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Data management

In document VergelTovar_unc_0153D_16265.pdf (Page 103-111)

CHAPTER 3: RESEARCH METHODS AND DESIGN

3.3. Research methods and design (Aim 2)

3.3.4. Data management

The data were collected at three different levels: segment, block and BRT station. The latter is the unit of analysis for this dissertation. Therefore, segment and block level data were aggregated at the station level. All variables were aggregated based on the proportion of

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segments with one variable and the presence of facilities and public spaces by counting its presence within the buffer area. The list of the complete built environment variables collected is shown in Table 14.

Table 14 List of built environment variables, definition and scale of data collection

Variable Definition

Level at which data was collected

Density

Population density Population by gross station area Station No building height % of segments with building heights = None Segment Low building height % of segments with building heights~ 1 story Segment Medium building height % of segments with building heights ~ 2 to 3 stories Segment High building height % of segments with building heights ~ 4 to 5 stories Segment Very high height % of segments with building heights > 5 stories Segment Low built-up density % of segments with low built-up density development Segment Medium built-up density % of segments with medium built-up density development Segment High built-up density % of segments with high built-up density development Segment Low development level % of segments with low development consolidation Segment Medium development level % of segments with medium development consolidation Segment High development level % of segments with high development consolidation Segment High rise developments % of Segments with high-rise developments Segment Diversity

Institutional % segments with institutional uses Segment

Industrial % segments with industrial uses Segment

Exclusively commercial % segments with commercial land uses Segment Mixed commercial % segments with commercial and other land uses Segment Residential single family

(attached) % segments with residential single uses Segment Residential multifamily % segments with residential multifamily uses Segment Mixed: Industrial-commercial % segments with industrial-commercial uses Segment Mixed: commercial residential % segments with commercial residential Segment

Vacant % segments with vacant uses Segment

Open Green Area % segments with undeveloped open green spaces Segment

Land use index # of land uses in station (1-10) Segment

BRT-oriented land uses Density of commercial, residential, and institutional uses Segment Other land uses Density of industrial, industrial & commercial, and vacant

uses Segment

Entropy evenness in the distribution of commercial, residential and

institutional land uses Segment

Design

Segment density # of segments by gross station area Station Number of blocks # of blocks within gross station area Block Number of 2 lanes segments # of segments with 2 lanes within gross station area Segment Number of 3 lanes segments # of segments with 3 lanes within gross station area Segment Number of pedestrian

segments # of pedestrian segments within gross station area Segment

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Access to destination

Distance to CBD Distance to closest activity node in Km Station Distance to transit

Vacant and BRT % of segments with vacant and on BRT corridor Segment Average distance to BRT

station Average distance of segments to BRT station Station Average segment length Average segment length within gross station area Station Segment on BRT corridor

density # of segments facing the BRT right of way by gross station area Station Parking

On-street parking % of segments with parking on street Segment Off-street parking % of segments with off-street parking Segment Commercial and parking % of segments with commercial and parking uses Segment Vacant and off-street parking % of Segments with Vacant and off-street parking

NMT infrastructure

Green areas’ density Density of # parks, squares, pocket squares, green areas,

boulevards Block

Pedestrian segments density # of pedestrian segments by gross station area Station NMT friendliness Density of parks, squares, pocket squares, boulevards,

pedestrian segments, pedestrian bridges, bike-paths Block Average block size Average size of blocks within the buffer area in square

meters Block

Park density Density of # parks, squares, pocket squares Block Socioeconomic characteristics

Affordable housing % segments with affordable housing Segment Informal settlements % segments with informal settlements Segment Urban decay % of segments in low condition of maintenance Segment Medium condition &

maintenance % of segments in medium condition of maintenance Segment High condition &

maintenance % of segments in high condition of maintenance Segment Total population # of people within the gross station area Station Facilities and public space

Public facility index Index of presence of seven facility types, excluding big

box development (0-7) Block

Public facility density Density of facilities (except big box development) Block BRT-oriented facility index Index of presence of hospitals, libraries, markets/ squares,

churches (0-4)

Block BRT-oriented facility density Density of hospitals, libraries, markets/ squares, churches Block

At the BRT station level, distance in kilometers to the closest activity node or central business district (CBD) was calculated using GIS for each BRT station. Segment density was calculated based on the total number of segments in the gross area (total segments/area: 0.19635 sq-km for single BRT stations; 0.785398 sq-km for BRT Terminals). Census data was provided by local authorities in order to calculate population within the buffer area. Population density

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was calculated based on the percentage share for each block within the census tract area using GIS.

With block level data, ten variables were calculated by counting the presence of facilities and public spaces and dividing them by the gross area (0.19635 sq-km for single BRT stations; 0.785398 sq-km for BRT Terminals). The public facility index consists on a measurement of the number of facilities present within the buffer area counting from zero (none) to seven (school, hospital, church, library, market/square, recreation facility, hotel) in this way the presence of each facility increase the index value up to seven (maximum). The public facility index excludes the presence of big-box developments (shopping centers or malls). Public facility density

measures the sum of facilities present in the BRT station per gross area. BRT-oriented facility index refers to the presence of supportive facilities for the BRT system such as hospitals

libraries, markets/squares and temples. BRT-oriented facility density was calculated by the sum of BRT supportive facilities per gross area. Green area’s density was determined by counting the presence of parks, squares, pocket squares, green areas and boulevards per gross area. Park density is also calculated by counting parks, squares and pocket squares per gross area. Non- motorized transport (NMT) friendliness measures the presence of parks, squares, pocket squares, boulevards, pedestrian segments, pedestrian bridges, bike-paths per gross area. Average block size was calculated using GIS by identifying the blocks within the buffer area and then

calculating its area in square meters.

With segment level data, forty two variables were calculated. Land use index measures the presence of one of the ten types of land uses identified for the present study (institutional, industrial, commercial, mixed-commercial, single residential, multifamily residential, mixed industrial commercial, mixed commercial residential, vacant and open green area). The intensity

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of land uses was determined by calculating the percentages of segments with each land use type in relation to the total number of segments. Given the lack of parcel level data, the presence of each land use was done by identifying all land uses present on each segment within the buffer area. The density of BRT oriented land uses (mixed commercial, single and multifamily residential and institutional) was calculated by summing these types of land uses and dividing their presence per gross area. The density of other land uses (industrial, industrial commercial and vacant) was also calculated by summing these types of land uses and dividing their presence per gross area. Building heights were identified by counting the presence of constructions with each of the 5 categories along each segment (no height -none, low –one story, medium -2 to 3 stories, high -4 to 5 stories and very high – 5 to 10 stories). The intensity of the building heights was calculated by the percentage of segments with each category. The urban density of built-up area variable seeks to determine the development density of constructions relative to the length of each segment (low, medium and high).

The development level on each segment was established by three levels as following: i) low, presence of vacant land or lack of urban infrastructure (unpaved roads); medium, almost all parcels developed with few vacant land and presence of some urban infrastructure (paved roads); high, all parcels along the segment are developed and there is full urban infrastructure (paved roads and sidewalks). The condition and maintenance of buildings along the segments was also assessed from low (lack of maintenance, abandonment and temporal construction materials) to high (good maintenance on the facades and completely permanent construction materials). The presence of affordable housing and slums was also part of the data collection process and the percentage of segments with these housing typologies was calculated. The intensity of parking was calculated by the percentage of segments with on-street parking and off-street parking. The

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number of segments facing the BRT corridor was calculated. Three combined variables were also calculated. The percentage of segments with commercial land uses and parking (on-street parking, off-street parking) was calculated in relation to the total number of segments within the buffer area. The percentage of segments with vacant land and facing the BRT right of way was calculated. The percentage of segments with vacant land and off-street parking was calculated.

Entropy was calculated by using the formula developed by Cervero and Kockelman (Cervero & Kockelman, 1997) in order to evaluate the evenness in the distribution of particular land uses (institutional, mixed-commercial, single and multifamily residential).

3.3.5. Data analysis

The data analysis is structured in three sections. First, one model was developed to test the associations between BRT ridership and population density in the sample of 120 BRT stations in seven cities in Latin America. This model was developed to answer research question 2.1. Second, different models expanded the first analysis by testing association per built

environment domain in the sample of 120 BRT stations. These models were developed in order to answer research question 2.2. Third, one model was developed testing associations between built environment factors and BRT ridership after running exploratory factor analysis (EFA). Then, one model was developed testing associations between typologies and BRT ridership after running cluster analysis. These two models were developed to answer research question 2.3.

3.3.5.1. Population density (research question 2.1)

The association between BRT ridership with population density, centrality and BRT terminals is tested with the following equation:

86 Where: 𝑦𝑖= 𝐡𝑅𝑇 π‘Ÿπ‘–π‘‘π‘’π‘Ÿπ‘ β„Žπ‘–π‘ π‘Žπ‘‘ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽0= π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘’π‘π‘‘ 𝛽1= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ π‘ƒπ‘œπ‘π·π‘’π‘›π‘ π‘–= π‘π‘œπ‘π‘’π‘™π‘Žπ‘‘π‘–π‘œπ‘› 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘Ÿπ‘œπ‘’π‘›π‘‘ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽2= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ πΆπ‘’π‘›π‘‘π‘Ÿπ‘–= πΆπ‘’π‘›π‘‘π‘Ÿπ‘Žπ‘™π‘–π‘‘π‘¦ (π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ π‘‘π‘œ 𝐢𝐡𝐷)π‘“π‘Ÿπ‘œπ‘š π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽𝑑𝑦𝑝𝑒= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ 𝑇𝑦𝑝𝑒𝑖= 𝑖𝑠 π‘Ž π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’ (𝐡𝑅𝑇 π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ = 1; 0 = π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) πœ€π‘–= π‘’π‘Ÿπ‘Ÿπ‘œπ‘Ÿ π‘‘π‘’π‘Ÿπ‘š

3.3.5.2. Built environment attributes (research question 2.2)

The association between BRT ridership and built environment attributes in seven cities is estimated with the following equation:

𝑦𝑖 = 𝛽0+ βˆ‘ 𝛽𝑗 𝑗=1 𝐡𝐸𝑖 + 𝛽𝑑𝑦𝑝𝑒𝑇𝑦𝑝𝑒𝑖 + 𝛽𝑐𝑖𝑑𝑦 𝐢𝑖𝑑𝑦𝑖 + πœ€π‘– Where: 𝑦𝑖= 𝐡𝑅𝑇 π‘Ÿπ‘–π‘‘π‘’π‘Ÿπ‘ β„Žπ‘–π‘ π‘Žπ‘‘ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽0= π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘’π‘π‘‘ βˆ‘ 𝛽𝑗 𝑗=1 = π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘π‘  π‘Žπ‘ π‘ π‘œπ‘π‘–π‘Žπ‘‘π‘’π‘‘ π‘€π‘–π‘‘β„Ž 𝑏𝑒𝑖𝑙𝑑 π‘’π‘›π‘£π‘–π‘Ÿπ‘œπ‘›π‘šπ‘’π‘›π‘‘ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘  π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝐡𝐸𝑖= π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝑏𝑒𝑖𝑙𝑑 π‘’π‘›π‘£π‘–π‘Ÿπ‘œπ‘›π‘šπ‘’π‘›π‘‘ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘  π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽𝑑𝑦𝑝𝑒= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ 𝑇𝑦𝑝𝑒𝑖= 𝑖𝑠 π‘Ž π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’ (𝐡𝑅𝑇 π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ = 1; 0 = π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) 𝑖 𝐢𝑖𝑑𝑦𝑖= 𝑖𝑠 π‘Ž π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝑠𝑖π‘₯ π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘ , π‘€π‘–π‘‘β„Ž π‘œπ‘›π‘’ 𝑒π‘₯𝑐𝑙𝑒𝑑𝑒𝑑 π‘“π‘œπ‘Ÿ π‘–π‘‘π‘’π‘›π‘‘π‘–π‘“π‘–π‘π‘Žπ‘‘π‘–π‘œπ‘› π‘π‘’π‘Ÿπ‘π‘œπ‘ π‘’π‘ : (𝐢𝑖𝑑𝑦𝑖= 1 𝑖𝑓 π‘ π‘‘π‘œπ‘/π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ 𝑖𝑠 𝑖𝑛 𝑐𝑖𝑑𝑦 𝑖, π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) πœ€π‘–= π‘’π‘Ÿπ‘Ÿπ‘œπ‘Ÿ π‘‘π‘’π‘Ÿπ‘šπ‘–

3.3.5.3. Transit oriented development features (research question 3.1)

The association between variables and BRT ridership within TOD domains are tested in two parts. First, the analysis identifies built environment factors by running exploratory factor analysis (EFA) based on primary built environment data collected around 120 BRT stations. Factors are determined where the covariance between variables is high but the covariance between groups is low. Factor analysis relies exclusively on the correlation between variables where the weight between factors summarizes the correlation (Kim & Mueller, 1978).

A previous factor analysis based on a subset of the data resulted in 9 factors, which map very closely to the TOD standard (Rodriguez & Vergel-Tovar, 2014). The EFA results identified

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built environment factors including TOD features. The association between BRT ridership and TOD features is tested first by running a regression analysis with these factors. The association between BRT ridership and built environment factors is estimated with the following equation:

𝑦𝑖 = 𝛽0+ βˆ‘ 𝛽𝑗 9 𝑗=1 𝐡𝑒𝐹𝑖 + 𝛽𝑑𝑦𝑝𝑒𝑇𝑦𝑝𝑒𝑖 + 𝛽𝑐𝑖𝑑𝑦 𝐢𝑖𝑑𝑦𝑖+ πœ€π‘– Where: 𝑦𝑖= 𝐡𝑅𝑇 π‘Ÿπ‘–π‘‘π‘’π‘Ÿπ‘ β„Žπ‘–π‘ π‘Žπ‘‘ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽0= π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘’π‘π‘‘ βˆ‘ 𝛽𝑗 9 𝑗=1 = π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘π‘  π‘Žπ‘ π‘ π‘œπ‘π‘–π‘Žπ‘‘π‘’π‘‘ π‘€π‘–π‘‘β„Ž 𝐡𝑒𝐹 π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝐡𝑒𝐹𝑖= π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝑏𝑒𝑖𝑙𝑑 π‘’π‘›π‘£π‘–π‘Ÿπ‘œπ‘›π‘šπ‘’π‘›π‘‘ π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽𝑑𝑦𝑝𝑒= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ 𝑇𝑦𝑝𝑒𝑖= 𝑖𝑠 π‘Ž π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’ (𝐡𝑅𝑇 π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ = 1; 0 = π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) 𝑖 𝐢𝑖𝑑𝑦𝑖= 𝑖𝑠 π‘Ž π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝑠𝑖π‘₯ π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘ , π‘€π‘–π‘‘β„Ž π‘œπ‘›π‘’ 𝑒π‘₯𝑐𝑙𝑒𝑑𝑒𝑑 π‘“π‘œπ‘Ÿ π‘–π‘‘π‘’π‘›π‘‘π‘–π‘“π‘–π‘π‘Žπ‘‘π‘–π‘œπ‘› π‘π‘’π‘Ÿπ‘π‘œπ‘ π‘’π‘ : (𝐢𝑖𝑑𝑦𝑖= 1 𝑖𝑓 π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘›/π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ 𝑖𝑠 𝑖𝑛 𝑐𝑖𝑑𝑦 𝑖, π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) πœ€π‘–= π‘’π‘Ÿπ‘Ÿπ‘œπ‘Ÿ π‘‘π‘’π‘Ÿπ‘šπ‘–

Second, cluster analysis is developed in order to classify BRT stations and identified those with high transit orientation. Then, regression analyses are developed in order to test the association between BRT ridership and TOD features by cluster focusing on BRT typologies with high transit orientation. The association is estimated with the following equation:

𝑦𝑖 = 𝛽0+ βˆ‘ 𝛽𝑗 13 𝑗=1 𝐢𝑖 + 𝛽𝑑𝑦𝑝𝑒𝑇𝑦𝑝𝑒𝑖 + 𝛽𝑐𝑖𝑑𝑦 𝐢𝑖𝑑𝑦𝑖+ πœ€π‘– Where: 𝑦 = 𝐡𝑅𝑇 π‘Ÿπ‘–π‘‘π‘’π‘Ÿπ‘ β„Žπ‘–π‘ 𝛽0= π‘–π‘›π‘‘π‘’π‘Ÿπ‘π‘’π‘π‘‘ βˆ‘ 𝛽𝑗 13 𝑗=1 = π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘π‘  π‘Žπ‘ π‘ π‘œπ‘π‘–π‘Žπ‘‘π‘’π‘‘ π‘€π‘–π‘‘β„Ž π‘π‘™π‘’π‘ π‘‘π‘’π‘Ÿ π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝐢𝑖= π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ π‘π‘™π‘’π‘ π‘‘π‘’π‘Ÿ π‘œπ‘“ π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘› 𝑖 𝛽𝑑𝑦𝑝𝑒= π‘’π‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘π‘œπ‘’π‘“π‘“π‘–π‘π‘–π‘’π‘›π‘‘ 𝑇𝑦𝑝𝑒 = 𝑖𝑠 π‘Ž π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’ (𝐡𝑅𝑇 π‘‡π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ = 1; 0 = π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) 𝑖 𝐢𝑖𝑑𝑦𝑖= 𝑖𝑠 π‘Ž π‘£π‘’π‘π‘‘π‘œπ‘Ÿ π‘œπ‘“ 𝑠𝑖π‘₯ π‘‘π‘’π‘šπ‘šπ‘¦ π‘£π‘Žπ‘Ÿπ‘–π‘Žπ‘π‘™π‘’π‘ , π‘€π‘–π‘‘β„Ž π‘œπ‘›π‘’ 𝑒π‘₯𝑐𝑙𝑒𝑑𝑒𝑑 π‘“π‘œπ‘Ÿ π‘–π‘‘π‘’π‘›π‘‘π‘–π‘“π‘–π‘π‘Žπ‘‘π‘–π‘œπ‘› π‘π‘’π‘Ÿπ‘π‘œπ‘ π‘’π‘ : (𝐢𝑖𝑑𝑦𝑖= 1 𝑖𝑓 π‘ π‘‘π‘Žπ‘‘π‘–π‘œπ‘›/π‘‘π‘’π‘Ÿπ‘šπ‘–π‘›π‘Žπ‘™ 𝑖𝑠 𝑖𝑛 𝑐𝑖𝑑𝑦 𝑖, π‘Žπ‘›π‘‘ 0 π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘€π‘–π‘ π‘’) πœ€π‘–= π‘’π‘Ÿπ‘Ÿπ‘œπ‘Ÿ π‘‘π‘’π‘Ÿπ‘šπ‘–

88

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