Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the t-expansion method to the calculation of the ground state energy E₀ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the t-expansion results are rather poor and exhibit considerable oscillations. In this Letter, we formulate the t-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the t-series, E₀ is assumed to be stationary with respect to the free parameters. A high accuracy of E₀ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than ¹⁰−4 (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy E₁, with the relative error smaller than ¹⁰−2 (1%).     

On connected dominating sets of restricted diameter

A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s-club. We prove that for any fixed positive integer s it is NP-complete to determine if a graph has a dominating s  -club, even when the graph has diameter s+1$s+1$. As a special case it is NP-complete to determine if a graph of diameter two has a dominating clique. We then propose a compact integer programming formulation for the related minimization problem, enhance the approach with variable fixing rules and valid inequalities, and present computational results.     

Designing an optimal connected nature reserve

We consider a landscape divided into elementary cells, each of these cells containing some species to be protected. We search to select a set of cells to form a natural reserve in order to protect all the species present in the landscape. A species is considered protected if it is present in a certain number of cells of the reserve. There is an important spatial constraint concerning the set of selected cells: a species must be able to go from any cell to any cell without leaving the reserve. An integer linear programming model was proposed by Önal and Briers [2] for this reserve selection problem, but the size of the problems which can be handled by this model is limited: several hours of computation are required for solving instances with hundred of cells and hundred of species. Having proposed an improvement of this model which reduces appreciably the computation time, we propose another integer linear programming model, easy to carry out, which allows to obtain, in a few seconds of computation, optimal or near-optimal solutions for instances with hundred of cells and hundred of species. However, the computation time becomes prohibitive for instances with more than 200 cells and 100 species. But, this approach can be particularly useful to solve the problem, in an approximate way, by aggregation of cells as proposed by Önal and Briers [2].     

Unobserved Component models applied to the assessment of wear in railway points: A case study

Railways are experiencing a fundamental transformation. The introduction of high speed networks and the increased traffic levels on suburban routes and freight lines require new technologies for both railway infrastructure and trains, all of which must be subjected to rigorous quality control before and during operation and must be supported with effective maintenance processes during their operating lives. Safety in railway infrastructure provision must be ensured by all the main components operating reliably all the time. From an economic, quality and safety point of view, points are probably one of the most critical infrastructure elements in railway transportation.     

The speaker''s formant in male voices

Spectral analysis of vowels during connected speech can be performed using the spectral intensity distribution within critical bands corresponding to a natural scale on the basilar membrane. Normalization of the spectra provides the opportunity to make objective comparisons independent from the recording level. An increasing envelope peak between 3,150 and 3,700 Hz has been confirmed statistically for a combination of seven vowels in three groups of male speakers with hoarse, normal, and professional voices. Each vowel is also analyzed individually. The local energy maximum is called “the speaker's formant” and can be found in the region of the fourth formant. The steepness of the spectral slope (i.e. the rate of decline) becomes less pronounced when the sonority or the intensity of the voice increases. The speaker's formant is connected with the sonorous quality of the voice. It increases gradually and is approximately 10 dB higher in professional male voices than in normal male voices at neutral loudness (60 dB at 0.3 min). The peak intensity becomes stronger (30 dB above normal voices) when the overall speaking loudness is increased to 80 dB. Shouting increases the spectral energy of the adjacent critical bands but not the speaker's formant itself.     

Components of the Net Current in Differential Pulse Polarography. Part 2. Kinetics and Adsorption

Components of the net response in differential pulse polarography were studied theoretically, assuming gradually changing electrode rate constant or strength of the reactant adsorption. The difference between the maximum potential of the peak component and the half‐wave potential of the wave component appear as an important parameter. From its value, the electrode rate constant can be calculated even when the standard potential is not known. In a reversible process, effects of the reactant adsorption on the mentioned separation are less pronounced. The results were compared with experimentally obtained effects. For deeper insight into the applicability of this approach, additional experimentally obtained polarograms (that reflect different potential/timing parameters or changing character of the electrode process) should be studied in terms of their components.     

LIBS对钛合金焊缝中成分的原位统计分布分析表征

钛合金凭借其强度高、耐蚀性好、耐热性高等特点已经被广泛应用于航天、海洋、生物医药等诸多领域,其中Ti-6Al-4V（TC4）合金的耐热性、强度、塑性、韧性、成形性、可焊性、耐蚀性和生物相容性均较好,已成为钛合金工业中的王牌合金。钛合金在激光焊接时,加入表面活性剂可以增加焊缝熔深、提高焊接效率、改善焊缝微观组织的不均匀性,但是可能会改变熔合区和焊缝区中元素含量及其分布状态,从而可能会对材料的性能产生一定的影响。运用LIBS分析技术对TC4钛合金焊接试样表面进行面扫描同步获得多元素成分信息,同时结合原位统计分布分析方法（OPA）,实现了对钛合金母材、熔合区、焊缝成分及其分布状态的快速表征,为活性剂的选择和焊接后钛合金的材料性能提供一种新的评价手段。选取了两个使用不同活性剂进行焊接的TC4钛合金薄板试样,选取焊缝纵切面方向作为分析面,采用320目的氧化铝砂纸进行表面处理,利用LIBSOPA系统进行成分分布统计表征。首先,对激发光斑和剥蚀条件进行条件优化,最终选择200 μm的激发光斑、10个预剥蚀脉冲10个剥蚀脉冲进行实验,并建立了钛合金中C,Al,V,Fe,Si和Ti六个元素的校准曲线（其中Si元素主要来自活性剂）;然后对钛合金焊接样品进行了区域扫描,并对元素含量和分布状态进行了统计表征。同时,在钛合金焊接样品的不同部位进行分区取样,采用高频红外法分析C元素含量,并与LIBSOPA结果进行比对,两种测试方法结果吻合。元素Al,V,Fe,Si和Ti分布结果与微束X荧光光谱法对应性较好。运用LIBSOPA 技术实现了对钛合金母材、熔合区、焊缝中多元素的成分分布表征,为快速判定钛合金焊缝中成分及分布状态提供了全新的评价表征手段。     

The interval function of a connected graph and road systems

Let V be a finite nonempty set. In this paper, a road system on V (as a generalization of the set of all geodesics in a connected graph G with V(G)=V) and an intervaloid function on V (as a generalization of the interval function (in the sense of Mulder) of a connected graph G with V(G)=V) are introduced. A natural bijection of the set of all intervaloid functions on V onto the set of all road systems on V is constructed. This bijection enables to deduce an axiomatic characterization of the interval function of a connected graph G from a characterization of the set of all geodesics in G.     

平坦的多项式剩余类环

本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.     

Comparing Zagreb indices for connected graphs

It was conjectured that for each simple graph G=(V,E) with n=|V(G)| vertices and m=|E(G)| edges, it holds M₂(G)/m≥M₁(G)/n, where M₁ and M₂ are the first and second Zagreb indices. Hansen and Vuki?evi? proved that it is true for all chemical graphs and does not hold in general. Also the conjecture was proved for all trees, unicyclic graphs, and all bicyclic graphs except one class. In this paper, we show that for every positive integer k, there exists a connected graph such that m−n=k and the conjecture does not hold. Moreover, by introducing some transformations, we show that M₂/(m−1)>M₁/n for all bicyclic graphs and it does not hold for general graphs. Using these transformations we give new and shorter proofs of some known results.