An analysis of moisture diffusion according to Fick’s law and the tensile mechanical behavior of a glass-fabric-reinforced composite

The properties of moisture diffusion parameters and their effect on the tensile mechanical behavior of a fabric composite (glass fiber/epoxy resin) in the warp and weft directions were investigated. The water up take by specimens conditioned in a humid environment under different relative humidities (0, 60, and 96% RH) at a constant temperature of 60°C was evaluated by weight gain measurements. The water absorption followed Fick’s diffusion law in the fabric composite. A comparison between the values obtained for the moisture diffusion coefficient and the equilibrium moisture content at the laboratory and those given by Loos and Springer showed that the parameters depended not only on the nature of materials, but also on environmental conditions. The effect of moisture absorption on tensile characteristics of the composite, which was tested in uniaxial tension in the warp and weft directions at constant imposed displacement rates up to failure, showed a significant reduction in the ultimate tensile strength of the specimens conditioned at 96% RH. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 43, pp. 479-488, May-June, 2009.     

Simulation analysis of ruin capital in Sparre Andersen’s model of risk

Ruin capital is a function of premium rate set to render the probability of ruin within finite time equal to a given value. The analytical studies of this function in the classical Lundberg model of risk with exponential claim sizes done in Malinovskii (2014) have shown that the ruin capital’s shape is surprisingly simple. This work presents the results of related simulation studies. They are focused on the question whether this shape remains similar in Sparre Andersen’s model of risk.     

An analysis of single-index model with monotonic link function

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.     

An efficient numerical approximation for the linear class of Fredholm integro-differential equations based on Cattani’s method

This paper provides with a generalization of the work by Cattani (Math. Probl. Eng. (2008) 1–24), who has introduced the connection coefficients of the Shannon wavelets. We apply the Shannon wavelets approximation based on Cattani’s connection coefficients together the collocation points for solving the linear Fredholm integro-differential equations. Finally, numerical results are included to demonstrate the validity and applicability of the method and some comparisons are made with existing results.     

On asymptotic efficiency of exponentiality tests based on Rossberg’s characterization

We construct new tests of exponentiality based on Rossberg’s characterization of the exponential law. We compute limiting distributions of new tests, local Bahadur efficiency for common alternatives, and describe conditions of their local asymptotic optimality. Bibliography: 13 titles.     

An approximation algorithm for quadratic dynamic systems based on N. Chomsky’s grammar for Taylor’s formula

Single-step methods for the approximate solution of the Cauchy problem for dynamic systems are discussed. It is shown that a numerical integration algorithm with a high degree of accuracy based on Taylor’s formula can be proposed in the case of quadratic systems. An explicit estimate is given for the remainder. The algorithm is based on N. Chomsky’s generative grammar for the language of terms of Taylor’s formula.     

A variant of Newton’s method based on Simpson’s three-eighths rule for nonlinear equations

We propose a new variant of Newton’s method based on Simpson’s three-eighth rule. It can be shown that the new method is cubically convergent.     

An Upper Bound on Korenblum’s Constant

Let be the Bergman space over the open unit disk in the complex plane. Korenblum conjectured that there is an absolute constant , such that whenever in the annulus , then . In 1999 Hayman proved Korenblums conjecture. But the sharp value of c (we use to denote this sharp value and call it Korenblums constant) is still unknown. In this paper we give an upper bound on , that is, < 0.685086, which improves an earlier result of the author.     

Improving discrimination in data envelopment analysis without losing information based on Renyi’s entropy

Data envelopment analysis (DEA) heavily depends on the dimensionality of the variables, and previous studies address the problem by decreasing the dimensionality with a minimal loss of information. Since the lost information can also have the impact on the evaluation performance, this paper accordingly proposes an approach to improve the discriminatory power of DEA without losing any variables information and without requiring any additional preferential information. Furthermore, an accelerating approach based on the concept of parallel computing is introduced to solve the multi-subsets problem. Listing all the possible variables subsets as the nodes, then the DEA efficiencies under each node are calculated, and the corresponding purity of information can be scientifically generated based on Renyi’s entropy. Subsequently, the important degrees of nodes are obtained by normalizing the purities of information, and the comprehensive efficiency scores can be finally generated by the weighted sum between the important degrees and the efficiencies under the corresponding node. Two specific examples are provided to evaluate the performance.     

Continuous approximations of Gol’dshtik’s model

We consider continuous approximations to the Gol’dshtik problem for separated flows in an incompressible fluid. An approximated problem is obtained from the initial problem by small perturbations of the spectral parameter (vorticity) and by approximating the discontinuous nonlinearity continuously in the phase variable. Under certain conditions, using a variational method, we prove the convergence of solutions of the approximating problems to the solution of the original problem.     

Bahadur’s efficiency of a test of exponentiality based on the loss-of-memory property

A test of exponentiality of Kolmogorov-Smirnov type based on the loss-of-memory characterization property is under study. The large-deviation asymptotics under the null-hypothesis is calculated. Local Bahadur efficiencies for commonly used parametric alternatives are found. Conditions of the Bahadur local optimality are obtained. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 315–329. Translated by S. Yu. Pilyugin     

Revisiting key schedule’s diffusion in relation with round function’s diffusion

We study the weakness of key schedules from an observation: many existing attacks use the fact that the key schedules poorly distribute key bits in the diffusion path of round functions. This reminds us of the importance of the diffusion’s relation between key schedules and round functions. We present new cryptanalysis results by exploring such diffusion relation and propose a new criterion for necessary key schedule diffusion. We discuss potential attacks and summarize the causes for key schedules without satisfying this criterion. One major cause is that overlapping between the diffusion of key schedules and round functions leads to information leakage of key bits. Finally, a measure to estimate our criterion for recursive key schedules is presented. Today designing key schedule still lacks practical and necessary principles. For a practical key schedule with limited diffusion, our work adds more insight to its requirements and helps to maximize the security level.     

An extension of Jung’s theorem

Theorem. Let a set X?Rⁿ have unit circumradius and let B be the unit ball containing X. Put C =conv \(\bar X\) D =diam C (=diam X), k =dim C,d _i = √(2i + 2)/i. Then: (i) D∈[d_n, 2]; (ii) k≧m where m∈{2,3,...,n} satisfies D∈[d_m, d_m?1) (d_i decreases by i); (iii) In case k=m (by (ii), this is always the case when m=n), C contains a k-simplex Δ such that: (α) its vertices are on δB; (β) the centre of B belongs toint Δ; (γ) the inequalitiesλ _k (D) ≦l ≦D with $$\lambda _k (D) = D\sqrt {\frac{{4k - 2D^2 (k - 1)}}{{2 - (k - 2)(D^2 - 2)}}, D \in (d_k ,d_{k - 1} )} $$ are unimprovable estimates for length l of any edge of Δ.     

Early box office prediction in China’s film market based on a stacking fusion model

Artificial intelligence has been increasingly employed to improve operations for various firms and industries. In this study, we construct a box office revenue prediction system for a film at its early stage of production, which can help management overcome resource allocation challenges considering the significant investment and risk for the whole film production. In this research, we focus on China’s film market, the second-largest box office in the world. Our model is based on data regarding the nature of a film itself without word-of-mouth data from social platforms. Combining extreme gradient boosting, random forest, light gradient boosting machine, k-nearest neighbor algorithm, and stacking model fusion theory, we establish a stacking model for film box office prediction. Our empirical results show that the model exhibits good prediction accuracy, with its 1-Away accuracy being 86.46%. Moreover, our results show that star influence has the strongest predictive power in this model.

     

Qualitative analysis on an SIRS reaction–diffusion epidemic model with saturation infection mechanism

In this paper, we deal with an SIRS reaction–diffusion epidemic model with saturation infection mechanism. Based on the uniform boundedness of the parabolic system, we investigate the extinction and persistence of the infectious disease in terms of the basic reproduction number. To better investigate the effects of infection mechanism and individual diffusion, we further analyze the asymptotic profiles of the endemic equilibrium for small or large motility rate and large saturation rate. In particular it is shown that large saturation may cause the elimination of disease. Our study may provide some significant useful insight on disease control and prevention.     

A new method of proof of Filippov’s theorem based on the viability theorem

Filippov??s theorem implies that, given an absolutely continuous function y: [t ₀; T] ?? ? ^d and a set-valued map F(t, x) measurable in t and l(t)-Lipschitz in x, for any initial condition x ₀, there exists a solution x(·) to the differential inclusion x??(t) ?? F(t, x(t)) starting from x ₀ at the time t ₀ and satisfying the estimation $$\left| {x(t) - y(t)} \right| \leqslant r(t) = \left| {x_0 - y(t_0 )} \right|e^{\int_{t_0 }^t {l(s)ds} } + \int_{t_0 }^t \gamma (s)e^{\int_s^t {l(\tau )d\tau } } ds,$$ where the function ??(·) is the estimation of dist(y??(t), F(t, y(t))) ?? ??(t). Setting P(t) = {x ?? ? ⁿ : |x ?y(t)| ?? r(t)}, we may formulate the conclusion in Filippov??s theorem as x(t) ?? P(t). We calculate the contingent derivative DP(t, x)(1) and verify the tangential condition F(t, x) ?? DP(t, x)(1) ?? ?. It allows to obtain Filippov??s theorem from a viability result for tubes.