An effective recursive partitioning approach for the packing of identical rectangles in a rectangle

In this work, we deal with the problem of packing (orthogonally and without overlapping) identical rectangles in a rectangle. This problem appears in different logistics settings, such as the loading of boxes on pallets, the arrangements of pallets in trucks and the stowing of cargo in ships. We present a recursive partitioning approach combining improved versions of a recursive five-block heuristic and an L-approach for packing rectangles into larger rectangles and L-shaped pieces. The combined approach is able to rapidly find the optimal solutions of all instances of the pallet loading problem sets Cover I and II (more than 50 000 instances). It is also effective for solving the instances of problem set Cover III (almost 100 000 instances) and practical examples of a woodpulp stowage problem, if compared to other methods from the literature. Some theoretical results are also discussed and, based on them, efficient computer implementations are introduced. The computer implementation and the data sets are available for benchmarking purposes. Journal of the Operational Research Society (2010) 61, 306-320. doi: 10.1057/jors.2008.141 Published online 4 February 2009

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Trapezoidal SOI FinFET analog parameters` dependence on cross-section shape

The trapezium is often a better approximation for the FinFET cross-section shape, rather than the design-intended rectangle. The frequent width variations along the vertical direction, caused by the etching process that is used for fin definition, may imply in inclined sidewalls and the inclination angles can vary in a significant range. These geometric variations may cause some important changes in the device electrical characteristics. This work analyzes the influence of the FinFET sidewall inclination angle on some relevant parameters for analog design, such as threshold voltage, output conductance, transconductance, intrinsic voltage gain (A V), gate capacitance and unit-gain frequency, through 3D numeric simulation. The intrinsic gain is affected by alterations in transconductance and output conductance. The results show that both parameters depend on the shape, but in different ways. Transconductance depends mainly on the sidewall inclination angle and the fixed average fin width, whereas the output conductance depends mainly on the average fin width and is weakly dependent on the sidewall inclination angle. The simulation results also show that higher voltage gains are obtained for smaller average fin widths with inclination angles that correspond to inverted trapeziums, i.e. for shapes where the channel width is larger at the top than at the transistor base because of the higher attained transconductance. When the channel top is thinner than the base, the transconductance degradation affects the intrinsic voltage gain. The total gate capacitances also present behavior dependent on the sidewall angle, with higher values for inverted trapezium shapes and, as a consequence, lower unit-gain frequencies.

THE PYROCHLORE SUPERGROUP OF MINERALS: NOMENCLATURE

A new scheme of nomenclature for the pyrochlore supergroup, approved by the CNMNC-IMA, is based on the ions at the A, B and Y sites. What has been referred to until now as the pyrochlore group should be referred to as the pyrochlore supergroup, and the subgroups should be changed to groups. Five groups are recommended, based on the atomic proportions of the B atoms Nb, Ta, Sb, Ti, and W. The recommended groups are pyrochlore, microlite, romite, betafite, and elsmoreite, respectively. The new names are composed of two prefixes and one root name (identical to the name of the group). The first prefix refers to the dominant anion (or cation) of the dominant valence [or H(2)O or rectangle] at the Y site. The second prefix refers to the dominant cation of the dominant valence [or H(2)O or rectangle] at the A site. The prefix "" keno-"" represents "" vacancy"". Where the first and second prefixes are equal, then only one prefix is applied. Complete descriptions are missing for the majority of the pyrochlore-supergroup species. Only seven names refer to valid species on the grounds of their complete descriptions: oxycalciopyrochlore, hydropyrochlore, hydroxykenomicrolite, oxystannomicrolite, oxystibiomicrolite, hydroxycalcioromite, and hydrokenoelsmoreite. Fluornatromicrolite is an IMA-approved mineral, but the complete description has not yet been published. The following 20 names refer to minerals that need to be completely described in order to be approved as valid species: hydroxycalciopyrochlore, fluornatropyrochlore, fluorcalciopyrochlore, fluorstrontiopyrochlore, fluorkenopyrochlore, oxynatropyrochlore, oxyplumbopyrochlore, oxyyttropyrochlore-(Y), kenoplumbopyrochlore, fluorcalciomicrolite, oxycalciomicrolite, kenoplumbomicrolite, hydromicrolite, hydrokenomicrolite, oxycalciobetafite, oxyuranobetafite, fluornatroromite, fluorcalcioromte, oxycalcioromite, and oxyplumboromite. For these, there are only chemical or crystalstructure data. Type specimens need to be defined. Potential candidates for several other species exist, but are not sufficiently well characterized to grant them any official status. Ancient chemical data refer to wet-chemical analyses and commonly represent a mixture of minerals. These data were not used here. All data used represent results of electron-microprobe analyses or were obtained by crystal-structure refinement. We also verified the scarcity of crystal-chemical data in the literature. There are crystalstructure determinations published for only nine pyrochlore-supergroup minerals: hydropyrochlore, hydroxykenomicrolite, hydroxycalcioromite, hydrokenoelsmoreite, hydroxycalciopyrochlore, fluorcalciopyrochlore, kenoplumbomicrolite, oxycalciobetafite, and fluornatroromite. The following mineral names are now discarded: alumotungstite, bariomicrolite, bariopyrochlore, bindheimite, bismutomicrolite, bismutopyrochlore, bismutostibiconite, calciobetafite, ceriopyrochlore-(Ce), cesstibtantite, ferritungstite, jixianite, kalipyrochlore, monimolite, natrobistantite, partzite, plumbobetafite, plumbomicrolite, plumbopyrochlore, stannomicrolite, stetefeldtite, stibiconite, stibiobetafite, stibiomicrolite, strontiopyrochlore, uranmicrolite, uranpyrochlore, yttrobetafite-(Y), and yttropyrochlore-(Y).

Bendadaite, a new iron arsenate mineral of the arthurite group

Bendadaite, ideally Fe(2+)Fe(2)(3+)(AsO(4))(2)(OH)(2 center dot).4H(2)O, is a new member of the arthurite group It was found as a weathering product of arsenopyrite on a single hand specimen from the phosphate pegmatite Bendada. central Portugal (type locality) Co-type locality is the granite pegmatite of La via do Almerindo (Almerindo mine), Linopolis, Divmo das Laranjeiras county, Minas Gerais, Brazil Further localities are the Vein Negra mine, Copiapo province, Chile, mid-East, Bou Azzer district, Morocco, and Para Inferida yard, Fenugu Sibirt mine, Gonnosfanadiga, Medio Campidano Province, Sardinia. Italy Type bendadaite occurs as blackish green to dark brownish tufts (<0 1 mm long) and flattened radiating aggregates. in intimate association with an intermediate member of the scorodite-mansfieldite series It is monoclinic. space group P2(l/c). with a = 10 239(3) angstrom. b = 9 713(2) angstrom, c = 5 552(2) angstrom. beta = 94 11(2)degrees. = 550 7(2) angstrom(3). Z = 2 Electron-microprobe analysis yielded (wt %). CaO 0 04, MnO 0 03. CuO 006, ZnO 004. Fe(2)O(3) (total) 43 92, Al(2)O(3) 115. SnO(2) 0 10, As(2)O(5) 43 27. P(2)O(5) 1 86, SO(3) 0.03 The empirical formula is (Fe(0 52)(2+)Fe(0 32)(3+)rectangle(0 16))(Sigma 1 00)(Fe(1 89)(3+)Al(0 11))(Sigma 2 00)(As(1 87)P(0 13))(Sigma 2 00)O(8)(OH)(2 00) 4H(2)O based. CM 2(As,P) and assuming ideal 80, 2(OH), 4H2O and complete occupancy of the ferric on site by Fe(3+) and Al Optically, bendadaite is biaxial, positive, 2V(est) = 85+/-4 degrees, 2V(eale) = 88 degrees, with alpha 1 734(3). 13 1 759(3), 7 1 787(4) Pleochrosim is medium strong X pale reddish brown. Y yellowish brown, Z dark yellowish brown. absorption Z > V > X, optical dispersion weak, r > v. Optical axis plane Is parallel to (010), with X approximately parallel to a and Z nearly parallel to c Bendadaite has vitreous to sub-adamantine luster, is translucent and non-fluorescent It is brittle, shows irregular fracture and a good cleavage parallel to 1010} 3 15 0 10 g/cm(3), 3 193 g/cm3 (for the empirical formula) The five strongest powder diffraction lines [d in angstrom (I)(hkl] are 10 22 (10)(100), 7 036 (8)(110), 4 250 (5)(11 I), 2 865 (4)(311), 4 833 (3)(020,011) The d spacings are very similar to those of its Zn analogue, ojelaite The crystal structure of bendadaite was solved and refined using a crystal from the co-type locality with the composition (Fe(0 95)(2+)rectangle(0 05))(Sigma 1 00)(Fe(1 80)(3+)Al(0 20))Sigma(2 00)(As(1 48)P(0 52))(Sigma 2 00)O(8)) (OH)(2) 4H(2)O (R = 16%) and confirms an arthurite-type atomic arrangement