Electron-impact ionization of Fe14+ and other atomic ions in the Mg isoelectronic sequence

Distorted-wave calculations are carried out for the electron-impact ionization of Fe¹⁴⁺ in both the ground 3s^{2 1}S₀ and metastable 3s3p ³P_0.2 levels. The cross sections and Maxwellian-average rate coefficients include direct ionization of the 2s, 2p, 3s, and 3p subshells, as well as inner-shell excitations from the 2s and 2p subshells leading to autoionization. The excitation—autoionization contributions are found to be large for both the ground the metastable levels. To assist modeling efforts of moderately dense plasmas, the direct and indirect rate coefficients are resolved as to the final level of the ionization process and assembled in a standard database file. A complete database for selected metallic ions in the Mg isoelectronic sequence will reside in electronic form at the Controlled Fusion Atomic Data Center at ORNL (//www-cfadc.phy.ornl.gov/data_and_codes/).     

A combinatorial algorithm for max csp

We consider the problem max csp over multi-valued domains with variables ranging over sets of size s_i?s and constraints involving k_j?k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A,B).The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp. on Theoret. Aspects of Comput. Sci., 1998, pp. 488-498] and gives ratio A which is bounded below by s^1−k. For k=2, our bound in terms of the individual set sizes is the minimum over all constraints involving two variables of , where s₁ and s₂ are the set sizes for the two variables.We then give a simple combinatorial algorithm which has approximation ratio B, with B>A/e. The bound is greater than s^1−k/e in general, and greater than s^1−k(1−(s−1)/2(k−1)) for s?k−1, thus close to the s^1−k linear programming bound for large k. For k=2, the bound is if s=2, 1/2(s−1) if s?3, and in general greater than the minimum of 1/4s₁+1/4s₂ over constraints with set sizes s₁ and s₂, thus within a factor of two of the linear programming bound.For the case of k=2 and s=2 we prove an integrality gap of . This shows that our analysis is tight for any method that uses the linear programming upper bound.     

Observational constraints on a hyperbolic potential in brane-world inflation

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P _R (k), the parameter f should be of order 0.1m _p to 0.001m _p , the brane tension must be in the range λ ~ (1?10)×10⁵⁷ GeV⁴, and the energy scale is around V₀ ^1/4 ~ 10¹⁵ GeV. We find that the inflationary parameters (n _s , r, and dn _s /d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.     

Organization of self-diagnosis of the discrete multicomponent systems a structure like bipartite quasicomplete graphs

Organization of an efficient self-diagnosis of the multicomponent computer and communication systems of diverse structures always attracted attention of the researchers and engineers. A method to solve these problems is presented in the paper by way of the example of a system whose structure is modeled by a uniform ordinary bipartite graph of diameter d = 3, any degree s > 1, and any number n of vertices, where n = s(s ? 1) + 1. The method requires checking of (s ? 1)³ graph loops of length eight each, which is smaller than the number s ²(s ? 1) + s of checks of single graph edges.     

Erzeugende Funktionen bei Spline-Interpolation mit äquidistanten Knoten

Using generating functions we obtain in the case ofn+1 equidistant data points a method for the calculation of the interpolating spline functions(x) of degree 2k+1 with boundary conditionss ^(κ) (x₀)=y ₀ ^(κ) ,s ^(κ) (x _n )=y _n ^(κ) , κ=1(1)k, which only needs the inversion of a matrix of orderk. The applicability of our method in the case of general boundary conditions is also mentioned.     

Studies of angular correlations in the decays Bs→J/ψφ by using the SIMUB generator

The performance of the method of angular moments on the ΔΓ_s determination from analysis of untagged decays is examined by using the SIMUB generator. The results of Monte Carlo studies with evaluation of measurement errors are presented. The method of angular moments gives stable results for the estimate of ΔΓ_s and is found to be an efficient and flexible tool for the quantitative investigation of the B⁰_s→J/ψφ decay. The statistical error of the ratio ΔΓ_s/Γ_s for values of this ratio in the interval [0.03,0.3] was found to be independent on this value, being 0.015 for 10⁵ events.     

Partitioning a Square into Rectangles: NP-Completeness and Approximation Algorithms

In this paper we deal with two geometric problems arising from heterogeneous parallel computing: how to partition the unit square into p rectangles of given area s ₁ , s ₂ , . . . ,s _p (such that Σ _i=1 ^p s _i = 1 ), so as to minimize either (i) the sum of the p perimeters of the rectangles or (ii) the largest perimeter of the p rectangles? For both problems, we prove NP-completeness and we introduce a 7/4 -approximation algorithm for (i) and a $(2/\sqrt{3})$ -approximation algorithm for (ii).     

A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n ? 6 and 1 ? m ? ⌈n/2⌉ − 1, a family of 2^m disjoint k-dimensional tori of size 2^s₁×2^s₂×?×2^s_k each can be embedded in an n-dimensional crossed cube with unit dilation, where each s_i ? 2, , and max_1?i?k{s_i} ? 3 if n is odd and ; otherwise, max_1?i?k{s_i} ? n − 2m − 1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.     

Kantowski-Sachs and Bianchi type models with a general non-canonical scalar field

The paper deals with spatially homogeneous and anisotropic Kantowski-Sachs and Bianchi universes with a general non-canonical scalar field with the Lagrangian L = F(X) ? Ω(?), where \(X = \frac{1}{2}{\phi _i}{\phi ^i}\). We discuss a general non-canonical scalar field in three different cosmologies: (i) cosmology with a constant potential, Ω(?) = Ω₀ = const, (ii) cosmology with a constant equation-of-state parameter, i.e., γ_? = const, and (iii) cosmology with a constant speed of sound, i.e., c _s ² = const. For a constant potential, we have shown that the k-essence Lagrangian and the Lagrangian of the present model are equivalent. Dissipation of anisotropy, when the universe is filled with a general non-canonical scalar field, is investigated. The existence of an average bounce in Kantowski-Sachs and locally rotationally symmetric Bianchi-I and Bianchi-III models is discussed in detail.     

Esistenza,unicità e calcolo della soluzione di un sistema non lineare

LetX be a point of the realn-dimensional Euclidean space ? ⁿ ,G(X) a given vector withn real components defined in ? ^u ,U an unknown vector withs real components,K a known vector withs real components andA a given reals×n matrix of ranks. Assuming that, for every pair of pointsX ₁ , X₂of ? ⁿ ,G(X) satisfies the conditions $$(G(X_1 ) - G(X_2 ), X_1 - X_2 ) \geqslant o (X_1 - X_2 , X_1 - X_2 )$$ and $$\left\| {(G(X_1 ) - G(X_2 )\left\| { \leqslant M} \right\|X_1 - X_2 )} \right\|$$ wherec andM are positive constants, we prove that a unique solution of the system $$\left\{ \begin{gathered} G(X) + A ^T U = 0 \hfill \\ AX = K \hfill \\ \end{gathered} \right.$$ exists and we show a method for finding such a solution     

活性污泥法污水处理数学模型的发展和应用

综述了活性污泥法污水处理数学模型自20世纪50年代以来的发展历程； 阐述了国际水协会（IWA）推出的活性污泥1号、2号、2D号、3号模型（ASM1、ASM2、ASM2D、ASM3）各自的特点和使用限制条件； 介绍了几种基于ASM系列模型的具有代表性的商业化仿真软件． 最后，还就ASM系列模型的三个应用难点——水质的分析测定、模型简化、参数校正进行了讨论．     

Optimal Path Embedding in the Exchanged Crossed Cube

The (s + t + 1)-dimensional exchanged crossed cube, denoted as ECQ(s, t), combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ(s, t) has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ(s, t). We prove the result in ECQ(s, t): if s ≥ 3, t ≥ 3, for any two different vertices, all paths whose lengths are between \( \max \left\{9,\left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +4\right\} \) and 2 ^s+t+1 ? 1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ(s, t) is \( \left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +2 \). The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ(s, t) preserves the path embedding capability to a large extent, while it only has about one half edges of CQ _n .     

Approximating Node-Connectivity Augmentation Problems

We consider the (undirected) Node Connectivity Augmentation (NCA) problem: given a graph J=(V,E _J ) and connectivity requirements $\{r(u,v): u,v \in V\}$ , find a minimum size set I of new edges (any edge is allowed) such that the graph J∪I contains r(u,v) internally-disjoint uv-paths, for all u,v∈V. In Rooted NCA there is s∈V such that r(u,v)>0 implies u=s or v=s. For large values of k=max? _u,v∈V r(u,v), NCA is at least as hard to approximate as Label-Cover and thus it is unlikely to admit an approximation ratio polylogarithmic in k. Rooted NCA is at least as hard to approximate as Hitting-Set. The previously best approximation ratios for the problem were O(kln?n) for NCA and O(ln?n) for Rooted NCA. In this paper we give an approximation algorithm with ratios O(kln?² k) for NCA and O(ln?² k) for Rooted NCA. This is the first approximation algorithm with ratio independent of?n, and thus is a constant for any fixed k. Our algorithm is based on the following new structural result which is of independent interest. If $\mathcal{D}$ is a set of node pairs in a graph?J, then the maximum degree in the hypergraph formed by the inclusion minimal tight sets separating at least one pair in $\mathcal{D}$ is O(? ²), where ? is the maximum connectivity in J of a pair in $\mathcal{D}$ .     

Dilatonic (quasi-) black holes without scalar charge

We consider static, spherically symmetric configurations of electrically charged dust in Einstein-Maxwell-dilaton gravity where the Lagrangian contains the interaction term P(χ)F _μν F ^μν with an arbitrary function P(χ). Unlike previous studies, we assume that the scalar field χ (which can be canonical or phantom) does not have a charge of its own and exists only due to this interaction. We discuss possible solutions to the field equations, in particular, those describing black holes (BHs) and quasi-black holes (QBHs). The latter are globally regular configurations whose size is very close to that of a BH of the same mass and which therefore are almost indistinguishable from BHs for a distant observer. Some general features are revealed, a family of explicitly integrable models is found, and some explicit examples are presented.     

Cops and Robbers from a distance

Cops and Robbers is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robbers, distance k Cops and Robbers, where the cops win if at least one of them is of distance at most k from the robber in G. The cop number of a graph G is the minimum number of cops needed to capture the robber in G. The distance k analogue of the cop number, written c_k(G), equals the minimum number of cops needed to win at a given distance k. We study the parameter c_k from algorithmic, structural, and probabilistic perspectives. We supply a classification result for graphs with bounded c_k(G) values and develop an O(n^2s+3) algorithm for determining if c_k(G)≤s for s fixed. We prove that if s is not fixed, then computing c_k(G) is NP-hard. Upper and lower bounds are found for c_k(G) in terms of the order of G. We prove that