Let λ1, . . . , λs be non-zero with λ1/λ2 irrational and let S be the set of values attained by the form λ1x 3 1 + · · ·+ λsxs when x1 has at most 6 prime divisors and the remaining variables are prime. In the case s = 4, we establish that most real numbers are “close” to an element of S. We then prove that if s = 8, S is dense on the real line.

Let L be a finite first-order language and 〈Mn | n < ω〉 be a sequence of finite L-models containing models of arbitrarily large finite cardinality. If the intersection of less than continuum-many dense open subsets of Cantor Space 2 is non-empty, then there is a non-principal ultrafilter U over ω such that the corresponding ultraproduct Q U Mn is infinite and has an automorphism that is not ind...

A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Although convenient for the development of the theory, using such objects as data deviates from the computational practice and has a drawback from a logico-philosophical point of view. Two ways to eliminate the using of such na...

dense medium cyclone is a high capacity device that is widely used in coal preparation. it is simple in design but the swirling turbulent flow, the presence of medium and coal with different density and size fraction and the presence of the air-core make the flow pattern in dmcs complex. in this article the flow pattern simulation of dmc is performed with computational fluid dynamics and fluent...

We develop and compare several fine-grained parallel algorithms to compute the Cholesky factorisation of a sparse matrix. Our experimental implementations are on the Connection Machine, a distributedmemory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special-purpose algorithms in which the matrix structure conforms to the connection s...

We investigate the polynomial time isomorphic type structure of PT ⊂ {A : A ⊆ {0}∗} (the class of tally, polynomial time computable sets). We partition PT into six parts: D−, D̂−, C, S, F, F̂ , and study their p-isomorphic properties separately. The structures of 〈deg1(F ); ≤〉, 〈deg1(F̂ ); ≤〉, and 〈deg1(C); ≤〉 are obvious, where F , F̂ , and C are the class of tally finite sets, the class of tally ...

Green’s functions are established tools for solving petroleum engineering flow problems. Their utility and rigor was extended to arbitrarily shaped reservoirs using the Boundary Element Method (BEM). Traditional BEMs are limited to single-phase flow in homogeneous reservoirs. Earlier authors have developed techniques to handle heterogeneity. These methods are perturbationbased and computation-i...

Graph mining is an important research area with a plethora of practical applications. Core decomposition in networks, is a fundamental operation strongly related to more complex mining tasks such as community detection, dense subgraph discovery, identification of influential nodes, network visualization, text mining, just to name a few. In this tutorial, we present in detail the concept and pro...