The 3D Prandtl fluid flow through a bidirectional extending surface is analytically investigated. Cattaneo–Christov fluid model is employed to govern the heat and mass flux during fluid motion. The Prandtl fluid motion is mathematically modeled using the law of conservations of mass, momentum, and energy. The set of coupled nonlinear PDEs is converted to ODEs by employing appropriate similarity relations. The system of coupled ODEs is analytically solved using the well-established mathematical technique of HAM. The impacts of various physical parameters (...) over the fluid state variables are investigated by displaying their corresponding plots. The augmenting Prandtl parameter enhances the fluid velocity and reduces the temperature and concentration of the fluid. The momentum boundary layer boosts while the thermal boundary layer mitigates with the rising elastic parameter strength. Furthermore, the enhancing thermal relaxation parameter ) reduces the temperature distribution, whereas the augmenting concentration parameter drops the strength of the concentration profile. The increasing Prandtl parameter declines the fluid temperature while the augmenting Schmidt number drops the fluid concentration. The comparison of the HAM technique with the numerical solution shows an excellent agreement and hence ascertains the accuracy of the applied analytical technique. This work finds applications in numerous fields involving the flow of non-Newtonian fluids. (shrink)

In our current era, a new rapidly spreading pandemic disease called coronavirus disease, caused by a virus identified as a novel coronavirus, is becoming a crucial threat for the whole world. Currently, the number of patients infected by the virus is expanding exponentially, but there is no commercially available COVID-19 medication for this pandemic. However, numerous antiviral drugs are utilized for the treatment of the COVID-19 disease. Identification of the appropriate antivirus medicine to treat the infection of COVID-19 is still (...) a complicated and uncertain decision. This study’s key objective is to develop a novel approach called _q_-rung orthopair probabilistic hesitant fuzzy rough set, which incorporates the _q_-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set structures. New _q_-ROPHFR aggregation operators have been established: the _q_-ROPHFR Einstein weighted averaging operator and the _q_-ROPHFR Einstein weighted geometric operator. In this study, we explored some basic features of the developed operators. Afterward, to demonstrate the viability and feasibility of the established decision-making approach in real-world applications, a case study related to selecting drugs for COVID-19 pandemic is addressed. Furthermore, a comprehensive comparison with the _q_-rung orthopair probabilistic hesitant fuzzy rough TOPSIS technique is also presented to illustrate the benefits of the new framework. The obtained results confirm the reliability and effectiveness of the proposed approach for finding uncertainty in real-world decision-making. (shrink)

We are in the midst of a fundamental shift, as more enterprises start to use services enabled by cloud technologies. This will heavily impact IT services providers, who must now consider strategies for coping with profound changes in the marketplace or risk being left behind. This research will be of interest to IT services vendors, as well as consumers of IT services.

Nature-inspired optimization techniques are useful tools in electrical engineering problems to minimize or maximize an objective function. In this paper, we use the firefly algorithm to improve the optimal solution for the problem of directional overcurrent relays (DOCRs). It is a complex and highly nonlinear constrained optimization problem. In this problem, we have two types of design variables, which are variables for plug settings (PSs) and the time dial settings (TDSs) for each relay in the circuit. The objective function is (...) to minimize the total operating time of all the basic relays to avoid unnecessary delays. We have considered four models in this paper which are IEEE (3-bus, 4-bus, 6-bus, and 8-bus) models. From the numerical results, it is obvious that the firefly algorithm with certain parameter settings performs better than the other state-of-the-art algorithms. (shrink)

Many real-world optimization problems usually require a large number of conflicting objectives to be optimized simultaneously to obtain solution. It has been observed that these kinds of many-objective optimization problems often pose several performance challenges to the traditional multi-objective optimization algorithms. To address the performance issue caused by the different types of MaOPs, recently, a variety of many-objective particle swarm optimization has been proposed. However, external archive maintenance and selection of leaders for designing the MaOPSO to real-world MaOPs are still (...) challenging issues. This work presents a MaOPSO based on entropy-driven global best selection strategy to solve the many-objective software package restructuring problem. EMPSO makes use of the entropy and quality indicator for the selection of global best particle. To evaluate the performance of the proposed approach, we applied it over the five MaOSPR problems. We compared it with eight variants of MaOPSO, which are based on eight different global best selection strategies. The results indicate that the proposed EMPSO is competitive with respect to the existing global best selection strategies based on variants of MaOPSO approaches. (shrink)

With the increasing volume of data transmission through insecure communication channels, big data security has become one of the important concerns in the cybersecurity domain. To address these concerns and keep data safe, a robust privacy-preserving cryptosystem is necessary. Such a solution relies on chaos encryption algorithms over standard cryptographic methods that possess multistage encryption levels, including high speed, high security, low compute overheads, and procedural power, among other characteristics. In this work, a secure image encryption scheme is proposed using (...) linear feedback shift register and chaos-based quantum chaotic map. The focus of the scheme is mainly dependent on the secret keys from the input of the algorithm. The threat landscape, the statistical test analysis, along critical comparisons with other schemes indicate that the presented algorithm is significantly secure and is resistant to a wide range of different attacks such as differential and statistical attacks. The proposed method has sufficiently higher sensitivity and security when compared to existing encryption algorithms. Several security parameters validated the security of proposed work such as correlation coefficient analyses among the neighboring pixels, entropy, the number of pixels change rate, unified average change intensity, mean square error, brute force, key sensitivity, and peak signal to noise ratio analyses. The randomness of the ciphers produced by the proposed technique is also passed through NIST-800-22. The results of NIST indicate that the ciphers are highly random and do not produce any type of periodicity or pattern. (shrink)

Measuring and evaluating a learner’s learning ability is always the focus of every person whose aim is to develop strategies and plans for their learners to improve the learning process. For example, classroom assessments, self-assessment using computer systems such as Intelligent Tutoring Systems, and other approaches are available. Assessment of metacognition is one of these techniques. Having the ability to evaluate and monitor one’s learning is known as metacognition. An individual can then propose adjustments to their learning process based on (...) this assessment. By monitoring, improving, and planning their activities, learners who can manage their cognitive skills are better able to manage their knowledge about a particular subject. It is common knowledge that students’ metacognitive and self-assessment skills and abilities have been extensively studied, but no research has been carried out on the mistakes that novice developers make because they do not use their self-assessment abilities enough. This study aims to assess the metacognitive skills and abilities of novice software developers working in the industry and to describe the consequences of awareness of metacognition on their performance. In the proposed study, we experimented with novice software developers and collected data using Devskiller and a self-assessment log to analyze their use of self-regulation skills. The proposed study showed that when developers are asked to reflect upon their work, they become more informed about their habitual mistakes, and using a self-assessment log helps them highlight their repetitive mistakes and experiences which allows them to improve their performance on future tasks. (shrink)

The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.

We discuss Robinson's model theoretic proof of Tarski's theorem on undefinability of truth. We present two other “diagonal-free” proofs of Tarski's theorem, and we compare undefinability of truth to other forms of undefinability in nonstandard models of arithmetic.

A good definition of process tracing should highlight what is distinctive about process tracing as a methodology of causal inference. I look at eight criteria that are used to define process tracing in the methodological literature, and I dismiss all eight criteria as unhelpful (some because they are too restrictive, and others because they are vacuous). In place of these criteria, I propose four alternative criteria, and I draw a distinction between process tracing for the ultimate aim of testing a (...) start--end hypothesis versus process tracing as an ultimate end in itself. Although it is clear enough how the former method works, there is still much methodological work to be done in understanding the latter method as a distinctive method of causal inference, I argue. (shrink)

How might Roland Barthes’ posthumously published account of the Neutral invite us to rethink the very activity of cultural analysis? How did Barthes the cultural critic change when, towards the end of his career, he described and desired Neutral Life? Cultural criticism has often taken Barthes’ early semiological work as a guide, but this essay examines how we might need to reorient ourselves as critics, shift our stance, learn to look and live differently in the light of Barthes’ later focus (...) on the Neutral. (shrink)

The ‘black box problem’ is a long-standing talking point in debates about artificial intelligence. This is a significant point of tension between ethicists, programmers, clinicians and anyone else working on developing AI for healthcare applications. However, the precise definition of these systems are often left undefined, vague, unclear or are assumed to be standardised within AI circles. This leads to situations where individuals working on AI talk over each other and has been invoked in numerous debates between opaque and (...) explainable systems. This paper proposes a coherent and clear definition for the black box problem to assist in future discussions about AI in healthcare. This is accomplished by synthesising various definitions in the literature and examining several criteria that can be extrapolated from these definitions. There are no data in this work. (shrink)

Among the main theorems obtained in mathematical logic in this century are the so called limitation theorems, i.e., the Löwenheim-Skolem theorem on the cardinality of models of first-order theories, Gödel’s incompleteness theorems and Tarski’s theorem on the undefinability of truth. Problems connected with the latter are the subject of this paper. In Section 1 we shall consider Tarski’s theorem. In particular the original formulation of it as well as some specifications will be provided. Next various meanings of the notion of (...) a satisfaction predicate will be studied. In Section 2 the problem of definability of the notion of truth, in particular of the notion of truth for the language of Peano arithmetic PA, will be discussed. It will be explicitly shown that the notion of satisfaction for the language of PA can be defined in a certain weak fragment of the second order arithmetic. Finally the axiomatic characterization of satisfaction and truth as well and its mathematical and philosophical meaning will be discussed. (shrink)

We prove that the class of trees with no branches of cardinality ≥κ is not RPC definable in L ∞κ when κ is regular. Earlier such a result was known for L κ + κ under the assumption $\kappa^{ . Our main result is actually proved in a stronger form which covers also L ∞λ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality κ.

Many attempts have been made to define analytic philosophy in a nonhistorical or otherwise deictic way, and to provide a set of necessary and sufficient conditions for a piece of philosophical work to be part of analytic philosophy. This is more difficult than might appear, for the conditions appealed to are normative and must be claimed by non-analytic philosophers to apply to their production as well. In fact, no such set of conditions has been forthcoming, and it is unlikely that (...) it ever will. Instead, I offer a holistic characterization of analytic philosophy as a mode of organization of philosophical work modeled on science. This accounts for analytic philosophy’s success in the academic world, its pedagogic virtues, and its ability to expand beyond its initial boundaries. Two related questions remain: one about the indirect justification analytic philosophy might be granted from outside of philosophy, the other about its ability to make contact with cultural realms other than those with which it has until now established a fruitful exchange. The answers are crucial for the potential renewal of analytic philosophy. (shrink)

We prove that the class of trees with no branches of cardinality $\geq\kappa$ is not RPC definable in $L_{\infty\kappa}$ when $\kappa$ is regular. Earlier such a result was known for $L_{\kappa^+\kappa}$ under the assumption $\kappa^{<\kappa} = \kappa$. Our main result is actually proved in a stronger form which covers also $L_{\infty\lambda}$ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality $\kappa$.

We show that if is not in the field generated by α1,…,αn, then no restriction of the function xβ to an interval is definable in . We also prove that if the real and imaginary parts of a complex analytic function are definable in Rexp or in the expansion of by functions xα, for irrational α, then they are already definable in . We conclude with some conjectures and open questions.

Insightful and fascinating studies of great men of French literature introduce the reader to that wonderful dialogue that takes place between writer and works of literature. Here we find that creative conversation which enchants the mind and forces it to become more deeply aware of its own creative reality. The discovery of the mind as a creative entity is man's most precious acquisition. This book is devoted to this creative activity.

We begin by proving that any Presburger-definable image of one or more sets of powers has zero natural density. Then, by adapting the proof of a dichotomy result on o-minimal structures by Friedman and Miller, we produce a similar dichotomy for expansions of Presburger arithmetic on the integers. Combining these two results, we obtain that the expansion of the ordered group of integers by any number of sets of powers does not define multiplication.

There exists a model in a countable language having a unique element which is not definable in $\scr{L}_{\omega _{1},\omega}$.

We prove the equivalence of the semantic version of Tarski’s theorem on the undefinability of truth with the semantic version of the diagonal lemma and also show the equivalence of a syntactic version of Tarski’s undefinability theorem with a weak syntactic diagonal lemma. We outline two seemingly diagonal-free proofs for these theorems from the literature and show that the syntactic version of Tarski’s theorem can deliver Gödel–Rosser’s incompleteness theorem.

Linked with existence of the almighty, the operation of division by zero which is considered as undefined or indeterminate or infinite sometimes, has been a topic of serious altercation among mathematicians and philosophers for so long. History is evident of the various attempts made to clearly define the algebra of zero, including the idea of division by zero. This includes the evolution of the idea of zero division and various insights from mathematicians like Euler, Craig and more. The realm (...) of the paper contains all such significant attempts and it deals with the idea of the history that wishes to explore the evolution of infinity and undefined. The prime aim of this paper is to clearly distinguish the three concepts of Undefined, Indeterminate and Infinity, along with the concept of division by zero. It strives to provide a notation to undefined expressions, along with citing justifications and results with the help of unpretentious examples from key branches. (shrink)

The questions what the future will bring and if and how it is possible to anticipate coming events have intrigued human beings since the dawn of time. Over the course of the centuries human beings have found better and more sophisticated ways to calculate and predict certain prospective occurrences, for example earthquakes, thunderstorms et cetera. In the Europe of the nineteenth century this potential of rational sciences led to the idea that it would once be possible to anticipate everything that (...) will happen in the universe, going as far as that it should even become predictable how human beings will develop and which actions they will choose. The French philosopher Henri Bergson verbally fought against this kind of belief and developed a so-called process ontology, which claims that nothing in the universe is ever fixed. In fact everything that exists is an ongoing and evolutionary process without a fixed goal. And since—according to Bergson—our rational mind is solely capable of understanding and therefore predicting rigid entities but not processes, any belief in the complete predictability of the universe must be abandoned. Instead, we should focus on the possibilities of an open, spontaneous and creative future, which we will only then be able to understand, if we get more in touch with our so-called intuitive faculty, which is able to fathom a process in its processual state. (shrink)

This paper describes Tarski’s project of rehabilitating the notion of truth, previously considered dubious by many philosophers. The project was realized by providing a formal truth definition, which does not employ any problematic concept.

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the (...) line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

Audrito and Viale introduced the new large cardinal notion of an (α)‐uplifting cardinal (for an ordinal α). We shall show that this notion cannot be defined (or expressed) in the standard first‐order language of set theory for every tranfinite α.

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the (...) line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness (...) and undefinability theorems. (shrink)

Clinician scientists have gained institutional support in the era of translational research, as the key solution to closing the ‘translational gap’ between biomedical research and medical practice. However, clinician scientists remain an ‘endangered species’ in search of a secure niche, while new grants and training programs attempt to counteract their measurable decline in numbers over the past decades. Our study asks how an occupational space for clinician scientists is currently situated between the politics of translation, professional dynamics, and the specialization (...) of academic disciplines. We interviewed clinician scientists, their adjacent professions—clinicians and biomedical researchers—, and contrast their views with expectations from the discourse on clinician scientists in the biomedical and policy literature. We identify professionalizable work and tasks that relate to, first, being able to speak the two languages of both clinic and research, second, translating patients’ needs and clinical experience for further research, and third, counteracting the trends towards specialization by providing an inclusive point of view. We find that clinician scientists are overburdened with fulfilling a hybrid role of simultaneously being clinicians and scientists. Based on these findings, we suggest a path for the future professional development of clinician scientists towards the role of a translator. (shrink)

This article addresses the issue of linguistic phenomena which, as a legacy of the centuries-old tradition of the Roman Empire, are rooted in Polish jurisdictional texts. The study focused on foreign-language expressions and short texts in Latin, used in judicial decisions. The aim of the study was to determine the function of Latinisms as foreign-language expressions in judicial decisions and how their use influences the communicativeness and persuasiveness of argumentation. During the analysis, it was noticed that Latinisms in jurisdictional texts (...) are used on four levels, including: legal maxims, terminology equivalence, linguistic ornaments and the description of taboo phenomena. On the basis of the identified categories, efforts were made to determine the extent to which Latin strengthens or weakens the power of persuasion of judicial decisions. (shrink)