The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...

Network in network (NiN) is an effective instance and an important extension of deep convolutional neural network consisting of alternating convolutional layers and pooling layers. Instead of using a linear filter for convolution, NiN utilizes shallow multilayer perceptron (MLP), a nonlinear function, to replace the linear filter. Because of the powerfulness of MLP and 1 x 1 convolutions in spa...

Let us recall some basics on infinitely divisible probability distributions or laws. We denote the set of strictly positive integers by N∗. Definition A distribution G is called infinitely divisible if for all n ∈ N∗ there exists a distribution Gn such that G equals the n-fold convolution of Gn with itself, denoted as (Gn) . In other words, the distribution of a random variable S is infinitely ...

Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A method is proposed for performing exact hypercube convolution in sub-quadratic time. The method outperforms FFTPACK, called via numpy, and FFTW, called via pyfftw...

In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.

Let P = Ca × Cb be a poset where Ci is the chain 1 < · · · < i. A chain blocker of P is an inlcusionwise minimal subset B ⊆ P with the property that every maximal chain in P contains at least one element of B. In [1] the chain blockers of P are being expressed in term of the Catalan numbers and k fold convolution of the Catalan numbers. In this paper we give a complete description of the chain ...

e〈x,tu〉 p(x) dx < ∞ for some linear functional u and all t ∈ (0, 1), then, for each t ∈ (0, 1) and all large enough n, the n-fold convolution of the ttilted density p̃t(x) := e〈x,tu〉p(x)/R(t) is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results are useful for saddle-point approximations. AMS 2000 subject class...