We cover the gap in the analysis of explosion time between one-dimensional and multidimensional case for a rather general class of stochastic Volterra integro-differential equations. By mimicking the classical techniques from Murge and Pachpatte (1986) and generalizing them to the multidimensional case, we prove that the class of equations under consideration has almost surely infinite explosion time.

A refined version of the stochastic Volterra integral model for an epidemic of the new corona virus SARS-CoV-2, causing the COVID-19 disease, is analysed. The system is constructed from the corresponding ordinary differential model by introducing the class of immunized individuals with the finite duration of immunity gained by vaccination. In addition, independent delays, represented as random time distribution functions, were introduced, which describe the duration of incubation, infectiousness, and immunity acquired through recovery from the disease or vaccination. Beside these refinements, the classical Ornstein-Uhlenbeck process is introduced as a model for the transmission coefficient describing the exposure of individuals from susceptible class. For this particular system, the existence and uniqueness of the positive global solution are proven. Furthermore, the conditions for extinction and persistence in mean of the disease are derived. The theoretical results are illustrated via numerical simulations.

In this paper we propose stochastic SIRS model which describes propagation of two independent computer viruses. Randomness is introduced in the model by perturbing transmission rates via Brownian motion and Poisson jump. For this model, we theoretically prove that its solution is unique, global and positive. Furthermore, we derive conditions under which viruses become extinct from population. Also, conditions for stochastic strong persistence in mean of viruses will be obtained. In the end, we will present numerical simulations to illustrate our theoretical results using Euler-Maruyama method.

A large class of backward doubly stochastic differential equations whose coefficients are linearly perturbed is observed in this paper. Their solutions are compared in the L^p-sense (p ≥ 2) with the solutions of the appropriate unperturbed equations of the same type, under the most global non-Lipschitz condition for the coefficients of the equations. Also, an interval [t̅(η), T] ⊂ [0, T], on which the L^p difference between the solutions of perturbed and unperturbed equations is less than a given value η, is established.

The authors correct part of Theorem 3.1 in the paper titled above [1] in order to avoid using inadequate inequalities and approximations while defining constant C. These corrections do not influence on the formulation of Theorem 3.1 and its conclusion. Also, parts of proof of Theorem 4.2 are corrected in order to avoid using inadequate inequalities. This corrections do not influence on conclusion of theorem. The authors apologize for any inconvenience that may have been caused.

Research on oral performance assessment in an English for Academic Purposes (EAP) learning context supported by Mobile Assisted Language Learning (MALL) is scarce. This research aimed to investigate whether rubrics may be expected to yield valid, reliable and replicable data when evaluating EAP speaking skills in remote classes supported by MALL. An action-based case study was conducted with a convenience sample of 93 students (from three different cohorts: 2019, 2020 and 2021) video-recording themselves delivering speeches with their smartphones in an English language university course including EAP writing and speaking skills as substantial requirements. The students' EAP speaking skills were evaluated over three years with descriptive, analytic, task-specific and teacher-created rubrics contextualised in real-world language. The rubrics were designed to include a rating scale, specific criteria, levels of achievement and descriptors. The results indicate that when implemented as a preparation and assessment tool, rubrics provide valid, reliable and replicable data for assessing EAP speaking skills in remote classes supported by MALL. The practical implications of these findings are significant since the data collected in this way can help language instructors evaluate the students' spoken communicative competence in remote classes that would otherwise be difficult to assess.

We analyze a stochastic optimal control problem for the PReP vaccine in a model for the spread of HIV. To do so, we use a stochastic model for HIV/AIDS with PReP, where we include jumps in the model. This generalizes previous works in the field. First, we prove that there exists a positive, unique, global solution to the system of stochastic differential equations which makes up the model. Further, we introduce a stochastic control problem for dynamically choosing an optimal percentage of the population to receive PReP. By using the stochastic maximum principle, we derive an explicit expression for the stochastic optimal control. Furthermore, via a generalized Lagrange multiplier method in combination with the stochastic maximum principle, we study two types of budget constraints. We illustrate the results by numerical examples, both in the fixed control case and in the stochastic control case.

Based on Framing Theory and Sociocognitive Discourse Studies, the study analyzes 1,010 comments following 15 news articles on four Serbian news websites about a Serbian actress accusing her acting teacher of rape. The hate speech in the comments results from five frames evident in the news headlines and includes discourse structures indicating victim blaming, victim shaming, and the lack of sympathy for the victim. The discourse structures are openly telling victims to remain silent about their experience, establishing a specific relationship between certain news frames, online hate speech that rape victims face, and the sociocognitive dimension forcing them into silence.

In this paper, we introduce a method of successive approximations for moment functions of logistic stochastic differential equations. We first reduce the system of the corresponding moment functions to an infinite system of linear ordinary differential equations. Then, we determine certain upper and lower bounds on the moment functions, and utilize these bounds to solve the resulting systems approximately via suitable truncations, iterations and a local improvement step. After obtaining some general theoretical results on the error norms and describing a general algorithm for logistic SDE, we focus on stochastic Verhulst systems in numerical implementations. We compare their moment approximations with numerical solutions via simulation-based methods that include discretizations of the pathwise solutions as well as other convergent numerical procedures like semi-implicit split-step Euler methods.

This research is based on bibliometric analysis to find out if Hate Speech in Spain and Latin America has consolidated as a mature research field in recent years (2021 and 2022). Through the consultation of the Web of Science (WoS) database and by searching specific terms, we obtained a universe of 153 articles that allowed us to address our objective. The results revealed that the analysis of hate speech in Spain and LATAM is mature, characterized by consistent publication trends and influential authors while productive researchers tend to be highly cited. Conceptual trends include Hate Speech, social media, Twitter, and Freedom of Expression. There is also evidence that new theoretical foundations and reference groups in this evolving field are emerging.

Esta investigación utiliza el análisis bibliométrico para conocer si el Discurso de Odio (DDO) en España y Latinoamérica (LATAM) se ha consolidado como un campo de investigación maduro en años recientes (2021 y 2022). A través de la consulta de la base de datos Web of Science (WoS) y mediante la búsqueda de términos específicos se obtuvo un universo de 153 artículos para abordar la cuestión. Los resultados revelan que el análisis del DDO en España y LATAM es maduro, caracterizado por tendencias de publicación consistentes y autores influyentes, mientras que los investigadores productivos tienden a ser altamente citados. Las tendencias conceptuales incluyen el DDO, las redes sociales, Twitter y la libertad de expresión. También hay evidencia de que están surgiendo nuevos fundamentos teóricos y grupos de referencia en este campo en evolución.

This paper reports the findings from an action-based case study conducted with a convenience sample of 42 students encouraged by their teacher to create digital videos as an additional practice tool to improve their oral performance in English as a Foreign Language. The students recorded themselves giving a 10-minute talk following their teacher's instructions. The comparison of the students' oral performance between the oral exam at the end of the fourth semester and the oral exams at the end of the previous three semesters provided evidence of improvement in the students' oral performance in the fourth semester due to the digital videos the students created. The students also completed a questionnaire focusing on their opinions about the additional tool to practice their oral performance. The analyses of the obtained results indicate a positive effect of digital videos created by students both on their oral performance and their attitude to digital video creation. The pedagogical implications of this study suggest three main applications of digital videos: a) as a practice tool to help students improve their oral performance in English, b) as a feedback tool to help teachers provide students with feedback on areas that need improvement and c) as an assessment tool to help teachers evaluate their students' speaking skills.

Dopamine is a crucial neurotransmitter that plays a central role in various aspects of brain functions, including reward processing, motivation, learning, and movement control. Its intricate involvement in these biological processes has made it a subject of extensive research across multiple disciplines, ranging from neuroscience and psychology to computational modeling. In this paper the non-linear stochastic model describing synthesis, storage, release, uptake and metabolism of dopamine in dopaminergic nerve terminal of the rat striatum is introduced. The model is driven by 9-dimensional Brownian motion with constant coordinate intensities. Existence and uniqueness of a positive global solution x(t) = [x(1)(t), ... , x(9)(t)](tau) on a corresponding time-domain are proved and lower and upper bounds for specific moments of coordinate processes {x(i)(t), 0 <= t <= T} are derived. These results are used for calculation of bounds for intensities of driving processes and time horizons ensuring that expected values of coordinate processes stay in the same time-interval as the corresponding expected starting values. Furthermore, positivity preserving balance implicit method is used for simulation of coordinate processes in order to illustrate theoretical results.

Most translation tasks in the entertainment industry involve multiple modes of communication, i.e. they are multimodal, not solely language-based. A translator is expected to analyse, evaluate and transfer each of those modes to render an accurate translation of the source text. This is especially important in films, documentaries, TV and animated shows - multimodal scripts which are being localised for various contexts. An important step in the translation process in the entertainment industry should be the identification of translation errors in the final product which should be based on a proper translation error classification. Given that available translation error classifications rely solely on linguistic modes of communication, the aim of this paper is to propose a multimodal translation error classification which would be based on the multimodality of scripts to be translated and thus provide a reliable tool for the quality check of the final translation product in the entertainment industry. In that way, translators in this industry will be alerted to recognise elements (e.g. tone of voice, facial expressions, proximity, etc.) existing in multimodal scripts where both the source and the target texts as essential parts of the scripts are multimodal products.

The aim of this paper is to analyse a WIS-stochastic differential equation driven by fractional Brownian motion with H>0.5. For this, we summarise the theory of fractional white noise and prove a fundamental L^2-estimate for WIS-integrals. We apply this to prove the existence and uniqueness of a solution in L^2(P) of a WIS-stochastic differential equation driven fractional Brownian motion with H>0.5 under Lipschitz conditions on its coefficients.

In this paper, we prove a result of existence and uniqueness of solutions to coupled forward–backward stochastic differential equations with delayed generators under a Lipschitz condition.

Backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short) are observed in this paper. Existence of M-solution established under functional Lipschitz assumptions. Duality principle between linear BDSIEVs and (forward) stochastic Volterra integral equations is obtained. Using duality principle, the comparison theorem for the adapted solutions of BDSIEVs is proven.

In this paper backward stochastic differential equations with interaction (shorter BSDEs with interaction) are introduced. Far to our knowledge, this type of equation is not seen in the literature before. Existence and uniqueness result for BSDE with interaction is proved under version of Lipschitz condition with respect to Wasserstein distance. Such kind of BSDE arises naturally when considering Monge-Kantorovich problem. In the proof we start from discrete measures using known result of Pardoux and Peng and approximate general measure via Wasserstein distance.

The growing internationalization of higher education and scientific research and publishing, characterized by the dominant use of English as the language of in-struction and publication, has spurred the need for highly specialized, tailor-made ESP courses for university staff and researchers. The proliferation of English Medium In-struction (EMI) has created a new requirement for university teaching staff to acquire not only general English and ESP proficiency, but also pedagogical and intercultural com-municative competences. ESP for particular scientific and technical disciplines, as well as EAP and academic writing instruction in particular, have already gained some ground and acquired a sound tradition in non-Anglophone academic institutions. Therefore ESP, broadly understood as an approach to language teaching that targets the academic or oc-cupational needs of learners, and focuses on the necessary language, genres and skills to address these needs, can now rise to the challenge of combining EMI, terminology -ori-ented ESP for particular disciplines, and EAP. The article presents a specialized course created for the purpose of developing competences for teaching in English and academic writing, as part of the Erasmus+ project Strengthening Teaching Competencies in Natu-ral and Mathematical Sciences (TeComp). In the empirical section, the article presents the results of a needs analysis carried out among prospective learners (university teach-ers and young researchers) in the fields of natural and mathematical sciences at four Serbian universities, included in TeComp. The proposed course, based on the theoretical principles of ESP (Dudley-Evans; Anthony) and EMI (Macaro), as well as on the needs analysis, combines certain components of EMI and academic writing, while addressing particular scientific disciplines and learners.