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Let G be a simple graph of order n, with no component of order two. Define an edge l-labeling θ:E(G)→{1,2,...,1}. Let xϵV(G), the weight of x is the sum of the l-labels of all its incident edges, denoted by α(x)=Σ░⟦θ(xy)⟧. The edge l-labeling is said modular irregular l-labeling of G if there exists a bijective weight α-function from V(G) to the group of integers modulo n. The smallest positive integer l such that G has a modular irregular l-labeling is said the modular irregularity strength of G, denoted by ms(G). Write ms(G)=∞, if G has no modular irregular strength. In this paper, we find ms of some graph classes, i.e. sunlet graphs, cycle barbell graphs, and m-Harary cycle graphs. [ABSTRACT FROM AUTHOR]

Ecological monitoring was performed on Chepelarska River using Barbus cyclolepis Heckel, 1837, and its parasite communities as bioindicators. Helminth parasites are recorded in 45.83% of the examined specimens of the round-scaled barbell from the freshwater ecosystem of the Chepelarska River. Two species of parasites are fixed: one acanthocephalan species Pomphorhynchus laevis (Zoega in Müller, 1776), and one nematode species (Rhabdochona hellichi (Sramek, 1901). The analysis of the dominant structure of the found parasite species is presented to the component and infracommunities level. In the component community of Barbus cyclolepis from Chepelarska River R. hellichi is core parasite species (P%=37.5), and P. laevis is an accidental parasite species (P%=7.41). The determined basic ecological characteristics, biotic indices, and bioindicator significance of the established parasite species were discussed for ecological evaluation of the state of the studied freshwater ecosystem. The established in this study parasite species are considered and compared with previous researches of parasite communities of Barbus cyclolepis in Bulgaria. This is the first report of Pomphorhynchus laevis and Rhabdochona hellichi from Chepelarska River, Bulgaria. [ABSTRACT FROM AUTHOR]

In this paper, new results of domination in graphs called bi-domination are determined. Some properties for bi-dominating set are presented. The bi-domination number of G is the minimum cardinality of a bi-dominating set of G. In this paper, we investigate the bi-domination number for web graph, tadpole graph, lollipop graph, daisy graph, Dutch windmill graph, windmill graph, dumbbell graph, barbell graph, grid graph, product of two path, and the corona H ⊙ K2 and H + K2. [ABSTRACT FROM AUTHOR]

Article presents hodographs of the arterial blood pressure relation to heart-rate enabling to evaluate organism sensitivity of trained weightlifter to the magnitude of lifted weight, lifting technique and weight repeatability. Variation regularities of the latter relation have been explained and approximate criterions of relative stability and skill level were formulated. Analysing variations of the relation of the arterial blood pressure to the heart-rate and barbell's lifting accelerations and velocities the weaknesses of trained weightlifters have been explained. It has shown that in most cases the blood pressure of the weightlifter can increase 8-13% after the barbell drop. [ABSTRACT FROM AUTHOR]

The present study sought to examine the effect of altering the position of external loads on the kinematics and kinetics of weighted vertical jumps in 29 resistance trained rugby union athletes. Vertical jumps were performed with loads of 20, 40 and 60% squat 1RM with the load positioned: 1) on the posterior aspect of the shoulder using a traditional barbell (TBJ); and 2) at arms' length using a hexagonal barbell (HBJ). Weighted jumps performed with the load held at arms' length resulted in significantly greater values for jump height, peak force, peak power, and peak rate of force development (p<0.05), indicating a greater training stimulus for the HBJ than TBJ. These results suggest that when using weighted vertical jumps to improve lower body muscular performance, the jumps should be performed with the external load at arms' length rather than on the shoulder. [ABSTRACT FROM AUTHOR]

This study is aimed at using the BCH angle which represents the relative movement of lifter's body and barbell to compare the snatch movement of two young female weightlifters. The snatch movements of these two female weightlifters were filmed by a high speed camera (120Hz) and analyzed by Kwon 3D motion analysis software. The BCH angle, defined as the angle between the projection vector of the 7th cervical spinous process to the barbell and the projection vector of the 7th cervical spinous process to the hip joint in the sagittal plane, was calculated. The differences of BCH angles during the whole snatch movement have been found between successful and unsuccessful lifts for S1, and even between successful lifts of S1 and S2. In conclusion, the BCH angle seems to be a simple and good variable to evaluate the snatch techniques of the weightlifters. [ABSTRACT FROM AUTHOR]

In Olympic Weightlifting it can be quite difficult to monitor subtle aspects of lifting technique even by a very experienced coach. For this project, the major markers for performance were identified by experts in bio mechanics and weightlifting, and these aspects were incorporated into this design. Three main areas of interest were recognized: ground reaction forces, barbell velocity and trajectory, and video for athlete analysis and feedback from the coaches. To measure ground reaction forces, an AMTI force platform was placed under each foot. Vertical forces and both X and Y moments (Mx, My) were input measures to the specialized hardware and software. Both bar end positions were measured continuously, and the computer screen image displayed bar velocities, trajectories, and any non-symmetrical aspects of the lift. A video image of the athlete in motion has the above data superimposed on the computer screen and is displayed in real-time. This displayed information can be reviewed by the athlete and coach immediately after the lift during the training session. [ABSTRACT FROM AUTHOR]

The article investigates the trajectory of the center of mass (COM) at different postures and loading of barbell squats weight lifting in Taiwan. The study shows that knee joint has less flexion and bore small moment and force. It suggests that free weight squats must be performed at less flexion angle to avoid knee injury. Moreover, joint moments and electromyography must be monitored and calculated to understand the muscle activity and joint power during squat.

The article examines the lower body joint kinematics between free high pulls and fixed high pull apparatus in the U.S. The study shows that the use of Cormax Smith Machine Plus provides power output advantages due to its ability to throw and release the barbell. However, the changes in kinematics using the method can affect the athletes' ability to properly perform the platform high pulls technique.