In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

Groupwise non-rigid image alignment is a difficult non-linear optimization problem involving many parameters and often large datasets. Previous methods have explored various metrics and optimization strategies. Good results have been previously achieved with simple metrics, requiring complex optimization, often with many unintuitive parameters that require careful tuning for each dataset. In this chapter, the problem is restructured to use a simpler, iterative optimization algorithm, with very few free parameters. The warps are refined using an iterative Levenberg-Marquardt minimization to the mean, based on updating the locations of a small number of points and incorporating a stiffness constraint. This optimization approach is eff

Consider a simple graph   on vertices and edges together with a total  labeling . Then ρ is called total edge irregular labeling if there exists a one-to-one correspondence, say  defined by  for all  where  Also, the value  is said to be the edge weight of . The total edge irregularity strength of the graph G is indicated by  and is the least  for which G admits   edge irregular h-labeling.  In this article,   for some common graph families are examined. In addition, an open problem is solved affirmatively.

Random throwing of industrial waste has a significant impact on the environment unless it takes into account the conditions of engineered destroying and/or re-used. Taking the advantage of re-using waste materials in engineering projects represents a well-planned project in order to resolve a lot of engineering problems for some difficult soils. The objective of this study was to evaluate the capability and effects of Rubber Shreds (RS) from scrap torn belts towards improving the shear strength of soft clay. A direct shear tests were conducted on soft clay-RS mixture. The following parameters were investigated to study the influence of RS content, water content, normal stress, and dilation ratio. From experimental test results it was fou

This paper demonstrates an experimental and numerical study on the behavior of reinforced concrete (RC) columns with longitudinal steel embedded tubes positioned at the center of the column cross-section. A total of 12 pin-ended square sectional columns of 150 × 150 mm having a total height of 1400 mm were investigated. The considered variables were the steel tube diameters of 29, 58, and 76 mm and the load eccentricity (0, 50, and 150) mm. Accordingly, these columns were divided into three groups (four columns in each group) depending on the load eccentricity (e) to column depth (h) ratio (e/h = 0, 1/3, and 1). For each group, one column was solid (reference), and the other three columns contained steel tubes with hollow rat