Mixed Modes and Asteroseismic Surface Effects. II. Subgiant Systematics

Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modeling error near the surface. This asteroseismic “surface term” must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic (p-mode) and gravity (g-mode) character, which defy description by the traditional p-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In Paper I, we generalized such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. Here, we apply those results, modeling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. While these systematics are smaller than those resulting from other choices of model construction, they persist for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modeling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from those of both main-sequence and red giant stars.

Spatial components dependence for bidimensional time-constant AR(1) model with $$\alpha $$-stable noise and triangular coefficients matrix

In this paper, we examine the bidimensional time-constant autoregressive model of order 1 with $$\alpha $$ α -stable noise. We focus on the case of the triangular coefficients matrix for which one of the spatial components of the model simplifies to the one-dimensional autoregressive time series. We study the asymptotic behaviour of the cross-codifference and the cross-covariation applied to describe the dependence in time between the spatial components of the model. As a result, we formulate the theorem about the asymptotic relation between both measures, which is consistent with the result that is correct for the case of the non-triangular coefficients matrix.

Large deflection nonlinear mechanics of curved cantilevers under contact point loading

Presented here is a comprehensive model for hook bending behavior under contact loading conditions, motivated by the relevance of this problem to reusable hook attachment systems in nature and engineering. In this work, a large deflection model that can describe the bending of hooks, taken as precurved cantilevers with uniform initial curvature, was derived and compared with physical testing. Physical testing was performed with stainless-steel and aluminum hooks shaped as semicircular arcs. The force versus displacement behavior exhibited a linear portion for small displacements but at large displacements there was an asymptotic relation where the force approached some limit and remained flat as further displacement occurred. Comparison with testing showed that the model developed in this paper gave good agreement with the physical testing. Surprisingly, in dimensionless form, all parameters to define the hook transform to approximately linear functions of displacement. Using these linear relations, several equations are presented that rapid calculation of the dimensional force versus displacement for a hook.

Wiener index via wirelength of an embedding

Embeddings are often viewed as a high-level representation of systematic methods to simulate an algorithm designed for one kind of parallel machine on a different network structure and/or techniques to distribute data/program variables to achieve optimum use of all available processors. A topological index is a numeric quantity of a molecule that is mathematically derived in an unambiguous way from the structural graph of a molecule. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. Arguably, the best known of these indices is the Wiener index, defined as the sum of all distances between distinct vertices. In this paper, we have obtained the exact wirelength of embedding Cartesian products of complete graphs into a Cartesian product of paths and cycles, and generalized book. In addition to that, we have found the Wiener index of generalized book and the relation between the Wiener index and wirelength of an embedding, which solves (partially) an open problem proposed in Kumar et al. [K. J. Kumar, S. Klavžar, R. S. Rajan, I. Rajasingh and T. M. Rajalaxmi, An asymptotic relation between the wirelength of an embedding and the Wiener index, submitted to the journal].

Block circulant matrices and the spectra of multivariate stationary sequences

Given a weakly stationary, multivariate time series with absolutely summable autocovariances, asymptotic relation is proved between the eigenvalues of the block Toeplitz matrix of the first n autocovariances and the union of spectra of the spectral density matrices at the n Fourier frequencies, as n → ∞. For the proof, eigenvalues and eigenvectors of block circulant matrices are used. The proved theorem has important consequences as for the analogies between the time and frequency domain calculations. In particular, the complex principal components are used for low-rank approximation of the process; whereas, the block Cholesky decomposition of the block Toeplitz matrix gives rise to dimension reduction within the innovation subspaces. The results are illustrated on a financial time series.

The Mysterious Souls of HellÉ and Debussy’s Toys

This article is a study of the piano version of Debussy’sLa Boîte à joujoux—a musical storybook with illustrations by André Hellé—in the context of literary discourses about the toy. The storybook’s exploration of the nature of toyhood illustrates what Barbara Johnson calls the ‘asymptotic relation between things and persons’. Hellé and Debussy’s characters invite a contribution to philosophical reflections on the role of mechanical bodies as signifying a relationship between subjecthood and objecthood. The characters ofLa Boîte à joujoux are, I suggest, entirely untroubled by the distinction between interiority and exteriority that haunted the modernist imagination. The final section answers a broader question prompted by the storybook’s opening: how toys could serve as comic ideals of the modern urban citizen.

A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

Sufficient conditions for the improved regular growth of entire functions in terms of their averaging

Let $f$ be an entire function of order $\rho\in (0,+\infty)$ with zeros on a finite system of rays $\{z: \arg z=\psi_{j}\}$, $j\in\{1,\ldots,m\}$, $0\le\psi_1<\psi_2<\ldots<\psi_m<2\pi$ and $h(\varphi)$ be its indicator. In 2011, the author of the article has been proved that if $f$ is of improved regular growth (an entire function $f$ is called a function of improved regular growth if for some $\rho\in (0,+\infty)$ and $\rho_1\in (0,\rho)$, and a $2\pi$-periodic $\rho$-trigonometrically convex function $h(\varphi)\not\equiv -\infty$ there exists a set $U\subset\mathbb C$ contained in the union of disks with finite sum of radii and such that $\log |{f(z)}|=|z|^\rho h(\varphi)+o(|z|^{\rho_1})$, $U\not\ni z=re^{i\varphi}\to\infty$), then for some $\rho_3\in (0,\rho)$ the relation \begin{equation*} \int_1^r {\frac{\log |{f(te^{i\varphi})}|}{t}}\, dt=\frac{r^\rho}{\rho}h(\varphi)+o(r^{\rho_3}),\quad r\to +\infty, \end{equation*} holds uniformly in $\varphi\in [0,2\pi]$. In the present paper, using the Fourier coefficients method, we establish the converse statement, that is, if for some $\rho_3\in (0,\rho)$ the last asymptotic relation holds uniformly in $\varphi\in [0,2\pi]$, then $f$ is a function of improved regular growth. It complements similar results on functions of completely regular growth due to B. Levin, A. Grishin, A. Kondratyuk, Ya. Vasyl'kiv and Yu. Lapenko.

Analysis of time of committing nearest malicious attack in information security system using apparatus of rare regenerating processes

The paper analyzes the model that describes the process of attacking the protected object, where closed information is stored, the model built on the basis of the apparatus of regenerating sequences of the successful completion of malicious attacks. The moments of the attacks are considered in detail. It is assumed that attacks originating from a single source are rare enough, have an isolated singled character and are quite distant in time, that is, the event of a successful attack is a rare event, but the losses upon its successful completion can be huge. For the studied characteristic there is chosen a nearest moment when the next attack is successful: this characteristic is very important with relation to the information security. Knowing the parameters of this characteristic will help, at appropriate time intervals, to take additional actions that increase the level of protection. Studies are conducted under the assumption that all characteristics of the model are heterogeneous, which more adequately corresponds to the real state in information security systems. There has been obtained an asymptotic relation for the moment of the next successful malicious attack under conditions when the time interval for analyzing the attack is constantly rising and the probability of attack is becoming less common, both values changing consistently.