Square meshes are not optimal for convex hull computation

Recently it has been noticed that for semigroup computations and for selection, rectangular meshes with multiple broadcasting yield faster algorithms than their square counterparts. The contribution of the paper is to provide yet another example of a fundamental problem for which this phenomenon occurs. Specifically, we show that the problem of computing the convex hull of a set of n sorted points in the plane can be solved in O(n^1/8 log ^3/4) time on a rectangular mesh with multiple broadcasting of size n^3/8 log^1/4 n×n^5/8/log^1/4n. The fastest previously known algorithms on a square mesh of size √n×√n run in O(n^1/6) time in case the n points are pixels in a binary image, and in O(n^1/6log^3/2 n) time for sorted points in the plane     

Monofunctionalized β-cyclodextrins as sensor elements for the detection of small molecules

β-Cyclodextrins functionalized by different moieties that were tethered to a single 6-deoxyaminoglucose unit were investigated with respect to their suitability for sensor applications. Derivatizing the cyclodextrins with hydrophobic moieties like dipalmitoylglycerol and cholesterol allowed us to study packing density and orientation of the cyclodextrin tori at the air–water interface. From the pressure-area isotherms, it was concluded that the cyclodextrins are positioned towards the water subphase, with their molecular axis predominately parallel to the interface. By introducing a disulfide group, we managed to immobilize cyclodextrins on gold surfaces via self-assembly. MALDI mass spectrometry (MALDI MS) and XPS confirmed that the molecules are chemisorbed on the gold substrate displaying high surface coverage as determined by means of impedance spectroscopy. The inclusion of various charged guest molecules was monitored by changes in the charge transfer resistance of the redox couple [Fe(CN)₆]³⁻/[Fe(CN)₆]⁴⁻. The charge transfer resistance is sensitive to the surface potential, which leads to either repulsion or attraction of the redox active species.     

Parallel dynamic programming

Recurrence formulations for various problems, such as finding an optimal order of matrix multiplication, finding an optimal binary search tree, and optimal triangulation of polygons, assume a similar form. A. Gibbons and W. Rytter (1988) gave a CREW PRAM algorithm to solve such dynamic programming problems. The algorithm uses O(n⁶/log n) processors and runs in O(log² n) time. In this article, a modified algorithm is presented that reduces the processor requirement to O(n⁶/log ⁵n) while maintaining the same time complexity of O(log² n)     

重金属捕集剂二甲基二硫代氨基甲酸对6种重金属螯合固化性能的量子化学研究

为探讨二甲基二硫代氨基甲酸盐螯合重金属离子的作用机理,本文采用密度泛函理论,在B3LYP/6-31++G（d,p）和B3LYP/LanL2DZ混合基组水平上,分别计算了二甲基二硫代氨基甲酸离子（DDC^-）和铬、铜、钴、锌、铁、镉6种重金属离子形成配合物的前线轨道能级、配位能△E、考虑基组重叠误差后的配位能△E_BSSE、零点振动能校正后的配位能△E_ZPE及自然电荷分布。研究结果表明:上述二甲基二硫代氨基甲酸配合物的稳定性与能级差△ε及配位能△E_BSSE、△E_ZPE的绝对值密切相关,△ε及△E_BSSE、△E_ZPE的绝对值越大,配合物越稳定。6种二甲基二硫代氨基甲酸重金属配合物的稳定性由大到小的顺序为:[CrDDC]²⁺>[CuDDC]⁺>[CoDDC]⁺>[ZnDDC]⁺>[FeDDC]⁺>[CdDDC]⁺。在形成配合物的过程中,电子从配体DDC^-流向重金属离子,电荷转移越多,配位能的绝对值越大。     

Temporal, spatial and thermal features of 3-D Rayleigh-Bénard convection by a least-squares finite element method

Numerical solutions of 3-D time-dependent Rayleigh-Bénard convection are presented in this work. The temporal, spatial and thermal features of convective patterns are studied for four different geometric aspect ratios, 2:1:2, 4:1:4, 5:1:5 and 3.5:1:2.1 at supercritical Rayleigh numbers Ra = 8 × 10³, 2.4 × 10⁴ and Prandtl numbers Pr = 0.71, 2.5. Several physical phenomena, such as multicellular flow pattern, oscillatory transient solution, ‘T-shaped’ rolls at the ends of a rectangular box, and roll alignment, are observed in our simulations. The numerical technique is based on an implicit, fully coupled, and time-accurate method, which consists of the Crank-Nicolson scheme for time integration, Newton's method for the convective terms with extensive linearization steps, and a least-squares finite element method. A matrix-free algorithm of the Jacobi conjugate gradient method is implemented to solve the symmetric, positive definite linear system of equations.     

Integration of beam functions

The beam functions satisfying d⁴φ/dξ⁴ = β⁴φ with the associated boundary conditions are convenient admissible comparison functions for the approximated solutions of complex structural problems by the well known Rayleigh-Ritz method. Reliable integration formulae for products of various beam functions φ and ψ with an arbitrary function θ are essential. Felgar's recurrence formula for ∫ θφψ dξ is found to be in error and is corrected here. The condition when the characteristic values of θ and ψ are identical is also considered. A simple subroutine is given to evaluate ∫ θ(ξ)(dⁿφ/dξⁿ)(d^mψ/dξ^mdξ for all possible sets of boundary conditions. Applications to the free vibration of nonuniform beams and plate systems are demonstrated.     

Petri net-based analysis on object assignment in distributed object-oriented systems

Object-oriented programming ^[9], which treats objects as processes in execution, has shown significant effectiveness in distributed systems. This effectiveness is greatly influenced by how objects are assigned to nodes. In this paper, we present a colored generalized stochastic Petri net (CGSPN) model to analyze the behavior of object invocations when an assignment strategy is applied. The effectiveness of an object assignment is also analyzed by our CGSPN model. Moreover, this analysis provides guidelines to develop an efficient object assignment strategy. ^[4–8]     

On application of differential geometry to computational mechanics

Developments in the fields of computational science—the finite element method—and mathematical foundations of continuum mechanics result in many new algorithms which give solutions to very complicated, complex, large scaled engineering problems. Recently, the differential geometry, a modern tool of mathematics, has been used more widely in the domain of the finite element method. Its advantage in defining geometry of elements [13–15] or modeling mechanical features of engineering problems under consideration [4–7] is its global character which includes also insight into a local behavior. This fact comes from the nature of a manifold and its bundle structure, which is the main element of the differential geometry.

Manifolds are generalized spaces, topological spaces. By attaching a fiber structure to each base point of a manifold, it locally resembles the usual real vector spaces; e.g. ³. The properties of a differential manifold M are independent of a chosen coordinate system. It is equivalent to say, that there exists smooth or C^r differentiable atlases which are compatible.

In this paper a short survey of applications of differential geometry to engineering problems in the domain of the finite element method is presented together with a few new ideas.

The properties of geodesic curves have been used by Yuan et al. [13–15], in defining distortion measures and inverse mappings for isoparametric quadrilateral hybrid stress four- and eight-node elements in ². The notion of plane or space curves is one of the elementary ones in the theory of differential geometry, because the concept of a manifold comes from the generalization of a curve or a surface in ³.

Further, the real global nature of differential geometry, has been used by Simo et al. [4,6,7]. A geometrically exact beam finite strain formulation is defined. The mechanical basis of such a nonlinear model can be found in the mathematical foundation of elasticity [18]. An abstract infinite dimensional manifold of mappings, a configuration space, is constructed which permits an exact linearization of algorithms, locally. A similar approach is used by Pacoste [5] for beam elements in instability problems.

Special attention is focused on quadrilateral hybrid stress membrane elements with curved boundaries which belong to a series of isoparametric elements developed by Yuan et al. [14]. The distortion measures are redefined for eight-node isoparametric elements in ² for which geodesic coordinates are used as local coordinates.     

An efficient parallel recognition algorithm forbipartite-permutation graphs

We present a parallel recognition algorithm for bipartite-permutation graphs. The algorithm can be executed in O(log n) time on the CRCW PRAM if O(n³/log n) processors are used, or O(log² n) time on the CREW PRAM if O(n³/log² n) processors are used. Chen and Yesha (1993) have presented another CRCW PRAM algorithm that takes O(log²n) time if O(n ³) processors are used. Compared with Chen and Yesha's algorithm, our algorithm requires either less time and fewer processors on the same machine model, or fewer processors on a weaker machine model. Our algorithm can also be applied to determine if two bipartite-permutation graphs are isomorphic     

On the complexity of ω-type Turing acceptors

Turing machines are considered as recognizers of sets of infinite (ω-type) sequences, so called ω-languages. The basic results on such ω-type Turing acceptors were presented in a preceding paper. This paper focuses on the theory of deterministic ω-type Turing acceptors (ω-DTA's) which turns out to be crucially different from the ‘classical’ theory of Turing machines. It is shown that there exists no ω-DTA which is universal for all ω-DTA's. Two infinite complexity hierarchies for ω-DTA's are established, the ‘states hierarchy’, corresponding to the number of states in the machine, and the ‘designated sets hierarchy’, corresponding to the number of designated sets of states used in the recognition. Concrete examples of ω-languages characterizing each of the complexity classes are exhibited. Two additional examples of interesting ω-languages are presented:

1. (i) An ω-language which is ‘inherently non-deterministic’, i.e. can be recognized by a non-deterministic Turing acceptor but by no deterministic acceptor.

2. (ii) An ω-language which cannot be recognized even by a non-deterministic Turing acceptor.

The above examples are constructed without using diagonalization. Oscillating ω-DTA's, i.e. ω-DTA's which are allowed to oscillate on ω-inputs, are also considered and are shown to be strictly more powerful than non-oscillating ω-DTA's, yet strictly less powerful than non-deterministic ω-Turing acceptors.     

Prefix computations on a generalized mesh-connected computer withmultiple buses

The mesh-connected computer with multiple buses (MC-CMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2D generalized MCCMB (2-GMCCMB) for the purpose of increasing the efficiency of executing some important applications of prefix computations such as solving Linear recurrences and tridiagonaI systems, etc. A k₁n₁ ×k₁n₂ 2-GMCCMB is constructed from a k ₁n₁×k₁n₂ mesh organization by enhancing the power of each disjoint n₁×n₂ submesh with multiple buses (sub-2-MCCMB). Given n data, a prefix computation can be performed in O(n^1/10) time on an n^3/5×n^2/5 2-GMCCMB, where each disjoint sub-2-MCCMB is of size n^1/2×n^3/10. This time bound is faster than the previous time bound of O(n^1/8) for the same computation on an n^5/8×n^3/8 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to O(n^1/11) if fewer processors are used. Our result can be extended to the d-dimensional GMCCMB, giving a time bound of O(n¹ (d2(d)+d)/) for any constant d; here, we omit the constant factors. This time bound is less than the previous time bound of O(n¹(d2(d))/) on the d-dimensional MCCMB     

A period-processor-time-minimal schedule for cubical meshalgorithms

Using a directed acyclic graph (dag) model of algorithms, we investigate precedence-constrained multiprocessor schedules for the n×n×n directed mesh. This cubical mesh is fundamental, representing the standard algorithm for square matrix product, as well as many other algorithms. Its completion requires at least 3^n-2 multiprocessor steps. Time-minimal multiprocessor schedules that use as few processors as possible are called processor-time-minimal. For the cubical mesh, such a schedule requires at least [3n²/4] processors. Among such schedules, one with the minimum period (i.e., maximum throughput) is referred to as a period-processor-time-minimal schedule. The period of any processor-time-minimal schedule for the cubical mesh is at least 3^n/2 steps. This lower bound is shown to be exact by constructing, for n a multiple of 6, a period-processor-time-minimal multiprocessor schedule that can be realized on a systolic array whose topology is a toroidally connected n/2×n/2×3 mesh     

Precise isotope abundance ratio measurement of nitrous oxide using diode lasers

High-precision measurement of the isotope abundance ratio ¹⁴N¹⁵N¹⁶O/¹⁵N¹⁴N¹⁶O/¹⁴N¹⁴N¹⁸O/¹⁴N¹⁴N¹⁶O (0.37/0.37/0.2/100) in nitrous oxide by a laser-spectroscopic method is demonstrated. The abundance ratio is determined from the absorbance ratio of selected absorption lines near 2 μm of the respective isotopic molecular species. Four wavelength-modulated diode lasers whose center wavelengths are stabilized on the selected lines are made to travel different distances in a multipass cell to compensate the large abundance differences. In the test experiment using pure nitrous oxide samples the abundance ratio can be measured with relative uncertainties of ±(2–6)×10⁻⁴ (±0.2–0.6‰). The laser-spectroscopic method is expected to complement mass spectrometry in isotope analyses to trace the geochemical cycles of environmental substances.     

On the type of a polynomial f, when f(0)f−f(0)f is a monomial

A polynomial is said to be of type (p₁, p₂, p₃) relative to a directed line in the complex plane if, counting multiplicities, it has p₁ zeros to the left of, p₂ zeros on, and p₃ zeros to the right of the line. In this paper we determine explicitly the types of all polynomials belonging to a very restricted (but infinite) family of polynomials. A polynomial ƒ belongs to this family if and only if its coefficients are such that the polynomial ƒ^*(0)ƒ(z)−ƒ(0) ƒ^*(z) is a monomial; here ƒ^* denotes the reflection of ƒ in the directed line.

A special case of the present result appeared in an earlier publication.     

On describing complex surface shapes

The fractal surface model¹ is extended to provide a formalism that is competent to describe complex, natural three-dimensional surfaces in either a quantitative or qualitative manner and which, in addition, closely mimics human perceptual judgments of surface structure (eg ‘peaks’, ‘ridges’ or ‘valleys’) and threedimensional texture. This representation is then used to develop a statistical version of scale-space filtering that is applicable to one-, two- or three-dimensional data.     

White organic light-emitting devices with non-doped-type structure

A non-doped-type structure was proposed for obtaining organic light-emitting devices with high-efficiency and full-spectrum white light emission. The device structure included indium tin oxide glass substrate/450 Å 4,4′,4″-tris{N-(3-methylphenyl)-N-phenylamin}triphenylamine (m-MTDATA) hole injection layer/100 Å N,N′-bis-(1-naphthyl)-N,N′-diphenyl-1,1′-biph-enyl-4,4′-diamine (NPB) hole transport layer/150 Å 4,4′-bis(2,2′-diphenylvinyl)-1,1′-biphenyl (DPVBi) blue emitting layer/ultrathin [2-methyl-6-[2-(2,3,6,7-tetrahydro-1H, 5H-benzo[ij] quinolizin-9-yl)ethenyl]-4H-pyran-4-ylidene] propane-dinitrile (DCM2) yellow-emitting layer/ 80 Å 4,7-diphenyl-1,10-phenanthroline (BPhen) electron transporting layer and hole blocking layer/600 Å tris (8-hydroxyquinoline) aluminium (Alq3) electron-transporting layer /10 Å lithium fluoride (LiF)/aluminum (Al). A white emission (Commission Internationale de l’Eclairage 1931 chromaticity coordinate) (X = 0.3556, Y = 0.3117) at 5 V and (X = 0.282, Y = 0.2658) at 15 V was obtained. Its luminance was 11,497 cd/m² at 15 V, and the maximum efficiency was 4.8 lm/W at 5 V.     

Polyominoes simulating arbitrary-neighborhood zippers and tilings

This paper provides a bridge between the classical tiling theory and the complex-neighborhood self-assembling situations that exist in practice.The neighborhood of a position in the plane is the set of coordinates which are considered adjacent to it. This includes classical neighborhoods of size four, as well as arbitrarily complex neighborhoods. A generalized tile system consists of a set of tiles, a neighborhood, and a relation which dictates which are the “admissible” neighboring tiles of a given tile. Thus, in correctly formed assemblies, tiles are assigned positions of the plane in accordance with this relation.We prove that any validly tiled path defined in a given but arbitrary neighborhood (a zipper) can be simulated by a simple “ribbon” of microtiles. A ribbon is a special kind of polyomino, consisting of a non-self-crossing sequence of tiles on the plane, in which successive tiles stick along their adjacent edge.Finally, we extend this construction to the case of traditional tilings, proving that we can simulate arbitrary-neighborhood tilings by simple-neighborhood tilings, while preserving some of their essential properties.     

Application of the independent molecule model to elucidate the dynamics of structure I methane hydrate

Raman spectroscopy has exhibited the C–H stretch (A₁ mode) frequency ν₁ of hydrated methanes at 2915 cm⁻¹ for the 5¹² cage and 2905 cm⁻¹ for the 5¹²6² cage. These values are lower than the frequency of 2916.5 cm⁻¹ in gaseous methane. In this paper, we theoretically examine the Raman spectra observed in methane hydrate by normal mode analysis using the independent molecule model. By a breakdown of the symmetry, the four frequencies in modes A₁, E, T₂ and T₂ observed in gaseous methane are separated into nine frequencies in the hydrate. It is necessary to consider the anharmonic potential energy within methane and hydrogen bonding between methane hydrogen and water oxygen in order to get a result in qualitative agreement with experiment. The frequency in the 5¹²6² cage is shifted downward in comparison to the one in 5¹², and the frequencies in the both cages are also shifted downward compared with the frequencies in gas. Calculations are also reported for the isotopic methane (CD₄, ¹³CH₄) hydrates.     

Quartic discriminants and tensor invariants

Discusses the calculation of discriminants of polynomials. The discriminant is a function of the coefficients that indicates if the polynomial has any double roots. The discriminant Δ₄ of a homogeneous quartic f(x,w) = Ax⁴+4Bx³w+6Cx² w²+4Dxw³+Ew⁴ = 0 is Δ₄ = 27(I₃)²-(I₂)³, where I₂ = AE-4BD+3C² and I₃ = ACE-AD ²-B²E+2BCD-C³ (this is the Hilbert representation). The author shows how to write the discriminant as a tensor diagram. The discriminant of a polynomial is an example of an invariant quantity. Tensor diagrams are particularly useful to express invariant quantities. Adding a dimension moves us from the world of (1D) homogeneous polynomials to 2D homogeneous (2DH) geometry (curves in the projective plane). It is shown that a relationship exists between the possible root structures of a 4th-order polynomial and the possible degeneracies of a 3rd-order curve