the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

Design consistency refers to the conformance of a highway's geometry with driver expectancy. Drivers make fewer errors in the vicinity of geometric features that conform with their expectations. Techniques to evaluate the consistency of a design documented within this report include alignment indices, speed distribution measures, and driver workload. Alignment indices are quantitative measures ...

Solar simulators are common laboratory devices to artificially reproduce the Sun emission spectrum. Their use in optic tests allows to study the effect of the solar radiation on both materials and components. This paper focuses on the effective design of the ellipsoidal reflector for concentrating solar simulators. A ray-tracing analytic model integrated to Monte Carlo simulation is proposed as...

Using urinary carisoprodol data from pain patients, our objectives were to determine the relationship between carisoprodol concentration and its conversion to meprobamate, and quantify the intra-subject and inter-subject variability in carisoprodol metabolism. Liquid chromatography-tandem mass spectrometry was used to quantitate carisoprodol and meprobamate concentrations in urine specimens. Th...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model--adding a slow, but significant, ...

Article history: Received 25 March 2013 Received in revised form 29 May 2013 Accepted 29 May 2013 Available online 1 June 2013 Editor: J. Hisano We propose a realistic A4 extension of the Standard Model involving a particular quark–lepton mass relation, namely that the ratio of the third family mass to the geometric mean of the first and second family masses are equal for down-type quarks and c...