Order Terms Research Articles

Anomalous Temperature-Induced Particle Size Reduction in Manganese Oxide Nanoparticles.

The intricate role of temperature in the structure-property relationship of manganese oxide nanoparticles (Mn3O4 NPs) remains an open question. In this study, we successfully synthesized Mn3O4 NPs using the hydrothermal method with two differing temperatures, namely, 90 and 150 °C. Interestingly, a smaller average particle size is found when Mn3O4 NPs are synthesized at 150 °C compared to 90 °C, corresponding to 46.54 and 63.37 nm, respectively. This was confirmed by the time variation of temperature setting of 150 °C where the size evolution was insignificant, indicating a competing effect of nucleation and growth particles. Under varying NaOH concentrations (2-6 M) at 150 °C, a reduction in the particle size is found at the highest NaOH concentration (6 M). The particle grows slightly, indicating that the growth state is dominant compared to the nucleation state at low concentrations of NaOH. This finding implies that the high nucleation rate originates from the excessive monomer supply in the high-temperature reaction. In terms of crystallinity order, the structural arrangement of Mn3O4 NPs (150 °C) is largely decreased; this is likely due to a facile redox shift to the higher oxidation state of manganese. In addition, the higher ratio of adsorbed oxygen and lattice oxygen in Mn3O4 NPs at 150 °C is indirectly due to the higher oxygen vacancy occupancies, which supported the crystallinity decrease. Our findings provide a new perspective on manganese oxide formation in hydrothermal systems.

Regularity results for local solutions to some anisotropic elliptic equations

In this paper we study the higher integrability of local solutions for a class of anisotropic equations with lower order terms whose growth coefficients lay in Marcinkiewicz spaces. A condition for the boundedness of such solutions is also given.

Revisiting Maxwell-Smoluchowski theory: Low surface roughness in straight channels

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction ϑ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction 1−ϑ undergoes specular reflection. From this assumption one obtains the value D=2−ϑϑDK for the self-diffusivity constant, where DK is a reference value corresponding to ϑ=1. In this paper we show that ϑ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry.Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry—a concept which incorporates both the actual surface microgeometry and the molecular radius—and using this operator approximation, we show that ϑ can be resolved into easily obtained geometric parameters, ϑ=λh/C, having the following interpretation: C is a macroscopic parameter determined by the shape of the channel cross-section; h is a parameter that precisely captures the degree of roughness of the effective microgeometry, and λ is a parameter that characterizes the overall curvature of the surface microgeometry independent of h. Thus ϑ is resolved as the quotient of microscopic (λh) over macroscopic (C) signature parameters of the channel geometry. The identity ϑ=λh/C holds up to higher order terms in the roughness parameter h, so our main result better applies to well polished, or low roughness, surfaces.

Circular Economy and Solid Waste Management: Connections from a Bibliometric Analysis

The aim of this study is to conduct a meta-analysis of the research published between 2012 and 2022 on solid waste management (SWM) and the circular economy (CE) using bibliometrics. To this end, the Scopus and Web of Science (WoS) databases were used as sources of publications. Processing was conducted using the R language version 4.2.2 and the Bibliometrix software package version 4.1.2. A theoretical basis was built on the terms in order to present their interactions in the context of scientific debate. The results show that there is a need to create indicators to facilitate the evaluation of SWM. They can be identified from the data collected during the management process. Examples include the volume of material collected, operating costs, and recycling rates. Indicators are important in the waste management process because they help quantify the effectiveness of the management practices adopted, help to identify areas that need improvement, and make it possible to monitor the progress of work over time and the achievement of previously set targets. Two other important results are the maximization of the use of resources by increasing the useful life of the product and the emergence of new sustainable business models with recycling as a driving force. Finally, and perhaps the most disruptive discovery, is the integration of SWM and CE with blockchain technology to reduce the levels of waste production. This shows how new technologies can be used as partners in solving complex problems, such as solid waste (SW).

Longtime behavior of the weakly coupled Euler-Bernoulli plate system with structural damping

In this paper, we study the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The system consists of two plate equations coupled by zero order terms. First, we show that when the coupling coefficient function is a nonzero constant and the damping coefficient function is a positive constant, the optimal energy decay rate of the system is t−23. Then we consider the case that the coupling and damping coefficient functions have compact supports. By Carleman estimate and the frequency domain method, we show that the energy of the system decays logarithmically when the supports of the coupling and damping coefficient functions satisfy suitable assumptions.

Entanglement Entropy of Ground States of the Three-Dimensional Ideal Fermi Gas in a Magnetic Field

We study the asymptotic growth of the entanglement entropy of ground states of non-interacting (spinless) fermions in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}^3$$\\end{document} subject to a constant magnetic field perpendicular to a plane. As for the case with no magnetic field we find, to leading order L2ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2\\ln (L)$$\\end{document}, a logarithmically enhanced area law of this entropy for a bounded, piecewise Lipschitz region LΛ⊂R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L\\Lambda \\subset {{\\mathbb {R}}}^3$$\\end{document} as the scaling parameter L tends to infinity. This is in contrast to the two-dimensional case since particles can now move freely in the direction of the magnetic field, which causes the extra ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ln (L)$$\\end{document} factor. The explicit expression for the coefficient of the leading order contains a surface integral similar to the Widom–Sobolev formula in the non-magnetic case. It differs, however, in the sense that the dependence on the boundary, ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}, is not solely on its area but on the “surface perpendicular to the direction of the magnetic field”. We utilize a two-term asymptotic expansion by Widom (up to an error term of order one) of certain traces of one-dimensional Wiener–Hopf operators with a discontinuous symbol. This leads to an improved error term of the order L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} of the relevant trace for piecewise C1,α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{C}^{1,\\alpha }$$\\end{document} smooth surfaces ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}.

A Multi-Objective Optimization-Algorithm-Based ANFIS Approach for Modeling Dynamic Customer Preferences with Explicit Nonlinearity

In previous studies, customer preferences were assumed to be static when modeling their preferences based on online reviews. However, in fact, customer preferences for products are dynamic and changing over time. Few research has been conducted to model dynamic customer preferences as the time series data of customer preference are difficult to be obtained. Based on online reviews, an adaptive neuro fuzzy inference system (ANFIS) was introduced to model customer preferences, which can take into account the fuzzy nature of customers’ emotions and the nonlinearity of the model. However, ANFIS is plagued with black box problems, and the nonlinearity of the model cannot be directly demonstrated. To address the above research issues, a multi-objective chaos optimization algorithm (MOCOA)-based ANFIS approach is proposed to generate customer preferences models by using online reviews, which has explicit nonlinear inputs. Firstly, a sentiment analysis approach is used to derive information from online reviews by periods, which is used as the time series data sets of the proposed model. A MOCOA is combined into ANFIS to identify the nonlinear inputs, which include single items, interactive items, and terms of second order and/or higher-order terms. Consequently, the fuzzy rules in ANFIS are expressed in polynomial form, which allows for the explicit representation of the nonlinearity between customer preferences and product attributes. A case study of sweeping robots is used to compare the validation results of the proposed approach with those of ANFIS, subtractive cluster-based ANFIS, fuzzy c-means-based ANFIS, and K-means-based ANFIS. Moreover, the proposed approach provides better performance than the other four approaches in terms of mean relative error and variance of error.

Characteristics of chloroplast and mitochondrial genomes and intracellular gene transfer in the Korean endemic shrub, Sophora koreensis Nakai (Fabaceae)

Sophora koreensis Nakai, an endemic species distributed only in the Korean Peninsula, is of great geographical, economic, and taxonomic importance. Although its complete chloroplast (cp) genome sequence has been reported, its mitochondrial (mt) genome sequence has not yet been studied. Therefore, in this study, we aimed to investigate its mt genome sequence and compare it with those reported for other Fabaceae species. Total genomic DNA was extracted from fresh S. koreensis leaves collected from natural habitats in Gangwon-do Province, South Korea. This was followed by polymerase chain reaction (PCR) amplification of cpDNA insertions in the mt genome and the detection of microsatellites and dispersed repeats in the cp and mt genomes. Finally, the cp and mt genomes of S. koreensis were compared with those reported for other Fabaceae species. The cp sequence of S. koreensis showed identical gene orders and contents as those previously reported. Only six substitutions and one deletion were detected with 99 % homology. Conversely, the complete mt genome sequence, which was 517,845 bp in length and encoded 61 genes, including 43 protein-coding, 15 transfer RNAs, and 3 ribosomal RNA genes, was considerably different from that of S. japonica in terms of gene order and composition. Further, the mt genome of S. koreensis included ca. 7 and 3 kb insertions, representing an intracellular gene transfer (IGT) event, and the regions with these insertions were determined to be originally present in the cp genome. This IGT event was also confirmed via PCR amplification. IGT events can be induced via biological gene expression control or the use of repetitive sequences, and they provide important insights into the evolutionary lineage of S. koreensis. However, further studies are needed to clarify the gene transfer mechanisms between the two organelles.

INFLUENCE OF HIGH-ORDER TERMS IN THE SOLUTION GENERALIZING THE APPROACH OF M. WILLIAMS, TAKING INTO ACCOUNT THE ANISOTROPY OF THE MATERIAL

The research is devoted to the study of the stress field at the crack tip in an anisotropic material with three mutually orthogonal axes of symmetry of the fourth order (with cubic symmetry). A plane case is considered when one of the axes of symmetry is orthogonal to the cracked plate, and the remaining two axes lie in the plane of the plate. The paper presents an asymptotic analysis of the contribution of higher approximations in the generalized asymptotic decomposition of mechanical fields near the crack tip in a linearly elastic anisotropic material with cubic symmetry of its elastic properties. In the article, based on the obtained solution of M. Nejati and co-authors for an infinite anisotropic plate with a central crack, circumferential apportionments of the stress tensor components at the crack tip at various distances fromthe crack tip are constructed, which makes it possible to estimate the contribution of non-singular (regular)terms to the general asymptotic representation of mechanical fields generated by an acute crack. In the work of M. Nejati, the contribution of exclusively T-stresses is analyzed, then, as shown in this work, the terms following the T-stress play a significant role in describing the fields induced by the crack. A comparison of the angular distributions of the stress tensor components constructed at different distances from the crack tip indicates that with the increase of distances from the crack tip, it is required to preserve in asymptotic series representing stresses, displacements and strains near the tip of the crack, the terms of high order of smallness. The preservation of the terms of high order of smallness can be used to expand the domain in which the asymptotic solution in the series is valid.

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation.

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

Tuning rules of filtered PID/PIDD2 controller for integrating processes with measurement noise

PID controllers are widely used in industrial processes. However, it is well-known that the derivative action is susceptible to measurement noise, so most of the practical PID controllers are of PI-type. To improve the control performance and lessen the impact of measurement noise on actuators, tuning formulas under arbitrary comprehensive robustness measures are proposed to meet more control needs, the filtered PID/PIDD2 (PID plus second derivative) is used under the promise of acceptable performance of robustness and disturbance rejection. Many chemical production processes can be approximated to the common model with integrators, to improve the chemical production process efficiency, tuning rules of filtered PID/PIDD2 controllers are proposed for different integrating processes in terms of relative order to make better trade-offs. Simulation results show that the proposed tuning formula can reduce the impact of noise and achieve proper compromising among robustness, disturbance rejection and measurement noise.

Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains

We consider elliptic operators in divergence form with lower order terms of the form Lu = -{{textrm{div}}}(A cdot nabla u + b u ) - c cdot nabla u - du, in an open set Omega subset mathbb {R}^n, n ge 3, with possibly infinite Lebesgue measure. We assume that the n times n matrix A is uniformly elliptic with real, merely bounded and possibly non-symmetric coefficients, and either b, c in L^{n,infty }_{text {loc}}({Omega }) and d in L_{text {loc}}^{frac{n}{2}, infty }(Omega ), or |b|^2, |c|^2, |d| in mathcal {K}_{text {loc}}(Omega ), where mathcal {K}_{text {loc}}(Omega ) stands for the local Stummel–Kato class. Let {mathcal {K}_{text {Dini}}}(Omega ) be a variant of mathcal {K}(Omega ) satisfying a Carleson-Dini-type condition. We develop a De Giorgi/Nash/Moser theory for solutions of Lu = f - {{textrm{div}}}g, where f and |g|^2 in {mathcal {K}_{text {Dini}}}(Omega ) if, for q in [n, infty ), any of the following assumptions holds: (i) |b|^2, |d| in {mathcal {K}_{text {Dini}}}(Omega ) and either c in L^{n,q}_{text {loc}}(Omega ) or |c|^2 in mathcal {K}_{text {loc}}(Omega ); (ii) {{textrm{div}}}b +d le 0 and either b+c in L^{n,q}_{text {loc}}(Omega ) or |b+c|^2 in mathcal {K}_{text {loc}}(Omega ); (iii) -{{textrm{div}}}c + d le 0 and |b+c|^2 in {mathcal {K}_{text {Dini}}}(Omega ). We also prove a Wiener-type criterion for boundary regularity. Assuming global conditions on the coefficients, we show that the variational Dirichlet problem is well-posed and, assuming -{{textrm{div}}}c +d le 0, we construct the Green’s function associated with L satisfying quantitative estimates. Under the additional hypothesis |b+c|^2 in mathcal {K}'(Omega ), we show that it satisfies global pointwise bounds and also construct the Green’s function associated with the formal adjoint operator of L. An important feature of our results is that all the estimates are scale invariant and independent of Omega , while we do not assume smallness of the norms of the coefficients or coercivity of the associated bilinear form.

A priori and a posteriori error analysis for semilinear problems in liquid crystals

In this paper, we develop a unified framework for the a priori and a posteriori error control of different lowest-order finite element methods for approximating the regular solutions of systems of partial differential equations under a set of hypotheses. The systems involve cubic nonlinearities in lower order terms, non-homogeneous Dirichlet boundary conditions, and the results are established under minimal regularity assumptions on the exact solution. The key contributions include (i) results for existence and local uniqueness of the discrete solutions using Newton–Kantorovich theorem, (ii) a priori error estimates in the energy norm, and (iii) a posteriori error estimates that steer the adaptive refinement process. The results are applied to conforming, Nitsche, discontinuous Galerkin, and weakly over penalized symmetric interior penalty schemes for variational models of ferronematics and nematic liquid crystals. The theoretical estimates are corroborated by substantive numerical results.

Challenges in the Receiving and Inspection of Supplies & Equipment in an International Organization in West Africa

The warehouse operation has enabled physical inspection activities, including receiving and inspection of materials and equipment. It has been found that there are certain challenges faced by inspectors during the receiving and inspection of materials. The warehouse custodian has performed the physical inspection, but not all cross-checking activities are accurate. Therefore, receiving and inspection are crucial to the delivery process, and distinct approaches must be implemented to deal with internal and external clients, including international and local suppliers. To effectively deal with these challenges, a process for entry document processing must be established. This process should include harmonizing the purchase order's terms and supporting it with the delivery note, packing list, invoice, bill of lading, and airway/waybill provided by the supplier. This will ensure that the material's quantity, quality, and specifications are accurately documented. A total of 14 responses were collected among managers and supervisors of receiving and inspection unit through interviews and survey questionnaires in the seven geographical locations of Mali, West Africa. The independent variables, namely (PI) physical inspection, (HOV) handover, and (DOC) documentation, significantly impact the dependent variable.

A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two

We prove a rigidity result for foliations on surfaces of genus two, which can be seen as a generalization to higher genus of Herman’s theorem on circle diffeomorphisms and, correspondingly, flows on the torus. We prove in particular that, if a smooth, orientable foliation with non-degenerate (Morse) singularities on a closed surface of genus two is minimal, then, under a full measure condition for the rotation number, it is differentiably conjugate to a linear foliation.The corresponding result at the level of Poincaré sections is that, for a full measure set of (standard) interval exchange transformations (IETs for short) with d=4 or d=5 continuity intervals and irreducible combinatorics, any generalized interval exchange transformation (GIET for short) which is topologically conjugate to a standard IET from this set and satisfies an obstruction expressed in terms of boundary operator (which is automatically satisfied when the GIET arises as a Poincaré map of a smooth foliation) is mathcal{C}^{1}-conjugate to it. This in particular settles a conjecture by Marmi, Moussa and Yoccoz in genus two. Our results also show that this conjecture on the rigidity of GIETs can be reduced to the study of affine IETs, or more precisely of Birkhoff sums of piecewise constant observables over standard IETs, in genus g geq 3.Our approach is via renormalization, namely we exploit a suitable acceleration of the Rauzy-Veech induction (an acceleration which makes Oseledets generic effective) on the space of GIETs. For in ly renormalizable, irrational GIETs of any number of intervals dgeq 2 we prove a dynamical dichotomy on the behaviour of the orbits under renormalization, by proving that either an orbit is recurrent to certain bounded sets in the space of GIETs, or it diverges and it is approximated (up to lower order terms) by the orbit of an affine IET (a case that we refer to as affine shadowing). This result can in particular be used, in conjunction with previous work by Marmi-Moussa and Yoccoz on the existence of wandering intervals for affine IETs, to prove, a priori bounds in genus two and is therefore at the base of the rigidity result.

Smooth integers and de Bruijn's approximation Ʌ

This paper is concerned with the relationship of $y$ -smooth integers and de Bruijn's approximation $\Lambda (x,\,y)$ . Under the Riemann hypothesis, Saias proved that the count of $y$ -smooth integers up to $x$ , $\Psi (x,\,y)$ , is asymptotic to $\Lambda (x,\,y)$ when $y \ge (\log x)^{2+\varepsilon }$ . We extend the range to $y \ge (\log x)^{3/2+\varepsilon }$ by introducing a correction factor that takes into account the contributions of zeta zeros and prime powers. We use this correction term to uncover a lower order term in the asymptotics of $\Psi (x,\,y)/\Lambda (x,\,y)$ . The term relates to the error term in the prime number theorem, and implies that large positive (resp. negative) values of $\sum _{n \le y} \Lambda (n)-y$ lead to large positive (resp. negative) values of $\Psi (x,\,y)-\Lambda (x,\,y)$ , and vice versa. Under the Linear Independence hypothesis, we show a Chebyshev's bias in $\Psi (x,\,y)-\Lambda (x,\,y)$ .

Existence of renormalized solutions to fully anisotropic and inhomogeneous elliptic problems

We will present the proof of existence and uniqueness of renormalized solutions to a broad family of strongly non-linear elliptic equations with lower order terms and data of low integrability. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak–Orlicz spaces. The setting considered in this paper generalized known results in the variable exponents, anisotropic polynomial, double phase and classical Orlicz setting.

Refusing Invitations: A Contrastive Pragmatic Study of Jordanian Arabic and Castilian Spanish

Objectives: The study aimed at examining the use of refusals by Jordanian Arabic and Castilian Spanish speakers when declining invitations from their friends, focusing on similarities and differences in terms of head strategies, adjuncts, order, and frequency. Methods: A discourse completion task (DCT) comprising various situations were designed to elicit refusals from the participants. Drawing on Beebe et al’s categorization (1990), the data were categorized into head acts (subdivided into direct and indirect strategies) and adjuncts to refusal. Results: Although the Jordanian and Spanish participants belong to two distant cultures (eastern and western), the findings revealed that they were more similar than different in their refusals. They both showed a stronger tendency for indirectness in refusing invitations, with the Jordanians being more indirect. Both groups commonly utilized the strategies of statement of regret, giving reason, and negative ability, with different degrees of preference and frequency. As for adjuncts, both groups were inclined to employ a high percentage of adjuncts either before or after head strategies of refusal. While the Jordanians preferred the adjuncts of gratitude and swearing, the Spanish participants preferred gratitude and positive opinion. Both groups showed predilection to combine the same typical components in their refusal responses but differ in the order in which these components appeared. The employment of indirect refusal strategies and adjuncts in the Jordanian and Spanish responses pragmatically served to mitigate potentially negative effects of refusal on the inviters. Conclusion: Further research on Jordanian and Spanish refusals in other situations is recommended.

New Variants of Newton's Method for Solving Nonlinear Equations

Two Newton-type iterative techniques have been created in this work to locate the true root of univariate nonlinear equations. One of these can be acquired by modifying the double Newton's method in a straightforward manner, while the other can be gotten by modifying the midpoint Newton's method. The iterative approach developed by McDougall and Wortherspoon is employed for the change. The study demonstrates that the modified double Newton's approach outperforms the current one in terms of both convergence order and efficiency index, even though both methods assess the same amount of functions and derivatives every iteration. In comparison to the midpoint Newton's technique, which has a convergence order of 3, the modified midpoint Newton's method has a convergence order of 5.25 and requires two extra functions to be evaluated per iteration. In order to evaluate the effectiveness of recently introduced approaches with current methods, some numerical examples are shown in the final section.

Approximate boundaries of resonance tongue for planar maps

A resonance tongue of a planar map with a weakly resonant equilibrium is a region of parameters in which periodic orbits appear on the invariant circle arising from the Neimark-Sacker bifurcation. Although conditions were given for the existence of resonance tongues, it is still difficult to compute boundaries of such a tongue. Known results give the common term of the lowest order and the different term of the lowest order only for the tongue with a mistake. In this paper we give a method to compute approximately all common terms and the first different term for the boundaries and correct the mistake for the normal form of planar maps having a weakly resonant equilibrium. Then, computing higher order derivatives of implicit functions and discussing Hölder smoothness of implicit functions, we use the inducing relation of parameters to compute approximately boundaries of resonance tongues for given planar maps. Finally, we apply our result to a planar discrete time prey–predator model.