Abstract: A search for prime factors of the generalized Fermat numbers $F_n(a,b)=a^{2^n}+b^{2^n}$ has been carried out for all pairs $(a,b)$ with $a,b\leq 12$ and GCD$(a,b)=1$. The search limit $k$ on the fact...
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Abstract: A search for prime factors of the generalized Fermat numbers $F_n(a,b)=a^{2^n}+b^{2^n}$ has been carried out for all pairs $(a,b)$ with $a,b\leq 12$ and GCD$(a,b)=1$. The search limit $k$ on the factors, which all have the form $p=k\cdot 2^m+1$, was $k=10^9$ for $m\leq 100$ and $k=3\cdot 10^6$ for $101\leq m\leq 1000$. Many larger primes of this form have also been tried as factors of $F_n(a,b)$. Several thousand new factors were found, which are given in our tables.—For the smaller of the numbers, i.e. for $n\leq 15$, or, if $a,b\leq 8$, for $n\leq 16$, the cofactors, after removal of the factors found, were subjected to primality tests, and if composite with $n\leq 11$, searched for larger factors by using the ECM, and in some cases the MPQS, PPMPQS, or SNFS. As a result all numbers with $n\leq 7$ are now completely factored.
作者：
Nordlund, PeterUhlin, Tomas
Department of Numerical Analysis Computing Science Royal Institute of Technology StockholmS-10044 Sweden
We present an integrated system, able to pursue a moving object by controlling a robot-head to maintain the moving object centered in the image. This system runs continuously in time and updates the object localizatio...
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We introduce the hypothesis testing problem (HTP). In HTP the input is a family of species F and a hypothesis, i.e., a tree where the leaves are labeled with species from some subfamily of F. The problem is to decide ...
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Despite the extensive work on human-computer interaction regarding methods of involving users and designing for high degrees of usability, there is surprisingly little published on how procurer organizations understan...
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Despite the extensive work on human-computer interaction regarding methods of involving users and designing for high degrees of usability, there is surprisingly little published on how procurer organizations understand, reason about, and require usability. This study focuses on how one taxi company dealt with usability requirements when procuring a new dispatch system. We have conducted ten interviews with various stakeholders in the company and analyzed related documentation in order to discover the process. The case shows how the concept of usability matured during over time. The taxi company dealt with requirement elicitation by developing prototypes in small reference groups. They did no formal analysis of the operators' cooperation with each other at the operator central, but they did include experienced users, which created implicit scenarios. The supplier company did not focus on the efficiency of the operators or, for that matter, the cooperative demands of the operator central in their original design, which became evident when the procurer organization requested a redesign that emphasized user tasks. This indicates, on one hand, the extent to which procurers must understand usability and cooperation to procure good systems design and, on the other hand, the extent to which designers must understand business and activity processes in order to design good systems.
A numerical method for simulating incompressible two-dimensional multiphase flow is presented. The method is based on a level-set formulation discretized by a finiteelement technique. The treatment of the specific fea...
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A numerical method for simulating incompressible two-dimensional multiphase flow is presented. The method is based on a level-set formulation discretized by a finiteelement technique. The treatment of the specific features of this problem, such as surface tension forces acting at the interfaces separating two immiscible fluids, as well as the density and viscosity jumps that in general occur across such interfaces, have been integrated into the finite-element framework. Using a method based on the weak formulation of the Navier-Stokes equations has its advantages. In this formulation, the singular surface tension forces are included through line integrals along the interfaces, which are easily approximated quantities. In addition, differentiation of the discontinuous viscosity is avoided. The discontinuous density and viscosity are included in the finite element integrals. A strategy for the evaluation of integrals with discontinuous integrands has been developed based on a rigorous analysis of the errors associated with the evaluation of such integrals. numerical tests have been performed. For the case of a rising buoyant bubble the results are in good agreement with results from a fronttracking method. The run presented here is a run including topology changes, where initially separated areas of one fluid merge in different stages due to buoyancy effects.
The approximability of several NP maximization problems is investigated and strong lower bounds for the studied problems are proved. For some of the problems the bounds are the best that can be achieved, unless P = NP...
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This article presents: (i) a multiscale representation of grey-level shape called the scale-space primal sketch, which makes explicit both features in scale-space and the relations between structures at different scal...
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This article presents: (i) a multiscale representation of grey-level shape called the scale-space primal sketch, which makes explicit both features in scale-space and the relations between structures at different scales, (ii) a methodology for extracting significant blob-like image structures from this representation, and (iii) applications to edge detection, histogram analysis, and junction classification demonstrating how the proposed method can be used for guiding later-stage visual processes. The representation gives a qualitative description of image structure, which allows for detection of stable scales and associated regions of interest in a solely bottom-up data-driven way. In other words, it generates coarse segmentation cues, and can hence be seen as preceding further processing, which can then be properly tuned. It is argued that once such information is available, many other processing tasks can become much simpler. Experiments on real imagery demonstrate that the proposed theory gives intuitive results.
MIN PB is the class of minimization problems whose objective functions are bounded by a polynomial in the size of the input. We show that there exist several problems which are MIN PB-complete with respect to an appro...
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An intertwine of two graphs H and H′ is a graph G such that G contains both H and H′ as minors, but no proper minor of G contains both H and H′ as minors. We give an upper bound on the size of an intertwine of two ...
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