The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.

X. J. Zhang, C. J. Xu (Corresponding Author), Z. Y. Wang, J. Li, L. W. Zhang, X.D. Peng. School of Materials and Metallurgy, University of Science and Technology Liaoning, China In this study, the mechanism of the formation in structure of Cold Core ingot which is prepared by cold core casting method in lab is studied. The structure of the CC ingot is obtained by optical microscopy and macrosco...

The study of decompositions of sets in U, n ^ 1, into disjoint, mutually isometric subsets has a long and distinguished history. In 1928 J. von Neumann [2] proved that an interval in U (with or without endpoints) is decomposable into Ko disjoint sets which are mutually isometric under translations. In 1951 W. Gustin [1] proved that no such decomposition into n, 2 ^ n < No, sets is possible. A b...

abstract study design: a cross-sectional non-experimental study. objectives: to collectively detect the reliability and feasibility of the five types of clinical tests that have been used to measure endurance of the trunk muscles in subjects with and without low back pain (lbp) and identify the sensitivity of each test to predict the probability of the occurrence oflbp. background: testing spin...

Simulating the dynamics of finite two-dimensional (2D) quantum many-body systems poses challenges to numerical methods due exponential growth Hilbert space. In this work, authors explore variational power recently introduced isometric tensor network states (isoTNS) --- a subset general tensor-network that allow an efficient simulation. As tool find ground states, density matrix renormalization ...

Objectives: It is well known that neuromuscular function is temperature sensitive. Changing of muscle temperature can effect voluntary muscle contraction. The aim of this study was to investigate the effects of cooling and heating on maximal isometric force generated by the elbow flexor musculature in male subjects. Methods: Forty five healthy males encompassing 3 groups participated in the ...

Objectives: Motor weakness is a notable symptom after stroke. Hence, the aim of this study was to find out the effect of bilateral quadriceps training compared to that of unilateral quadriceps training on balance, functional mobility and functional gait in patients with stroke. Subjects: Male and female hemiparetic patients between 40-60 years of age with post-stroke of 1-6 months were included...