Free vibration analysis of porous beams with gradually varying mechanical properties

This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

Symmetry and unification from soft theorems and unitarity

We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

Is Zero Void? Attentional Mechanism of Hidden-zero Effect in Risky Decision-making

The frame of risky choice could alter and shape an individual’s risky preferences. Within an option of typical risky choice, that is, "p% chance to win Q dollar," naturally embedded a hidden-zero outcome, namely, "(1-p)% chance to win 0 dollar." Despite its pervasive existence, there is insufficient evidence of the existence or a cognitive mechanism of the hidden-zero effect in risky choice. To this end, we proposed an attentional based risk-aversion model for behavior and process level to interpret the mechanism of the hidden-zero effect. We presented participants’ explicit or hidden-zero outcomes in pairs of certain versus risky options and measured their choice preferences and eye-movement characteristics. We observed that participants were less risk avoidant in the explicit-zero condition than in the hidden-zero condition, and a descriptive attentional bias shifted this preference to favor certain options in the hidden-zero condition (Study 1). We further combined the eye-tracking data with hierarchical Bayesian modeling (Study 2). We observed that a model combining behavioral and process attention provided better predictions regarding participants’ preference. When presenting zero outcomes, an empirical attentional bias integrating eye-movement features indicated that attention plays a central role to alter the attention allocation and consequent choice preference from certainty options to risky options in risky decision-making. These findings highlight the potential mechanism of the hidden-zero effect in risk decision-making on cognitive and computational levels.

ANALYSIS OF WATER QUALITY ZERO CONDITION IN THE AREA OF SILICON MATERIAL FACTORY

Construction of the silica material factory named "R-S Silicon", with an annual production capacity of15,210 ton of Si-metal, was planned in the village of Bjelajce, municipality of Mrkonjić Grad. The factoryfor production of Si-metal shall have direct and indirect environmental impacts, especially on waters, bywashing off working areas, leachate and other waste water that must be treated due to contamination, so thattheir quality would be at least the quality of surface recipient into which they are discharged.Before the construction, i.e. commissioning of subject factory, it is necessary to determine the zerocondition of waters quality around the factory in order to have a realistic picture of its impact on the waterquality during its operation.

Higher-Order Approximations for Testing Neglected Nonlinearity

We illustrate the need to use higher-order (specifically sixth-order) expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity. The test statistic is a quasi-likelihood ratio (QLR) statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activation function violating the no-zero condition in Cho, Ishida, and White ( 2011 ). This statistic is also shown to be asymptotically equivalent under the null to the Lagrange multiplier (LM) statistic of Luukkonen, Saikkonen, and Teräsvirta ( 1988 ) and Teräsvirta ( 1994 ). In addition, we compare the power properties of our QLR test to one satisfying the no-zero condition and find that the latter is not consistent for detecting a DGP with neglected nonlinearity violating an analogous no-zero condition, whereas our QLR test is consistent.

Normal characterization by zero correlations

Suppose Xi, i = 1,…,n are indepedent and identically distributed with E/X1/r < ∞, r = 1,2,…. If Cov (( − μ)r, S2) = 0 for r = 1, 2,…, where μ = EX1, S2 = , and , then we show X1 ~ N (μ, σ2), where σ2 = Var(X1). This covariance zero condition charaterizes the normal distribution. It is a moment analogue, by an elementary approach, of the classical characterization of the normal distribution by independence of and S2 using semi invariants. More generally, if Cov = 0 for r = 1,…, k, then E((X1 − μ)/σ)r+2 = EZr+2 for r = 1,… k, where Z ~ N(0, 1). Conversely Corr may be arbitrarily close to unity in absolute value, but for unimodal X1, Corr2( < 15/16, and this bound is the best possible.