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The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to evaluate the appropriateness of such unconventional calculus.

The nonlocal fractal integro-differential equations describing RL, RC, LC and RLC circuits with arbitrary source terms defined on middle b cantor set have been formulated and solved by means of fractal Laplace transformation. Numerical simulations based on the derived solutions have been performed where an LC circuit has been studied by means of Lagrangian and Hamiltonian formalisms. The nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been derived and the local fractal calculus-based ones have been revisited.

The author has found that the LC circuit defined on a middle b cantor set become a physically unsound system due to the unreasonable associated Hamiltonian unless the local fractal calculus has been applied instead.

For the first time, the nonlocal fractal calculus-based analyses of electrical circuits with arbitrary source terms have been performed where those circuits with order higher than 1 have also been analyzed. For the first time, the nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been proposed. The revised contradiction free local fractal calculus-based Lagrangian and Hamiltonian equations have been presented. A comparison of local and nonlocal fractal calculus in terms of Lagrangian and Hamiltonian formalisms have been made where a drawback of the nonlocal one has been pointed out.

The purpose of this paper is to verify the possibility of ultrasonic intensification of drug dissolution of cholesterol calculi of the gallbladder using conventional ultrasound frequency and intensity from 0.1 to 0.5 W/cm².

For research purposes, the physical model was developed containing pig bile, pig liver, pigskin, fat and muscles, as well as human cholesterol calculus removed by surgery and a drug with ursodeoxycholic acid.

The studies have shown the possibility of accelerating the drug dissolution of calculi of the gallbladder with ultrasound exposure. The ultrasound intensity of 0.4 W/cm² is the most preferable to intensify the dissolution of calculus.

The results will be used to advance with development of the device and methodology for ultrasonic intensification of drug dissolution of gallbladder calculi.

This paper aims to present the application of situation calculus for knowledge representation in missing persons investigations.

The development of a knowledge representation model for the missing persons investigation process based upon situation calculus, with a demonstration of the use of the model for a missing persons example case.

Situation calculus is valuable for knowledge representation for missing persons investigations, as such investigations have state changes over time, and due to the complexity of the differing investigation activities applicable to different situations, can be difficult to represent using simpler approaches such as tables or flowcharts.

Situation calculus modelling for missing persons investigations adds formalism to the process beyond that which can be afforded by the current use of text, tables or flowcharts. The additional formalism is useful in dealing with the uncertainty present in such investigations.

The implications are a simplification of the application of the current police guidelines, and thoroughness in the application of such guidelines for missing persons investigations via situation calculus modelling.

This paper supports the management of missing person investigations, by using the most critical variables in a missing persons investigation to determine relevant investigation and search activities applicable to the circumstances of a given case.

The novelty of the knowledge representation approach is the application of situation calculus via state and action vectors and a matrix of fluents to the process of missing persons investigations.

This paper aims to evaluate the possibilities of fractional calculus application in electrical circuits and magnetic field theories.

The analysis of mathematical notation is used for physical phenomena description. The analysis aims to challenge or prove the correctness of applied notation.

Fractional calculus is sometimes applied correctly and sometimes erroneously in electrical engineering.

This paper provides guidelines regarding correct application of fractional calculus in description of electrical circuits’ phenomena. It can also inspire researchers to find new applications for fractional calculus in the future.

This paper aims to show how a sociological description – a swarm analysis of the Nazi dictatorship – initially made with the means borrowed from George Spencer-Brown’s Calculus of Indications, can be transformed into a digital circuit and with which methods and tools of digital mathematics this digital circuit can be analyzed and described in its behavior. Thus, the paper also aims to contribute to a better understanding of Chapter 11 of “Laws of Form.”

The analysis uses methods of automata theory for finite, deterministic automata. Basic set operations of digital mathematics and special set operations of the Boolean Differential Calculus are used to calculate digital circuits. The software used is based on ternary logic, in which the binary Boolean logic of the elements {0, 1} is extended by the third element “Don’t care” to {0, 1, −}.

The paper confirms the method of transforming a form into a digital circuit derived from the comparative functional and structural analysis of the Modulator from Chapter 11 of “Laws of Form” and defines general rules for this transformation. It is shown how the indeterminacy of re-entrant forms can be resolved in the medium of time using the methods of automata theory. On this basis, a refined definition of the degree of a form is presented.

The paper shows the potential of interdisciplinary approaches between sociology and information technology and provides methods and tools of digital mathematics such as ternary logic, Boolean Differential Calculus and automata theory for application in sociology.

The purpose of this paper is to enhance students’ mastery of course material in a second semester calculus course and assess the effectiveness of a traditional “lecture-based” instructional model compared to a modified “flipped classroom” model using a mixed method research design.

Evaluation of effectiveness was measured by having students in all four courses take the same pre-post exams and participate in a survey to assess their opinion of each instructional model. Undergraduate students covered the same content using two different modes of instruction.

Within a comparable group of students, participants in the flipped course had similar content knowledge gains as the lecture-based course. Based on responses obtained in blinded student surveys, the authors found that the use of an online homework system (WebAssign) and in-class quizzes were critical motivating factors that likely contributed to the increase in student performance. The flipped classroom instruction was more effective at increasing interest in the subject and promoting student discourse around problem solving. Taken together, the findings support the flipped classroom model as an equally effective means in which to disseminate key calculus concepts to undergraduate students.

Findings from this study are limited to content knowledge gains in calculus over a 14-week time period, and student attitudes toward the mode of instruction they received. More research is needed to study the depth of learning that occurs in small group problem solving and interactions between faculty-and-student and student-to-student.

While many course redesigns focus on incorporating more project-based or laboratory-based learning opportunities, the redesign used in this study was focussed on different ways to deliver the same content. Results from this study suggest that a blended type of learning would be optimal for learning calculus concepts with a strategic use of video content concepts.

The purpose of this paper is to identify funders’ motivations for investing in crowdfunding. It applies trust theory to propose a research model including three subject measures – fundraiser-related, project-related and platform-related factors. Trust has been categorized into cognitive and affective dimensions to specifically analyze the influential factors.

Bootstrapping is employed to analyze data collected from respondents with investment experience on equity crowdfunding projects. Structural equation modeling techniques are adopted to examine the factors that influence trust between funders and crowdfunding as well as the outcomes of this trust.

The results indicate that calculus trust and relationship trust collectively or separately transmit the effect of some antecedents to investment intention. However, there is no evidence indicating the mediating effects of calculus trust and relationship trust on the relationship of structural assurance and value congruence to investment intention.

This paper provides insights for crowdfunding fundraisers on how to build a strong relationship with funders, and it also gives crowdfunding designers advice on how to improve and perfect the platform functions.

This study contributes to a better understanding of the driving forces of calculus and relationship trust and their influence on investment intention. It is also the first to address a funder’s trust using a theoretical model describing the investor intention in crowdfunding and thereby extending the knowledge base of trust theory.

The privacy calculus based on a single stakeholder failed to explain users' co-owned information disclosure owing to the uniqueness of co-owned information. Drawing on collective privacy calculus theory and impression management theory, this study attempts to explore the co-owned information disclosure of social network platform users from a collective perspective rather than an individual perspective.

Drawing on collective privacy calculus theory and impression management theory, this study explores the co-owned information disclosure of social network platform users from a collective perspective rather than an individual perspective based on a survey of 740 respondents.

This study finds that self-presentation and others presentation directly positively affect users' co-owned information disclosure. Also, self-presentation, others presentation and relationship presentation indirectly positively affect users' co-owned information disclosure via relationship support. Furthermore, personal privacy concern, others' privacy concern and relationship privacy concern indirectly negatively affect users' co-owned information disclosure via relationship risk.

The findings develop the theory of collective privacy calculus and impression management, which offer insights into the design of the collective privacy protection function of social network platform service providers.