439 research outputs found
On a Deterministic Property of the Category of -almost Primes: A Deterministic Structure Based on a Linear Function for Redefining the -almost Primes (, ) in Certain Intervals
In this paper based on a sort of linear function, a deterministic and simple
algorithm with an algebraic structure is presented for calculating all (and
only) -almost primes ( , ) in
certain interval. A theorem has been proven showing a new deterministic
property of the category of -almost primes. Through a linear function that
we obtain, an equivalent redefinition of the -almost primes with an
algebraic characteristic is identified. Moreover, as an outcome of our
function's property some relations which contain new information about the
-almost primes (including primes) are presented.Comment: 10 pages. Accepted and presented article in the 11th ANTS, Korea,
2014. The 11th ANTS is one of international satellite conferences of ICM
2014: The 27th International Congress of Mathematicians, Korea. (Expanded
version
Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations
One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology
Realizability and uniqueness in graphs
AbstractConsider a finite graph G(V,E). Let us associate to G a finite list P(G) of invariants. To any P the following two natural problems arise: (R) Realizability. Given P, when is P=P(G) for some graph G?, (U) Uniqueness. Suppose P(G)=P(H) for graphs G and H. When does this imply G ≅ H? The best studied questions in this context are the degree realization problem for (R) and the reconstruction conjecture for (U). We discuss the problems (R) and (U) for the degree sequence and the size sequence of induced subgraphs for undirected and directed graphs, concentrating on the complexity of the corresponding decision problems and their connection to a natural search problem on graphs
Fast multiplication of multiple-precision integers
Multiple-precision multiplication algorithms are of fundamental interest for both theoretical and practical reasons. The conventional method requires 0(n2) bit operations whereas the fastest known multiplication algorithm is of order 0(n log n log log n). The price that has to be paid for the increase in speed is a much more sophisticated theory and programming code. This work presents an extensive study of the best known multiple-precision multiplication algorithms. Different algorithms are implemented in C, their performance is analyzed in detail and compared to each other. The break even points, which are essential for the selection of the fastest algorithm for a particular task, are determined for a given hardware software combination
- …