Two Tree-Width-Like Graph Invariants

In this paper we introduce two tree-width-like graph invariants. The first graph invariant, which we denote by ⁼(G), is defined in terms of positive semi-definite matrices and is similar to the graph invariant (G), introduced by Colin de Verdière in [J. Comb. Theory, Ser. B., 74:121–146, 1998]. The second graph invariant, which we denote by (G), is defined in terms of a certain connected subgraph property and is similar to (G), introduced by van der Holst, Laurent, and Schrijver in [J. Comb. Theory, Ser. B., 65:291–304, 1995]. We give some theorems on the behaviour of these invariants under certain transformations. We show that ⁼(G)=(G) for any graph G with ⁼(G)4, and we give minimal forbidden minor characterizations for the graphs satisfying ⁼(G)k for k=1,2,3,4.This paper is extracted from two chapters of [7]. This work was done while the author was at the Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.     

Sr_2ZnSi_2O_7∶Eu~(3+)的低温合成与发光性能

以介孔二氧化硅MCM-41为硅源,采用低温水热反应与后续煅烧相结合的方法合成Sr2-xZnSi2O7∶xEu3+红色荧光粉。实验结果表明,150℃水热处理16 h后的反应产物含Sr2ZnSi2O7相,经后续950℃煅烧3h得到Sr2ZnSi2O7纯相。在392 nm近紫外光的有效激发下,Sr2-xZnSi2O7∶xEu3+荧光粉显示Eu3+离子的特征跃迁发射,以615 nm的5D0→7F2跃迁发射峰为最强。适量Eu3+的掺杂对Sr2ZnSi2O7相结构几乎没有影响,当Eu3+离子的掺杂量x=0.10时,荧光粉发光强度最大。     

A novel methodological approach for δ18O analysis of sugars using gas chromatography-pyrolysis-isotope ratio mass spectrometry

Although the instrumental coupling of gas chromatography-pyrolysis-isotope ratio mass spectrometry (GC-Py-IRMS) for compound-specific δ¹⁸O analysis has been commercially available for more than a decade, this method has been hardly applied so far. Here we present the first GC-Py-IRMS δ¹⁸O results for trimethylsilyl-derivatives of plant sap-relevant sugars and a polyalcohol (glucose, fructose, sucrose, raffinose and pinitol). Particularly, we focus on sucrose, which is assimilated in leaves and which is the most important transport sugar in plants and hence of utmost relevance in plant physiology and paleoclimate studies. Replication measurements of sucrose standards and concentration series indicate that the GC-Py-IRMS δ¹⁸O measurements are not stable over time and that they are amount (area) dependent. We, therefore, suggest running sample batch replication measurements in alternation with standard concentration series of reference material. This allows for carrying out (i) a drift correction, (ii) a calibration against reference material and (iii) an amount (area) correction. Tests with ¹⁸O-enriched water do not provide any evidence for oxygen isotope exchange reactions affecting sucrose and raffinose. We present the first application of GC-Py-IRMS δ¹⁸O analysis for sucrose from needle extract (soluble carbohydrate) samples. The obtained δ¹⁸O_{sucrose/ Vienna Standard Mean Ocean Water (VSMOW)} values are more positive and vary in a wider range (32.1–40.1 ‰) than the δ¹⁸O_{bulk/ VSMOW} values (24.6–27.2 ‰). Furthermore, they are shown to depend on the climate parameters maximum day temperature, relative air humidity and cloud cover. These findings suggest that δ¹⁸O_sucrose of the investigated needles very sensitively reflects the climatically controlled evaporative ¹⁸O enrichment of leaf water and thus highlights the great potential of GC-Py-IRMS δ¹⁸O_sucrose analysis for plant physiology and paleoclimate studies.     

Graded Steinberg algebras and partial actions

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space which is totally disconnected, the Steinberg algebra of the associated groupoid is graded isomorphic to the corresponding partial skew group ring. We show that there is a one-to-one correspondence between the open invariant subsets of the topological space and the graded ideals of the partial skew group ring. We also consider the algebraic version of the partial $C^{?}$-algebra of an abelian group and realise it as a partial skew group ring via a partial action of the group on a topological space. Applications to the theory of Leavitt path algebras are given.     

Gas sensing properties of nanostructured MoO3 thin films prepared by spray pyrolysis

Thin films of molybdenum trioxide (MoO₃) were deposited on common glass using the chemical spray pyrolysis technique. A (NH₄)₆Mo₇O₂₄4H₂0 solution 0.1 M was used as the precursor one. The influence of substrate temperature on the crystallographic structure, surface morphology and electrical behavior of MoO₃ thin films was studied. MoO₃ can exist in two crystalline forms, the thermodynamically stable orthorhombic α-MoO₃ and the metastable monoclinic β-MoO₃ phase. XRD-spectra showed a growth of α-MoO₃ phase percentage as substrate temperature increases from 420 K up to 670 K. Films deposited in the 500–600 K range have a clearly porous surface structure of nanometer order as can be seen in SEM images. Changes up to six magnitude orders were observed in MoO₃ thin films electrical resistance when films temperature varied from 100 K up to 500 K. The sensing property of these MoO₃ films was also studied. The sensitivity was investigated in the temperature range 160 and 360 K for H₂O and CO gases, respectively. Both of them are of reducing nature. In all studied cases sensitivity decreases slowly as film temperature is raised. At room temperature the sensitivity changes from 12 up to 75% depending on substrate temperature. The sensitivity for CO gas was found to be lower than that of H₂O.     

Monte Carlo study of the universal area distribution of clusters in the honeycomb O（n） loop model

We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A-1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method.     

Krylov type subspace methods for matrix polynomials

We consider solving eigenvalue problems or model reduction problems for a quadratic matrix polynomial Iλ² − Aλ − B with large and sparse A and B. We propose new Arnoldi and Lanczos type processes which operate on the same space as A and B live and construct projections of A and B to produce a quadratic matrix polynomial with the coefficient matrices of much smaller size, which is used to approximate the original problem. We shall apply the new processes to solve eigenvalue problems and model reductions of a second order linear input-output system and discuss convergence properties. Our new processes are also extendable to cover a general matrix polynomial of any degree.     

Syzygies and the Rees algebra

Let a,b,c be linearly independent homogeneous polynomials in the standard Z-graded ring R?k[s,t] with the same degree d and no common divisors. This defines a morphism P¹→P². The Rees algebra of the ideal I=〈a,b,c〉 is the graded R-algebra which can be described as the image of an R-algebra homomorphism h: . This paper discusses one result concerning the structure of the kernel of the map h and its relation to the problem of finding the implicit equation of the image of the map given by a, b, c. In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox.     

Fast data extrapolating

Data-extrapolating (extension) technique has important applications in image processing on implicit surfaces and in level set methods. The existing data-extrapolating techniques are inefficient because they are designed without concerning the specialities of the extrapolating equations. Besides, there exists little work on locating the narrow band after data extrapolating—a very important problem in narrow band level set methods. In this paper, we put forward the general Huygens’ principle, and based on the principle we present two efficient data-extrapolating algorithms. The algorithms can easily locate the narrow band in data extrapolating. Furthermore, we propose a prediction–correction version for the data-extrapolating algorithms and the corresponding band locating method for a special case where the direct band locating method is hard to apply. Experiments demonstrate the efficiency of our algorithms and the convenience of the band locating method.