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The most common ways used to generate indistinguishability operators, namely as transitive closure of reflexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, are related for archimedean t-norms introducing the notion of length of indistinguishability operators.

Materialized view selection (MVS) improves the query processing efficiency and performance for making decisions effectively in a data warehouse. This problem is NP-hard and constrained optimization problem which involves space and cost constraint. Various optimization algorithms have been proposed in literature for optimal selection of materialized views. Few works exist for handling the constraints in MVS. In this study, authors have proposed the Cuckoo Search Algorithm (CSA) for optimization and Stochastic Ranking (SR) for handling the constraints in solving the MVS problem. The motivation behind integrating CS with SR is that fewer parameters have to be fine tuned in CS algorithm than in genetic and Particle Swarm Optimization (PSO) algorithm and the ranking method of SR handles the constraints effectively. For proving the efficiency and performance of our proposed algorithm Stochastic Ranking based Cuckoo Search Algorithm for Materialized View Selection (SRCSAMVS), it has been compared with PSO, genetic algorithm and the constrained evolutionary optimization algorithm proposed by Yu et al. SRCSAMVS outperforms in terms of query processing cost and scalability of the problem.

A novel approach called the YUV dimension method is proposed in this study to indirectly characterize fractured rock surface topography. This model is based on YUV color model theory in iconography and graphics. The process is described in detail as follows. A true-color photo with m pixels is selected. Y is denoted by gray scale, U by hue, and V by the saturation components of the pixel color. These components are applied to create the z, x and y coordinates of the point in the coordinate system that originates from the pixel. A similar method is applied in each pixel. M points are created in the coordinate space. The number of created points is equivalent to one of the pixels. The m points are then connected and a rough YUV surface is established. Otherwise, the calculation method for the self-affine dimension of a n - 1 ~ n-dimensional fractal body is presented by fractal Brownian motion theory and then degenerated to one between the 2D and 3D case. The approach is applied to evaluate the dimension of the YUV surface, i.e. the YUV dimension. To validate the feasibility of YUV dimension theory, numerical studies on the YUV dimension are conducted through a laser profilometer scanning experiment and scanning electron microscopy with the same specimens. The surface characteristics of similar samples are analyzed by probing into the YUV, general and grayscale dimensions of the specimens. The comparison shows that the YUV and general dimensions of similar specimens are fundamentally identical, and the complete trends of the YUV and gray dimensions remain consistent with changing specimens. The result indicates that YUV dimension theory is reasonable and feasible. In short, the YUV dimension is a new method that exhibits more advantages than the general and grayscale dimensions. This method characterizes surface configuration indirectly.

As a part of serial work about the application of a tetra-needle-shaped whisker (T-ZnOw) with a spatial structure in polymer composites, this work is focused on the effect of T-ZnOw dimension on the properties of polymer composites. Two kinds of T-ZnOw whiskers with different dimensions (big and small one) are introduced into PA6 composites. Our results show that for the big whisker and the small whisker both, the addition of T-ZnOw induces the mechanical property improvement of T-ZnOwT-ZnOw/PA6 composites. Especially, the reinforcement effect of small whisker is more apparent than the bigger one. The toughening mechanism of T-ZnOw is comparatively studied through the analyzing of impact-fractured surface morphologies and the single-edge-single-notched 3-point-bend test. Finally, the effect of T-ZnOw on thermal properties of the composite is also investigated, and the results show that small whisker reinforced composites exhibit much higher heat deflection temperatures compared with the big whisker reinforced composites possibly due to the greater volume effect.

Currently, many new materials including nanomaterials exhibit exotic properties like, mention a few, unconventional superconductivity, reduced magnetism, reduced Pauli repulsion. These exotic properties could not be explained completely with the existing quantum mechanical theories which did not take into account the dimension of angle. Now, there arises a necessity to invoke the forgotten dimension of angle, for explaining these exotic interesting properties. So far angle is considered as a dimensionless quantity even though its all time partner $r$ is endowed with dimension. In materials, where surface plays a dominant role, this new dimension, of angle becomes an important tool for exploring their morphology and exotic properties. This new dimension of angle restores the orbital degrees of freedom to the s electrons whose orbital degrees of freedom are suppressed ($\ell =0$). It compensates for the missed signature of s electron orbital angular momentum.

The symbolic representation of quantities, units, and dimensions is reviewed with regard to information carried by conventional notation. The formal structure of unit systems like the International System of Units (SI) has been an efficient way for scientists to share data about the magnitudes of quantities, but it is an unsatisfactory basis for digitalisation. SI notation does not convey information about kind of quantity, which must be obtained from some other source, and the use of dimensional expressions in the SI also loses information about kinds of quantity. It is argued that digitalisation of quantities, units, and dimensions should focus on the more fundamental measurement concepts of quantity kinds and scales of measurement to provide strong foundations on which to build support for quantities, including features familiar from SI unit notation.