Calculus (dental) ≈ Calculus (dental)
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Fractional Calculus: Models and Numerical Methods Open
Survey of Numerical Methods to Solve Ordinary and Partial Fractional Differential Equations Specific and Efficient Methods to Solve Ordinary and Partial Fractional Differential Equations Fractional Variational Principles Continuous-Time Ra…
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Central limit theorem: the cornerstone of modern statistics Open
According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a vari…
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Mechanics of Fluids Open
Contents Preface to the eighth edition 1 Fundamental Concepts Problems 2 Fluid Statics Problems 3 The Principles Governing Fluids in Motion Problems 4 The Momentum Equation 5. Physical Similarity and Dimensional Analysis Problems 6 Laminar…
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Journal of Theoretical and Applied Mechanics Open
Along with increasing dimensions, speed, and output of modern machines, many newly appearing problems are being encountered in design and manufacturing of such machines.Vibrations occuring in certain technological processes create undesira…
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Determination of 50% endpoint titer using a simple formula Open
Two commonly used methods for calculating 50% endpoint using serial dilutions are Spearman-Karber method and Reed and Muench method. To understand/apply the above formulas, moderate statistical/mathematical skills are necessary. In this pa…
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From Frege to Gödel: a source book in mathematical logic, 1879-1931 Open
The fundamental texts of the great classical period modern logic, some of them never before available English translation, are here gathered together for the first time. Modern logic, heralded by Leibniz, may be said to have been initiated…
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A Conceptual Introduction to Hamiltonian Monte Carlo Open
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, …
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Fractal calculus and its geometrical explanation Open
Fractal calculus is very simple but extremely effective to deal with phenomena in hierarchical or porous media. Its operation is almost same with that by the advanced calculus, making it much accessible to all non-mathematicians. This pape…
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Introduction to structural equation modeling Open
This chapter introduces the basic concepts, terminology, and conceptual sequence of structural equation modeling (SEM) steps. The chapter describes the formulation of the general structural equation model and presents the principles of mod…
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The Journal of Mathematical Behavior Open
The Journal of Mathematical Behavior solicits original research on the learning and teaching of mathematics, from young children to adults, with a focus on how mathematical ideas are developed in learners under certain conditions that supp…
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On a new class of fractional operators Open
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these…
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Theoretical Study on Light Trajectories in Traversable Wormholes and Temporal Displacements Open
This work presents a theoretical study on the feasibility of temporal displacements through traversable wormholes, combining general relativity with modern approaches to the behavior of light and particles. While the idea of traveling to t…
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Fractional viscoelastic models for power-law materials Open
Power law materials exhibit a rich range of behaviours interpolating continuously from the linear elastic to the linear viscous responses.
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Bernstein Polynomials Open
Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obta…
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Numerical Solution of Richards' Equation: A Review of Advances and Challenges Open
Core Ideas The numerical solution of Richards' equation remains challenging. Space/time discretization affects both computational effort and accuracy. Adaption of space and time discretizations produces benefits. Dissemination of codes and…
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Moore–Gibson–Thompson thermoelasticity Open
We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parameter in the Green–Naghdi type III model. We…
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Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit Open
The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this p…
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A FORMAL PROOF OF THE KEPLER CONJECTURE Open
This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck pr…
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The Koopman Operator in Systems and Control Open
This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the…
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Two-scale mathematics and fractional calculus for thermodynamics Open
A three dimensional problem can be approximated by either a two-dimensional or one-dimensional case, but some information will be lost. To reveal the lost information due to the lower dimensional approach, two-scale mathematics is needed. …
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Applications of variable-order fractional operators: a review Open
Variable-order fractional operators were conceived and mathematically formalized only in recent years. The possibility of formulating evolutionary governing equations has led to the successful application of these operators to the modellin…
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New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle Open
Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally use…
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Modeling and Verifying Security Protocols with the Applied Pi Calculus and ProVerif Open
International audience
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Calculus: Early Transcendentals Open
Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Editi…
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Mathematical Methods for Physicists Open
"The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical fram…
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A Review of Topology Optimisation for Fluid-Based Problems Open
This review paper provides an overview of the literature for topology optimisation of fluid-based problems, starting with the seminal works on the subject and ending with a snapshot of the state of the art of this rapidly developing field.…
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On two-scale dimension and its applications Open
Dimension or scale is everything. When a thing is observed by different scales, different results can be obtained. Two scales are enough for most of practical problems, and a new definition of a two-scale dimension instead of the fractal d…
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Eighty Years of the Finite Element Method: Birth, Evolution, and Future Open
This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics. We present a historical overview beginning with t…
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Proofs Without Words: Exercises in Visual Thinking Open
1. Geometry and algebra 2. Trigonometry, calculus and analytic geometry 3. Inequalities 4. Integer sums 5. Sequences and series.
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Equations of Mathematical Physics Open
This concise volume presents an overview of mathematical physics & generalized functions, an in-depth study of the "generalized" differential equation.