Mathematical precision

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  • Stewart's CALCULUS, Fifth Edition has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that have characterized the first four editions. Stewart retains the focus on problem solving and the pedagogical system that has made the book a favorite of students and instructors in a wide variety of colleges and universities throughout the world.

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  • The pronunciations of the most common mathematical expressions are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary).

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  • This is an advanced course on modeling, design, integration and best practices for use of machine elements such as bearings, springs, gears, cams and mechanisms. Modeling and analysis of these elements is based upon extensive application of physics, mathematics and core mechanical engineering principles (solid mechanics, fluid mechanics, manufacturing, estimation, computer simulation, etc.).

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  • This fourth edition of the best-selling Illustrated Maths Dictionary is a comprehensive update of the most thorough mathematics dictionary for primary school students, student teachers and teachers in Australia. It features a new design, new illustrations and the addition of computer terminology in the useful information section. The new edition comes with an electronic version of the dictionary for use on your computer.

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  • Game theory is a mathematical system for analyzing and predicting how humans behave in strategic situations. Standard equilibrium analyses assume all players: 1) form beliefs based on analysis of what others might do (strategic thinking); 2) choose a best response given those beliefs (optimization); 3) adjust best responses and beliefs until they are mutually consistent (equilibrium).

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  • In a Global scenario, economically progressive nations have developed medical sciences. But still it lacks precise information during the enhancement of potent drugs to combat ailment, which is the legacy of the organisms that generate diseases. Rising countries had long been perceived the threat, which at times, down the lane has been the major factor for magnanimous economic disaster and human poverty. Lot of resources was put into force by the world community to abscond the microbial fauna and genetically inherited diseases to contain them within the safe limits.

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  • It is well known that not every orientation-preserving homeomorphism of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is “almost” a welding in a precise way. The proofs are based on Koebe’s circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings. 1. Introduction Let D ⊂ R2 be the open unit disk, let D∗ = S 2 \D and let T = ∂D = ∂D∗ be the unit circle. ...

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  • We find the exact value of the best possible constant C for the weak-type (1, 1) inequality for the one-dimensional centered Hardy-Littlewood maximal operator. We prove that C is the largest root of the quadratic equation 12C 2 − 22C + 5 = 0 thus obtaining C = 1.5675208 . . . . This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.

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  • The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erd˝s-Szemer´di [E-S]. (see also [El], [T], o e and [K-T] for related aspects.) Only much weaker results or very special cases of this conjecture are presently known. One approach consists of assuming the sum set A + A small and then deriving that the product set AA is large (using Freiman’s structure theorem) (cf. [N-T], [Na3]). We follow the...

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  • We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms nevertheless remain bounded. Moreover, we show that in Hartree-Fock theory the radius of an atom (properly defined) is bounded independently of its nuclear charge. Contents 1. Introduction and main results 2. Notational conventions and basic prerequisites 3. Hartree-Fock theory 4. Thomas-Fermi theory ...

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  • The goal of this work is to give a precise numerical description of the K¨hler cone of a compact K¨hler manifold. Our main result states that the a a K¨hler cone depends only on the intersection form of the cohomology ring, the a Hodge structure and the homology classes of analytic cycles: if X is a compact K¨hler manifold, the K¨hler cone K of X is one of the connected components of a a the set P of real (1, 1)-cohomology classes {α} which are numerically positive on analytic cycles, i.e. Y αp 0 for every irreducible analytic...

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  • There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diffeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove first that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...

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  • We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere. 1. Introduction 1.1. In 1916, D. E. Menshov constructed an example of a nontrivial trigonometric series on the circle T ∞ (1) n=−∞ c(n)eint which converges to zero almost everywhere (a.e.). Such series are called nullseries. This result was the origin of the modern theory of uniqueness in Fourier analysis, see [Z59], [B64], [KL87], [KS94]. Clearly for such a series |c(n)|2 = ∞.

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  • The purpose of this paper is to introduce the principles of GPS theory, and to provide a background for more advanced material. With that in mind, some of the theoretical treatment has been simplified to provide a starting point for a mathematically literate user of GPS who wishes to understand how GPS works, and to get a basic grasp of GPS theory and terminology.

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  • Humidity promotes the growth of moulds Credit: Infrogmation The majority of the health effects linked to dampness and moisture of buildings are those of the respiratory system. They range from irritation of mucous membranes, respiratory symptoms, and infections to diseases such as asthma and allergy. However , it is still not known precisely how dampness leads to these symptoms and which are the main substances responsible. Humidity problems in buildings may originate from leaks, condensation, or the ground.

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  • Note that the computation of the equivalent units of production involves adding the num- ber of units transferred out of the department to the equivalent units in the department’s ending inventory. There is no need to compute the equivalent units for the units trans- ferred out of the department—they are 100% complete with respect to the work done in that department or they would not be transferred out. In other words, each unit transferred out of the department is counted as one equivalent unit. Consider the Shaping and Milling Department at Double Diamond.

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  • VNU. JOURNAL OF SCIENCE, Mathematics - Physics, T.xXI, n02, 2005 Nguyen Thi Minh Hanga,b, Chien-Hung Hoc, Vu Ngoc Hungb, Nguyen Phu Thuyb,d a d Center for Micro Electronic and Information Technology (IMET) International Training Institute for Materials Science (ITIMS) c Precision Instrument Development Center (PIDC) College of Technology, Vietnam National University, Hanoi (VNU) b Abstract. Thanks to almost transparent property of SU8 for wavelength of 365400nm, UV-LIGA technology using this photoresist has been applied to fabricate high-aspect-ratio (HAR) microstructures.

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  • Another limitation of the literature is that minorities have been dramatically under- represented in psycho-oncology research (Anderson, 1992). Further, although the research demonstrates the importance of the spousal relationship during the cancer experience, there is a lack of controlled research concerning couples or family interventions. Finally, a crucial question that remains unanswered is determining what these findings mean in terms of clinical intervention and care.

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  • On completion of this chapter students will know how to: Declare variables and constants, format output, work with character data, create mathematical expressions, work with mixed data types and casting, use different data types for precision, utilize available math functions.

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  • Microsoft@ Excel is a ‘number crunching’ application with the accountant as its primary target. However, it also provides the scientist or engineer with a very powerful computational tool. True, there are more sophisticated mathematical applications, such as Mathematica, MathCAD, Maple, etc., but none are as widely available as Microsoft Excel.

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