This paper shows the reliability of the symmetrical columns with eccentric loading about one and two axes due to the maximum intensity stress and minimum intensity stress. In this paper, a new lifetime distribution is introduced which is obtained by compounding exponential and gamma distributions (named as Lindley distribution). Hazard rates, mean time to failure and estimation of single parameter Lindley distribution by maximum likelihood estimator have been discussed. It is observed that when the load and the area of the cross section increase, failure of the column also increases at two intensity stresses. It is observed from the results that reliability decreases when scale parameter increases.

Some of the spherical distributions can be constructed through proper transformation of the densities on plane. Since the logistic density on the Euclidean space has similar behavior to the normal distribution, it is of interest to extend it for spherical data. In this paper, we introduce spherical logistic distribution on the unit sphere and then study relevant statistical inferences including parameters estimation through method of moments and maximum likelihood techniques. It is shown that the spherical logistic distribution is a multimodal distribution with the marginal logistic density function. Proposed density has rotational symmetry property and this plays a key role to drive some important results related to first two moments. To investigate the proposed density in more details, some simulation studies along with analyzing real-life data are also considered.

In this paper, we will propose a way to accurately model certain naturally occurring collections of data. Through this proposed model, the proportion of d as leading digit, $d\in \llbracket 1,9\rrbracket $, in data is more likely to follow a law whose probability distribution is determined by a specific upper bound, rather than Benford’s Law, as one might have expected. These probability distributions fluctuate nevertheless around Benford’s values. These peculiar fluctuations have often been observed in the literature in such data sets (where the physical, biological or economical quantities considered are upper bounded). Knowing beforehand the value of this upper bound enables to find, through the developed model, a better adjusted law than Benford’s one.

The performance of feature learning for deep convolutional neural networks (DCNNs) is increasing promptly with significant improvement in numerous applications. Recent studies on loss functions clearly describing that better normalization is helpful for improving the performance of face recognition (FR). Several methods based on different loss functions have been proposed for FR to obtain discriminative features. In this paper, we propose an additive parameter depending on multiplicative angular margin to improve the discriminative power of feature embedding that can be easily implemented. In additive parameter approach, an automatic adjustment of the seedling element as the result of angular marginal seed is offered in a particular way for the angular softmax to learn angularly discriminative features. We train the model on publically available dataset CASIA-WebFace, and our experiments on famous benchmarks YouTube Faces (YTF) and labeled face in the wild (LFW) achieve better performance than the various state-of-the-art approaches.

The purpose of this paper is twofold. We first solve the Dirichlet problem for $\tau $-Hermitian–Einstein equations on holomorphic filtrations over compact Hermitian manifolds. Secondly, by using Uhlenbeck–Yau’s continuity method, we prove the existence of approximate $\tau $-Hermitian–Einstein structure on holomorphic filtrations over closed Gauduchon manifolds.

We consider the inhomogeneous incompressible Navier–Stokes equation on thin domains ${\mathbb {T}}^2 \times \epsilon {\mathbb {T}}$, $\epsilon \rightarrow 0$. It is shown that the weak solutions on ${\mathbb {T}}^2 \times \epsilon {\mathbb {T}}$ converge to the strong/weak solutions of the 2D inhomogeneous incompressible Navier–Stokes equations on ${\mathbb {T}}^2$ as $\epsilon \rightarrow 0$ on arbitrary time interval.