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The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell‐wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high‐order and high‐smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points. [ABSTRACT FROM AUTHOR]

A proof that Wronskians of non-zero B-splines are positive is given, using only recursive formulas for B-splines and their derivatives. This could be used to generalize the de Boor–DeVore geometric proof of the Schoenberg–Whitney conditions and total positivity of B-splines to Hermite interpolation. For Wronskians of maximal order with respect to a given degree, positivity follows from a simple formula. [ABSTRACT FROM AUTHOR]

Time-fractional parabolic equations with a Caputo time derivative of order α ∈ (0 , 1) are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness of their solutions. Two approaches are explored: the Lax–Milgram Theorem and the eigenfunction expansion. The resulting sufficient conditions, which involve certain m × m matrices (where m is the order of the collocation scheme), are verified both analytically, for all m ≥ 1 and all sets of collocation points, and computationally, for all m ≤ 20 . The semilinear case is also addressed. [ABSTRACT FROM AUTHOR]

Collocational priming is a priming effect induced by collocationally related words; it has been taken to explain the cognitive reality of collocation. Collocational priming has largely been observed in first language (L1) speakers, whereas work on the representation of collocation in a second language (L2) is still limited. In the present study, we sought to investigate this phenomenon in L1 and L2 speakers of Italian. We used a lexical decision task to explore collocational priming in verb–noun and noun–adjective collocations differing in frequency and collocational strength. Both L1 and L2 speakers were found sensitive to the frequency of collocations. Importantly, exposure to L2 Italian was found to play a role. The results suggest that collocational priming occurs both in L1 and L2 speakers, and that the mechanisms associated with collocation processing and representation in L1 and L2 speakers may be comparable. [ABSTRACT FROM AUTHOR]

In this paper, we survey selected software packages for the numerical solution of boundary value ODEs (BVODEs), time-dependent PDEs in one spatial dimension (1DPDEs), and initial value ODEs (IVODEs). A unifying theme of this paper is our focus on software packages for these problem classes that compute error-controlled, continuous numerical solutions. A continuous numerical solution can be accessed by the user at any point in the domain. We focus on error-control software; this means that the software adapts the computation until it obtains a continuous approximate solution with a corresponding error estimate that satisfies the user tolerance. The second section of the paper will provide an overview of recent work on the development of COLNEWSC, an updated version of the widely used collocation BVODE solver, COLNEW, that returns an error-controlled continuous approximate solution based on the use of a superconvergent interpolant to the underlying collocation solution. The third section of the paper gives a brief review of recent work on the development of a new 1DPDE solver, BACOLIKR, that provides time- and space-dependent event detection for an error-controlled continuous numerical solution. In the fourth section of the paper, we briefly review the state of the art in IVODE software for the computation of error-controlled continuous numerical solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the collocations produced by a set of fictive motion verbs found in a specialized corpus representing the language of adventure tourism. Since our ultimate aim is to contribute to the characterization of this specialized language, we defined two specific objectives: (1) to analyze the motion verbs and their meanings extracted from the Advencor corpus, and (2) to identify the collocates of these verbs as well as the semantic roles they express. After the application of our methodology, eight motion verbs produced 35 collocations satisfying all the established criteria. The results focus on different aspects: (1) the verbs convey distinct meanings, such as motion on a vertical axis or direction towards a destination; (2) the most recurrent combination is noun + verb, where the former describes the inanimate entity that seems to perform motion; (3) collocation production and collocation strength are not correlated; and (4) the collocates accompanying the verbs under analysis shed light on the argument structure of these verbs, for they represent one of the participants. In conclusion, this work provides relevant information about the phraseology of fictive motion verbs in the language of adventure tourism and proves the specialization of this domain. [ABSTRACT FROM AUTHOR]

This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legendre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton's method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution. [ABSTRACT FROM AUTHOR]

In this paper, we utilise the Nineteenth Century Newspaper Corpus to examine reporting surrounding William Gladstone's Midlothian campaign, a key point in the democratization of British politics where a politician not only communicated with ordinary people through hustings but indirectly to a wider electorate via media reporting of those hustings. With the use of social actor analysis (van Leeuwen 2008), approached through collocation, we find that a distinctive feature of media reporting was a focus on Gladstone's family. This surprising intersection of family and electioneering reveals a powerful hierarchy of social relationships in terms of gender and seniority, which became an effective propaganda strategy as Gladstone, enabled by Liberal-supporting newspapers, utilised his family as a political tool. [ABSTRACT FROM AUTHOR]

This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legen-dre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton’s method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution.

This research aims to reveal Korean’s perspectives on plastic surgery practices through a corpus-based text analysis of Korean online newspapers. The research used quantitative and qualitative methods to observe keywords, significant collocates, and semantic preference. The data used were 106 opinion articles about plastic surgery in Chosun Ilbo and Donga Ilbo (2010–2019). Keyword analysis shows that the most frequently used keywords are seonghyeong (189 times) and seonghyeongsusul (116 times). Analysis of significant collocates and semantic preferences revealed that plastic surgery was frequently discussed in relation to body parts, people (collocate yeoseong (women), junggukin (Chinese), hwanja (patient), gwangganggek (tourist)), country (collocate jungguk (China), hangguk (Korea)), intensity (gwadohan (excessive)), and effect (phihae (loss)), and others. Plastic surgery clinics are frequently addressed in terms of location (collocate Gangnam, Seoul), intensity (collocate daehyong (big scale)), and others. Based on the findings of this study, plastic surgery is primarily performed on local women and international patients, particularly Chinese tourists. Plastic surgery is also perceived as having a negative impact, being overdone, and causing numerous difficulties. Plastic surgery performed on foreign patients is considered as beneficial to Korean economic progress, but it should not be performed on Koreans.

In order to predict the static deformations and free vibration behaviour of thin and thick cross-ply laminated plates, we integrate Carrera’s unified formulation with a radial basis function collocation technique on a pseudospectral framework, using Reissner’s mixed variational theorem. Numerical examples illustrate the precision and effectiveness of this collocation technique for static and vibration problems.

This study presents the findings of a corpus analysis regarding the media studies of the concept of a healthy lifestyle as a paramount regulatory value in contemporary society. The empirical foundation of the research is based on the British segment of the News on Web (NOW) corpus. Semantic categorization and quantification of collocations reveal that in the media narratives of British outlets, the value of a healthy lifestyle is increasingly framed within psychological and mental dimensions, reflecting shifting societal perceptions of its content. An interpretative analysis of contexts capturing behavioral types indicates that excesses in healthy lifestyle practices are met with disapproval. Concerns and anxieties are linked to mental health domains and psychologically healthy relationships. A critical stance is observed towards the most manipulable area of healthy eating. It has been established that media narratives politicize healthy lifestyle practices, associating the challenges of their implementation with economic issues as well as the phenomenon of psychological fatigue. Thematic modeling of discursive practices demonstrates the predominance of mental health topics in quality press, alongside rational discursive strategies grounded in scientific research findings. In popular media, emphasis is placed on appearance as a result of a healthy lifestyle, with extensive use of emotional appeal strategies referencing well-known personalities as role models.

The study introduces OnomOs, a new corpus of Czech texts with annotation of proper names. The corpus was compiled by onomasticians from the Department of Czech Language, Faculty of Arts, University of Ostrava, and made available by the Institute of the Czech National Corpus, Faculty of Arts, Charles University in Prague. The paper briefly discusses the content and structure of the corpus, the selection of texts for inclusion, and the onomastic-geographical classification of the identified names. The text consists chiefly of three preparatory analyses, which focus on the most frequent surnames, collocations found in Western and Eastern countries in the pre-1989 period, and the declension patterns of three types of onyms. In the summary, further possibilities of onomastic corpus research are presented.

In this paper, we introduce second derivative multistep collocation meth-ods for the numerical integration of ordinary differential equations (ODEs). These methods combine the concepts of both multistep methods and col-location methods, using second derivative of the solution in the collocation points, to achieve an accurate and efficient solution with strong stability properties, that is, A-stability for ODEs. Using the second-order deriva-tives leads to high order of convergency in the proposed methods. These methods approximate the ODE solution by using the numerical solution in some points in the r previous steps and by matching the function values and its derivatives at a set of collocation methods. Also, these methods utilize information from the second derivative of the solution in the colloca-tion methods. We present the construction of the technique and discuss the analysis of the order of accuracy and linear stability properties. Finally, some numerical results are provided to confirm the theoretical expecta-tions. A stiff system of ODEs, the Robertson chemical kinetics problem, and the two-body Pleiades problem are the case studies for comparing the efficiency of the proposed methods with existing methods.

The meshless global radial basis function (RBF) collocation method is widely used to model physical phenomena in science and engineering. The method produces highly accurate solutions with an exponential convergence rate. However, due to the global approximation structure of the method, dense node distributions lead to long computation times and hinder the applicability of the technique. In order to overcome this issue, this study proposes a parallel meshless global RBF collocation algorithm. The algorithm is applied to 2-D neutron diffusion problems. The multiquadric is used as the RBF. The algorithm is developed with Mathematica and eight virtual processors are used in calculations on a multicore computer with four physical cores. The method provides accurate numerical results in a stable manner. Parallel speedup increases with the number of processors up to five and seven processors for external and fission source problems, respectively. The speedup values are limited by the constrained resource sharing of the multicore computer’s memory. On the other hand, significant time savings are achieved with parallel computation. For the four-group fission source problem, when 4316 interpolation nodes are employed, the utilization of seven processors instead of sequential computation decreases the computation time of the meshless approach by 716 s.

We consider the Galerkin and Collocation Isogeometric approximations of the acoustic wave equation with absorbing boundary conditions, while the time discretization is based on second-order Newmark schemes. A numerical study investigates the properties of the two IGA methods as concerns stability thresholds, convergence errors, accuracy, computational time, and sparsity of the stiffness matrices varying the polynomial degree p , mesh size h , regularity k , and time step Δ t. In order to compare the two IGA methods, we focus on two meaningful examples in the framework of wave propagation simulations: a test problem with an oscillatory exact solution having increasing wave number, and the propagation of two interfering Ricker wavelets. Numerical results show that the IGA Collocation method retains the convergence and stability properties of IGA Galerkin. In all examples considered, IGA Collocation is in general less accurate when we adopt the same choices of parameters p , k , h , and Δ t. On the other hand, regarding the computational cost and the amount of memory required to achieve a given accuracy, we observe that the IGA Collocation method often outperforms the IGA Galerkin method, especially in the case of maximal regularity k = p − 1 with increasing NURBS degree p. [ABSTRACT FROM AUTHOR]

This research paper aims to re-evaluate Arabic grammatical heritage through a contemporary lens of text linguistics. This approach emphasizes the text as a unified linguistic unit, focusing on how language elements work together to create meaning. Modern linguists refer to this as "text grammar. "The study unfolds across two sections. Section I provides a conceptual overview of Sahih al-Bukhari and its methodology. It further explores the concept of text linguistics, its objectives, and the tools it employs. Section II delves into the phenomenon of cohesion, demonstrating how it fosters coherence, harmony, and connections within models of the Prophet's (peace be upon him) hadiths in Sahih al-Bukhari. This section also analyzes the foundational elements and principles of textual linkage that the Prophet relied upon in his teachings. The research concludes that the concept of collocation, or the way words habitually appear together within a text, has been present in Arabic for centuries. This is evident through the cohesion displayed in the text's components and the various methods of textual linking, such as stylistic choices, thematic integration, and organization. [ABSTRACT FROM AUTHOR]

This article is a corpus-based study, exploring three synonymous verbs: "join," "participate," and "attend," in terms of the degree of formality and collocation. The data were derived from the Corpus of Contemporary American English (COCA). The results demonstrated that "participate" is the most formal word as it commonly appears in academic texts. Similarly, "attend" is as formal as "participate" and frequently emerges in newspapers. On the other hand, "join" has the highest number of occurrences in informal contexts, that is, spoken and television and movie subtitles. For the purposes of this study, the top-thirty frequently listed noun collocates with MI scores higher than three were examined. The collocates were categorized into themes according to semantic preference. It was found that "participate" and "attend" are more synonymous as these two verbs share a number of particular noun collocates. Moreover, "participate" and "attend" have some overlapping collocates as represented by the emerging themes. These shared themes highlight the close sense of relation between the two verbs. However, "join" is the least synonymous among these three verbs as it has its own unique sets of noun collocates. The conclusion made from distinctions in object noun collocates and the degree of formality can illustrate the usage of the three target synonyms. [ABSTRACT FROM AUTHOR]

Research into vocabulary knowledge often differentiates between breadth (how many words a person knows) and depth (how well the words are known). Both theoretical categories are essential for understanding language learners' lexical development, but how the different aspects of vocabulary knowledge interconnect has not received the same attention as each individual dimension, especially in terms of productive knowledge. This study analyses lexis from mid-frequency lemmas in the K3–K9 frequency bands from the learner corpus PELIC (The University of Pittsburgh English Language Institute Corpus). Critically for learners, mastery of lexis in this frequency range is essential for achieving the English proficiency required for university study. From these mid-frequency items, a dataset of 7,554 tokens were collected from word families with multiple derivations and manually annotated. The findings showed high rates of collocational and derivational accuracy for the forms learners opted to use. However, compared to expert speaker texts in the Corpus of Contemporary American English (COCA), learners overused the verb forms and underused the noun forms of these lexical items. These patterns provide evidence of the interplay between breadth and depth in learners' productive vocabulary usage, suggesting that increased lexical depth will naturally lead to greater lexical breadth and vice versa. Pedagogical implications reaffirm the importance of developing learners' explicit morphological awareness and collocational accuracy. Suggestions for mid-frequency lexical items to prioritize in language learning are also provided, with a view to helping learners achieve academic readiness. [ABSTRACT FROM AUTHOR]

This article investigates semantic prosody in a diachronic perspective. Although prosodies have been shown to change over time, there is no consensus regarding the source of such changes. The present study explores this further through a corpus study of the development of the lemmas fabric, fabricate and fabrication from the late 15th century to the late 20th century, drawing on material from Early English Books Online, the Corpus of Late Modern English Texts and the British National Corpus. The results of the study show that prosodic changes coincide with the emergence of new senses and indicate that these processes are related to and possibly caused by semantic transfer induced by persistent prosodies over time. [ABSTRACT FROM AUTHOR]

Satellite radar interferometry (InSAR) enables large-scale monitoring of displacement with precision akin to ground-based methods. Using measurements from Sentinel-1 satellites, persistent scatterer networks cover areas up to hundreds of kilometers in size. One of the current challenges for the InSAR community is to tie these networks into a current and country-specific global terrestrial reference system through collocation with other geodetic techniques, especially Global Navigation Satellite Systems (GNSS). In this work, an optimal procedure for assessing a suitable collocation properties for InSAR and GNSS techniques is discussed, along with the proposal for the methodology to determine the spatial relationship between the reference points of both techniques. The study analyzes three collocation stations in Slovakia using their radar backscattering characteristics. InSAR achieves an intrinsic accuracy of up to 1 mm but has uncertainties several orders of magnitude larger in 3D space. A collocation of InSAR measurements with GNSS can tie relative InSAR displacement estimates to an absolute reference frame. [ABSTRACT FROM AUTHOR]

The conditioning and spectral properties of the mass and stiffness matrices for acoustic wave problems are here investigated when isogeometric analysis (IGA) collocation methods in space and Newmark methods in time are employed. Theoretical estimates and extensive numerical results are reported for the eigenvalues and condition numbers of the acoustic mass and stiffness matrices in the reference square domain with Dirichlet, Neumann, and absorbing boundary conditions. This study focuses in particular on the spectral dependence on the polynomial degree p, mesh size h, regularity k, of the IGA discretization and on the time step size Δ t and parameter β of the Newmark method. Results on the sparsity of the matrices and the eigenvalue distribution with respect to the number of degrees of freedom d.o.f. and the number of nonzero entries nz are also reported. The results show that the spectral properties of the IGA collocation matrices are comparable with the available spectral estimates for IGA Galerkin matrices associated with the Poisson problem with Dirichlet boundary conditions, and in some cases, the IGA collocation results are better than the corresponding IGA Galerkin estimates, in particular for increasing p and maximal regularity k = p - 1 . [ABSTRACT FROM AUTHOR]

This article introduces and explores the 3.5-million-word Victorian Anti-Vaccination Discourse Corpus (VicVaDis). The corpus is intended to provide a (freely accessible) historical resource for the investigation of the earliest public concerns and arguments against vaccination in England, which revolved around compulsory vaccination against smallpox in the second half of the 19th century. It consists of 133 anti-vaccination pamphlets and publications gathered from 1854 to 1906, a span of 53 years that loosely coincides with the Victorian era (1837–1901). This timeframe was chosen to capture the period between the 1853 Vaccination Act, which made smallpox vaccination for babies compulsory, and the 1907 Act that effectively ended the mandatory nature of vaccination. After an overview of the historical background, this article describes the rationale, design and construction of the corpus, and then demonstrates how it can be exploited to investigate the main arguments against compulsory vaccination by means of widely accessible corpus linguistic tools. Where appropriate, parallels are drawn between Victorian and 21st-century vaccine-hesitant attitudes and arguments. Overall, this article demonstrates the potential of corpus analysis to add to our understanding of historical concerns about vaccination. [ABSTRACT FROM AUTHOR]

Periodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids. While various bifurcations of periodic orbit families around asteroids have been extensively studied, period-multiplying bifurcations have received less attention. This paper focuses on studying period-multiplying bifurcations of periodic orbit families around asteroids. In particular, orbits with periods of approximately 7 and 17 times that of the rotational period of asteroid 216 Kleopatra were computed. The computation of high-period orbits provides insights into the numerical aspects of simulating long-duration trajectories around asteroids. The previous literature uses single-shooting and multiple-shooting methods to compute bifurcations of periodic orbit families around asteroids. Computational difficulties were encountered while using the shooting methods to obtain period-multiplying bifurcations of periodic orbit families around asteroids. This work used the Legendre–Gauss collocation method to compute period-multiplying bifurcations around asteroids. This study recommends the use of collocation methods to obtain long-duration orbits around asteroids when computational difficulties are encountered while using shooting methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce second derivative multistep collocation methods for the numerical integration of ordinary differential equations (ODEs). These methods combine the concepts of both multistep methods and collocation methods, using second derivative of the solution in the collocation points, to achieve an accurate and efficient solution with strong stability properties, that is, A-stability for ODEs. Using the second-order derivatives leads to high order of convergency in the proposed methods. These methods approximate the ODE solution by using the numerical solution in some points in the r previous steps and by matching the function values and its derivatives at a set of collocation methods. Also, these methods utilize information from the second derivative of the solution in the collocation methods. We present the construction of the technique and discuss the analysis of the order of accuracy and linear stability properties. Finally, some numerical results are provided to confirm the theoretical expectations. A stiff system of ODEs, the Robertson chemical kinetics problem, and the two-body Pleiades problem are the case studies for comparing the efficiency of the proposed methods with existing methods. [ABSTRACT FROM AUTHOR]

Acknowledging the critical role of working memory in language acquisition, this study examines the effects of multimodal input enhancement on working memory capacity (WMC) and collocation learning in adolescent and adult EFL learners. A cohort of 117 participants was randomly assigned to either experimental groups, receiving enhanced textual and auditory inputs, or control groups, experiencing standard inputs. Assessments included the Preliminary English Test, n-back test, and immediate and delayed collocation posttests. The results indicated that multimodal input significantly improved WMC and the recall and retention of collocations for all learners. Adolescents, in particular, excelled in both immediate and delayed tests and adapted their WMC more effectively in a multimodal context than adults. Additionally, an interaction between age and WMC was noted, affecting collocation recall and retention. These findings affirm the benefits of multimodal materials in enhancing cognitive functions and memory resources, thus improving language learning. The study offers practical insights for educational practices, advocating for the use of varied modalities in teaching materials to cater to different learning styles and cognitive needs. It also highlights the significance of designing age-appropriate materials and managing cognitive load in curriculum development, providing a tailored approach to language education for diverse learner populations. [ABSTRACT FROM AUTHOR]

The experimental and theoretical analysis of viscous dissipation and heat generation/absorption management is crucial in engineering, medical, biological, and exploration activities. This study investigates the analytical solution of viscous heating and thermal gyration of magneto-micropolar fluid particles across a resistive medium with internal non-uniform heat generation/absorption. The formulated partial differential equations were appropriately converted into coupled ordinary differential equations employing similarity variables along with the boundary conditions. The simulation of the resultant equations is carried out using the collocating weighted residual scheme, and the result is validated using the shooting technique via the Runge-Kutta method of order four, Adomian decomposition technique, variational iteration scheme, differential transform method, and quasi-linearization technique as the control methods. Tabular and graphical representations are provided to illustrate the flow characteristics. Taking from the results, the existence of a magnetic field retards the gyration of the fluid particle motion. The spin gradient and vortex viscosity terms reveal the reverse occurrence of micro-rotation distribution, and it is seen that the porosity term suppresses the velocity field. Furthermore, it is observed that the parameters that enhance internal heat generation decrease the viscosity of the fluid in the region. Hence, these findings will assist scientists and engineers to effectively manage heat generation/absorption in industries where effective heat transfer activities are crucial to achieving ideal performance and reducing energy waste.

The paper proves convergence of unsymmetric radial basis functions (RBFs) collocation for second order elliptic boundary value problems on the bounded domains. By using Schaback’s linear discretization theory, L2 error is obtained based on the kernel-based trial spaces generated by the compactly supported radial basis functions. The present theory covers a wide range of kernel-based trial spaces including stationary and non-stationary approximation. The convergence rates depend on the regularity of the solution, the smoothness of the computing domain, and the approximation of scaled kernel-based spaces. Some numerical examples are added for illustration.

Accurate atmospheric 3D wind observations are one of the top priorities for the global scientific community. To address this requirement, and to support researchers’ needs to acquire and analyze wind data from multiple sources, the System for Analysis of Wind Collocations (SAWC) was jointly developed by NOAA/NESDIS/STAR, UMD/ESSIC/CISESS, and UW-Madison/CIMSS. SAWC encompasses the following: a multi-year archive of global 3D winds observed by Aeolus, sondes, aircraft, stratospheric superpressure balloons, and satellite-derived atmospheric motion vectors, archived and uniformly formatted in netCDF for public consumption; identified pairings between select datasets collocated in space and time; and a downloadable software application developed for users to interactively collocate and statistically compare wind observations based on their research needs. The utility of SAWC is demonstrated by conducting a one-year (September 2019–August 2020) evaluation of Aeolus level-2B (L2B) winds (Baseline 11 L2B processor version). Observations from four archived conventional wind datasets are collocated with Aeolus. The recommended quality controls are applied. Wind comparisons are assessed using the SAWC collocation application. Comparison statistics are stratified by season, geographic region, and Aeolus observing mode. The results highlight the value of SAWC’s capabilities, from product validation through intercomparison studies to the evaluation of data usage in applications and advances in the global Earth observing architecture.

In this paper, we develop and implement numerical method for the solution of non-linear Volterra integro-differential equations of fractional order using collocation method. We obtain the integral form of the problem and transform it into system of algebraic equations, we solve the algebraic equations using matrix inversion method. The analysis of the developed method is investigated and solution found to be q-contraction and convergent. The uniqueness of the solution also proven. Numerical examples were considered to test the efficiency of the method which shows that the method compete favourably with the existing methods.

This study reflects the importance of semantic mapping strategy knowledge and students' speaking proficiency. The goal of this study is to find out how grade nine students who are studying English as a second language perceive and have experienced successful education in the classroom with respect to their productive skills. The study proposes that semantic mapping can help students discover the relationships between known words and learn new ones, improving their understanding of English. This strategy motivates students to learn and avoids boredom. The researcher followed a deduction analysis method revealing some of the important case studies examining the significance of semantic mapping strategy on enhancing students" vocabulary. It is to show the effectiveness of Semantic Mapping Technique in helping students retain vocabulary in long-term memory. This method can enhance students' vocabulary learning abilities, making it crucial for teachers to learn if this method can help them. The goal is to minimize lack of retention and recognition in students. The current study explores vocabulary learning strategies students prefer and find effective, considering their experiences and beliefs. It provides information for both learners and teachers about vocabulary learning strategies. The study covers the theoretical discussion of Semantic Mapping Technique, its applications, methods, materials, findings, and concludes with a final chapter. It takes the learner as an individual and provides insights for both learners and teachers. It emphasizes the importance of considering learners' experiences and beliefs when using vocabulary strategies. [ABSTRACT FROM AUTHOR]

This paper describes a protocol for using dictionaries in classroom activities to support language learning and develop language awareness (Nied Curcio 2022). A group of undergraduate foreign language students was guided through the process of compiling a multilingual Covid-19 dictionary, which provides collocational data to support language production and improve fluency in an L2. The activities were an integral part of a BA course in Lexicology and Lexicography. Lexonomy was used as the project editing tool. The compilation process not only shed light on the students' challenges in basic language skills, such as syntactic analysis, but also highlighted the importance of refining the proposed teaching programme to include more detailed metalinguistic explanation and an augmented dictionary microstructure. Besides, the skills that emerged from the experiments conducted also provide valuable insights for research into dictionary use and the design of effective dictionaries. [ABSTRACT FROM AUTHOR]

Since at least as far back as the infamous Derek Bentley case of the 1950s in which an unarmed 19-year-old was convicted and executed for murder based on his alleged uttering of the words let him have it to his gun-wielding accomplice, the issue of incitement has been positioned firmly as an object of interest for forensic linguists. An example of a language crime—i.e. an unlawful speech act (as reported by Shuy in Language crimes: The use and abuse of language evidence in the courtroom, Wiley Blackwell, Hoboken, 1993) the features of incitement—formalized as intentionally encouraging or assisting others to commit an offence in the law of England & Wales under section 44 of the Serious Crime Act 2007 (https://www.legislation.gov.uk/ukpga/2007/27/contents)—have been widely debated by linguists and legal scholars alike. This paper draws on two webinars hosted by The Hunting Office in August 2020, which were subsequently leaked by the Hunt Saboteurs Association. Featuring senior figures from the hunting community addressing a nationwide audience of hunt masters, the webinars led to a police investigation and subsequent prosecution and conviction of one of the main speakers, Mark Hankinson, for encouraging or assisting others to commit an offence under the Hunting Act 2004. In this paper I explore what, linguistically, is meant by encouraging or assisting. Through corpus-assisted pragmatic and discourse analyses I interrogate the webinars to address the question of how precisely Hankinson implied his encouragement of illegal hunting with dogs. The phenomena of collocation and semantic prosody are crucial for understanding how such meanings came to be attached to the contributions Hankinson makes to the webinars. Moreover the paper will examine the contributions of other speakers and demonstrate that the same incriminating linguistic patterns in Hankinson's talk are also evident in that of those who were not prosecuted. [ABSTRACT FROM AUTHOR]

In this study, an exact and a numerical method namely direct algebraic method and collocation finite element method are proposed for solving soliton solutions of a special form of fifth-order KdV (fKdV) equation that is of particular importance: Caudrey-Dodd-Gibbon (CDG) equation. For these aims, homogeneous balance method and septic B-spline functions are used for exact and numerical solutions, respectively. Next, it is proved by applying von-Neumann stability analysis that the numerical method is unconditionally stable. The error norms L2 and L∞ have been computed to control proficiency and conservation properties of the suggested algorithm. The obtained numerical results have been listed in the tables. The graphs are modelled so that easy visualization of properties of the problem. Also, the obtained results indicate that our method is favourable for solving such problems. [ABSTRACT FROM AUTHOR]

Accurate atmospheric 3D wind observations are one of the top priorities for the global scientific community. To address this requirement, and to support researchers' needs to acquire and analyze wind data from multiple sources, the System for Analysis of Wind Collocations (SAWC) was jointly developed by NOAA/NESDIS/STAR, UMD/ESSIC/CISESS, and UW-Madison/CIMSS. SAWC encompasses the following: a multi-year archive of global 3D winds observed by Aeolus, sondes, aircraft, stratospheric superpressure balloons, and satellite-derived atmospheric motion vectors, archived and uniformly formatted in netCDF for public consumption; identified pairings between select datasets collocated in space and time; and a downloadable software application developed for users to interactively collocate and statistically compare wind observations based on their research needs. The utility of SAWC is demonstrated by conducting a one-year (September 2019–August 2020) evaluation of Aeolus level-2B (L2B) winds (Baseline 11 L2B processor version). Observations from four archived conventional wind datasets are collocated with Aeolus. The recommended quality controls are applied. Wind comparisons are assessed using the SAWC collocation application. Comparison statistics are stratified by season, geographic region, and Aeolus observing mode. The results highlight the value of SAWC's capabilities, from product validation through intercomparison studies to the evaluation of data usage in applications and advances in the global Earth observing architecture. [ABSTRACT FROM AUTHOR]

Since collocation knowledge is integral to second language vocabulary depth, it necessitates a careful examination of various measurement approaches. To this end, the current paper provides an overview and evaluation of extant collocation measurements used in empirical studies on L2 English (N = 153) published between 1980 and 2023 indexed in the SSCI, SCIE, AHCI, SCOPUS, and ERIC databases. Six instruments, seven item formats, and three other assessment tools were identified and reviewed for the assessment of receptive and productive collocation knowledge. The review focused on the collocation knowledge measured by each tool, the instrument and/or item format employed, item design, reported reliability, and potential drawbacks of employing each instrument and item format in research or practice. The review proposes several theoretical and practical considerations for future assessments of and research on English collocation knowledge. [ABSTRACT FROM AUTHOR]

The meshless global radial basis function (RBF) collocation method is widely used to model physical phenomena in science and engineering. The method produces highly accurate solutions with an exponential convergence rate. However, due to the global approximation structure of the method, dense node distributions lead to long computation times and hinder the applicability of the technique. In order to overcome this issue, this study proposes a parallel meshless global RBF collocation algorithm. The algorithm is applied to 2-D neutron diffusion problems. The multiquadric is used as the RBF. The algorithm is developed with Mathematica and eight virtual processors are used in calculations on a multicore computer with four physical cores. The method provides accurate numerical results in a stable manner. Parallel speedup increases with the number of processors up to five and seven processors for external and fission source problems, respectively. The speedup values are limited by the constrained resource sharing of the multicore computer's memory. On the other hand, significant time savings are achieved with parallel computation. For the four-group fission source problem, when 4316 interpolation nodes are employed, the utilization of seven processors instead of sequential computation decreases the computation time of the meshless approach by 716 s. [ABSTRACT FROM AUTHOR]

Background: This study reports on new contexts in which formulaic language has been used in the years since 2013 when the last synthesis was carried out. The background presents an old but still useful definition and lists themes under which research was arranged in 2013 and which continue to be used. Aims: This study has a particular emphasis on the relevance of formulaic language to people living with dementia. Methods: Section 3, identifying new directions, reviews new 'third waves' of research priorities in several fields in which formulaic sequences play a major role, including sociolinguistic variation, corpus‐based and corpus‐driven analyses, pragmatics, human‐computer interaction, and psycholinguistics, all of which are relevant to speech‐language therapists. Section 4, outreach and expansions, illustrates new contributions from cognitively impaired person‐to‐person exchanges in online environments, recent examinations of infant‐ and pet‐directed speech incorporating formulaic language, and online graphic explorations such as emojis. Section 5 focuses on growth of research in theoretical and clinical applications by Van Lancker Sidtis, as illustrated by references to her recent work. Main Contribution: The paper's main contribution is to summarize the work on formulaic language over the last 10 years, to indicate its continued importance and relevance in ordinary conversation, and especially in allowing people living with dementia to continue to interact with others. Conclusion: The paper concludes by suggesting that more focus be placed on the analysis of formulaic language with an emphasis on its relevance for speech‐language therapists and other clinicians. WHAT THIS PAPER ADDS: What is already known on the subject: Research has been growing since the late 1970s and early 1980s on non‐propositional language (as opposed at that time to the Chomskyan paradigm) and especially on lexical bundles, idioms, second language acquisition and multiword expressions. Studies beginning with Hughlings Jackson (1874) have been annotated through early 2012 (Wray, 2013). What this study adds: This study examines 'third waves' in pragmatics, sociolinguistics and areas of neurology and speech perception contributing to what Van Lancker Sidtis (2021) calls the third wave of acceptance of the range and depth of formulaic sequences in ordinary or familiar language. What are the clinical implications of this work?: Conversations with pet robots or web‐based composition with emojis are but two of the developing areas built on formulaic sequences currently being used for communication interventions with persons living with dementia or other major neurocognitive disorder. Overviews of major contributions in theory and social contexts by Wray (2020, 2021) and theoretical and cognitive applications by Van Lancker Sidtis (2021) detail new areas for the study of formulaic sequences and their contributions to a range of neurocognitive disorders. [ABSTRACT FROM AUTHOR]

This study explores the unique linguistic characteristics of bitcoin, which has significantly changed the financial world over the past few years. As the concept of bitcoin, cryptocurrency and the digital network behind them are not dealt with in LSP (Language for Specific Purposes) coursebooks yet, this small-scale research is intended to fill this niche. In order to see what terminology has to be acquired to be able to understand the basic issues about bitcoin, online sources dealing with this innovative technology and its regulatory systems have been used. The selected online texts are analysed by TextStat software, which is capable of making word counts and collocation frequency. The results show us the most common collocations with bitcoin, and blockchain processing within context, as well as the most frequently used words (e.g., cryptocurrency or exchange), which definitely need to be learned by students majoring in Business English. My aim with this research is that LSP teachers get a comprehensive picture of what terminology to teach to their student when dealing with the topic of cryptocurrencies. In addition, bitcoin-related vocabulary can be integrated into other subjects, such as economics, finance or technology, allowing students to explore the connections between different fields of knowledge. [ABSTRACT FROM AUTHOR]

Through consultations with the online version of the Longman Dictionary of Contemporary English (LDOCE) and the Corpus of Contemporary American English (COCA), this study focuses on distinguishing between the two synonymous verbs 'restrict' and 'constrain', both part of Coxhead's (2000) Academic Word List, in terms of formality and collocations. The COCAinformed findings revealed that both near-synonyms are most prevalent in academic genres, sharing an equally high level of formality, and exhibit six overlapping groups of noun collocates. Interestingly, the target synonyms, along with their left- and right-sided noun collocates, form context-specific clusters. The verb 'restrict' is associated with terms related to governance and rights (i.e., laws and regulations restrict liberties) while 'constrain' with governance and commerce (i.e., rules constrain spending). The two are also characterized by unique patterns of collocating with nouns that have opposite morphological meanings: 'restrict' pairs with noun collocates containing morphemes representing inbound activities (e.g., acc-in access, as in restrict access), while 'constrain' with those indicating outbound directions (e.g., ex- in expansion, as in constrain expansion). [ABSTRACT FROM AUTHOR]

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Collocations is a term for a linguistic phenomenon that can be and is variously understood and defined. The aim of this article is to give an overview of the narrow concept of collocations suggested by Hausmann. The author of the article describes the semantic (phraseological) approach to the term, which stands in opposition to the syntactic, or corpus-based one. Collocations, according to Hausmann, take into account the process of thinking and language production of language learners. The hierarchical structure of collocations consisting of the collocation base and the collocator, which was suggested for the first time, is presented, and the individual elements of this phraseme are characterised in the article. Also, the author of the article attempts to transfer the concept of collocations according to Hausmann to the Polish language, and indicates a possible classification of Polish collocations in the semantic approach. [ABSTRACT FROM AUTHOR]