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We propose the first technique that can deal with more general surfaces in three dimensions. ... A favorite open problem in combinatorial geometry is to determine the worst-case complexity of a level in an arrangement. ... Introduction Given an arrangement of n surfaces in IR d , the level of a point p ∈ IR d is the number of surfaces strictly below p. ...doi:10.1007/s00454-012-9428-2 fatcat:vpj6rjuq3nhvrfhtaj4yytc6qu
However, the transformation from one to three dimensions is not straightforward, as described in the main text of the paper. ... In one dimension the ions may be arranged as linear chains of alternating positive and negative ions; in two dimensions as a square chequer board array with alternate positive and negative ions; and in ...doi:10.1039/c2cp23901a pmid:22441396 fatcat:ftllliqylvfaval6rjpjcy4hnu
The study was aimed to optimize the process of lamella grinding -the final stage in the manufacturing of the oak surface layer. ... The authors introduce the problem of excessive waste of raw material in the wood industry on the basis of the floorboard manufacturing process. ... The expected 12% wood moisture level was obtained in all the three procedures. ...doi:10.12783/dtetr/icpr2017/17664 fatcat:37bswrjnxfb5zoj5xrjsoyybua
of approximately 7 nm in diameter, wound around one another in a left helical manner, with a 7-nm center-to-center separation. ... Based on the shapes of these sectional profiles and their vertical dimensions, paired helical filaments appeared to be composed of two identical integral subunits, each of a circular cross-sectional profile ... The greater density of immunolabeling on the surface of straight filaments suggests that the arrangement of tau molecules in PHFs and straight filaments is different. ...pmid:7639341 pmcid:PMC1869818 fatcat:bhcphh4h3jfkdmab6m5yp54ani
Journal of the ACM
It was shown that the vertical decomposition of the (≤ k)-level in an arrangement of surfaces in R 3 has complexity O(n 2+ε k) . ... We show that the complexity of the vertical decomposition of an arrangement of n fixeddegree algebraic surfaces or surface patches in four dimensions is O(n 4+ε ), for any ε > 0. ... Acknowledgements I would like to thank Micha Sharir for his help in the preparation of this paper. In particular, he suggested extending Theorem 3.1 to higher dimensions, as described in Section 4. ...doi:10.1145/1017460.1017461 fatcat:2g4w3lnbizfh3o2fe7n24fczqe
Selection of experimental factors such as particle size fractal dimension D ps , particle orientation fractal dimension D di , equivalent diameter D e , design the experiments using response surface method ... , Study on the relationship between the mechanical strength index and the optimal microstructure parameters of lime solidified saline soil ,and is verified. ... The particle size fractal dimension D Results and Analysis Results of the Test The response surface analysis test of three factors and three levels of the microstructure index of solidified soil ...doi:10.12783/dtetr/amma2017/13337 fatcat:obf2yfg43nch3j2eztxejftnpy
levels. ... We develop a new type of correlation analysis of the preferred conductance values that provide new type of information on a few-atomic-nanocontact formation dynamics. ... However, due to hybridization between different bands, or on few-atom level, between different orbitals usually T n < 1. Its value strongly depends on particular atomic arrangement in a QPC. ...doi:10.12693/aphyspola.115.384 fatcat:7nau7mss2ffb7arkbckc3f42wq
In this study, a fifty six points third order rotatable design is constructed by adding a set of factors to a second order rotatable design in four dimensions and a practical hypothetical example is given ... This design permits a response surface to be fitted easily and provide spherical information contours besides the economic use of scarce resources in relevant production processes. ... The point sets in (3.1) and (3.2) form a rotatable arrangement of order three for the values of constants given in (3.4) . ...doi:10.9734/cjast/2019/v33i630110 fatcat:qm7jpjvgcfdm3f4qayplckv5oa
This quadratic response surface methodology focuses on finding the levels of some (coded) predictor variables x = (x1u, x2u, x3u)' that optimize the expected value of a response variable yu from natural ... The expected second order rotatable design model in three dimensions is available where the responses would then facilitate the estimation of the linear and quadratic coefficients. ... ... points form second order specific rotatable arrangement in three dimensions in the twenty six points if the non- Mutiso(1998) shows that the expansion of var(yu) is given by var(ŷ u ) [(k + 2)β 2 ...doi:10.14419/ijasp.v8i1.30122 fatcat:xlcxie7m5vh2dm5qyxpyihulsy
The Annals of Mathematical Statistics
classes of sequential third order rotatable designs in three dimensions. ... In this paper, third order rotatable designs in three dimensions are discussed. ...
Asian Journal of Probability and Statistics
We present an illustration on how to obtain the mathematical parameters of the coded values and its corresponding natural levels for a third order rotatable design in four dimensions by utilizing response ... This design permits a response surface to be fitted easily and provides spherical information contours besides the economic use of scarce resources in relevant production processes. ... The point set forms a rotatable arrangement of order three for the values of the constants given in 15. ...doi:10.9734/ajpas/2019/v4i430119 fatcat:7ynar2dt25a35ms5iewhri6xte
We also present a randomized algorithm for computing the envelope in three dimensions, with expect,ed running time O(n?+'), a.nd give several applications of the new bounds. ... We show that the combinatorial complexity of the lower envelope of n surfaces or surface patches in dspace ( d 2 3), all algebraic of constant maximum degree, and bounded by algebraic surfaces of constant ... In Section 2 we prove the upper bound for the complexity of the envelope of surface patches in three dimensions. ...doi:10.1007/bf02574384 fatcat:hb64hlthtnbltdinotfev2yw4i
We conducted two experiments in which observers were asked to estimate the spatial dimensions (size of the room dimensions in meters and centimeters) and to judge subjective spaciousness of various rooms ... Despite the ubiquity of interior space design, there is virtually no scientific research on the influence of furnishing on the perception of interior space. ... Acknowledgments We are grateful to Agnes Münch for programming the virtual reality experiment and to Oliver Daum and Elsa Krauss for their assistance in constructing the model rooms. ...doi:10.1371/journal.pone.0113267 pmid:25409456 pmcid:PMC4237397 fatcat:dwav5yi37veodjqdexwqihk2ke
This arrangement resulted in three levels. Level one contained the representative elements; level two, the re- lated metals; and level three, the rare earths. ... Obviously, it is of no value as a teaching aid. His opinion has not deterred others from continuing to make charts on a plane or models in three dimensions. ...
Motivated by frequency assignment in office blocks, we study the chromatic number of the adjacency graph of a 3-dimensional parallelepiped arrangement. ... In the case each parallelepiped is within one floor, a direct application of the Four-Colour Theorem yields that the adjacency graph has chromatic number at most 8. ... The third author thanks Louigi Addario-Berry, Frédéric Havet, Ross Kang, Colin McDiarmid and Tobias Müller for stimulating discussions on the topic of this paper during a stay in Oxford, in 2005. ...doi:10.7155/jgaa.00344 fatcat:oulq75r4zjeorjonqj7sqwr3wi
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