The mathematical model of physical problems interprets physical phenomena closely. This research work is focused on numerical solution of a nonlinear mathematical model of fractional Maxwell nanofluid with the finite difference element method. Addition of nanoparticles in base fluids such as water, sodium alginate, kerosene oil, and engine oil is observed, and velocity profile and heat transfer energy profile of solutions are investigated. The finite difference method involving the discretization of time and distance parameters is applied (...) for numerical results by using the Caputo time fractional operator. These results are plotted against different physical parameters under the effects of magnetic field. These results depicts that a slight decrease occurs for velocity for a high value of Reynolds number, while a small value of Re provides more dominant effects on velocity and temperature profile. It is observed that fractional parameters α and β show inverse behavior against u y, t and θ y, t. An increase in volumetric fraction of nanoparticles in base fluids decreases the temperature profile of fractional Maxwell nanofluids. Using mathematical software of MAPLE, codes are developed and executed to obtain these results. (shrink)

In this paper, we present an intensive investigation of the finite volume method compared to the finite difference methods. In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the (...) other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A DIFFERENT METHOD; A DIFFERENT CASE: THE THEOLOGICAL PROGRAM OF JULIAN HARTT AND AUSTIN FARRER WILLIAM M. WILSON University of Virginia, OharlottesvUZe, Virginia, WRITERS COVERING the work of Julian Hartt or Austin Farrer-the :llew that there ar~generally find that the hest introduction is a straightforward acknowledgement that what is to come is unique. Basil Mitchell, for instance, has said that no matter how one catalogues contemporary theologians, a footnote (...) will be needed, reading " and then of course there is Austin Farrer." 1 Likewise, David Kelsey has said that Hartt's work "is not identi:firuble as a variant on any of the options on the present scene." 2 Those already aicquainted with Hartt and Farrer will no dorurbt agree with the sense o[ these assessments; but if they have heen carefol students they will demand, nev,ertheless, a slight qualification : Hartt,and Farrer.are unique as a party of two. Farrer is a " variant " on Hartt; Hartt belongs down in the footnote aibout Farrer. But from the claim that these two are unique it does not follow that their wo:vk is something akin to those bold " new theologies " fashioned from the innocent's quest for a faith untouched hy either the hands of tradition or the perplexities of our time. Farrer's: anchorage in tradition is obvious throughout his writing and clearly stated in the preiface to his first 1 ' Austin Marsden Farrer,' A Oelebmtion of Fa,ith, ed. Leslie Houlden (London: Hodder and Stoughton, 1970), pp.13-14. 2" Christian Sense Making: Hartt's 'Theological Method and Imagination,"' The J owrna,Z of ReUgion Vol. 58 (4), October 1978, p. 428. 599 600 WILLIAM M. WILSON work. There he said that he was " possessed hy the Thomistic vision" and w:as incapable of "thinking it wrong."3 As to novelty, he had this to say:. •. it is indeed absurd to propose new grounds for belief in the existence of God. The belief has stood for more than ~.ooo years if we are to speak of the essentials of transcendental theism. If belief has been reasona9le it has had a reason, and our only business must be to draw this out and restate it.4 It is.fair to say, to 1be sure, that Farrer "drew out" and "restated " that reason in a. way unlike that of any other contemporary Thomist. There are some who would deny him even the label.5 And it is in this sense that Mitchell's statement about him must remain: If " transcendental," " Neo-," and " traditional " Thomist are three current categories, Farrer is a footnote to them. Hartt, unlike Farrer, has ne,ver labeled himself, hut none of his readers can miss his hostility to any pretense to novelty, even to those which have become our standard fare. The good ship theology (has taken) on a radioactive cargo, its company attracted by the dynamic and dazzle of it all. Relevance~ Historicism, several varieties of analysis, Secularism-what a promising manifest! 6 The " spirit of the age " is not to illuminate the gospel, according to Hartt, rather it is the gospel which illuminates the spirit of the age.7 s Finite and Infinite: A Philosophical Essay, Ibid., p. 1. 11 But see note 5 above. JULIAN HARTT AND AUSTIN FARRER 603 I. The Uniqueness of Hartt and Farrer In a recent encydopedia entry, David Kelsey arranges a useful chart of contemporary theology according to the answers given to " the array o:f decisions theologians must make in the course of doing theology." 12 According to Kelsey, theologians must decide the subject matter o:f theology, the importance o:f cultural context, the 1wudience, the significance of the theologian 's vantage point, the goals o:f theology and the best means o:f accomplishing them. For our purposes o:f identifying Hartt and Farrer, however, we need concentrate only on the first and the last-the question o:f subject matter and the question o:f the hest means £or attaining theological ends. The latter (being the last question the theologian must face) best :identifies the overall mind o:f the theologian at work. Thus, against the standard answers given here, I shall try... (shrink)

In [4], I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek [2]) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski [1] to the non-associative variant NL of L (cf. Lambek [3]). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). (...) We present it below to the use of those who refer to the results of [1] and [4]. (shrink)

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state (...) delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method. (shrink)

We give a proof of the finite model property of some fragments of commutative and noncommutative linear logic: the Lambek calculus, BCI, BCK and their enrichments, MALL and Cyclic MALL. We essentially simplify the method used in [4] for proving fmp of BCI and the Lambek ca culus and in [5] for proving fmp of MALL. Our construction of finite models also differs from that used in Lafont [8] in his proof of fmp of MALL.

A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same (...) is true of higher order probabilities. However, when higher order probabilities are normalized to obtain weights that are used to average the probabilities of the next lower level, the averaging process will yield convergence towards a single first order probability condensing higher order information. An infinite averaging process can be finitely calculated to obtain a coherent assignment. Hence there is no vicious regress of probabilities. Memory beliefs illustrate the convergence of an infinite hierarchy. (shrink)

A theory of probabilities of probabilities is articulated and defended. Hume's argument against higher probabiHties is critically evaluated. Conflicting probability assignments for a hypothetis or theory may result from the appHcation of different methods or perspectives, for example, those of consensual authority and individual ratiocination. When we have conflicting probabilities we may assign probabilities to the diverse probabilities initially obtained. These second level probabilities may also conflict as a result of applying diverse methods or perspectives, and the same (...) is true of higher order probabilities. However, when higher order probabilities are normalized to obtain weights that are used to average the probabilities of the next lower level, the averaging process will yield convergence towards a single first order probability condensing higher order information. An infinite averaging process can be finitely calculated to obtain a coherent assignment. Hence there is no vicious regress of probabilities. Memory beliefs illustrate the convergence of an infinite hierarchy. (shrink)

The method of Quasi-Analysis used by Carnap in his program of theconstitution of concepts from finite observations has the following twogoals: (1) Given unsharp observations in terms of similarity relations thetrue properties of the observed objects shall be obtained by a suitablelogical construction. (2) From a single relation on a finite domain,different dimensions of qualities shall be reconstructed and identified. Inthis article I show that with a slight modification Quasi-Analysis iscapable of fulfilling the first goal for a single (...) observable dimension. Weobtain a partition of the so-called Quality Classes representing thepairwise disjoint and exhaustive extensions associated to the ``values'''' ofthe observable. On the other hand, an example demonstrates that the methodfails, as Goodman has pointed out, for a relation expressing similarity withregard to at least one out of many properties.Since it seems to be impossible in general to reconstruct more-dimensionalqualities from a single similarity relation, the constitution of at least asmany similarity relations as there are qualities have to be presumed. Thenit is possible to state adequate sufficient conditions for the dimension ofthe observable space, even if some of the similarity relations might dependon others. The concept of topological dimension cannot be used for thispurpose on finite sets of observations. We replace it by a set-algebraicalcondition on the Quality Classes. (shrink)

Model theory is concerned mainly, although not exclusively, with infinite structures. In recent years, finite structures have risen to greater prominence, both within the context of mainstream model theory, e.g., in work of Lachlan, Cherlin, Hrushovski, and others, and with the advent of finite model theory, which incorporates elements of classical model theory, combinatorics, and complexity theory. The purpose of this survey is to provide an overview of what might be called the model theory of finite structures. (...) Some topics in finite model theory have strong connections to theoretical computer science, especially descriptive complexity theory. In fact, it has been suggested that finite model theory really is, or should be, logic for computer science. These connections with computer science will, however, not be treated here.It is well-known that many classical results of ‘infinite model theory’ fail over the class of finite structures, including the compactness and completeness theorems, as well as many preservation and interpolation theorems. The failure of compactness in the finite, in particular, means that the standard proofs of many theorems are no longer valid in this context. At present, there is no known example of a classical theorem that remains true over finite structures, yet must be proved by substantially different methods. It is generally concluded that first-order logic is ‘badly behaved’ over finite structures.From the perspective of expressive power, first-order logic also behaves badly: it is both too weak and too strong. Too weak because many natural properties, such as the size of a structure being even or a graph being connected, cannot be defined by a single sentence. Too strong, because every class of finite structures with a finite signature can be defined by an infinite set of sentences. Even worse, every finite structure is defined up to isomorphism by a single sentence. In fact, it is perhaps because of this last point more than anything else that model theorists have not been very interested in finite structures. Modern model theory is concerned largely with complete first-order theories, which are completely trivial here. (shrink)

How should we conceive of the relationship between finite subjectivity and reflection? And what implications does this have for the phenomenological method? This article addresses these questions by reconstructing the main pillars of Patočka’s theory of the subject. I present three of Patočka’s key arguments related to finitude, consciousness, and the world (the primacy of the sum, the reduction to immanence, and temporality); then, after every argument, I outline their implications for Patočka’s philosophy. In particular, I highlight how Patočka’s (...) thought implies a repositioning of the subject in the world to which it ontologically belongs and a reassessment of the meaning of reflection. These theoretical assumptions open phenomenology to a different understanding of the subject than it had previously possessed and promote rich analysis of the movements of existence. The most important implication of Patočka’s theory of finite subjectivity, however, concerns the concept of the world, which bear a significance that extends beyond its critical position vis-à-vis transcendental subjectivity. (shrink)

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

SummaryFinite, or Fermat arithmetic, as we call it, differs from Peano arithmetic in that it does not involve the existence of an infinite set or Peano's induction postulate. Fermat's method of infinite descent takes the place of bound induction, and we show that a con‐structivist interpretation of logical connectives and quantifiers can account for the predicative finitary nature of Fermat's arithmetic. A non‐set‐theoretic arithemetical logic thus seems best suited to a constructivist‐inspired number theory.

The article examines the role of Hegel's theory of finite cognition in Marx's critique of classical political economy. I argue that Hegel's distinction of finite cognition between analytic and synthetic in the Science of Logic constitutes the methodological framework through which Marx delineates the different stages of the development of political economy. Focusing on the Grundrisse, I reveal the Hegelian influence behind Marx's statements on previous political economists’ methods. Thus, Marx's immanent critique of the classical political economy (...) is construed as undertaken from the level of the systematic dialectical method of Capital, and is modelled on Hegel's immanent critique of analytic and synthetic cognition from the perspective of absolute cognition. In this context, and focusing on Marx's critique of Ricardo's method, I argue that the latter's limitations are associated with the deficiencies of synthetic cognition as presented by Hegel. Therefore, the article sheds light on an important yet underexplored topic of the Hegel-Marx relationship. By indicating the centrality of Hegel's theory of finite cognition in Marx's methodological underpinnings, the article provides a new perspective on Hegel-Marx scholarship. (shrink)

Shoenfield [8] has shown that a hierarchy for the functions recursive in a type-2 object can be set up whenever E2 (the type-2 object that introduces numerical quantification) is recursive in that type-2 object. With a restriction that we will discuss in the next paragraph, Moschovakis [4, pp. 254–259] has solved the analogous problem for type-3 objects. His method seems to generalize for any type-n object, where n ≥ 2. We will solve this same problem of finding hierarchies based on (...) type-n objects by a different method. Instead of using ordinal notations for indexing stages of hierarchies, as do Shoenfield and Moschovakis, we will define notation-independent stages. (shrink)

The demand of many scientific areas for the usage of fractional partial differential equations to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations. (...) The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference method and standard finite difference technique, which are popular in the literature for solving engineering problems. (shrink)

The pessimistic induction and the problem of underdetermination in the philosophy of science have a rich history. In their recent incarnation as the problem of unconceived alternatives, most fully articulated by Kyle Stanford (2010) in Exceeding Our Grasp, the induction is more specific and underdetermination is construed more epistemically than is typical…The problem is not that there are empirically equivalent alternatives, that is, alternative between which no empirical evidence could ever distinguish. The problem is that multiple radically different alternative that (...) are empirically inequivalent might be equally well-confirmed by current evidence, and we might fail to even conceive one or more of those alternatives… In “Of German Tanks and Scientific Theories: Estimating the Number of Unconceived Alternatives,” Burkay Ozturk (2016) challenges Stanford on a distinct front. By applying a method of statistical estimation to scientific alternatives, Ozturk argues that the possibility space within which the alternatives are located allows for probable knowledge. The particular frequentist estimation method Ozturk employs requires that we assume the alternative pool is finite, which seems to be both false and wildly implausible. At first glance. I argue in this comment that Ozturk’s postulate of finitude is actually defensible in circumstances that might actually hold for ordinary scientific contexts. (shrink)

Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor-immune system to design an optimal chemotherapy strategy. For this, we first propose a mathematical model (...) of tumor-immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman equation. Here, we use an upwind finite-difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects. (shrink)

In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. Two different analytical approximations are obtained: for the first approximation, the ansatz method with the help of Chebyshev approximate polynomial is employed to derive an approximation in the form of trigonometric functions. For the second analytical approximation, a novel hybrid homotopy with Krylov–Bogoliubov–Mitropolsky method is introduced (...) for the first time for analyzing the evolution equation. For the numerical approximation, both the finite difference method and Galerkin method are presented for analyzing the strong nonlinear quadratically damped pendulum equation that arises in real life, such as nonlinear phenomena in plasma physics, engineering, and so on. Several examples are discussed and compared to the Runge–Kutta numerical approximation to investigate and examine the accuracy of the obtained approximations. Moreover, the accuracy of all obtained approximations is checked by estimating the maximum residual and distance errors. (shrink)

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering (...) the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

Consciousness is defined as operating with the meanings of representations, which are what arises in mind under the influence of a stimulus (primary representations) as well as what arises as a result of their transformation (secondary, combined representations). In a first approximation, a representation is expressed by words. The concept of “representation” is a special case of the concept of “information-certainty”, which is the result of distinction. Any distinction is a distinction by a specific attribute and representation is the value (...) of the attribute. In relative ontology, distinction is an essential condition of being that is formalized quantitatively through the operation of ontological subtraction, which is a quantitative expression of representation in relation to consciousness. The finite set of representations for one attribute can always be sorted in ascending order of this attribute values. In the order constructed, each representation corresponds to an attribute number, the only difference of which from a number in mathematics is that the one is always associated with a specific attribute, and the other is not associated with any attribute. The meaning of a representation expressed by an attribute number has a place in an ordered quantitative series of other representations of the same attribute, which is the basis of distinction. Operating with meanings is operating with attributive numbers-meanings. This method of the meaning describing is called the relative method. All operations with the meanings of representations are performed in a multidimensional cognitive space. Each axis of the cognitive space corresponds to an attribute by which representations differ. On each axis there are attribute numbers corresponding to the meanings of representations for the attribute. This approach is a quantitative method of describing of all experimental processes of consciousness, which allows to build a scientific, i.e. quantitative, theory of consciousness with laws written down in a quantitative way. Based on this, it is possible to construct a quantitative calculation of this theory predictions. Such a prediction allows to make an accurate (unambiguous) experimental verification. Due to the quantitative way of describing the operation of meanings, such a theory of consciousness is easily modeled in information technologies, since the latter are also based on the numerical nature of all their processes. The main difference between the relative method and the vast majority of methods using information technologies for text processing is that the relative method, firstly, is not statistical, and secondly, conveys the meaning of the text fully and most adequately. The relative method is effective in operating not only with text data, but also with any data of a different nature, for example, with video data, audio data. (shrink)

A perfectly matched layer (PML) absorbing material composed of a uniaxial anisotropic material is presented for the truncation of finite-difference time-domain (FDTD) lattices. It is shown that the uniaxial PML material formulation is mathematically equivalent to the perfectly matched layer method published by Berenger (see J. Computat. Phys., Oct. 1994). However, unlike Berenger's technique, the uniaxial PML absorbing medium presented in this paper is based on a Maxwellian formulation. Numerical examples demonstrate that the FDTD implementation of the uniaxial (...) PML medium is stable, equal in effectiveness as compared to Berenger's PML medium, while being more computationally efficient. (shrink)

My article is a rejoinder to Gert Biesta’s, ‘“This is My Truth, Tell Me Yours”. Deconstructive pragmatism as a philosophy of education.’ Biesta attempts to place Jacques Derrida’s deconstruction in ‘the very heart’ of John Dewey’s pragmatism. My article strives to impress Deweyan pragmatism in the heart of Derridian deconstruction. It does so by offering Dewey’s denotative, naturalistic, empirical perspectivalism as an alternative to Derrida’s anti-empirical quasi-transcendentalism for understanding otherness and difference. The first section of my article shows Biesta (...) offers a catastrophically mistaken and confused argument. The second section imprints Deweyan pragmatism in the heart of Derrida’s deconstruction. Dewey specifically makes philosophical use of a version of the genetic method he calls the ‘empirical denotative method’ to trace the exclusions as well as the inclusions of our perspectival selections driven by our finite embodied needs, interest, desires, and purposes. We may derive the trace of quasi-transcendental différance from the trace of empirically perspectival inclusions and exclusions. Specifically, différance is a reified hypostatic abstraction. Next, I respond to Biesta’s claim that since the metaphysics of presence still entangles Dewey, he cannot appreciate the fact that presence depends on absence. Actually, presence in Dewey always depends on absence. Finally, we will find that Biesta’s own deconstructive pragmatism flounders on his commitment to self-refuting relativism. (shrink)

This research aims to evaluate the calculation accuracy and efficiency of the artificial neural network-based important sampling method on reliability of structures such as drum brakes. The finite element analysis result is used to establish the ANN sample in ANN-based reliability analysis methods. Because the process of FEA is time-consuming, the ANN sample size has a very important influence on the calculation efficiency. Two types of ANNs used in this study are the radial basis function neural network and (...) back propagation neural network. RBF-IS and BP-IS methods are used to conduct reliability analysis on training samples of three different sizes, and the results are compared with several reliability analysis methods based on ANNs. The results show that the probability of failure of the RBF-IS method is closer to that of the Monte-Carlo simulation method than those of other methods. In addition, the RBF-IS method has better calculation efficiency than the other methods considered in this study. This research demonstrates that the RBF-IS method is well suited to structure reliability problems. (shrink)

In 1949, Richard Feynman published the essentials of his solution to the recalcitrant problems that plagued quantum theories of electrodynamics of his days. The main problem was that the theory, that was considered to be correct and often led to correct observable consequences, also implied that some quantities should be infinite, while by common sense or empirical evidence they were finite. Feynman devised a method of solving the relevant theoretical equations in which particular combinations of elementary solutions yielded empirically (...) adequate results even when applied to complex problems. The combination of the basic solutions was guided by relatively simple graphical considerations... (shrink)

Tuberculosis is caused by bacillus Mycobacterium tuberculosis. In this study, a mathematical model of tuberculosis is analyzed. The numerical behaviour of the considered model is analyzed including basic reproduction number and stability. We applied three numerical techniques to this model, i.e., nonstandard finite difference scheme, Runge–Kutta method of order 4, and forward Euler scheme. NSFD scheme preserves all the essential properties of the model. Acquired results corroborate that NSFD scheme converges for each step size. While the other two (...) schemes failed to preserve some properties of the model such as positivity and convergence. A graphical comparison presented in this study confirms the numerical stability of the NSFD technique shown here is maintained over a large area. (shrink)

The encounter between two fundamentally different approaches in seminal research in molecular biology-the problems, aims, methods and metaphysics - is delineated and analyzed. They are exemplified by the microbiologist Oswald T. Avery who, in line with the reductionist mechanistic metaphysics of Jacques Loeb, attempted to explain basic life phenomena through chemistry; and the theoretical physicist Max Delbrück who, influenced by Bohr’s antimechanistic views, preferred to explain these phenomena without chemistry. Avery’s and Delbrück’s most important studies took place concurrently. Thus (...) analysis of their contrasting approaches lends itself to examination of the Weltanschauungen view concerning the role of fundamental (metaphysical) assumptions in scientific change, that is, the view that empirical research cannot be neutral in regard to the worldviews of the researchers. This study shows that the initial ostensible disparity (non-integratibility) of the two approaches lasted for just a short time. Ironically it was a student of Delbrück’s school, James Watson, who (with Crick) proposed a chemical model, the DNA double helix, as a solution to Delbrück’s problem. The structure of DNA has not been seriously challenged over the past half century. Moreover, Watson’s and Crick’s work did not call into question the validity of Delbrück’s research, but opened it up to entirely new approaches. The case of Avery and Delbrück demonstrates that after initial obstacles were overcome the different fundamental attitudes and the resulting research practices were capable of integration. © 2008 Stazione Zoologica Anton Dohrn. (shrink)

Humans constantly produce strings of characters in symbolic languages, e.g., sentences in natural languages. We show that for any given moment in human history, the set of character strings that have been produced up to that moment, i.e., the sum total of human symbolic output up to that moment, is finite and so Turing computable. We then prove a much stronger result: a Turing machine can produce any particular set of symbolic output that we could possibly have produced. We (...) then discuss metaphysical and/or theological systems, e.g., Spinoza’s, Leibniz’s, or Aquinas’s. We argue that any particular metaphysical system could be the output of a Turing machine. We then briefly discuss (i) automated theorem proving, the attempt to generate and/or prove theorems using computers, and (ii) computational metaphysics, the attempt to apply methods from computer science such as automated theorem proving to metaphysics. We conclude by arguing that: (i) computational metaphysics can succeed, at least in theory; indeed, all human metaphysical reasoning could be automated; (ii) computational metaphysics – and indeed metaphysical systems in general – will have the same limitations as Turing machines; and (iii) a number of different methods – not currently used in computational metaphysics – could be used to advance metaphysical research. (shrink)

The present study addresses the fluid transport behaviour of the flow of gold -copper /biomagnetic blood hybrid nanofluid in an inclined irregular stenosis artery as a consequence of varying viscosity and Lorentz force. The nonlinear flow equations are transformed into dimensionless form by using nonsimilar variables. The finite-difference technique is involved in computing the nonlinear transport dimensionless equations. The significant parameters like angle parameter, the Hartmann number, changing viscosity, constant heat source, the Reynolds number, and nanoparticle volume fraction (...) on the flow field are exhibited through figures. Present results disclose that the Lorentz force strongly lessens the hybrid nanofluid velocity. Elevating the Grashof number values enhances the rate of blood flow. Growing values of the angle parameter cause to reduce the resistance impedance on the wall. Hybrid nanoparticles have a superior wall shear stress than copper nanoparticles. The heat transfer rate is amplifying at the axial direction with the growing values of nanoparticles concentration. The applied Lorentz force significantly reduces the hybrid and unitary nanofluid flow rate in the axial direction. The hybrid nanoparticles expose a supreme rate of heat transfer than the copper nanoparticles in a blood base fluid. Compared to hybrid and copper nanofluid, the blood base fluid has a lower temperature. (shrink)

The main question of this article is whether there is a family closed under finite differences (i.e., if A belongs to the family and B=∗A, then B also belongs to the family) that can be enumerated by any noncomputable c.e. degree, but which cannot be enumerated computably. This question was formulated by Greenberg et al. (2020) in their recent work in which families that are closed under finite differences, close to the Slaman–Wehner families, are deeply studied.

The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström [17] (...) with a counting argument. We extend his method to arbitrary similarity types. (shrink)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles (...) of one, the finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof (...) is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic’s coming of age in the 20th century: Godel’s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs. (shrink)

Problem: There is currently a great deal of mysticism, uncritical hype, and blind adulation of imaginary mathematical and physical entities in popular culture. We seek to explore what a radical constructivist perspective on mathematical entities might entail, and to draw out the implications of this perspective for how we think about the nature of mathematical entities. Method: Conceptual analysis. Results: If we want to avoid the introduction of entities that are ill-defined and inaccessible to verification, then formal systems need to (...) avoid introduction of potential and actual infinities. If decidability and consistency are desired, keep formal systems finite. Infinity is a useful heuristic concept, but has no place in proof theory. Implications: We attempt to debunk many of the mysticisms and uncritical adulations of Gödelian arguments and to ground mathematical foundations in intersubjectively verifiable operations of limited observers. We hope that these insights will be useful to anyone trying to make sense of claims about the nature of formal systems. If we return to the notion of formal systems as concrete, finite systems, then we can be clear about the nature of computations that can be physically realized. In practical terms, the answer is not to proscribe notions of the infinite, but to recognize that these concepts have a different status with respect to their verifiability. We need to demarcate clearly the realm of free creation and imagination, where platonic entities are useful heuristic devices, and the realm of verification, testing, and proof, where infinities introduce ill-defined entities that create ambiguities and undecidable, ill-posed sets of propositions. Constructivist content: The paper attempts to extend the scope of radical constructivist perspective to mathematical systems, and to discuss the relationships between radical constructivism and other allied, yet distinct perspectives in the debate over the foundations of mathematics, such as psychological constructivism and mathematical constructivism. (shrink)

We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th has the same computational complexity as the true first-order arithmetic.

In this paper, particular key aspects of the philosophies of Plotinus and Wang Yangming have been analysed comparatively on the basis of important passages of their works. The method used for this investigation can be defined as that of transversal comparative induction, in which the focus is more on working out the details of affinities and similarities. As this means a first step in an encompassing systematic context, differences will be introduced more briefly. The present investigation aims to provide a (...) foundation for a more differentiating and therefore complementing second part, which will consider other contents and topics in both philosophies. The present analysis is performed in three systematic steps and with regard to three basic philosophical ideas: (1) the idea that human consciousness is a central medium in the universal process and interrelatedness of (biological) life as a whole; (2) the idea that the self-unfoldment of reality represents a meta-cognitive process beyond the limits of subjectivity and finite consciousness; and (3) the idea that it is our major task to perfect and know ourselves by means of a “return” to the highest underlying foundation of this universal process. In their own ways, Plotinus and Wang Yangming both show that by enfolding human reflexivity toward the ineffable source of all reality in thought, feeling, human activity, and natural processes, namely by actively pursuing the path of moral and intellective perfection, we become fulfilled mediators of a universal process and of that which all of it represents. (shrink)

Based on the heterogeneous multiscale method, this paper presents a finite volume method to solve multiscale convection-diffusion-reaction problem. The paper constructs an algorithm of the optimal order convergence rate in H1-norm under periodic medias.

This paper, which is mainly based on unpublished material, focuses on the scientific influence that Felice Casorati exerted on Salvatore Pincherle. This influence can be traced, in particular, in Casorati’s work on the finite-difference calculus as conceived and published between 1879 and 1880 when Pincherle was living in Pavia. Casorati’s work has an interesting back story related to his entry to the 1880 Grand Prix of the French Académie des Sciences that helps us in understanding Casorati’s personality. Moreover, (...) the correspondence that Casorati exchanged with other mathematicians on his work reveals that some of the results contained in Casorati :10–45, 1880b) had been obtained—though in a narrower context—in an early paper by Christoffel. Finally, the letters between Casorati and Pincherle contain a short unpublished note by Pincherle on a paper by Jules Tannery :113–182, 1875). This note offers the first evidence of the influence of Casorati :10–45, 1880b) on Pincherle’s work on the finite-difference calculus. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, (...) an evaluation of arguments and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in (the foundations of) mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem (why is mathematics so successful in its applications?). Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

This paper deals with two different problems in which infinity plays a central role. I first respond to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and I argue that we should use the subset principle for measuring knowledge. I then turn to the normalizability and coarse tuning objections to (...) fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, I hope to blunt much of the force of these objections to fine-tuning arguments. (shrink)

The primary method by which science endeavors to order the world is the analytic approach, consistent with Cartesian principles of dividing the problem in as many sections as required for an optimal solution, and progressing from the simplest to the most complex reasoning. When the interactions among the various elements of the system being studied are minimal, such a procedure indeed makes it possible to formulate laws that describe chains of causality. However, when the variables are interdependent and linked by (...) non-linear equations, the atomistic method cannot account for the phenomenon in its entirety. Spurred by this inadequacy, scientists sought to discover synthetic methods which, early in the twentieth century, led to the conceptualization of holistic theories in a number of disciplines. The most highly developed fields are the psychology of form, structural anthropology (1), and the various systems theories (2). More recently, the development of epigenetic concepts in biology has corresponded to the appearance of different theories of pattern in physics and mathematics (3, 4) and to the progressive emergence of the concept of self-organization (5, 6, 7). The objective is to explain the production of complex structures on the basis of interacting elements, none of which contains a guiding scheme that dictates these structures. In biology, the challenge is to locate the constraints that are expressed in a space of possibilities (8) in order to develop a theory of organization that is capable of predicting the finite number of forms that living creatures can assume (9). This school of thought can be described as structuralist, emergentist, self-organizational, or epigeneticist, depending on the theoretical version that is emphasized. (shrink)

Hypersequents are finite sets of ordinary sequents. We show that multiple-conclusion sequents and single-conclusion hypersequents represent two different natural methods of switching from a single-conclusion calculus to a multiple-conclusion one. The use of multiple-conclusion sequents corresponds to using a multiplicative disjunction, while the use of single-conclusion hypersequents corresponds to using an additive one. Moreover: each of the two methods is usually based on a different natural semantic idea and accordingly leads to a different class of algebraic structures. (...) In the cases we consider here the use of multiple-conclusion sequents corresponds to focusing the attention on structures in which there is a full symmetry between the sets of designated and antidesignated elements. The use of single-conclusion hypersequents, on the other hand, corresponds to the use of structures in which all elements except one are designated. Not surprisingly, the use of multiple-conclusion hypersequents corresponds to the use of structures which are both symmetrical and with a single nondesignated element. (shrink)