We systematically provide a similarity transformation reducing the (3 + 1)-dimensional inhomogeneous coupled nonlinear Schrödinger (CNLS) equation with variable coefficients and parabolic potential to the (1 + 1)-dimensional coupled nonlinear Schrödinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimension...

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and veloci...

In this paper, we studied MHD two dimensional flow of an incompressible tangent hyperbolic fluid flow and heat transfer towards a stretching sheet with velocity and thermal slip. Lie group analysis is used to develop new similarity transformation, using these similarity transformation the governing nonlinear partial differential equation are reduced into a system of coupled nonlinear ordinary d...

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three grou...

This paper presents a new method for exemplar-based image inpainting using transformed patches. We build upon a recent affine invariant self-similarity measure which automatically transforms patches to compare them in an appropriate manner. As a consequence, it intrinsically extends the set of available source patches to copy information from. When comparing two patches, instead of searching fo...

In this paper we present a disjoint camera track matching algorithm based on a “cumulative colour histogram transformation”, the “major colour” histograms matching and the post-matching integration algorithms. In order to reduce the “effects of variable illuminations” in disjoint camera environment, a cumulative colour histogram transformation is applied to located moving object image first. Th...

The classical absolute orientation method is capable of transforming tie points (TPs) from a local coordinate system to a global (geodetic) coordinate system. The method is based only on a unique set of similarity transformation parameters estimated by minimizing the total difference between all ground control points (GCPs) and the fitted points. Nevertheless, it often yields a transformation w...

To address the problem of 3D point matching where the poses of two point sets are unknown, we adapt a recently proposed path following based method to use similarity transformation instead of the original affine transformation. The reduced number of transformation parameters leads to more constrained and desirable matching results. Experimental results demonstrate better robustness of the propo...

Predicting entailment between two given texts is an important task upon which the performance of numerous NLP tasks depend on such as question answering, text summarization, and information extraction. The degree to which two texts are similar has been used extensively as a key feature in much previous work in predicting entailment. However, using similarity scores directly, without proper tran...

Voxel based non-rigid registration of images involves finding a similarity maximising transformation that deforms a source image to the coordinate system of a target image. In order to do this, interpolation is required to estimate the source intensity values corresponding to transformed target voxels. These interpolated source intensities are used when calculating the similarity measure being ...