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...

Similarity search in multimedia databases is typically performed on abstractions of multimedia objects, also called the features, rather than on the objects themselves. Though the feature extraction process is application speci c, the resulting features are most often considered as points in high-dimensional vector spaces (e.g. the color indexing method of Stricker and Orengo [SO95]). Similarit...

the effect of a transverse magnetic field on the boundary layer flow and heat transfer of anisothermal stretching cylinder is analyzed. the governing partial differential equations for themagnetohydrodynamic, temperature, and concentration boundary layers are transformed into a setof ordinary differential equations using similarity transformations. the obtained ordinarydifferential equations ar...

In several real-life data-mining applications, data reside in very high (1000 or more) dimensional space, where both clustering techniques developed for low-dimensional spaces (k-means, BIRCH, CLARANS, CURE, DBScan, etc.) as well as visualization methods such as parallel coordinates or projective visualizations, are rendered ineffective. This paper proposes a relationship-based approach that al...

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property results in great simplification of the governing partial differential equations. In addition, some self-similar solutions can describe the asymptotic behavio...

Biological sequence similarity analysis presents visualization challenges, primarily because of the massive amounts of discrete, multi-dimensional data. Genomic data generated by molecular biologists is analyzed by algorithms that search for similarity to known sequences in large genomic databases. The output from these algorithms can be several thousand pages of text, and is difficult to analy...

Four experiments investigated memory for timbre using the interpolated-tone paradigm [Deutsch, Science 168, 1604-1605 (1970)], in which participants discriminate pairs of tones (standard and comparison) separated by intervening (interpolated) tones. Interpolated tones varied from the standard tone in spectral similarity (within-dimensional variation), fundamental frequency (cross-dimensional va...

The Gaussian kernel encourages similarity between inputs based on their Euclidean distance. Because we’re not dealing with probabilities which must sum to 1, we can omit the normalization constant found in the Gaussian distribution. But the shape is the same: we strongly encourage similarity among nearby inputs, while as inputs get further away, we encourage similarity by an amount that decreas...

Similarity analysis is made of the three dimensional incompressible laminar boundary layer flow of general class of non-Newtonian fluids. This work is an extension of previous analysis by Na and Hansen (1967), where the similarity solution of laminar three dimensional boundary layer equations of Power-law fluids was investigated. For the present flow situation, it is observed that the similarly...

In the study of nonlinear physics, the search of new exact solutions of nonlinear evolution equations (NEEs) is one of the most important problems. Various methods for obtaining exact solutions to NEEs have been proposed, such as the Lie group method of infinitesimal transformations [1], the nonclassical Lie group method [2], the Clarkson and Kruskal direct method (CK) [3 – 5], the conditional ...