We define a new metric on the set of all closed linear operators between Hilbert spaces and investigate its properties. In particular, we show that the set of all closed operators with a closed range is an open subset of the set of all closed operators and the map T®T+ is an isometry in this metric. We also investigate the relationships between the topology induced by this metric and the gap metric.

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In this study, pressure-strain elastic MODULUS, stiffness, distensibility, cross-sectional ‎compliance and Young MODULUS of the common carotid artery were evaluated in 30 ‎subjects, normal and atherosclerosis, non-invasively. The diameter changes and cross-‎sectional changes in systolic and diastolic phases of the carotid artery were measured ‎by real time B-mode sonography and color Doppler, respectively. Indirect blood ‎pressure measurement was made by manometer immediately after measurement of the ‎pulsatile vessel diameter and area. Elastic parameters were estimated from the ‎diameter relative changes, cross-section relative changes and the systolic and diastolic ‎blood pressure in the brachial artery. The relative diameter changes in mild stenosis ‎and severe stenosis compared to normal group are not expected‏.‏‎‎ The results of evaluation of elastic parameters show that in mild stenosis, pressure-‎strain elastic MODULUS, stiffness and Young MODULUS decreased but in severe stenosis ‎they increased relative to normal arteries. In mild stenosis, distensibility and cross-‎sectional compliance increased but in severe stenosis these parameters decreased ‎relative to normal. Of course, mechanical parameters of atherosclerotic group are ‎significantly different from the normal carotid artery. By applying this method, we ‎can detect atherosclerosis from normal carotid artery (Iranian Heart Journal 2003; 4 ‎‎(2,3): 68-74).‎

The harmonic index of a graph G is dened as H (G) =å uuÎE(G) 2 d(u)+d (u), where d (u) denotes the degree of a vertexu in G. Let G (n; k) be the set of simple n -vertex graphs with MINIMUM degree at leastk. In this work we consider the problem of determining the MINIMUM value of the harmonic index and the corresponding extremal graphs among G (n; k). We solve the problem for each integerk (1 £ k £ n/2) and show the corresponding extremal graph is the complete split graph K *k, n-k. This result together with our previous result which solve the problem for each integer k (n/2 £ k £ n - 1) give a complete solution of the problem.

Despite its numerous potential applications, two-dimensional monolayer graphyne, a novel form of carbon allotropes with sp and sp2 carbon atoms, has received little attention so far, perhaps as a result of its unknown properties. Especially, determination of the exact values of its elastic properties can pave the way for future studies on this nanostructure. Hence, this article describes a density functional theory (DFT) investigation into elastic properties of graphyne including surface Young’s MODULUS and Poisson’s ratio. The DFT analyses are performed within the framework of generalized gradient approximation (GGA), and the Perdew–Burke–Ernzerhof (PBE) exchange correlation is adopted. This study indicates that the elastic MODULUS of graphyne is approximately half of that of graphene due to its lower number of bonds.

The main purpose of this paper is to characterize norm-additive in MODULUS, not necessarily linear, maps defined between function algebras (not necessarily unital or uniformly closed). In fact, for function algebras A and B on locally compact Hausdorff spaces X and Y, respectively, we study surjections T, S:A®B satisfying |||T¦|+|Sg|||Y=|||¦|+|g|||X for all ¦, gÎA.

The present study attempts to investigate different factors affecting the resilient MODULUS of hot mix asphalt. So a fractional factorial analysis of experiment was carried out considering five factors, each at two different levels. These factors were the maximum nominal aggregate size, specimen diameter and thickness, the load pulse form and duration. During the course of analysis, two types of hot mix asphalts with different maximum aggregate sizes were taken into consideration, while Marshall compaction method was used to prepare the specimens. Furthermore, measuring the resilient MODULUS, sinusoidal and triangular load pulse forms were applied. Finally, our investigation examined the different factors interrelations which affect the resilient MODULUS. Analysis of the factorial experimental design showed that the maximum nominal aggregate size was the most important factor affecting the resilient MODULUS, then the load duration, the specimen geometry (thickness and diameter), and finally the interactions between the different factors.