs, facilitating the development of new drugs and therapies for addiction and related disorders.

For every nonconstant rational function ϕ ∈ ℚ (x) , the Galois groups of the dynatomic polynomials of ϕ encode various properties of ϕ are of interest in the subject of arithmetic dynamics. We study here the structure of these Galois groups as ϕ varies in a particular one-parameter family of maps, namely, the quadratic rational maps having a critical point of period 2. In particular, we provide explicit descriptions of the third and fourth dynatomic Galois groups for maps in this family. [ABSTRACT FROM AUTHOR]

The present work deals with a FLRW cosmological model with spatial curvature and minimally coupled scalar field as the matter content. The curvature term behaves as a perfect fluid with the equation of state parameter ωK = -13. Using suitable transformation of variables, the evolution equations are reduced to an autonomous system for both power law and exponential form of the scalar potential. The critical points are analyzed with center manifold theory and stability has been discussed. Also, critical points at infinity have been studied using the notion of Poincaré sphere. Finally, the cosmological implications of the critical points and cosmological bouncing scenarios are discussed. It is found that the cosmological bounce takes place near the points at infinity when the non-isolated critical points on the equator of the Poincaré sphere are saddle or saddle-node in nature. [ABSTRACT FROM AUTHOR]

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features. [ABSTRACT FROM AUTHOR]

Our main aim is introduced some concepts in dynamical system in rough theory. We give the definition of periodic points and critical points and investigate their properties in rough actions. Also, we illustrated the relation between them. [ABSTRACT FROM AUTHOR]

We carry out complete membership to Kaplan classes of functions given by formula { ζ ∈ C : | ζ | < 1 } ∋ z ↦ ∏ k = 1 n (1 - z e - i t k ) p k , where n ∈ N , t k ∈ [ 0 ; 2 π) and p k ∈ R for k ∈ N ∩ [ 1 ; n ] . In this way we extend Sheil-Small’s, Jahangiri’s and our previous results. Moreover, physical and geometric applications of the obtained gap condition are given. The first one is an interpretation in terms of mass and density. The second one is a visualization in terms of angular inequalities between vectors in R 2 . [ABSTRACT FROM AUTHOR]

Accurate structure elucidation of biologically active molecules is crucial for designing and developing new drugs, as well as for analyzing their pharmacological activity. In this study, density functional theory calculations are applied to explore the electronic structure and properties of phenethylamine derivatives, including Amphetamine, Methamphetamine, and Methylene Dioxy Methamphetamine(MDMA). The investigation encompasses various aspects such as geometry optimization, vibrational analysis, electronic properties, Molecular Electrostatic Potential analysis, and local and global descriptor analysis. Additionally, the study utilizes Natural Bond Orbital analysis and Quantum Theory of Atoms in Molecules to investigate the chemical bonding and charge density distributions of these compounds. Experimental techniques such as Fourier transform infrared (FT-IR) and Raman spectroscopic analysis are employed in the range of 4000-400 c m - 1 and 4000-50 c m - 1 , respectively. Theoretical vibrational analysis with Potential Energy Distribution(PED) assignments is conducted, and the resulting frequencies are compared to experimental spectral data, revealing good agreement. By correlating various structural parameters with the pharmacological activity of each derivative, computational structure elucidation aids in understanding the unique actions of phenethylamine derivatives. The obtained results offer a comprehensive understanding of the molecular behavior and properties of these drugs, facilitating the development of new drugs and therapies for addiction and related disorders. [ABSTRACT FROM AUTHOR]

This article presents a novel and powerful goodness-of-fit test specifically designed for the Cauchy distribution. The motivation behind our research stems from the need for a more accurate and robust method to assess the fit of the Cauchy distribution to data. This distribution is known for its heavy tails and lack of finite moments. To compute the proposed test statistic, we utilize the maximum likelihood estimators of the unknown parameters, ensuring the test efficiency and reliability. In addition, Monte Carlo simulations are employed to obtain critical points of the test statistic for different sample sizes, enabling precise determination of the threshold for rejecting the null hypothesis. To assess the performance of the proposed test, we conduct power comparisons against several well-known competing tests, considering various alternative distributions. Through extensive simulations, we demonstrate the superiority of our test in the majority of the cases examined, highlighting its effectiveness in distinguishing departures from the Cauchy distribution. The contributions of our study are twofold. Firstly, we introduce a novel goodness-of-fit test tailored specifically for the Cauchy distribution, taking into account its unique characteristics. By incorporating the maximum likelihood estimate and employing Monte Carlo simulations, our test offers improved accuracy and robustness compared to existing methods. Furthermore, we provide practical validation of the proposed test through the analysis of a financial dataset. The application of the test to real-world data underscores its relevance and applicability in practical scenarios. [ABSTRACT FROM AUTHOR]

The 3D point cloud deep neural network (3D DNN) has achieved remarkable success, but its black-box nature hinders its application in many safety-critical domains. The saliency map technique is a key method to look inside the black-box and determine where a 3D DNN focuses when recognizing a point cloud. Existing point-wise point cloud saliency methods are proposed to illustrate the point-wise saliency for a given 3D DNN. However, the above critical points are alternative and unreliable. The findings are grounded on our experimental results which show that a point becomes critical because it is responsible for representing one specific local structure. However, one local structure does not have to be represented by some specific points, conversely. As a result, discussing the saliency of the local structure (named patch-wise saliency) represented by critical points is more meaningful than discussing the saliency of some specific points. Based on the above motivations, this paper designs a black-box algorithm to generate patch-wise saliency map for point clouds. Our basic idea is to design the Mask Building-Dropping process, which adaptively matches the size of important/unimportant patches by clustering points with close saliency. Experimental results on several typical 3D DNNs show that our patch-wise saliency algorithm can provide better visual guidance, and can detect where a 3D DNN is focusing more efficiently than a point-wise saliency map. Finally, we apply our patch-wise saliency map to adversarial attacks and backdoor defenses. The results show that the improvement is significant. [ABSTRACT FROM AUTHOR]

In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem $ -\Delta u = f(x, y) $ finding a geometric condition involving the curvature of the boundary and the normal derivative of $ f $ on the boundary to ensure uniqueness of the critical point. In the second part we consider stable solutions of the nonlinear problem $ -\Delta u = f(u) $ in perturbation of convex domains. [ABSTRACT FROM AUTHOR]

We relate the Brasselet number of a complex analytic function-germ defined on a complex analytic set to the critical points of its real part on the regular locus of the link. Similarly we give a new characterization of the Euler obstruction in terms of the critical points on the regular part of the link of the projection on a generic real line. As a corollary, we obtain a new proof of the relation between the Euler obstruction and the Gauss–Bonnet measure, conjectured by Fu. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions for the quasilinear elliptic equations \[ -\Delta_{p}u-\Delta_{p}(|u|^{2\alpha})|u|^{2\alpha-2}u+V(x)|u|^{p-2}u=|u|^{q-2}u,\quad x\in \mathbb{R}^{N}, \] − Δ p u − Δ p (| u | 2 α) | u | 2 α − 2 u + V (x) | u | p − 2 u = | u | q − 2 u , x ∈ R N , where $ \alpha \geq 1 $ α ≥ 1 , 10 $ V (x) > 0 is a continuous function. In this work, we mainly focus on nontrivial solutions. When $ 2\alpha p 2 αp < q < p ∗ , we establish the existence of nontrivial solutions by using Mountain-Pass lemma; when $ q\geq 2\alpha p^{\ast } $ q ≥ 2 α p ∗ , by using a Pohozaev type variational identity, we prove that the equation has no nontrivial solutions. [ABSTRACT FROM AUTHOR]

This paper investigates various aspects of the distribution of roots and critical points of a complex polynomial, including their variance and the relationships between their moduli using an inequality due to de Bruijn. Making use of two other inequalities-again due to de Bruijn-we derive two probabilistic results concerning upper bounds for the average moduli of the imaginary parts of zeros and those of critical points, assuming uniform distribution of the zeros over a unit disc and employing the Markov inequality. The paper also provides an explicit formula for the variance of the roots of a complex polynomial for the case when all the zeros are real. In addition, for polynomials with uniform distribution of roots over the unit disc, the expected variance of the zeros is computed. Furthermore, a bound on the variance of the critical points in terms of the variance of the zeros of a general polynomial is derived, whereby it is established that the variance of the critical points of a polynomial cannot exceed the variance of its roots. Finally, we conjecture a relation between the real parts of the zeros and the critical points of a polynomial. [ABSTRACT FROM AUTHOR]

In this note we prove a result that highlights an interesting connection between the structure of the zeros of a polynomial \(p(z)\) and Sendov's conjecture.

In this paper, we consider a fractional p-Laplacian elliptic Dirichlet problem that possesses one control parameter and has a Lipschitz nonlinearity order of p - 1 {p-1} . The multiplicity of the weak solutions is proved by means of the variational method and critical point theory. We investigate the existence of at least three solutions to the problem. [ABSTRACT FROM AUTHOR]

A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynomials, we show that there are only finitely many continuous selections of it and each one is semi-algebraic. Then, we establish some generic properties regarding the critical points, defined by the Clarke subdifferential, of these continuous selections. In particular, given a set of finitely many polynomials with generic coefficients, we show that the critical points of all continuous selections of it are finite and the critical values are all different, and we also derive the coercivity of those continuous selections which are bounded from below. We point out that some existing results about Łojasiewicz’s inequality and error bounds for the maximum function of some finitely many polynomials can be extended to all the continuous selections of them. [ABSTRACT FROM AUTHOR]

AbstractEnzymes are absolutely essential biological catalysts in human body that catalyze all cellular processes in physiological network. However, there are certain low molecular weight chemical compounds known as inhibitors, that reduce or completely inhibit the enzyme catalytic activity. Mathematical modeling plays a key role in the control and stability of metabolic enzyme inhibition. Enzyme stability is an important issue for protein engineers, because of its great importance and impact on optimal utility of material in biological tissues. In this outlook, we have first determined the existence of traveling wave solution for the enzyme-inhibitor system and then emphasized the stability of critical points that arise in the reactions. The study of traveling wave solution of an enzyme-inhibitor system with reaction diffusion equations involve quite complex mathematical analysis. The results obtained in this model indicate that the traveling wave solution may give a well explained method for improving enzyme kinetic stability. The present study will be helpful in understanding the stability of critical points of an enzyme-inhibitor system to give an idea about the inhibition of less stable enzymes. Moreover, the role of diffusion on the enzyme activity has been exhaustively discussed using mathematical tools related to eigen values and eigen function analysis. [ABSTRACT FROM AUTHOR]

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the first serious step. This yields a descent direction for the original objective function, and it is shown that a stepsize of at least one is accepted in this way. Using a line search, even larger stepsizes are possible. The overall method is shown to be globally convergent to critical points of DC programs. The new algorithm is tested and compared to some other solution methods on several examples and realistic applications. [ABSTRACT FROM AUTHOR]

We show that robustly transitive endomorphisms of a closed manifold must have a non-trivial dominated splitting or be a local diffeomorphism. This allows to get some topological obstructions for the existence of robustly transitive endomorphisms. To obtain the result, we must understand the structure of the kernel of the differential and the recurrence to the critical set of the endomorphism after perturbation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse the Italian dubbed and subtitled translations of selected episodes from the American TV series Sex and the City and its sequel And Just Like That. The analysis delves into the translation from English into Italian of the dialogues that are imbued with cultural references. The study examines the translation choices concerning swear words and idiomatic expressions by comparing the dubbed and subtitled versions. Starting from Munday's theories, it aims to identify critical points in translational decision-making, namely, phrases and fragments of dialogues that require particular interpretations on the part of the translator. The study attempts to determine the extent to which the approach to translation from English into Italian is target audience-oriented. Finally, by considering the concept of linguaculture, the work explores the impact of this approach on the target culture in order to compare the American and Italian linguacultures. [ABSTRACT FROM AUTHOR]

In the theory of gene networks, the mathematical apparatus that uses dynamical systems is fruitfully used. The same is true for the theory of neural networks. In both cases, the purpose of the simulation is to study the properties of phase space, as well as the types and the properties of attractors. The paper compares both models, notes their similarities and considers a number of illustrative examples. A local analysis is carried out in the vicinity of critical points and the necessary formulas are derived. [ABSTRACT FROM AUTHOR]

In this article, we mainly study the critical points of solutions to the Laplace equation with Dirichlet boundary conditions in an exterior domain in ℝ2. Based on the fine analysis about the structures of connected components of the super-level sets {x ∈ ℝ2 Ω: u(x) > t} and sub-level sets {x ∈ ℝ2 Ω: u(x) < t} for some t, we get the geometric distributions of interior critical point sets of solutions. Exactly, when Ω is a smooth bounded simply connected domain, u ∣ ∂ Ω = ψ (x) , lim ∣ x ∣ → ∞ u (x) = − ∞ and ψ(x) has K local maximal points on ∂Ω, we deduce that ∑ i = 1 l m i ≤ K , where m1, ..., ml; are the multiplicities of interior critical points x1, ..., xl; of solution u respectively. In addition, when ψ(x) has only K global maximal points and K equal local minima relative to ℝ2 Ω on ∂Ω, we have that ∑ i = 1 l m i = K . Moreover, when Ω is a domain consisting of l disjoint smooth bounded simply connected domains, we deduce that ∑ x i ∈ Ω m i + 1 2 ∑ x j ∈ ∂ Ω m j = l − 1 , and the critical points are contained in the convex hull of the l simply connected domains. [ABSTRACT FROM AUTHOR]

In this paper, we study the multiplicity of weak nonzero solutions for the following fractional Hamiltonian systems: t D ∞ α - ∞ D t α u (t) - L (t) u + λ u + ∇ W (t , u) = 0 , u ∈ H α (R , R N) , t ∈ R , where α ∈ (1 2 , 1 ] , λ ∈ R , - ∞ D t α and t D ∞ α are left and right Liouville–Weyl fractional derivatives of order α on real line R , the matrix L(t) is not necessarily coercive nor uniformly positive definite and W : R × R N → R satisfies some new general and weak conditions. Our results are proved using new symmetric mountain pass theorem established by Kajikia. Some recent results in the literature are generalized and significantly improved and some examples are also given to illustrate our main theoretical results. [ABSTRACT FROM AUTHOR]

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In this paper, the precise design of a high-power amplifier (HPA) is shown, along with the problems associated with the stability of "on-wafer" measurements. Here, techniques to predict possible oscillations are discussed to ensure the stability of a monolithic microwave-integrated circuit (MMIC). In addition, a deep reflection is made on the instabilities that occur when measuring both on wafer and using a mounted chip. Stability techniques are used as tools to characterize measurement results. Both a precise design and instabilities are shown through the design of a three-stage X-band HPA in gallium nitride (GaN) from the WIN Semiconductors Corp. foundry. As a result, satisfactory performance was obtained, achieving a maximum output power equal to 42 dBm and power-added efficiency of 32% at a 20 V drain bias. In addition to identifying critical points in the design or measurement of the HPA, this research shows that the stability of the amplifier can be verified through a simple analysis and that instabilities are often linked to errors in the measurement process or in the characterization of the measurement process. [ABSTRACT FROM AUTHOR]

The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in studying the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where these two situations happen simultaneously. The rational map obtained by applying a method in the Chebyshev–Halley family to a polynomial has both super-attracting extraneous fixed points and super-attracting cycles different from the roots of the polynomial. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions for a class of integrodifferential Kirchhoff equations. These equations involve a nonlocal operator with a measurable kernel that satisfies "structural properties" that are more general than the standard kernel of the fractional Laplacian operator. Additionally, the potential can be periodic or asymptotically periodic, and the nonlinear term exhibits critical exponential growth in the sense of Trudinger–Moser inequality. To guarantee the existence of solutions, we employ variational methods, specifically the mountain-pass theorem. In this context, it is important to emphasize that we have additional difficulties due to the lack of compactness in our problem, because we deal with critical growth nonlinearities in unbounded domains. Moreover, the Kirchhoff term adds complexity to the problem, as it requires suitable calculations for control the estimate the minimax level, representing the main challenge in this work. Finally, we consider two different approaches to estimate the minimax level. The first approach is based on a hypothesis proposed by D. M. Cao, while the second one involves a slightly weaker assumption addressed by Adimurthi and Miyagaki. [ABSTRACT FROM AUTHOR]

In a one-way design with unknown and unequal error variances, we are interested in testing the null hypothesis H 0 : μ 1 = μ 2 = ⋯ = μ k against the ordered alternative H 1 : μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k (with at least one strict inequality). We propose the likelihood ratio test (LRT) as well as two Min-T tests (Min-T and AMin-T) and study their asymptotic behaviour. For better finite sample properties, a parametric bootstrap procedure is used. Asymptotic accuracy of the parametric bootstrap is established. Simulation results show that all the tests control the nominal level in case of small, moderate, and highly unbalanced sample sizes. This even holds for combinations with large variances. However, the asymptotic likelihood ratio test (ALRT) achieves the nominal size only for large samples and k = 3 . Power comparisons between LRT and Min-T test show that the LRT has more power than Min-T. However, the Min-T test is easier to use as it does not require evaluation of MLEs. Similar observations are made while comparing ALRT and AMin-T test. The robustness of these tests under departure from normality is also investigated by considering five non-normal distributions (t-distribution, Laplace, exponential, Weibull, and lognormal). When high variances are combined with small or highly unbalanced sample sizes, the tests are observed to be robust only for symmetric distributions. If variances of groups are equal and sample sizes of each group are at least 10, the proposed tests perform satisfactorily for symmetric and skewed distributions. R packages are developed for all tests and a practical example is provided to illustrate their application. [ABSTRACT FROM AUTHOR]

In this paper, a two-way ANOVA model is considered when interactions between two factors are present and errors are normally distributed with heteroscedastic cell variances. The problem of testing the homogeneity of simple effects against their ordered alternatives has not been studied before in the literature for this model. Here, we develop the likelihood ratio test and two heuristic tests based on multiple contrasts. Two algorithms are proposed for finding solutions of the likelihood equations under the null and full parameter spaces. The existence and uniqueness of solutions and convergence of the algorithms are established. Hence, this paper also finds the maximum likelihood estimators of simple effects when they are order restricted. A parametric bootstrap procedure is used to implement all the tests and the asymptotic accuracy of the parametric bootstrap is proved. An extensive simulation study is carried out to study the size and power performance of the tests. Results show that all the parametric bootstrap-based test procedures achieve nominal sizes for small, moderate, and highly unbalanced sample sizes. Nominal size is controlled even in the case when small samples are combined with large and heterogeneous variances. The robustness of tests is also investigated under departure from normality. The proposed tests are illustrated with the help of three examples. Finally, an "R" package has been developed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse the Italian dubbed and subtitled translations of selected episodes from the American TV series Sex and the City and its sequel And Just Like That. The analysis delves into the translation from English into Italian of the dialogues that are imbued with cultural references. The study examines the translation choices concerning swear words and idiomatic expressions by comparing the dubbed and subtitled versions. Starting from Munday’s theories, it aims to identify critical points in translational decision-making, namely, phrases and fragments of dialogues that require particular interpretations on the part of the translator. The study attempts to determine the extent to which the approach to translation from English into Italian is target audience-oriented. Finally, by considering the concept of linguaculture, the work explores the impact of this approach on the target culture in order to compare the American and Italian linguacultures. Keywords: Sex and the City, And Just like That, translation, critical points.

Abstract This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents ( S ± ε ) : Δ 2 u − c n Δ u + d n u = K u n + 4 n − 4 ± ε $(S_{\pm \varepsilon}): \Delta ^{2}u-c_{n}\Delta u+d_{n}u = Ku^{ \frac{n+4}{n-4}\pm \varepsilon}$ , u > 0 $u>0$ on S n $S^{n}$ , where n ≥ 5 $n\geq 5$ , ε is a small positive parameter and K is a smooth positive function on S n $S^{n}$ . We construct some solutions of ( S − ε ) $(S_{-\varepsilon})$ that blow up at one critical point of K. However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation ( S + ε ) $(S_{+\varepsilon})$ .

This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents (S ± ε) : Δ 2 u − c n Δ u + d n u = K u n + 4 n − 4 ± ε , u > 0 on S n , where n ≥ 5 , ε is a small positive parameter and K is a smooth positive function on S n . We construct some solutions of (S − ε) that blow up at one critical point of K. However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation (S + ε) . [ABSTRACT FROM AUTHOR]

According to the Gauss–Lucas theorem, the critical points of a complex polynomial where always lie in the convex hull of its zeros. In this paper, we prove certain relations between the distribution of zeros of a polynomial and its critical points. Using these relations, we prove the well-known Sendov's conjecture for certain special cases. [ABSTRACT FROM AUTHOR]

The paper deals with the Fermi-Pasta-Ulam type systems that describe an infinite systems of nonlinearly coupled particles with nonlocal interaction on a two dimensional lattice. It is assumed that each particle interacts nonlinearly with several neighbors horizontally and vertically on both sides. The main result concerns the existence of traveling waves solutions with periodic relative displacement profiles. We obtain sufficient conditions for the existence of such solutions with the aid of critical point method and a suitable version of the Mountain Pass Theorem for functionals satisfying the Cerami condition instead of the Palais-Smale condition. We prove that under natural assumptions there exist monotone traveling waves. [ABSTRACT FROM AUTHOR]

We prove the existence of a solution for an equation where the nonlinearity is singular at zero, namely - Δ u = (- u - β + f (u)) χ { u > 0 } in Ω ⊂ R 2 with Dirichlet boundary condition. The function f grows exponentially, which can be subcritical or critical with respect to the Trudinger–Moser embedding. We examine the functional I ϵ corresponding to the ϵ -perturbed equation - Δ u + g ϵ (u) = f (u) , where g ϵ tends pointwisely to u - β as ϵ → 0 + . We show that I ϵ possesses a critical point u ϵ in H 0 1 (Ω) , which converges to a genuine nontrivial nonnegative solution of the original problem as ϵ → 0 . We also address the problem with f(u) replaced by λ f (u) , when the parameter λ > 0 is sufficiently large. We give examples. [ABSTRACT FROM AUTHOR]