A compact kernel for the calculus of inductive constructions.

by Asperti, A., Ricciotti, W., Coen, C. Sacerdoti, Tassi, E. [2009-02-01]

Academic Journal

pages 74

The paper describes the new kernel for the Calculus of Inductive Constructions (CIC) implemented inside the Matita Interactive Theorem Prover. The design of the newkernel has been completely revisited since the first release, resulting in a remarkably compact implementation of about 2300 lines of OCaml code. The work is meant for people interested in implementation aspects of Interactive Provers, and is not self contained. In particular, it requires good acquaintance with Type Theory and functional programming languages. [ABSTRACT FROM AUTHOR]


The Design and Formalization of Mezzo, a Permission-Based Programming Language.

by BALABONSKI, THIBAUT, POTTIER, FRANÇOIS, PROTZENKO, JONATHAN [2016-08-01]

Academic Journal

pages 94

The programming language Mezzo is equipped with a rich type system that controls aliasing and access to mutable memory. We give a comprehensive tutorial overview of the language. Then we present a modular formalization of Mezzo's core type system, in the form of a concurrent λ-calculus, which we successively extend with references, locks, and adoption and abandon, a novel mechanism that marries Mezzo's static ownership discipline with dynamic ownership tests. We prove that well-typed programs do not go wrong and are data-race free. Our definitions and proofs are machine checked. [ABSTRACT FROM AUTHOR]


POLY-GENOCCHI POLYNOMIALS WITH UMBRAL CALCULUS VIEWPOINT.

by TAEKYUN KIM, DAE SAN KIM, GWAN-WOO JANG, JONGKYUM KWON [2019-01-01]

Academic Journal

pages 18

In this paper, we would like to exploit umbral calculus in order to derive explicit expressions, some properties, recurrence relations and identities for poly-Genocchi polynomials. [ABSTRACT FROM AUTHOR]


UMBRAL CALCULUS APPROACH TO DEGENERATE POLY-GENOCCHI POLYNOMIALS.

by TAEKYUN KIM, DAE SAN KIM, LEE CHAE JANG, GWAN-WOO JANG [2019-01-01]

Academic Journal

pages 17

In this paper, we apply umbral calculus techniques in order to derive explicit expressions, some properties, recurrence relations and identities for degenerate poly-Genocchi polynomials. Furthermore, we derive several explicit expressions of degenerate poly-Genocchi polynomials as linear combinations of some of the well-known families of special polynomials. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 24

We investigate the complexity of the standard translation of lambda calculus into combinatory logic. The main result shows that the asymptotic growth rate of the size of a trans- lated term is Θ(n3) in worst-case, where n denotes the size of the lambda term. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 14

In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 24

I argue that European schools of thought on memory and memorization were critical in enabling growth of the scientific method. After giving a historical overview of the development of the memory arts from ancient Greece through 17th century Europe, I describe how the Baconian viewpoint on the scientific method was fundamentally part of a culture and a broader dialogue that conceived of memorization as a foundational methodology for structuring knowledge and for developing symbolic means for representing scientific concepts. The principal figures of this intense and rapidly evolving intellectual milieu included some of the leading thinkers traditionally associated with the scientific revolution; among others, Francis Bacon, Renes Descartes, and Gottfried Leibniz. I close by examining the acceleration of mathematical thought in light of the art of memory and its role in 17th century philosophy, and in particular, Leibniz's project to develop a universal calculus. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 4

An explicit, coupled, single-step method for the numerical solution of initial value problems for systems of ordinary differential equations is presented. The method was designed to be general purpose in nature but to be especially efficient when dealing with stiff systems of differential equations. it is, in general, second order except for the case of a linear system with constant coefficients and linear forcing terms; in that case, the method is third order. It has been implemented and put to routine usage in biological applications—where stiffness frequently appears—with favorable results. When compared to a standard fourth order Runge-Kutta implementation, computation time required by this method has ranged from comparable for certain nonstiff problems to better than two orders of magnitude faster for some highly stiff systems. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 4

The solution of the nonlinear differential equation Y" = F(x, Y, Y') with two-point boundary conditions is opproximated by a quintic or cubic spline function y(x). The method is well suited to nonuniform mesh size and dynamic mesh size allocation. For uniform mesh size h, the error in the quintic spline y(x) is O(h4), with typical error one-third that from Numerov's method. Requiring the differential equation to be satisfied at the mesh points results in a set of difference equations, which are block tridiagonal and so are easily solved by relaxation or other standard methods. [ABSTRACT FROM AUTHOR]


PERFORMANCE ANALYSIS OF INTRODUCTORY STATISTICS COURSE DUE TO DIFFERENT MATHEMATICAL BACKGROUND.

by Choudhury, Askar H., Radhakrishnan, Ramaswamy [2009-06-01]

Conference

pages 1

This paper addresses the issue of students' different mathematical background that differentiates students' performance in statistics course. Students can choose one of several mathematics based prerequisite to gain necessary background knowledge for the Statistics course. Statistics is one of the required courses for business and economics majors. Among several possible prerequisite courses we considered two different calculus courses (Applied Calculus and Calculus-I) as background knowledge for statistics course to compare. Therefore, the objective of this paper is to observe the significance and magnitude of differential effect of two different calculus courses on statistics course performance. Statistical tests provided evidence that differential effect exist due to different calculus background knowledge. Specifically, we have found that students who took the Calculus-I received higher average grade in Statistics course than students who took Applied Calculus. Thus, students with added traditional calculus orientation do have greater statistical proficiency. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 16

We present an approach to the numerical integration of ordinary differential equations based on the algebraic theory of Butcher (Math. Comp. 26, 79–106, 1972) and the [InlineMediaObject not available: see fulltext.]-series theory of Hairer and Wanner (Computing 13, 1–15, 1974). We clarify the differences of these two approaches by equating the elementary weight functions and showing the differences of the composition rules. By interpreting the elementary weight function as a mapping from input values to output values and introducing some special mappings, we are able to derive the order conditions of several types of integration methods in a straight-forward way. The simplicity of the derivation is illustrated by linear multistep methods that use the second derivative as an input value, Runge-Kutta type methods that use the second as well as first derivatives, and general two-step Runge-Kutta methods. We derive new high stage-order methods in each example. In particular, we found a symmetric and stiffly-accurate method of order eight in the second example. [ABSTRACT FROM AUTHOR]


Sorting realization of well-ordered sets based on π-calculus.

by Hao Bu, Rong Zhu, Shihong Chen, Xiaoqiong Tan [2017-09-01]

Academic Journal

pages 17

π-calculus is one of the most effective means for the modeling of the concurrent mobile system at the present stage. The paper starts with a brief introduction of π-calculus, which concerns mutual simulation, the fundamentals of mobile computing, and the concept of interaction with some basic grammars and regulations of π-calculus while the system mobility is discussed with special focuses on the relation between the referent and the mobility, and the relation between the granular size and mobility. Then the analysis goes on to discuss the sorting problems that frequently occur in modeling concurrent systems. Through the discussion of the underlying sorting algorithms based on π-calculus, five processes are established by applying such artless thoughts as "looking for the seats in the cinema" or "changing keys among a group" to do quick concurrent locating and instant sorting, so that the sorting problems of specific elements in the well-ordered sets could be solved on the basis of π-calculus. In this way, the sorting results will eventually be displayed in the specified process and conveniently help the readings of other processes. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 18

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for college calculus success by high school instructional experiences that emphasized mathematical definitions, vocabulary, reasoning, functions, and hands-on activities. These findings serve to inform high school mathematics teachers about promising instructional practices. They can also inform teacher education programs about how to better prepare secondary mathematics educators to discuss conceptual understanding on the widely used Educative Teacher Performance Assessment (edTPA). [ABSTRACT FROM AUTHOR]


Miraculous Mathematics: André Bazin's Film Theory.

by Vacche, Angela Dalle [2016-05-01]

Academic Journal

pages 25

The article focuses on assessment of film critic André Bazin's theory for films. Topics discussed include adoption of Henri Bergson's philosophy for mathematical analysis by Bazin with calculus method for computation; criticism of the "Miracle in Milan" film under supervision of director Vittorio De Sica by Bazin with analysis of its special effects; and examination of neorealism in the film "The Bicycle Thief" by Bazin.


Academic Journal

pages 6

In this article we prove a theorem on the definitional embeddability of the combinatory logic into the first-order predicate calculus without equality. Since all efficiently computable functions can be represented in the combinatory logic, it immediately follows that they can be represented in the first-order classical predicate logic. So far mathematicians studied the computability theory as some applied theory. From our theorem it follows that the notion of computability is purely logical. This result will be of interest not only for logicians and mathematicians but also for philosophers who study foundations of logic and its relation to mathematics. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 6

In this article we prove a theorem on the definitional embeddability into first-order predicate logic without equality of such well-known mathematical theories as group theory and the theory of Abelian groups. This result may seem surprising, since it is generally believed that these theories have a non-logical content. It turns out that the central theory of general algebra are purely logical. Could this be the reason that we find them in many branches of mathematics? This result will be of interest not only for logicians and mathematicians but also for philosophers who study foundations of logic and its relation to mathematics. [ABSTRACT FROM AUTHOR]


Calculus of directional coderivatives and normal cones in Asplund spaces.

by Long, Pujun, Wang, Bingwu, Yang, Xinmin [2017-09-01]

Academic Journal

pages 28

We study the directional Mordukhovich normal cones to nonsmooth sets, coderivatives of set-valued mappings in Asplund spaces and establish extensive calculus results on these constructions under various operations of sets and mappings. We also develop calculus of the directional sequential normal compactness both in general Banach spaces and in Asplund spaces. [ABSTRACT FROM AUTHOR]


Academic Journal

pages 41

Over the last ten years, Finite Element Exterior Calculus (FEEC) has been developed as a general framework for linear mixed variational problems, their numerical approximation by mixed methods, and their error analysis. The basic approach in FEEC, pioneered by Arnold, Falk, and Winther in two seminal articles in 2006 and 2010, interprets these problems in the setting of Hilbert complexes, leading to a more general and complete understanding. Over the last five years, the FEEC framework has been extended to a broader set of problems. One such extension, due to Holst and Stern in 2012, was to problems with variational crimes, allowing for the analysis and numerical approximation of linear and geometric elliptic partial differential equations on Riemannian manifolds of arbitrary spatial dimension. Their results substantially generalize the existing surface finite element approximation theory in several respects. In 2014, Gillette, Holst, and Zhu extended FEEC in another direction, namely to parabolic and hyperbolic evolution systems by combining the FEEC framework for elliptic operators with classical approaches for parabolic and hyperbolic operators, by viewing solutions to the evolution problem as lying in Bochner spaces (spaces of Banach-space valued parametrized curves). Related work on developing an FEEC theory for parabolic evolution problems has also been done independently by Arnold and Chen. In this article, we extend the work of Gillette-Holst- Zhu and Arnold-Chen to evolution problems on Riemannian manifolds, through the use of framework developed by Holst and Stern for analyzing variational crimes. We establish a priori error estimates that reduce to the results from earlier work in the flat (non-criminal) setting. Some numerical examples are also presented. [ABSTRACT FROM AUTHOR]


Yet Another Calculus Text

by Dan Sloughter [2007]

Book

pages unknown

I intend this book to be, firstly, a introduction to calculus based on the hyperreal number system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such as Abraham Robinson’s Non-standard Analysis or Robert Goldblatt’s Lectures on the Hyperreals.


Active Calculus Multivariable

by Steven Schlicker [2017]

Book

pages unknown

Active Calculus Multivariable is different from most existing texts in at least the following ways: The style of the text requires students to be active learners; there are very few worked examples in the text, with there instead being 3 or 4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas. Each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class. The exercises are few in number and challenging in nature. The book is open source and can be used as a primary or supplemental text


Active Calculus 2.0

by Matthew Boelkins [2017]

Book

pages unknown

Active Calculus is different from most existing texts in that: the text is free to read online in .html or via download by users in .pdf format; in the electronic format, graphics are in full color and there are live .html links to java applets; the text is open source, so interested instructor can gain access to the original source files via GitHub; the style of the text requires students to be active learners … there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas; each section begins with motivating questions, a brief introduction, and a preview activity; each section concludes (in .html) with live WeBWorK exercises for immediate feedback, followed by a few challenging problems


Academic Journal

pages 14

The purpose of this research is to investigate the phenomenon of online technology enhanced mathematics education. This is a mixed methods technology intervention action research case study on investigating the impact on secondary geometry and calculus students' academic achievement and affect when their face-to-face lessons are mirrored to the Cloud as lesson videos and note files for students to access outside of the classroom. The investigator discovered educational benefits from this intervention based on the results of a quantitative analysis of the students' assessment scores and a qualitative analysis of interview, questionnaire, and observational data collected during the intervention. This work is the result of an inquiry by the school's stakeholders on how to use online technologies to enhance mathematics education. [ABSTRACT FROM AUTHOR]


OPTIMAL CONTROL OF SOME QUASILINEAR MAXWELL EQUATIONS OF PARABOLIC TYPE.

by NICAISE, SERGE, TRÖLTZSCH, FREDI [2017-12-01]

Academic Journal

pages 17

An optimal control problem is studied for a quasilinear Maxwell equation of nondegenerate parabolic type. Well-posedness of the quasilinear state equation, existence of an optimal control, and weak Gâteaux-differentiability of the control-to-state mapping are proved. Based on these results, first-order necessary optimality conditions and an associated adjoint calculus are derived. [ABSTRACT FROM AUTHOR]


Conference

pages 3

This abstract discusses the results of two studies that assess the privacy attitudes, intensions, and behaviors of Millennials. Study 1 considers broadly how prevalent the privacy paradox is among Millennials (assessing whether there is an incongruity between Millennials' privacy attitudes and their personal information disclosure behavior). Using an online questionnaire, study participants were prompted to read and respond to various privacy policy statements from contemporary tech companies (blinded and generically presented as Company A, Company B, Company C, and Company D), and then later asked to identify the tech companies to which they currently have membership (e.g., Facebook, Google, LinkedIn, and Angry Birds). Participant attitudes and intensions toward various policy statements were then cross tabulated with their declared online service memberships. Study 2 considers the issues of how product relevance and product value serve as factors that predict a positive or accepting attitude toward a brand/firm and its privacy policies. Establishing baselines of product relevance and value from a pretest of Millennials, study 2 also tests for the moderating effect of a perceived privacy invasion on consumer attitudes and intensions. It was hypothesized that Millennials are less disapproving of aggressive customer profiling as product relevance and perceived product value increase (i.e., the larger the promotional offer for relevant products, the less disapproving they are of a firm's aggressive customer profiling techniques). Results indicate that both product relevance and value moderate consumer attitudes and intensions, and interestingly, product relevance and value stand independent (as moderators). The privacy paradox, the primary focus of study 1, is a wellestablished construct in the marketing academic literature, and very recently it was the impetus for framing the two leading normative theories or models for privacy protection for the FTC in the United States: the Notice-and-Choice Model and the Harm-Based Model (Ohlhausen 2014). Several explanations in the marketing literature attempt to explain the gap between consumer attitudes and behavior as a privacy paradox, however. They include a consumer bias or tendency to discount future risk (Acquisti, 2004); the allure or pull of immediate gratification (Acquisti, 2004); the prominence or sway of brand trust (Metzger, 2004; Norberg et al., 2007); and consumer knowledge deficiencies (Dommeyer and Gross, 2003; Pötzsch, 2009). Our focus in study 1 is on how the paradox is manifest among Millennials and yet not likely resulting from (misguided) consumer subjective knowledge (e.g., as discussed in Coupey and Narayanan, 1996). Closely connected with the privacy paradox is a consumer decision process known in the academic marketing literature as the "privacy calculus" (Smith, Dinev, and Xu, 2011). The privacy calculus is one attempt to account for the apparent inconsistencies of the privacy paradox by identifying an implicit cost-benefit analysis performed by the consumer when trading firmly held attitudes and beliefs about personal privacy, on one hand, with a willingness to trade/share personal information for services and consumer value, on the other. Having its origins in economic theory, the privacy calculus aims to explain behavior as a cost-benefit trade-off between perceived risk and perceived information control (Dinev, Xu, Smith, and Hart, 2013). Study 2 also considers how product relevance and perceived value are potential moderators of attitude-behavior incongruence. Study 1 The goal of study 1 is to examine how Millennials' attitudes about personal privacy and personal information relate to their actions and online behavior. Using a survey-questionnaire among 261 undergraduate business students at two mid- Atlantic universities (one private, the other public), we assessed the objective knowledge of technologies, current methods of information collection, privacy protection best practices, and current industry standards. Using Qualtrics and its logic/branching capabilities for various questions, we presented the "terms and conditions" of four social networking sites and popular phone apps that Millennials currently have (own, maintain, or use) and had respondents indicate whether they approve or not of the conditions to which they have previously or already consented. The four social media platforms used in the study one include Facebook, Google, LinkedIn, and Angry Birds. Respondents who disagree or disclose disapproving attitudes and/or intentions toward various clauses of the conditions they are currently or implicitly consented to are identified as exhibiting the privacy paradox. The hypotheses for study 1 are as follows: H1-1: Current users of an online service shows negative intention to disclose personal information for the online service after they read actual parts of privacy policy of the service provider. H1-2: Privacy concerns for an online service are heightened after consumers read actual parts of privacy policy of the service provider. To test the hypotheses regarding the privacy paradox, we visited the homepages of several popular tech companies that are widely used by the general public in the United States and examined their privacy policies to identify provisions about collecting and sharing customers' personal information. Next, using some recent high-profile media stories that involved the aggressive use of company/firm use of customers' personal information (reported in The New York Times, The Wall Street Journal, and Tech Crunch, for example) we selected several privacy policy statements from tech companies that could reasonably be seen to induce a company's current customers to perceive a loss of control or a heighten sense of insecurity. After responding to a series of qualifying and conditioning questions on brand product design, participants in the study were asked to read and respond to privacy policy statements. Study 2 The participants for study 2 were the same 261 undergraduate students who participated in study 1, and the experimental procedures were administrated prior to collecting data for study 1 in the same online pages. The design was a 2 × 2 (offer size, offer relevancy) between-subjects factorial design. The offer size was experimentally manipulated with coupon offers with two different levels of discount (5% off vs. 30% off). The offer relevancy was determined by the brand of cell phone that the participants were using. Because the coupon offered to all participants regardless of the experimental conditions was for cel lphone accessories for a particular brand (iPhone), the coupon offer was relevant to iPhone users but not for others who used phones other than the iPhone. The hypotheses for study two are as follows: H2-1: Perceived privacy invasion is reduced when the company provides bigger and more relevant promotional offers than when the offer is small or less relevant. H2-2: Attitude toward a company that collected and utilized their personal information when the company provides bigger and more relevant promotional offers than when the offer is small or less relevant In the experimental questionnaire, informed consent was obtained and participants completed filler tasks disguising the true purpose of the study. After that, participants were exposed to the simulated data processing procedure that asked for personal information and showed the graphical icons and messages about data processing. Participants were prompted to believe that a simultaneous privacy invasion took place (in which his/her personal information was being used/collected for a marketing purpose without consent or permission). Next, each individual participant was then randomly exposed to one of two different promotions (5% off vs. 30% off) for iPhone accessories. After participants reported their responses to several dependent variables and other measures including the brand of cellphone that they were currently using, they were thanked and debriefed. Results Two sets of analysis of covariance (ANCOVA) were performed for each dependent variable with the coupon proneness as the covariate, which had significant effects for both dependents (p < .05). The gender and sampling school had no effects on the following results. Two independent variables were the offer size (5% off vs. 30% off coupon) and the offer relevance (iPhone users vs. other). In regard to the attitude toward the brand, the interaction effect between the offer size and relevance was not significant (p > .05). However, both main effects were significant. First, participants who received the offer of 30% off coupon (M = 3.70, SD = 1.38) showed more positive brand attitude than others offered 5% off coupon (M = 3.24, SD = 1.39) (F(1, 256) = 5.24, p < .05). Second, the brand attitudes of iPhone users (M = 3.63, SD = 1.40) were more positive than other who used other cellphones (M = 3.03, SD = 1.32) (F(1, 256) = 9.47, p < .01). For the second dependent variable, perceived privacy invasion, there was no significant interaction between the offer size, and relevance was not significant (p >.05). Also, the main effect of the offer size was not significant (p > .05). The main effect of the offer relevance was marginally significant, showing higher perceived privacy invasion of participants who did not use an iPhone (M = 5.74, SD = 1.02) than iPhone users (M = 5.45, SD = 1.21) (F(1, 256) = 3.07, p = .08). Implications and Future Research These studies support the presence of a privacy paradox, specifically among a sample of Millennials who have largely grown up online and can be classified as digital native consumers. This incongruity between thoughts and behaviors may have several plausible explanations. A "herd mentality" for well-known sites and apps may certainly explain much of this behavior. For example, consumers may simply think that if millions of others are comfortable with liberally sharing personal information, then it must be okay and no "real" harm will likely materialize. Left to their own devices, it is foreseeable that a large number of app developers will continue to push the envelope as far as what is acceptable and necessary in terms of tracking online behavior and capturing personal information. Without some form of self-regulation by the community of developers, there may continue to be an erosion of consumer privacy, whether informed or not. A similar form of self-regulation does exist within the online behavioral advertising industry and is led by the Direct Marketing Association (DMA). Given the breadth of parties currently involved in the app development industry, however, any form of selfregulation and omnibus agreement seems unlikely. Thus the government or tech oligopoly which controls the flow of apps may need to create some form of regulation to protect consumers' privacy. A greater onus of responsibility could certainly be placed on the firms that review and approve the content of apps that are offered through digital storefronts. Just as media companies have an obligation to protect their audiences from seeing inappropriate content, app distributors (i.e., Apple App Store) may also have a responsibility to protect consumers from flagrant invasions of privacy. These companies already have processes in place to review content and look for other forms of malicious intent before making apps publicly available, so creating some minimum standard for the types of information that can be collected and how it is communicated to customers does not seem unreasonable. Several options may address the privacy paradox issues. The first would be the creation of standardized terms and conditions, or acceptable language for participating app developers to use in order to have their apps offered for acquisition. The second, rather than terms and conditions which are several pages long and contain a level of complexity well beyond the reading comprehension levels of the average consumer, perhaps specific statements which are likely to be objectionable are flagged and offered individually for consent. Third, a rating system could be created by the digital storefronts which evaluated the "intrusiveness" or "risk" of a given app prior to download. While offering a substantial incentive seemed to off-set the privacy violation in the second experiment, this quid pro quo exchange was perhaps more evident than that which exists in many scenarios. For instance, an app developer may consider their "free" offering to warrant some invasion of privacy which can be monetized to off-set the cost of the game development and yield a reasonable profit, however the consumer may not attribute the same perceived value to the exchange. While the courts may ultimately decide how much of our rights regarding the protection of our personal privacy can be waived through a mere click of an "I accept" check-box, the first step in addressing the privacy paradox is an admission and understanding of how a consumer's intent often does not mirror his/her actual behavior. [ABSTRACT FROM AUTHOR]