Singular Ones Research Articles

Some novel different solutions for Boussinesq-type models including bright, singular, and dark soliton ones

Some new different kinds of one-soliton solutions for various forms of Boussinesq-type equations are presented in thispaper to describe the nonlinear wave phenomena in coastal and ocean areas such as tsunami waves. These one-solitonsolutions include bright, dark, and singular ones. The property of each solution in coastal and ocean engineering isexplained.

Linearisation techniques and the dual algorithm for a class of mixed singular/continuous control problems in reinsurance. Part II: Numerical aspects

This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the no-reinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations.

Analyzing optical soliton propagation in perturbed nonlinear Schrödinger equation: A multi-technique study

In this study, the extended hyperbolic function method and unified solver method are applied to examine the propagation of optical solitons in perturbed nonlinear Schrodinger equation. The proposed techniques are characterized as simpler, more concise, and straightforward. They allow for the extension of the class of solutions and the retrieval of a diverse range of optical solitons, including singular, periodic singular, bright, and dark ones. This highlights the significance of the results. The authors emphasize the novelty of these techniques, as they have not been previously applied to recover optical solitons in this model These out comes may be beneficial for further understanding of numerous phenomena that arises in various physical systems and can be castoff for the optical communication resolution. The existence measures for these solutions are also unveiled in the form of constraint parameters. In addition, the pictorial representations of certain solutions depicted in figures undoubtedly play a key role in understanding the behavior and apprehending some of the physical features of the the discovery of a plethora of novel soliton solutions and their accompanying behaviors.

Optical Solitons for the Dispersive Concatenation Model

The study undertakes a comprehensive exploration of optical solitons within the context of the dispersive concatenation model, utilizing three distinct integration algorithms. These approaches, namely the enhanced Kudryashov' s method, the Riccati equation expansion approach, and the Weierstrass' expansion scheme, offer distinct perspectives and insights into the behavior of optical solitons. By employing the enhanced Kudryashov' s approach, the research uncovers a spectrum of soliton solutions, including straddled, bright, and singular optical solitons. This algorithm not only provides a nuanced understanding of the various soliton types but also highlights the occurrence of singular solitons that exhibit unique characteristics. The Riccati equation expansion approach, on the other hand, yields dark solitons in addition to singular solitons. This particular method expands our comprehension of soliton behavior by encompassing the presence of dark solitons alongside singular ones. This diversification contributes to a more comprehensive grasp of soliton phenomena. Furthermore, the application of the Weierstrass' expansion scheme extends the analysis to encompass bright, singular, and other variations of straddled solitons. This method introduces further complexity and diversity to the optical soliton. Importantly, the study meticulously addresses the parameter constraints that govern the behavior of these solitons. By providing a comprehensive presentation of these constraints, the research enhances the practical applicability of the findings, offering insights into the conditions under which these soliton solutions emerge.

The modular class of a singular foliation

The modular class of a regular foliation is a cohomological obstruction to the existence of a volume form transverse to the leaves which is invariant under the flow of the vector fields of the foliation. It has been used in dynamical systems and operator theory, from which the name modular comes from. By drawing on the relationship between Lie algebroids and regular foliations, this paper extends the notion of modular class to the realm of singular foliations. The singularities are dealt with by replacing the singular foliations by any of their universal Lie ∞-algebroids, and by picking up the modular class of the latter. The geometric meaning of the modular class of a singular foliation F is not as transparent as for regular foliations: it is an obstruction to the existence of a universal Lie ∞-algebroid of F whose Berezinian line bundle is a trivial F-module. This paper illustrates the relevance of using universal Lie ∞-algebroids to extend mathematical notions from regular foliations to singular ones, thus paving the road to defining other characteristic classes in this way.

Analysis of new soliton type solutions to generalized extended (2 + 1)-dimensional Kadomtsev-Petviashvili equation via two techniques

In this paper, we examine the solitary wave solutions of the generalised (2 + 1) extended Kadomtsev–Petviashvili (eKP) equation, which is used as model for the surface waves and internal waves in straits or channels and describes the dynamics of nonlinear waves in plasma physics and fluid dynamics. We secure distinct soliton solutions by employing two amelioration methodologies, namely the improved F-expansion method and the new Kudryashov method. These methods explore several unique forms of solitary wave solutions, including dark, rational, singular, periodic, and exponential ones. In order to illustrate propagation of some reported wave solutions, the graphs associated with these solutions are presented by choosing appropriate parametric values in 2D, 3D, contour, and density plots with the use of the symbolic software Mathematica 13.0. The presented solutions realize very significant fact for investigation the qualitative interpretations for various phenomena in our nature. The computed solutions revealed that the applied methods are influential, efficious and skilful and can be a best way to handle other higher order nonlinear evolution equations.

Non-Prototypical Uses of Personal Pronouns and Their Grammaticalization in Chinese

With an interesting typological study on the non-prototypical uses of personal pronouns, Helmbrecht (2015) demonstrates that the form-meaning mismatch with regards to personal pronouns is essentially based on discourse. It is claimed that the referents of personal pronouns dynamically keep changing with a particular context, and some kind of additional pragmatic meaning tends to be encoded into them. Based on his study, Helmbrecht proposes two hypotheses about how the phenomena at issue could be grammaticalized: (i) Plural pronouns may shift to singular ones; (ii) third-person pronouns may shift to second- or first-person ones, but not vice versa. Drawing on a more comprehensive typological perspective, this article presents various patterns in Mandarin Chinese that supplement Helmbrecht’s generalization and adjust his hypotheses concerning the grammaticalization of personal pronouns (Hu, 2018).

Singular flat bands in the modified Haldane-Dice model

Flat bands can be divided into singular and non-singular ones according to the behavior of their Bloch wave function around band-crossing points in momentum space. We analyze the flat band in the Dice model, which can be tuned by a uniaxial strain in the zigzag direction and a Haldane-type next-nearest neighbor interaction, and derive the topological phase diagram of the modified Haldane-Dice model to obtain all band-gap closings with the central band. When the central band is flat, we determine its compact localized state and classify its behavior at all band-touching points by means of the Hilbert–Schmidt quantum distance. We find that the flat band remains singular for all band-touching points (topological phase transitions) with a maximal quantum distance and give expressions for the resulting non-contractible loop states on the real-space torus.

Superscars for arithmetic point scatters II

Abstract We consider momentum push-forwards of measures arising as quantum limits (semiclassical measures) of eigenfunctions of a point scatterer on the standard flat torus ${\mathbb T}^2 = {\mathbb R}^2/{\mathbb Z}^{2}$ . Given any probability measure arising by placing delta masses, with equal weights, on ${\mathbb Z}^2$ -lattice points on circles and projecting to the unit circle, we show that the mass of certain subsequences of eigenfunctions, in momentum space, completely localizes on that measure and are completely delocalized in position (i.e., concentration on Lagrangian states). We also show that the mass, in momentum, can fully localize on more exotic measures, for example, singular continuous ones with support on Cantor sets. Further, we can give examples of quantum limits that are certain convex combinations of such measures, in particular showing that the set of quantum limits is richer than the ones arising only from weak limits of lattice points on circles. The proofs exploit features of the half-dimensional sieve and behavior of multiplicative functions in short intervals, enabling precise control of the location of perturbed eigenvalues.

Three-dimensional unsteady axisymmetric vortex solutions to the Bellamy-Knights equation and the distribution of boundary conditions

The Bellamy-Knights equation gives three-dimensional unsteady axisymmetric incompressible vortex solutions that are disconnected from the known exact steady solutions. In this paper, by introducing a new parameter that allows a change of the time scale, the Bellamy-Knights equation is transformed into an integro-differential equation that continuously connects with the equation for steady vortices. The new equation is viewed as describing the one-dimensional motion of a particle under conserved and nonconserved forces and leads to new regular solutions, in which the particle initially undergoes almost sinusoidal oscillations around the minimum of potential followed by a very rapid approach to the extrema of the potential. The regular solutions distribute discretely in the space of boundary conditions and are classified into types that are specified by the pattern of sequence of small and large oscillations of the axial component of velocity. Extending the solutions to singular ones, the boundary conditions for solutions of the same type are shown to form a continuous one-dimensional set, which we call a branch. The set of branches forms dense self-similar patterns with accumulation points, some of which coalesce to a single point. In an arbitrary neighborhood of the accumulation or coalescent point, any two distinct boundary conditions whose distance in the space of boundary conditions is arbitrarily small give mutually distinctive solutions with a finite difference at some region of the spatial distance. This feature of the equations signifies the extreme sensitivity of inflowing vortex solutions to boundary conditions.

Singular poeta acadêmico: António Serrão de Crasto (1614-1685)

Poet António Serrão de Crasto (1614-1685) was a member of the Academy of the Singular Ones (Academia dos Singulares) from 1628 to 1665, and penned two tomes of academic poetic works in 1665 and 1668. This article aims to briefly present the 72 poems contained in those academic publications, and two occasional speeches given as he presided over academic sessions. It also includes some separate poems found in handwritten form or in books authored by others. In this article, I seek to put forward a short bibliography of Serrão de Crasto by collating several bibliographical sources known to date. Generally, the rhetorical artifice present in the texts lies in switching around serious and jocular styles, as the poet shifts between the seriousness of the subject and the playfulness of the concepts, ornaments and words with which he treats the argument or, conversely, as he clothes a trivial or low subject with high ornaments. Most of his romances, sonnets and gloses feature this shifting between serious and facetious styles.

Error Analysis on the Students' Construction of English Irregular Plural Nouns

In English, the forms of singular nouns commonly different from those of the plural ones. Many students are confused with how to construct the irregular plural noun forms. The formation of irregular plural nouns has complex and unique patterns. This current study aims to get information about the types of errors commonly made by EFL learners in constructing irregular plural nouns and to know how the errors occurred. This study is descriptive qualitative applying error analysis theory. The data were collected by giving the respondents a test consisting of 28 questions on irregular plural construction. The result of analysis shows that the errors made by the respondents can be classified into three types: misformation, addition, and omission. Misformation was the kind of error most respondents made. The error specifically occurred with the nouns that had quite dissimilar plural forms from the singular ones (e.g., foot – feet, goose – geese).

ERROR ANALYSIS ON THE STUDENTS’ CONSTRUCTION OF ENGLISH IRREGULAR PLURAL NOUNS

In English, the forms of singular nouns commonly different from those of the plural ones. Many students are confused with how to construct the irregular plural noun forms. The formation of irregular plural nouns has complex and unique patterns. This current study aims to get information about the types of errors commonly made by EFL learners in constructing irregular plural nouns and to know how the errors occurred. This study is descriptive qualitative applying error analysis theory. The data were collected by giving the respondents a test consisting of 28 questions on irregular plural construction. The result of analysis shows that the errors made by the respondents can be classified into three types: misformation, addition, and omission. Misformation was the kind of error most respondents made. The error specifically occurred with the nouns that had quite dissimilar plural forms from the singular ones (e.g., foot – feet, goose – geese).

Smooth solutions to the complex plateau problem

The paper builds on work of Du, Gao, and Yau. The main result provides a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi–Yau CR manifolds of dimension $2n - 1 \geq 5$ and in the hypersurface case when $n = 2$. The latter case was completely solved by Yau for $n \geq 3$ but only partially solved by Du and Yau for $n = 2$. As an application, we determine the existence of a link-theoretic invariant of normal isolated singularities that distinguishes smooth points from singular ones.

Unstable operations on K-theory for singular schemes

We study the algebraic structures, such as the lambda ring structure, that arise on K-theory seen as an object of some homotopy categories coming from model categories of simplicial presheaves. In particular, we show that if we take the Jardine local injective model category of simplicial presheaves over the category of divisorial, hence possibly singular, schemes with respect to the Zariski topology, these structures are in bijection with the ones we have on K0 seen as a presheaf of sets. This extends some results of Riou ([63]) from smooth schemes to singular ones and does not require A1-invariance. We also discuss similar results for symplectic K-theory.

Finite Rank Perturbations of Linear Relations and Matrix Pencils

We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their number of Jordan chains of length at least n. In the operator case, it was recently proved that the difference of these numbers is independent of n and is at most the defect between the operators. One of the main results of this paper shows that in the case of linear relations this number has to be multiplied by n+1 and that this bound is sharp. The reason for this behavior is the existence of singular chains. We apply our results to one-dimensional perturbations of singular and regular matrix pencils. This is done by representing matrix pencils via linear relations. This technique allows for both proving known results for regular pencils as well as new results for singular ones.

The analysis of science textbooks: science-chemistry teachers’ book and students’ book of junior high school

This study aims to analyse the science textbooks for teachers and students of junior high school students. The method used in this research is a qualitative method that used text analysis as a content analysis. The issue of school science textbooks has been a major research topic within the science education research tradition. The analysis of textbooks is divided into three formality values, namely: terminology and notation, nominalisations, and the use of passive voice. The categories of terminology and notation for teachers’ book and students’ book showed the result of high (H) value, the nominalisations for teachers’ book and students’ book also showed the result of high (H) value. Meanwhile, the use of passive voice for teachers’ book and students’ book showed the result of a low (L) value. By nominalising verbs in writing, more information can be packed into each clause so that the noun phrases can extend and carry more content. On the other hand, the analysis showed the result of low value in the use of passive voice while the verbs in passive voice appeared less than the verbs in the active voice. The result also showed weak power relationship and weak involvement in both textbooks. The weak power (hierarchical) relationship was shown by more occurrences of interrogatives and declarative rather than imperatives in both textbooks. Meanwhile, the weak involvement was shown by the frequency of the use of personal pronouns (more use of plural personal pronouns than singular ones). In conclusion, the analysis in both Chemistry textbooks (teachers’ book and students’ book) in the content of acid and base was high value in the formality markers of both terminologies, notation, and the nominalisations.

Spectrum of the Laplacian on regular polyhedra

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Class of Uzawa-NPHSS iteration method for solving nonsingular and singular saddle point problems

ABSTRACT Based on the non-alternating preconditioned HSS iteration scheme, a class of the Uzawa-NPHSS iteration method for solving nonsingular and singular non-Hermitian saddle point problems with the (1,1) part of the coefficient matrix being non-Hermitian positive definite is established. The convergence properties for the nonsingular saddle point problems and the semi-convergence properties for the singular ones of the proposed method are carefully discussed under suitable conditions. Meanwhile, the distribution of eigenvalues and the forms of the eigenvectors of the preconditioned matrix are analysed in detail. Additionally, the parameter selection strategy for the Uzawa-NPHSS iteration method is provided. Numerical experiments are implemented to confirm the theoretical results, which show the feasibility and effectiveness of the proposed method.

ReSIde: Reusable service identification from software families

The clone-and-own approach becomes a common practice to quickly develop Software Product Variants (SPVs) that meet variability in user requirements. However, managing the reuse and maintenance of the cloned codes is a very hard task. Therefore, we aim to analyze SPVs to identify cloned codes and package them using a modern systematic reuse approach like Service-Oriented Architecture (SOA). The objective is to benefit from all the advantages of SOA when creating new SPVs. The development based on services in SOA supports the software reuse and maintenance better than the development based on individual classes in monolithic object-oriented software. Existing service identification approaches identify services based on the analysis of a single software product. These approaches are not able to analyze multiple SPVs to identify reusable services of cloned codes. Identifying services by analyzing several SPVs allows to increase the reusability of identified services. In this paper, we propose ReSIde (Reusable Service Identification): an automated approach that identifies reusable services from a set of object-oriented SPVs. This is based on analyzing the commonality and the variability between SPVs to identify the implementation of reusable functionalities corresponding to cloned codes that can be packaged as reusable services. To validate ReSIde, we have applied it on three product families of different sizes. The results show that the services identified based on the analysis of multiple product variants using ReSIde are more reusable than services identified based on the analysis of singular ones.