Academic literature on the topic 'Sum connectivity index'

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

We introduce some new atom bond sum connectivity indices: second, third and fourth atom bond sum connectivity indices of a graph. In this paper, we compute the atom bond sum connectivity index, the second, third and fourth atom bond sum connectivity indices and neighborhood sum atom bond connectivity index of some important chemical drugs such as chloroquine, hydroxychloroquine and remdesivir.

The sum-connectivity index of a simple graph G is defined in mathematical chemistry as R+(G) = ? uv?E(G)(du+dv)?1/2, where E(G) is the edge set of G and du is the degree of vertex u in G. We give a best possible lower bound for the sum-connectivity index of a graph (a triangle-free graph, respectively) with n vertices and minimum degree at least two and characterize the extremal graphs, where n ? 11.

For a simple finite graph G, general sum-connectivity index is defined for any real number α as χα(G) = , which generalises both the first Zagreb index and the ordinary sum-connectivity index. In this paper, we present some new bounds for the general sum-connectivity index. We also present relation between general sum-connectivity index and general Randić index.

In this paper, we introduce the domination atom bond sum connectivity index, multiplicative domination atom bond sum connectivity index and domination atom bond sum connectivity exponential of a graph. Also we determine these newly defined domination atom bond sum connectivity indices for some chemical drugs such as chloroquine and hydroxychloroquine.

In Chemical Graph Theory, the connectivity indices are applied to measure the chemical characteristics of compounds. In this paper, we compute the multiplicative product connectivity index and the multiplicative sum connectivity index of three infinite families NS₁[n], NS₂[n], NS₃[n] dendrimer nanostars. &nbsp; <strong>Mathematics Subject Classification :</strong> 05<em>C</em>05, 05<em>C</em>012, 05<em>C</em>090

The atom-bond sum-connectivity (ABS) index of a connected graph G = (V,E) is defined as ABS(G) = ∑uv∈E√((d(u)+d(v)-2)/(d(u)+d(v))), where d(w) is the degree of vertex w ∈ V. It was shown that this recently proposed topological index has comparable predictive applicability in chemistry with some famous indices, such as the Randić index, sum-connectivity index, and atom-bond connectivity index. Recently, the chemical bicyclic graphs with minimum ABS index were characterized. It was conjectured that this result also holds for general bicyclic graphs. We confirm this conjecture in the present paper.

Indoor air quality (IAQ) is among the topmost environmental hazards associated with the health of human beings. The concentrations of indoor pollutants could be several times more than outdoors. Increasing environmental pollution and global warming are also responsible for climate change. Variations in climatic conditions also add to the worsening of IAQ. The majority of time is spent indoors and adequate ventilation, thermal performance and desirable IAQ are important parameters of concern in indoor settings. Usage of HVAC (heating, ventilation, air conditioning) equipment accounts for the huge consumption of energy and reduced energy consumption can be met by reduced air circulation leading to more airtight buildings which compromise the air quality and health of inhabitants. Several strategies have been devised and being implemented to monitor indoor air quality. Smart environments are insidious systems consisting of integrable net-aware devices. Smart environments are augmented with computational resources providing information and services when and where needed. Over the last few years, IAQ monitoring has developed into smart environment monitoring (SEM) which is based on the internet of things (IoT) and the development of sensor technology. This chapter is an attempt to summarize the automated, computational aids and machine learning techniques that can predict the IAQ in smart environment. It is imperative to know the pollutants and factors governing the IAQ and the chapter has critically analyzed the available technological interventions based on IoT like sensors, Fuzzy logic controller and cloud computing technology which aid in the prediction of air quality in smart environment. Different types of sensors including infrared and electrochemical cells, Metal oxide semiconductor (MOS) gas sensor along with their principle has been discussed in context to IAQ. Recent developments in the field like the usage of the fuzzy logic controller for the calculation of air quality index by combining PM10, PM2.5, CO, and NO2 etc. has also been explored. The information can be utilized in dynamic situations to suggest alternative methods https://worldpopulationreview.com/world-cities/lucknow-population for the improvement of air quality which can be influenced by artificial intelligence and machine learning for futuristic predictions. However, there are some challenges as well including the development of systems working on a real-time basis and evaluation of the impact of different pollutants in diverse geographic conditions and variable living set-ups by highly accurate and calibrated systems. Nevertheless, as compared to the conventional solutions which predict IAQ instantly, the computational predictions furnish futuristic data and imminent crucial changes in the indoor air quality to implement anticipatory measures to prevent hazardous health impacts. Nevertheless there are several challenges like data security, data conversion, and connectivity issues etc. which have been discussed in the chapter.

Abstract Objective/scope Demonstrate technology effectiveness following improvements to system to increase robustness and refine operations following the initial Pilot Well deployed January 2016. The first Abu Dhabi Offshore well was deemed to be a success (reference SPE-183465-MS) despite deployment challenges during the lower completion phase. There was an opportunity to address these challenges for the second well, in the deployment of well -1 which from an operational perspective was textbook. In the search for an improvement to the Productivity index (PI), multi-lateral acid jetting technology was adopted as a more effective approach to typical drainage methods. With conventional stimulation techniques being limited in effectiveness and often leaving significant volumes of recoverable reserves out of reach, an alternative approach was required to create new connections within the reservoir. This technology effectively creates connections to layers previously separated by very tight, low permeability barriers to dramatically increase recovery factors across carbonate reservoirs. Method, procedures, process In a single multi-rate pumping sequence, needles were extended to create channels into the reservoir layers, using acid jetting technology to achieve vertical connectivity and improve production rates. Currently, up to 60 subs can be deployed in a signle well bore. With each sub capable of deploying 4 needles at 90 degrees perpendicular to the wellbore and up to 40 feet in length, multiple micro-laterals are created throughout the reservoir. During this case study, 10 sub-assemblies of the multi-lateral acid jetting technology system were installed, creating 40 micro-laterals, which significantly improved access to reserves. These laterals remain in the well, essentially leaving a permanently installed lower liner with full bore access to TD. Results, observations, conclusions Following successful adoption of this technology, the well has been producing for a year with positive results. Multi Rate test/PLT/Memory Gauge data all confirms a productivity index increase of 120%. This paper describes the process of candidate selection, completion design, operational challenges, deployment, post job analysis, system improvement and lessons learnt. Additional Information Multilateral acid jetting technology has evolved and improved over recent years and the primary differentiators highlighted in this paper are as follows: The continuous enhancement of multi-lateral acid jetting technology is playing a key role in driving increased efficiency in field development planning. By reducing the total well requirement for the reservoir, whilst simultaneously increasing recoverable reserves, the technology is at the forefront of facilitating the future state of field development.

Abstract Integrated solutions are important to formulate plans for mature reservoirs under waterflooding due to related dynamic changes and uncertainties. The reservoir and field management need to be handled as an integrated system, and therefore needing a multidisciplinary approach. This paper demonstrates how the integrated multidisciplinary team has developed several workflows covering water-flooding management, production enhancement and maximizing the economic recovery of reservoirs in the North Kuwait asset. Many integrated workflows were developed for water flooding and production optimization. The main integrated workflows that were implemented are as follows: PVT Properties Tool: is designed to estimate the fluid properties throughout the reservoir taking into consideration areal and vertical variations based on trends, and existing data coverage. Opportunity Maps: is a combination of updated reservoir pressure and fluids properties to provide a fast way to identify areas of opportunity to increase/decrease injection or production based on the development strategy. Waterflooding Patterns/segments Review Workflow and Allowable Tool: This integrated analytical workflow applied on predefined reservoir patterns or segments based on geological distribution and/or hydraulic communication, includes several tools like the analysis of production and injection trends, diagnostic plots to assess good vs bad water, Hall plots, Reservoir Pressure data, tracer data, salinity changes and pump intake pressure trends. Geological analysis (cross-sections, well correlations, sand thickness maps) for each layer are integrated in each pattern/segment review to support reservoir connectivity (or the lack thereof). Instantaneous and cumulative VRR are calculated and compared with the overall exploitation strategy and water injection efficiency. Other sub-workflows were developed to improve and manage waterflooding performance such as water recirculation tool and streamline sector modeling simulation. Structured integrated proactive production and ESP optimization workflows: Production optimization is a continuous iterative process (cycles) to improve production, especially in mature fields. This workflow facilitates the identification of opportunities for production optimization with a pro-active approach focusing on flowing wells and rig-less interventions to tackle production challenges and achieve production targets. The Heterogeneity Index (HI) process is utilized to rapidly demonstrate production gain opportunities. This provides family-type problems that are then represented by type-wells for detailed diagnostics. Continuous application and embedding of such structured integrated workflows as standard best practices, deliver significant value in terms of improving the understanding of reservoir performance in order to inject smart (where and when required) and produce smart (sweet healthy spots). This is done on reservoir, segment, pattern and individual well levels in multidisciplinary team domains. The ultimate results reflected in continuous improvement in waterflooding management (injection efficiency, vertical and areal sweep efficiency, sweep new oil via changing streamlines). This in turn contributes to significant added oil gain and recoverable reserves with best practices reservoir management. These integrated workflows are user friendly and can be applied across different reservoirs and fields. The application of such workflows in a structured, consistent and proactive approach improves the overall asset management in terms of maximizing production and recoverable reserves.