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Euclidean Clifford analysis has become a well‐established theory of monogenic functions in higher‐dimensional Euclidean space with a variety of applications both inside and outside of mathematics. Noncommutativity of the geometric product in Clifford algebras leads to what are now known as inframonogenic functions, which are characterized by certain elliptic system associated to the orthogonal Dirac operator in ℝm. The main question we shall be concerned with is whether or not a higher‐order Lipschitz function on the boundary Γ of a Jordan domain Ω⊂ℝm can be decomposed into a sum of the two boundary values of a sectionally inframonogenic function with jump across Γ. To this end, a kind of Cauchy‐type integral and singular integral operator, very specific to the inframonogenic setting, are widely used. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to solve a kind of the Riemann–Hilbert boundary value problem for (φ , ψ) -harmonic functions, which are linked with the use of two orthogonal bases of the Euclidean space ℝ m . We approach this problem using the language of Clifford analysis for obtaining an explicit expression of the solution of the problem in a Jordan domain Ω ⊂ ℝ m with fractal boundary. Since our study is concerned with a second order differential operator, the boundary data are restricted to involve the higher order Lipschitz class Lip ⁡ (1 + α , Γ) . [ABSTRACT FROM AUTHOR]

In Mexico, approximately 504,000 students pursue a bachelor's degree by means of distance or blended programmes. However, only 42% of these students conclude their degree on time. In the context of blended learning, the focus of this research is to present a causal model, based on a theoretical framework, which describes the relationships concerning motivations, emotions, cognitive strategies, metacognitive strategies, and learning strategies, and their impact on learning performance. The results suggest that negative emotions play a meaningful role between expectancy (a component of motivation) and learning strategies. Also, the expectancy component of motivation positively influences metacognitive strategies. Concerning the relationship between cognition and metacognition, metacognitive strategies take preference concerning the relationship between metacognitive and learning strategies, supporting the theoretical hypothesis that metacognitive processes are on a higher plane than cognition, and affect cognitive process directly. Moreover, the learning outcomes are directly influenced by cognitive and learning strategies, but not by metacognitive ones. Similarly, motivation has direct effects on metacognitive and learning strategies but not on cognitive ones. Lay Description: What is currently known about the subject matter: Several studies describe separately the causal relationships among motivation, emotions, cognition, metacognition, and learning performance in various learning contexts (mainly in distance and face‐to‐face learning).Although the fuzzy boundaries of metacognition have been recognized and a well‐sounded definition has been established, the theoretical relations with motivation, emotions, and cognition have barely been confirmed. What this paper adds to this: From the systems theory point of view, motivation, emotions, cognition, and metacognition are emergent subsystems of the human mind. Thus, studying each of them separately cuts off the relationships that conform the whole system and gives us a limited view of it.This integrating idea is depicted in a causal model, based on a theoretical framework, which describes the relationships among motivations, emotions, cognitive strategies, metacognitive strategies, and learning strategies, and their impact on learning performance.This research offers practical evidence that supports the theoretical relation between motivation and metacognition. The implications of study findings for practitioners. The motivation (expectancy) increases the use of metacognitive and learning strategies; this finding has practical implications, because metacognition may be positively stimulated by knowing that an individual's efforts to learn (control of learning beliefs) and judgments about the individual's abilities to accomplish a given task (self‐efficacy)Moreover, the results suggest that metacognitive, cognitive, and learning strategies are tightly related, in a hierarchical structure where metacognition plays an important role.The causal relations from positive emotions to metacognitive, cognitive, and learning strategies were not significant. Thus, the impact of negative emotions on the reviewed learning content (which captures the computer‐assisted nature of blended learning) and overall grade was explored. Students that face several obstacles in reviewing the learning content have not enough control to overcome this situation, and frustration is instigated. Also, anxious students think in advance that they will may fail the course, and this thought negatively impacts on their overall grade. [ABSTRACT FROM AUTHOR]

Abstract In this paper we prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator naturally arising in polyanalytic function theory. This result provides a generalization of the well-known theorem by Joseph Plemelj [16] and Ivan Privalov [17]. [ABSTRACT FROM AUTHOR]

The aim of this paper is to offer a new definition of Cauchy integral associated with Maxwell equations on 3-dimensional domains with fractal boundaries. This new Cauchy integral leads to several types of integral representation formulas, including the Cauchy representation formula for time-harmonic electromagnetic fields. Our approach is based on the framework of exploiting the close and well-defined connection between the quaternionic analysis and Maxwell equations. [ABSTRACT FROM AUTHOR]

One of the most challenging problems of electrochemical therapy is the design and selection of suitable electrode array for cancer. The aim is to determine how two-dimensional spatial patterns of tissue damage, temperature, and pH induced in pieces of potato (Solanum tuberosum L., var. Mondial) depend on electrode array with circular, elliptical, parabolic, and hyperbolic shape. The results show the similarity between the shapes of spatial patterns of tissue damage and electric field intensity, which, like temperature and pH take the same shape of electrode array. The adequate selection of suitable electrodes array requires an integrated analysis that involves, in a unified way, relevant information about the electrochemical process, which is essential to perform more efficiently way the therapeutic planning and the personalized therapy for patients with a cancerous tumor. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to estimate the Hölder norm of a fractal version of the Hilbert transform in the Douglis analysis context acting from Hölder spaces of Douglis algebra valued functions defined on h-summable curves. [ABSTRACT FROM AUTHOR]

In this note, we consider poly-analytic Cauchy integral operators introduced in a rather natural way on the higher order Lipschitz classes. We prove some boundary properties of the function represented by such an integral operator in the general context of rectifiable Jordan curves. [ABSTRACT FROM AUTHOR]

We present a brief survey of results on the Riemann boundary value problem for non-rectifiable curves. The solution of the Riemann problem for piecewise smooth curves and arcs was one of the well-known achievements of the complex analysis in the first half of the twentieth century. But, for non-rectifiable contours, the problem was solved only during the latter three decades. In the present paper, we consider this solution and certain related questions such as various generalizations of the Cauchy integral over non-rectifiable curves. We describe the technique of investigations, recent results and open problems. [ABSTRACT FROM PUBLISHER]

Global liquidity shortage as well as the availability on the market of overpriced assets and derivatives led to the situation where the global economy depends primarily on liquidity, becoming prone to chain-consistent world crises. Only for the last 15 years, the world has witnessed a continuous series of crises. Therefore, the study of the processes and phenomena of crisis is one of the most important scientific and practical tasks. The aim of this work consisted in the development of methods and models for the early detection of crises in the economy. The significance of the work is to develop an econometric model and tools for detection of crisis. [ABSTRACT FROM AUTHOR]

Currently, blended learning (BL) is trending among higher education institutions (HEIs) around the globe. Despite its popularity, no model exists that describes the motivation that affects instructors' opinions and beliefs regarding online learning. Therefore, the purpose of this study is to identify the factors responsible for motivating instructors at HEIs to integrate the BL approach into their courses. Two categories of motivational factors, namely, extrinsic and intrinsic, have been identified in the BL literature. These factors have been used to design a motivation model based on the cause-effect relationship between them. Survey data were collected from 362 HEI instructors in Turkey and North Cyprus for analysis using a structural equation modelling method. The results indicated that both extrinsic and intrinsic motivational factors have a significant impact on the instructors' motivation to apply the BL approach. However, the extrinsic factor, i.e., "academic workload", did not influence the instructors' motivation. In general, the findings confirmed that, the consideration of both extrinsic and intrinsic factors for motivating the application of blended learning has a 79% impact on the adoption of BL. The findings of this study provide practical solutions for educational managers, curriculum designers and faculty members towards creating a cohesive BL environment in HEIs. [ABSTRACT FROM AUTHOR]