Convolution is a critical component in modern deep neural networks, thus several algorithms for convolution have been developed. Direct convolution is simple but suffers from poor performance. As an alternative, multiple indirect methods have been proposed including im2colbased convolution, FFT-based convolution, or Winograd-based algorithm. However, all these indirect methods have high memory-...

In an earlier paper [1], the author introduced the notion of convolution of Riemannian manifolds. In [1] he also provided some examples and applications of convolution manifolds. In this paper we use tensor product to construct more examples of convolution manifolds and investigate fundamental properties of convolution manifolds. In particular, we study the relationship between convolution mani...

An oriented equator of [Formula: see text] is the image an embedding such that it divides into two equal area halves. Following Chekanov, we define Hofer distance between equators as infimal norm a Hamiltonian diffeomorphism taking one to another. Consider space equators. We girth infimum diameter text], where homotopic text]. There natural sending point on sphere positively great circle perpen...

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

We establish general versions of a variety results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our extend well-known from the literature to large class spaces random variables. sometimes obtain sharper versions, even well-studied case bounded approach builds on two fundamental structural functionals: equivalence law invariance Schur convexity, i.e., monotonicity with r...

Recursive inverse filtering with non-stationary filters is becoming a useful tool in a range of applications, from multi-dimensional inverse problems to wave extrapolation. I formulate causal non-stationary convolution and combination and their adjoints in such a way that it is apparent that the corresponding non-stationary recursive filters are true inverse processes. Stationary recursive inve...

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...