ORIGINAL ARTICLE

Diagnosis of landslide risk for individual buildings:insights from Prahova Subcarpathians, Romania

Iuliana Armas

Received: 3 January 2012 / Accepted: 6 October 2013 / Published online: 17 October 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract The aim of this study is to quantify the land-

slide risk for individual buildings using spatial data in a

GIS environment. A landslide-prone area from Prahova

Rivers’ Subcarpathian Valley was chosen because of its

associated landslide hazards and its impact upon human

settlements and activities. The bivariate landslide suscep-

tibility index (LSI) was applied to calculate the spatial

probability of landslides occurrence. The Landslide Sus-

ceptibility Index map was produced by numerically adding

the weighted thematic maps for slope gradient and aspect,

water table, soil texture, lithology, built environment and

land use. Validation curves were obtained using the ran-

dom-split strategy for two combinations of variables: (a) all

seven variables and (b) three variables which showed

highest individual success rates with respect to landslides

occurrences (slope gradient, water table and land use). The

principal pre-disposing factors were found to be slope

steepness and groundwater table. Vulnerability was estab-

lished as the degree of loss to individual buildings resulting

from a potential damaging landslide with a given return

period in an area. Risk was calculated by multiplying the

spatial probability of landslides by the vulnerability for

each building and summing up the losses for the selected

return period.

Keywords Specific risk analysis � Landslides

susceptibility � Bivariate statistical method � Building

stock vulnerability � Prahova Subcarpathians

Introduction

Landslides are related to erosion-prone areas, being com-

mon processes in mountainous or hilly regions with steep,

unstable slopes. There is evidence to proof that landslides

have the biggest impact on human communities and on

natural ecosystems (e.g., Alexander 1991, 2000; Schuster

1995; Schuster and Fleming 1986; U.S. Geological Survey

1997).

It was estimated that about 1 % of lives lost in natural

catastrophes between 1991 and 2005 can be attributed to

landslides, with an average of approximately 20 landslide

disasters occurring each year (EM-DAT 2010).

From a legislative point of view, only four European

countries have official landslide risk assessment method-

ologies (France, Italy, Sweden, and Switzerland). Romania

has a general framework of risk policy, but does not have

an official landslide Risk Assessment Methodology.

In Romania, during 1974–2006, the proportional distri-

bution of the different hazards shows that landslides rep-

resent only 1 %, affecting over 1,000,000 ha, of which

700,000 ha is agricultural land (EM-DAT 2010). Most

landslide-prone areas are located in the Subcarpathian area

and the Carpathian Flysch.

Landslide risk is commonly defined in literature as the

expected level of damage to property, disruption of eco-

nomic activity, and the probable number of lives lost and/or

persons injured due to a particular landslide hazard for a

given area and reference period (Varnes 1984). In a quan-

titative way, this specific risk is calculated as the product of

probability (spatial and temporal probability of occurrence

of a landslide with a given magnitude), vulnerability (the

degree of damage of the element at risk due to the occur-

rence of a landslide with a given magnitude) and damage

potential of the elements at risk. In recent years, the interest

I. Armas (&)

Faculty of Geography, University of Bucharest, Balcescu Bd. 1,

010041 Bucharest, Romania

e-mail: iulia_armas@geo.unibuc.ro

123

Environ Earth Sci (2014) 71:4637–4646

DOI 10.1007/s12665-013-2854-5

in this topic has increased greatly and many approaches

have been developed worldwide. Advances in GIS tech-

nology and the statistical tools have led to the growing

application of quantitative techniques for assessing land-

slide risks. Overview publications on GIS-based landslide

susceptibility assessment and risk methods have been

published by Yin and Yan (1988), Carrara et al. (1991,

1995, 1999), Chung et al. (1995), Soeters and van Westen

(1996), Atkinson and Massari (1998), Aleotti and Chow-

dhury (1999), Guzetti et al. (1999), Guzzetti (2002), Clerici

et al. (2002), Dai et al. (2002), van Westen (2004), van

Westen et al. (1997, 1999, 2006).

In this paper we discuss an applied investigation related

to the landslide risk assessment in human settlements,

based on a landslide-prone area along a Subcarpathian

Valley from Romania.

In particularly, this study stresses the investigation of

landslide risk to individual buildings based on the quanti-

tative risk equation (Eq. 1).

To support the research, the bivariate landslide suscep-

tibility index was used aiming to predict the landslides

occurrence, as well as vulnerability and risk approaches.

Landslides were defined as the gravitational movement of a

mass of rock, debris or earth down a slope (e.g., Cruden

1991; Cruden and Varnes 1996).

The following topics describe the geological/morpho-

logical characteristics of our research area and its related

landslide dynamic features as well as the methodological

advance. In the end, the paper presents/discusses the results

and conclusions of our study.

Study area

The study area is situated between 45�0802400N and

45�1002300N latitudes and 25�4103000E and 25�4302500Elongitudes, laying 100 km north of the Romanian capital

city, in the Prahova Subcarpathians (Fig. 1).

Fig. 1 Study area. Location

and geomorphological

background

4638 Environ Earth Sci (2014) 71:4637–4646

123

The area is located in the southern part of the Breaza

syncline. The northern fringe of the studied area is shaped

in loamy flysch from the facies of Pucioasa Series–Fusaru

sandstone, outcropping in the left slope of Prahova Valley

(Oligocene–Lower Miocene) (Mutihac 1990). In the

southern shank of the syncline, on the left bank of Prahova

Valley, in a 60–80 m wall Brebu conglomerates of Burd-

igalian age, are outcroping (Spataru and Trasnea 1993).

In a sedimentary continuity, the Ribbed Suite (Burdi-

galian–Lower Badenian) is present in the study area with a

thickness of about 650–700 m. The Ribbed Suite is formed

by pelites (60–70 %), which interfere with mica sandstone,

with fine or medium clast rocks. Especially in the left limb

of the syncline, appear gypsum-ferrous marls with small

interlayers or nodules of gypsum, and, in the upper region

of the shank, appear fine yellowish calcareous slate and

levels of green-white tuff, 4–5 m thick.

South of Breaza fault, the Upper Palaeogene deposits

appear to date.

The stepped topography is characteristic for this area

(Fig. 1). The highest reference surface is represented by a

ridge that descends gradually in altitude on a northwest–

southeast direction, from 664 to 500 m. A glacis with a

250–750 m width, a relative altitude of 25–70 m and with a

10–20 % slope in its forehead is shaped at the base of the

ridge. The glacis overlay the bench of Cornu terrace that

slightly descends from 550 to 440 m. 20 % of the study

area is represented by the slope surfaces affected mostly by

translational landslides.

The landscape change due to the increasing human

pressure in this area after 1950, has led to the continuous

extension of built space, especially in the slope area (Armas

and Manea 2002). A consequence of this fact was the reac-

tivation of the landslides through man-made activities such

as slope excavation and loading, land use changes, strong

vibrations or water leakage from utilities (Armas et al.

2003). Some of the most recent events were the landslides

from 21.04.2010 or 11.02.2011. For example, in the Febru-

ary 2011 event, more than 400 m2 were affected, including

the road between the two parts of Cornu’s village, blocking

also a small tributary, due to the landslide rock mass.

Method

In this study, the risk assessment for individual buildings

was calculated accordantly with the basic quantitative risk

equation:

Risk ¼ Hazard Hð Þ � Vulnerability Vð Þ� Amount of elements at risk Að Þ ð1Þ

The term ‘hazard’ in the general risk equation represents

the temporal probability of a landslide event (e.g. the

annual probability/return period) in a given area (e.g. the

spatial probability). The temporal probability of the

surveyed landslides was calculated based on the

correlations between daily rainfalls in the last 15 years

and landslides reactivation according to historical

information.

The spatial probability of landslides occurrence was

calculated from the susceptibility map. In this study, we

applied the bivariate index method in landslide sus-

ceptibility mapping (LSI). LSI is a bivariate statistical

approach that compares the spatial distribution of

landslides with each individual factor that is being

considered. In the last decades, the bivariate statistical

approach developed initially by Yin and Yan (1988)

and van Westen (1997) has been successfully employed

by researchers mapping landslide susceptibility all over

the world (Cevik and Topal 2003; Mehmet and Doyu-

ran 2004; Yaclin 2008; Kelarestaghi and Ahmadi 2009;

Nandi and Shakoor 2009; Bai et al. 2009; Thaiyuen-

wong and Maireang 2010). The most considered factors

for the bivariate method were slope, distance from

rivers, distance from human settlements and distance

from roads.

The LSI method requires the following steps, systema-

tised after Aleotti and Chowdhury (1999):

• Selection and mapping of significant factors and their

categorisation into a number of relevant classes

• Landslide mapping

• Overlay mapping of the landslide map with each pre-

disposing factor map

• Determination of density of landslides in each factor

class and assignment of weighting values to the various

factor maps according to the formula:

Wi ¼ ln Dclas=Dmap

� �

¼ ln Area Lið Þ=Area Nið Þ.X

Area Lið Þ.X

Area Nið Þh i

ð2Þ

where, Wi = the weight given to a certain parameter class

(e.g. a slope class or aspect class), Dclas = the landslide

density within the parameter class, Dmap = the landslide

density within the entire map, Area (Li) = area, which

contain landslides, in a certain parameter class, Area

(Ni) = total area in a certain parameter class.

We used the natural logarithm to emphasis negative

weights when the landslide density is lower than normal

and positive when it is higher than normal.

• Final overlay mapping and calculation of the final

susceptibility values

• Reclassification of the final susceptibility map accord-

ing to the histogram values

• Validation test

Environ Earth Sci (2014) 71:4637–4646 4639

123

The bivariate method can be used only after a thorough

analysis of which environmental condition is area specific

and important in the landslide process within the study

sector. In this research, the analysed factors were slope

gradient and aspect, water table, soil texture, weathered

rock material, built environment and land use. These fac-

tors were assumed to be independent.

Figure 2 illustrates the main steps of the LSI method

applied in this study.

Vulnerability was established as the degree of loss to a

given element (or a set of elements at risk) resulting from a

potential damaging landslide with a given intensity in an

area (IUGS Working Group on Landslides 1997). Vandine

et al. (2004) considered landslide vulnerability a measure

of the exposure to the expected potentially damaging

landslide. Vulnerability is expressed on a scale from 0 to 1,

0 meaning no damage and 1 expressing complete loss or

destruction.

Little is known about the vulnerability to landslides

(Alexander 1989, 2005; Lee and Jones 2004; Glade and

Crozier 2005; Roberds 2005; Galli and Guzzetti 2007).

There are no accepted standards for the landslide vulnera-

bility measurement, which is often estimated as the total

destruction of the elements at risk (Carrara et al. 1991). In

this paper, the vulnerability assessment was limited to the

building stock vulnerability to landslides according to the

building type and size. Only these characteristics of

the buildings were considered, due to the complexity of the

landslide vulnerability evaluation (van Westen et al. 2006).

Secondly, it was assumed that harmful landslide should

always affect the entire element at risk considered as per-

manent and fixed feature.

To calculate the ‘amount’ of the exposed elements at

risk, we crossed the susceptibility classes with the different

building types, and calculated the number of houses in

high, moderate and low landslide susceptibility areas.

The first step in the loss estimation was the calculation of

destroyed houses for the 0.1 return scenarios. This recurring

scenario was calculated based on the frequency of landslide

episodes pertaining to the daily rain quantity for the last

15 years. The next step was to calculate the losses to each

single building for the 10-year return period, by multiplying

the spatial probability by the vulnerability for each building

and summing up the losses. Figure 3 illustrates the main

methodological steps of the study.

Identification of significant factors and creation

of input maps

The pre-processing data involved the generation of a

number of thematic layers in GIS, concerning the occur-

rence of landslides. A number of maps were geo-refer-

enced, so that they could all be tied to the same projection

system. All spatial analysis were performed using ILWIS

3.6 software (van Westen 1997; ITC 2001).

The database included:

1. Basic data sources as topographic maps (1/25,000

scale)

2. An inventory of existing landslides including their

nature, size, location, obtained from field mapping

(surveys 2007–2011)

3. Thematic layers (e.g. lithology, tectonic structures,

land use, stream network, and soil characteristics)

resulted following the fieldtrip campaigns of 2007 and

2009

4. The Digital Elevation Model (DEM) of the study area

with a cell size of 5 m. Different terrain features such

as slope gradient and aspect originated from further

DEM processing

Slope data layer comprises seven classes, namely, flat

(\3�), 3�–7�, 7�–15�, 15�–25�, 25�–35�, 35�–45�, 45�–90�.

Aspect was referred to as the direction of maximum slope

of topography and was divided into nine classes, namely,

N, NE, E, SE, S, SW, W, NW and Flat (\3).

Fig. 2 Simplified flowchart of

the bivariate statistical landslide

analysis

4640 Environ Earth Sci (2014) 71:4637–4646

123

After the creation of the primary layers, various

advanced GIS techniques such as vector to raster conver-

sion, reclassification, filtering, distance operations and

raster calculations were applied.

LSI index was obtained by adding all the LSI individual

maps obtained by the statistical correlation of the landslide

map with the different factor maps. Weights were derived

from densities in each attribute class within each factor (see

‘‘Method’’).

More details on methodology for calculating the LSI

index can be found in van Westen (1997), Suzen and

Doyuran (2004), Armas (2011).

Next we calculated the risk at individual building levels,

based on the general Risk formula (Eq. 1).

The analysis was done only on the basis of the new

constructions—built after 1990—because before this year

houses were built traditionally only on the bridge of the

terraces, with no vulnerability to landslides. After 1990,

and especially after the year 2000, houses were built on

vulnerable slopes, exposed to the risk of sliding. New

buildings were mapped in the summer of 2008 with the

GPS, together with information on the structure, material

of construction, number of floors, land use, utilities and

type of property.

The risk analysis was made on the number of present

new buildings in high, moderate and low landslide sus-

ceptibility classes, according to the building type: auto-

claved aerated concrete (AAC), AAC and brick, brick,

wood, reinforced concrete, and size: small (bungalows),

medium (one to two floors) and large buildings (over two

floors) Table 1.

Results

The resulted weight values obtained from the LSI analysis

for each factor class are shown in Table 2.

Highest weights were registered in case of higher slope

gradient and low groundwater table. The values obtained

were in good agreement with the field observations.

Regarding the groundwater table, the measurements

made to over 40 wells and in over 30 bore holes (Parichi

et al. 2006a, b, 2008) showed that this is quartered at dif-

ferent depths as follows: between 0.51 and 1.0 m depth in

the Prahova and Campinita floodplain, between 1 and 2 m

in the floodplain terrace, and at greater depths (2 and over

10 m) in the terrace bench and glacis.

The groundwater table deepens significantly (to over

10 m, even 16 m) only in the area of the terrace bench, on

which Cornu locality was built.

The analysis of the weathered rock deposits reveals high

values of the ‘in situ’ (eluvia, carbonate or fine-grained

siliciclasts) material resulting from weathering and/or

Fig. 3 Flowchart of the

analytical process

Table 1 Pressure on land caused by human activities (1984, 2000

and 2008)

Human pressure index (ha/inhabitant)

Agricultural land use

Arable Pasture and meadow

1984 2000 2008 1984 2000 2008

0,073 0,075 0,07 0,166 0,154 0,147

Source: Prahova County’s Directory of Statistics

Environ Earth Sci (2014) 71:4637–4646 4641

123

physical disintegration acting on the interfluves, where the

landslide scarps advance progressively.

The soil mapping demonstrates that the largest part of

the soils (73 %) show a middle texture (clayey sand to

clay), as well as high values of landslide susceptibility

(Parichi et al. 2006, 2006–2007, 2008).

Weights were assigned to the classes of each thematic

layer, respectively, to produce weighted thematic maps

(Fig. 2). The Landslide Susceptibility Index map (LSI) was

produced by numerically adding the weighted thematic

maps, according to Eq. (3).

LSI ¼ Sl þ As þ W þ Li þ St þ Dbþ Lu; ð3Þ

where Sl, As, W, Li, St, Db and Lu are distribution-derived

weights for slope, aspect, groundwater depth, lithology,

soil texture, distances from built environment and land use,

respectively.

The spatial analysis shows the presence of two sectors

with maximum values of landsliding susceptibility: the

slopes of the upper terraces and the dens gullies frag-

menting the slope of the second terrace (Fig. 4).

For validation of the model, the landslides in the study

area were split into an analysis and a validation group and

the analysis was repeated.

The success rate is calculated by decreasing order of

pixels in the susceptibility map, on intervals based on the

histogram frequency values. Landslide inventory map was

overlapped with the LSI map and a common frequency was

calculated. The validation curve indicates what percentage

of the total number of slides occur in areas with the highest

rates of susceptibility of pixels on LSI map. The higher the

percentage of landslide occurrence in most susceptible

pixels, the better is the predictability of the model (Re-

mondo et al. 2003).

Figure 5a, b show validation curves obtained using the

random-split strategy for two combinations of variables:

(a) all seven variables and (b) three variables which

showed highest individual success rates with respect to

landslides occurrences (slope gradient, water table and land

use). The principal pre-disposing factor was found to be

slope steepness (99 % of landslides in the validation

sample fall in the highest susceptibility classes), followed

by groundwater table and land use. Slope aspect showed no

relation to the landslide occurrence. This fact could be also

explained through the general uniform western exposition

of slopes in the study area.

Figure 5a shows that almost 90 % of landslides in the

validation sample fall on pixels corresponding to the 45 %

of the study area with the highest susceptibility. Curve ‘b’

has a slightly better prediction rate with respect to land-

slides occurrences.

To derive the risk map, the susceptibility map was

combined with the vulnerability information of the

Table 2 Distribution of weight values (Wi) obtained from the LSI

analysis

Data layers Parameter classes Landslidearea (%)

Weights

Slope angle 0–3� 1 -2.67

3–7� 10 -0.27

7–15� 25 0.62

15–25� 21 0.43

25–35� 18 0.28

35–45� 15 0.08

45–90� 10 -0.34

Slope aspect NE 13 0.07

E 14 0.30

SE 15 0.24

S 6 -1.18

SV ? flat 15 0.20

V 14 0.19

NV 14 0.32

N 9 0.56

Groundwatertable

1–2 m 1 -2.55

1.5–2.5 m 8 -0.74

2–3 m 1 -6.31

2.5–3.5 m 6 -1.10

2–5 m 35 0.75

3.5–5.5 m 5 -1.27

5.5–10 m 3 -1.77

6–11 m 4 -3.97

Over 11 m 1 -7.41

Various depths (in the landslidebody)

36 0.79

Weathered rockmaterial

Torrential bed-loads 3 -1.73

Prahova and Campinita river-beds

10 -7.41

‘‘In situ’’ (eluvia, carbonate orfine-grained siliciclastic)material

7 0.31

Floodplain and terrace gravels 25 -1.23

Fine-grained deluvial-colluvialmaterial of the terrace IIglacis

19 -0.86

Terrace scarps 36 0.89

Soil texture Middle texture (clayey sand toclay)

73 1.19

Clay (terrace II glacis) 8 -2.16

Clayey sandy and sandy clay 15 -1.34

Various textures in thefloodplain

4 -7.41

Distances tobuiltenvironment

0–20 m 4 -1.20

20–50 m 11 -0.28

50–100 m 25 0.43

100–150 m 18 0.54

150–200 m 17 0.53

200–300 m 12 0.32

300–500 m 9 0.20

500–1,000 m 5 -0.16

Land use Prahova meadow 0 -12.2

Households/gardens/ 8 -0.93

Forests 35 0.43

Hay field/shrubs 57 0.92

4642 Environ Earth Sci (2014) 71:4637–4646

123

elements at risk. All of the over 300 new buildings ana-

lysed in this study have a residential function. Most

buildings are brick buildings (40 %), 17 % laying in the

high susceptibility class. Houses of the AAC type are the

second frequent building type in this area (31 % of all

buildings), 23 % of them laying in the high susceptibility

class. Although wooden and brick houses are traditional

building types for this Subcarpathian sector, newer con-

structions are of the ACC type because they are cheap and

have flexible wall construction blocks.

Figure 6 shows in a cumulative histogram the sus-

ceptibility class of each building type. Referring to the

general Risk formula (Eq. 1) the amount (A) represents

the number of buildings in different susceptibility

classes.

The hazard occurrence probability is expressed by the

spatial and temporal probability of landslides occurrence.

Because a complete historic record of landslide occur-

rences is absent, we used interviews to obtain information

about landslide activity. Unfortunately, we could not cover

a period of 15–20 years based on over 50 interviews with

local people. The analysis made on a 15-year period

(1990–2005) between the daily quantity of precipitations

and the start of gliding processes, showed a 10-year mean

return period of landslides reactivation. The annual land-

slide probability was estimated by multiplying the temporal

probability (1/return period for annual probability) with the

spatial susceptibility (e.g. the spatial distributed return

probability of a landslide to affect a building).

Table 3 shows the chance of occurrence of a landslide at

each location.

The building’s landslide vulnerability was considered as

being 1 in the case of complete destruction after a landslide

event. The estimation of landslide’s vulnerability is very

complex and necessitates data on the building type and

dimensions, as well as the expected landslide size and

speeds (van Westen et al. 2006).

The result was an annual risk of about three houses

located within high susceptibility areas that could be

affected by landslides and completely destroyed (vulnera-

bility is assumed to be 1). Equally, this value was divided

by brick houses and the AAC building type.

In estimating individual building vulnerability, the

damage percentages were calculated as a function of the

building type and size (e.g. number of floors). Table 4

presents the assigned value of vulnerability based on the

type of building material and building’s size. We defined

three classes: small (bungalows), medium (one to two

floors) and large buildings (over two floors).

Each building, based on its susceptibility class, was

assigned a spatial probability of a landslide occurrence.

The information showing that a landslide will strike a

particular part of a building is very important when cal-

culating the risk to landslides for individual buildings. The

next step was to calculate the losses for the 10-year return

period scenario, based on the equation: R ¼ H � V .

Each building contributes with its losses in the general

amount of losses, which is expressed in the number of

buildings lost for the 10-year return scenario. For all sus-

ceptibility levels there are five houses that could be lost.

The areas with the highest individual risk levels are located

on the steep and vulnerable slopes (Fig. 7).

Conclusions

The landslide risk assessment undertaken here represents

the first to follow an internationally recognised quantitative

Fig. 4 Landslide susceptibility map. a susceptibility weights; b sus-

ceptibility classes

Environ Earth Sci (2014) 71:4637–4646 4643

123

landslide risk assessment methodology applied to calculate

the landslide risk for individual buildings in a hilly area

from Romania.

Firstly, the most important aspects sought through this

research were to properly define disaster prone areas and to

weight up the spatial probability of a landslide occurring at

the location of a building. This value derived from the

landslide density within a susceptibility class. To calculate

the landslides susceptibility classes, the bivariate statistical

method was applied, which is suited for local or regional-

scale landslide susceptibility mapping.

The use of this statistical method has also a number of

drawbacks. Some of the most important are the simplifi-

cation and generalisation of conditional factors throughout

the study area. Another conclusion derived from the vali-

dation method used in this study is that an increase in the

number of variables included in the LSI analysis does not

necessarily increase the quality of the model.

Fig. 5 Landslide samples a and

b. Validation curves: all

variables (a); slope gradient,

groundwater table and land use

(b). The percentage of predicted

landslides was ordered from

high to low susceptibility values

0%

20%

40%

60%

80%

100%

1 2 3 4 5

Fig. 6 Cumulative histogram of building types in susceptibility

classes: 1 AAC and brick, 2 AAC, 3 reinforced concrete, 4 brick, 5

wood

Table 3 Landslides density within landslides susceptibility classes

Susceptibility class Area in the

susceptibility

classes

Landslides (% of

susceptibility areas)

Spatial probability of landslides

occurrence (cumulative landslide

area/susceptibility class areas)

Hazard for the

annual probability

of 0.1

[0 (low) 189,900 2.91 0 0

0–2.5 (moderate) 302,700 4.61 0.5 0.05

2.5–5 (high) 898,800 13.77 0.8 0.08

Table 4 Vulnerability of buildings according to building type and

size

Building material Building size

Small Medium Large

AAC 1.0 0.9 0.9

Brick 1.0 0.8 0.7

Wood 0.4 0.5 0.6

Concrete 0.6 0.5 0.4

AAC ? brick 1.0 0.9 0.9

4644 Environ Earth Sci (2014) 71:4637–4646

123

Secondly, this paper has provided new information on

the individual building risk estimation to landslides based

on the quantitative risk formula.

If the buildings continue to be developed on the hill

slopes, the risk of landslide occurrence will increase.

Therefore, landslide risk management should become a key

factor to be considered by risk mitigation strategies for the

protection of human life and property.

This case study is only an initial step in the complex

process of risk mitigation. We are aware that the man-

agement of slope instability/landslides has the potential to

become efficient only in connection with the real world of

land use planning.

Acknowledgments This research was partially supported by the

National Research Council (CNCS) of Romania through the project

No. 2916/31 GR, having Prof. I. Armas as principal investigator. The

author wishes to express sincere thanks to the two anonymous ref-

erees who provided constructive comments on the manuscript and

helped in improving the paper.

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