Principles of mathematics

3D animation software is extensively used to create graphics for special effects sequences in live-action films, in animated feature film production and for the generation of computer games and virtual reality content. It is a commonly held view within the computer graphics community that 3D animation software is ―just another tool‖ for self-expression. This research questions that view by examining the inherent nature of the tool itself. In doing so, some of the philosophical assumptions embedded in the design of the new digital tool are revealed.

99p runthenight05 01-03-2023 6 2   Download

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

68p dontetvui 17-01-2013 46 6   Download

By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables. 1. Introduction Early work of Lewis [14] and Birch [3], [4], now almost a half-century old, shows that pairs of quite general homogeneous cubic equations possess non-trivial integral solutions whenever the dimension of the corresponding intersection is suitably large (modern refinements have reduced this permissible affine dimension to 826; see [13]). ...

32p noel_noel 17-01-2013 60 6   Download

Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are “well-distributed” in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working with the “uncertainty principle”. In this article we find that these ideas have a natural setting in the analysis of distributions of sequences in analytic number theory, formulating a general principle, and giving several examples. ...

44p noel_noel 17-01-2013 53 6   Download

A Hausdorff measure version of the Duffin-Schaeffer conjecture in metric number theory is introduced and discussed. The general conjecture is established modulo the original conjecture. The key result is a Mass Transference Principle which allows us to transfer Lebesgue measure theoretic statements for lim sup subsets of Rk to Hausdorff measure theoretic statements. In view of this, the Lebesgue theory of lim sup sets is shown to underpin the general Hausdorff theory. This is rather surprising since the latter theory is viewed to be a subtle refinement of the former. ...

23p noel_noel 17-01-2013 48 6   Download

We prove an identity of Kloosterman integrals which is the fundamental lemma of a relative trace formula for the general linear group in n variables. 1. Introduction One of the simplest examples of Langlands’ principle of functoriality is the quadratic base change. Namely, let E/F be a quadratic extension of global fields and z
→ z the corresponding Galois conjugation. The base change associates to every automorphic representation π of GL(n, F) an automorphic representation Π of GL(n,E). If n = 1 then π is an id`ele class character and Π(z) = π(zz)....

26p tuanloccuoi 04-01-2013 37 6   Download

Giới thiệu Sau khi giấy Khamsi [8] theo nguyên tắc KKM-bản đồ trong không gian hyperconvex số liệu, một số tác giả đã thiết lập các ứng dụng chính của nguyên tắc này, chẳng hạn như Kỳ Fan minimax bất bình đẳng, định lý điểm cố định, định lý minimax, định lý điểm cân bằng, ...

9p phalinh21 01-09-2011 51 4   Download

Solid modeling (or modelling) is a consistent set of principles for mathematical and computer modeling of three dimensional solids. Solid modeling is distinguished from related areas of Geometric modeling and Computer graphics by its emphasis on physical fidelity [1]. Together, the principles of geometric and solid modeling form the foundation of Computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects....

19p xuanchienhui 12-05-2010 112 20   Download