Multiplicity factor and diffraction geometry factor for single crystal X-ray diffraction analysis and measurement of phase content in cubic GaN/GaAs(001) epilayers

On the basis of integrated intensity of rocking curves, the multiplicity factor and the diffraction geometry factor for single crystal X-ray diffraction (XRD) analysis were proposed and a general formula for calculating the content of mixed phases was obtained. With a multifunction four-circle X-ray double-crystal diffractometer, pole figures of cubic (002), 1₁₁₁ and hexagonal 1010 and reciprocal space mapping were measured to investigate the distributive character of mixed phases and to obtain their multiplicity factors and diffraction geometry factors. The contents of cubic twins and hexagonal inclusions were calculated by the integrated intensities of rocking curves of cubic (002), cubic twin 111, hexagonal 1010 and 1011.     

On a special case of the intersection of quadric and cubic surfaces

The intersection curve between two surfaces in three-dimensional real projective space RP³ is important in the study of computer graphics and solid modelling. However, much of the past work has been directed towards the intersection of two quadric surfaces. In this paper we study the intersection curve between a quadric and a cubic surface and its projection onto the plane at infinity. Formulas for the plane and space curves are given for the intersection of a quadric and a cubic surface. A family of cubic surfaces that give the same space curve when we intersect them with a quadric surface is found. By generalizing the methods in Wang et al. (2002) [6] that are used to parametrize the space curve between two quadric surfaces, we give a parametrization for the intersection curve between a quadric and a cubic surface when the intersection has a singularity of order 3.     

Surface forces in model hexagonal and cubic planar structures

Conclusions 1. Perturbation in the structure of the surface layer of hexagonal and cubic crystal structures produces attraction between the surface particles.2. The surface tension of a fiber depends qualitatively on the surface interaction forces. The nature of these forces is determined by the peculiarities of the microstructures, surface expansion of the lattice, microdefects, and perturbations on the surface.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 799–801, September–October, 1978.     

Note on the cubic decreasing region of the Chebyshev method

In this paper we reduce the two-dimensional cubic decreasing region considered in Hernandez and Salanova (2000) [1], [2] into one-dimensional region or interval for the Chebyshev method. It means that we find a simple sufficient condition for the semilocal convergence of the method.     

On a Frank-Wolfe type theorem in cubic optimization

ABSTRACT

A classical result due to Frank and Wolfe [An algorithm for quadratic programming. Naval Res Log Quart. 1956;3:95–110] says that a quadratic function f attains its supremum on a nonempty polyhedron M if f is bounded from above on M. In this note, we present a stringent proof of the extension of this result to cubic optimization (known from Andronov, Belousov and Shironin [On solvability of the problem of polynomial programming (In Russian). Izvestija Akadem. Nauk SSSR, Tekhnicheskaja Kibernetika. 1982;4:194–197. Translation appeared in News of the Academy of Science of USSR, Dept. of Technical Sciences, Technical Cybernetics.]). Further, we discuss related results. In particular, we bring back to attention Kummer's [Globale Stabilität quadratischer Optimierungsprobleme. Wissenschaftliche Zeitschrift der Humboldt- Universität zu Berlin, Math-Nat R. 1977;XXVI(5):565–569] generalization of the Frank-Wolfe theorem to the case that f is quadratic, but M is the Minkowski sum of a compact set and a polyhedral cone.     

Dominating and total dominating partitions in cubic graphs

In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating set is at most (n+2)/2, and this bound is essentially best possible.     

The local integro cubic splines and their approximation properties

We show the integro cubic splines proposed by Behforooz [1] can be constructed locally by using B-representation of splines. The approximation properties of the local splines are also considered.     

Complete cubic spline estimation of non-parametric regression functions

Summary For regression functions on [0, 1] with bounded fourth derivatives, a complete cubic spline estimate is proposed and shown to have an asymptotically optimal error rate among all estimates. The error is measured by the supremum norm.     

Global optimality conditions for cubic minimization problem with box or binary constraints

In this article, we provide optimality conditions for global solutions to cubic minimization problems with box or binary constraints. Our main tool is an extension of the global subdifferential approach, developed by Jeyakumar et al. (J Glob Optim 36:471–481, 2007; Math Program A 110:521–541, 2007). We also derive optimality conditions that characterize global solutions completely in the case where the cubic objective function contains no cross terms. Examples are given to demonstrate that the optimality conditions can effectively be used for identifying global minimizers of certain cubic minimization problems with box or binary constraints.     

The enumeration of rooted cubic c-nets

This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].     

Preconditioning cubic spline collocation discretizations of elliptic equations

Summary. This work considers the uniformly elliptic operator defined by in (the unit square) with boundary conditions: on and on and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix . We discuss the condition numbers and the distribution of -singular values of the preconditioned matrices where is the stiffness matrix associated with the finite element discretization of the positive definite uniformly elliptic operator given by in with boundary conditions: on on . The finite element space is either the space of continuous functions which are bilinear on the rectangles determined by Gauss points or the space of continuous functions which are linear on the triangles of the triangulation of using the Gauss points. When we obtain results on the eigenvalues of . In the general case we obtain bounds and clustering results on the -singular values of . These results are related to the results of Manteuffel and Parter [MP], Parter and Wong [PW], and Wong [W] for finite element discretizations as well as the results of Parter and Rothman [PR] for discretizations based on Legendre Spectral Collocation. Received January 1, 1994 / Revised version received February 7, 1995     

Estimates for Tamagawa numbers of diagonal cubic surfaces

For diagonal cubic surfaces, we give an upper bound for E. Peyre's Tamagawa type number in terms of the coefficients of the defining equation. This bound shows that the reciprocal admits a fundamental finiteness property on the set of all diagonal cubic surfaces. As an application, we show that the infinite series of Tamagawa numbers related to the Fano cubic bundles considered by Batyrev and Tschinkel (1996) [BT] are indeed convergent.     

High‐girth cubic graphs are homomorphic to the Clebsch graph

We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5‐colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph (Fig. 1 ). Hopkins and Staton [J Graph Theory 6(2) (1982), 115–121] and Bondy and Locke [J Graph Theory 10(4) (1986), 477–504] proved that every (sub)cubic graph of girth at least 4 has an edge‐cut containing at least of the edges. The existence of such an edge‐cut follows immediately from the existence of a 5‐edge‐coloring as described above; so our theorem may be viewed as a coloring extension of their result (under a stronger girth assumption). Every graph which has a homomorphism to a cycle of length five has an above‐described 5‐edge‐coloring; hence our theorem may also be viewed as a weak version of Ne?et?il's Pentagon Problem (which asks whether every cubic graph of sufficiently high girth is homomorphic to C₅). Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 66: 241—259, 2011     

Data compression based on the cubic B-spline wavelet with uniform two-scale relation

The aim of this paper is to investigate the potential artificial compression which can be achieved using an interval multiresolution analysis based on a semiorthogonal cubic B-spline wavelet. The Chui-Quak [1] spline multiresolution analysis for the finite interval has been modified [2] so as to be characterized by natural spline projection and uniform two-scale relation. Strengths and weaknesses of the semiorthogonal wavelet as regards artificial compression and data smoothing by the method of thresholding wavelet coefficients are indicated.     

Minimum path decompositions of oriented cubic graphs

Pullman [3] conjectured that if k is an odd positive integer, then every orientation of a regular graph of degree k has a minimum decomposition which contains no vertex which is both the initial vertex of some path in the decomposition and the terminal vertex of some other path in the decomposition. In this paper, the conjecture is established for cubic graphs, and its connection with Kelly's conjecture for tournaments is described.     

Asymptotic solutions of an extended Korteweg–de Vries equation describing solitary waves with weak or strong downstream decay in turbulent open-channel flow

Solitary waves in turbulent open-channel flow over a strip of enlarged bottom roughness are considered. Slightly supercritical, fully developed flow far upstream and downstream is assumed. An analysis by Schneider [1] yielded an extended Korteweg–de Vries equation that is solved in the present paper by matched asymptotic expansions up to second order. Solutions for the surface elevation and the location of the wave crest are given. It is shown that a minimum enlargement of the bottom roughness is required for the stationary wave to exist. The surface elevation exhibits either a weak downstream decay, i.e. a shallow ‘tail’, or, if the enlargement of the bottom roughness equals an eigenvalue, the strong decay of the classical soliton solution. Numerical results available for the latter case [2] are in very good agreement with the present analytical solution. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Annealing behavior of hexagonal phase content in cubic GaN thin films grown on GaAs (001) by MOCVD

The annealing behavior of the hexagonal phase content in cubic GaN (c-GaN) thin Films grown on GaAs (001) by MOCVD is reported. C-GaN thin films are grown on GaAs (001) substrates by metalorganic chemical vapor deposition (MOCVD). High temperature annealing is employed to treat the as-grown c-GaN thin films. The characterization of the c-GaN films is investigated by photoluminescence (PL) and Raman scattering spectroscopy. The change conditions of the hexagonal phase content in the metastable c-GaN are reported. There is a boundary layer existing in the c-GaN/GaAs film. When being annealed at high temperature, the intensity of the T0_B and LO_B phonon modes from the boundary layer weakens while that of the E₂ phonon mode from the hexagonal phase increases. The content change of hexagonal phase has closer relationship with annealing temperature than with annealing time period.     

On cubic non‐Cayley vertex‐transitive graphs

In 1983, the second author [D. Maru?i?, Ars Combinatoria 16B (1983), 297–302] asked for which positive integers n there exists a non‐Cayley vertex‐transitive graph on n vertices. (The term non‐Cayley numbers has later been given to such integers.) Motivated by this problem, Feng [Discrete Math 248 (2002), 265–269] asked to determine the smallest valency ?(n) among valencies of non‐Cayley vertex‐transitive graphs of order n. As cycles are clearly Cayley graphs, ?(n)?3 for any non‐Cayley number n. In this paper a goal is set to determine those non‐Cayley numbers n for which ?(n) = 3, and among the latter to determine those for which the generalized Petersen graphs are the only non‐Cayley vertex‐transitive graphs of order n. It is known that for a prime p every vertex‐transitive graph of order p, p² or p³ is a Cayley graph, and that, with the exception of the Coxeter graph, every cubic non‐Cayley vertex‐transitive graph of order 2p, 4p or 2p² is a generalized Petersen graph. In this paper the next natural step is taken by proving that every cubic non‐Cayley vertex‐transitive graph of order 4p², p>7 a prime, is a generalized Petersen graph. In addition, cubic non‐Cayley vertex‐transitive graphs of order 2p^k, where p>7 is a prime and k?p, are characterized. © 2011 Wiley Periodicals, Inc. J Graph Theory 69: 77–95, 2012     

Bounds on the extensional strains in elastic homogeneous crystals under simple tension

Within the context of the linearized theory of elasticity, weconsider homogeneous crystals, which have orthorhombic, tetragonal,hexagonal symmetry or cubic symmetry (‘RTHC’ crystals).When such a crystal is subjected to a simple tension (or compression)of amount T in the direction n, there will be three, generallydifferent, extensional strains along the three mutually perpendiculardirections corresponding to the principal axes of strain. Thepurpose of this paper is to present a simple procedure to placebounds, upper and lower, on the possible extensional strainsin the crystal, both in the case when n is fixed in directionand in the case when n is arbitrary. The procedure allows usto determine whether the bounds are attained or not.