The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

Abstract Transcranial Doppler (TCD) blood flow velocity has been extensively used in biomedical research as it provides a cost-effective and relatively simple approach to assess changes cerebral dynamics track cerebrovascular health status. In this article we introduce new TCD-based timing index, TITCD, an indicator of vascular stiffening health. We investigate the correlati...

Due to the lack of water quality of resourses in country, exact review of available water resources quality, especially in terms of heavy elements (heavy metals) has a particular importance. Due to industrial towns 1 and 2 of Yasuj city and also Yasuj wastewater treatment, surveying environmental harmful effects of heavy metals on this river is very important. To investigate the changes of heav...

We introduce and study a semi-random multigraph process, which forms no-replacement variant of the process that was introduced in [3]. The starts with an empty graph on vertex set [n]. For every positive integers q \(1\le r\le n\), \(((q-1)n+r)\)th round decision-maker, called Builder, is offered \(\pi _q(r)\), where _1, \pi _2, \ldots \) sequence permutations \(S_n\), chosen independently unif...

Validation of a 5-covariate prognostic index (PI;) (performance status, stage, residual tumor size, histolÃ3gica!grade, and ascitcs) derived from a group of 268 Dutch patients with advanced ovarian carcinoma was performed in a similar study of 301 Danish patients. Analysis of survival suggested an alternative 4-covariate PI (performance status, residual tumor size, age, weight/body surface) for...

Present study was conducted with the objectives of determining the renal vascular resistance in dogs with diabetes mellitus and to study the correlation between the indices of renovascular resistance with glycemic status, systolic blood pressure (SBP) and proteinuria in dogs with diabetes mellitus. This study was conducted on seventeen diabetic dogs and ten apparently healthy dogs. Increa...

We investigate the virtual specialness of a compact cube complex X that splits as graph nonpositively curved complexes. prove when each vertex space has word-hyperbolic $$\pi _1$$ and _1X$$ “finite stature” relative to its edge groups. The results generalize motivating case tree $$\times $$ lattices are products.

BACKGROUND Among numerous modalities applied for evaluation of kidney diseases, Doppler ultrasonography (DU) provides information about the hemodynamic status of the kidneys. Meanwhile, the variability in DU parameters of the right and left kidney is a matter of controversy. The aim of this study was to determine whether any difference exists between the DU indices of the right and left kidney....

Background & Aims: Diabetes is the most common cause of renal insufficiency throughout the world. The main cause of renal failure in diabetic patients is microvascular endothelial injuries that is secondary to atherosclerosis and ischemia. The efficacy of renal Doppler indices such as resistive index (RI) and pulsetile index (PI) for the evaluation of intrarenal arteries has been shown. This st...