. We investigate and study on mathematical structures involving mathematical models and others associated with seismic waves in an earthquake. Our first aim is to give some novel formulas and certain finite sums including the Bernoulli numbers and the Hermite polynomials with the aid of generating functions, the Riemann integral, and the Volkenborn integral. The second aim is to examine the seismic wave propagation in different geological units with the help of special polynomials containing the Hermite polynomials and their graph fitting of functions. To evaluate the shape of the seismic waves propagating within the ground (rock and/or soil), we use comparing method with the graph of the Hermite polynomials and functions and the polynomial Rocking Bearings. Furthermore, we also define generating function for the polynomial type Rocking Bearings. We give open problems on this generating function and earthquake facts. By applying partial derivative operator to the generating function for the m-parametric Hermite type polynomials, we give a novel recurrence relation and derivative formulas for these polynomials. We also give a new general formula for monomials in terms of these polynomials. Moreover, for the purpose of visualizing curve fitting approach to the seismic waves, we draw many plots of the Hermite functions with Mathematica (Version 12.0.0) with their codes. Finally, with the aid of these graphs, we give useful evaluation on the shapes of the seismic waves propagated in the ground (rock and/or soil).

Natural and anthropogenic water pollution caused by heavy metals has become a major problem worldwide. As a result of these processes, many harmful heavy metals are mixed into the water and endanger the environment and human health. Therefore, this study aimed to investigate the hydrogeochemical properties of the stream waters of G & ouml;yn & uuml;k Canyon (G & ouml;yn & uuml;k Stream), which is located in southern Turkey, an important touristic region of Antalya. A total of 44 water samples were retained to evaluate the geochemical type, heavy metal contamination level, and suitability for drinking and irrigation of G & ouml;yn & uuml;k Canyon Stream waters. All samples were analysed by inductively coupled plasma mass spectrometry (ICP-MS), X-ray fluorescence (XRF), and multi-parameter portable water quality assessment. Analysed water samples were found to be of classes II and III in terms of overall water quality. The average hardness level is above the limit values. The results of geochemical analyses showed that the common water types in the region are Mg-Ca-HCO3, Ca-Mg-HCO3, Ca-Mg-HCO3-SO4, and Ca-Mg-HCO3-Cl-water facies. Most of the samples belong to the "rock weathering dominated" region represented in the Gibbs diagram. The hydrogen ion concentration (pH), electrical conductivity (EC), and total dissolved solids (TDS) values vary between respectively 6.5-7.9; 230.4-720.8 mu S/cm, and 149-468 mg/L. Cations and anions followed the order Ca2+ > Mg2+ > Na+ > K+ and HCO3- > SO42- > Cl- > F- > NO3-. Heavy metal anomalies in water followed an increasing order: Cu < As < Pb < Ni < Ba < Fe < Cr < Mn < Zn < Sr. These heavy metals showed high index values (Poseidon index (PoS), contamination factor (CF), enrichment factor (EF), geochemical index (Igeo), heavy metals pollution index (HPI), contamination degree (Cd), in some water samples. There is a spatial anomaly in these locations related to limestone and ophiolite. This water can be used for irrigation purposes according to Wilcox, the United States salinity laboratory diagram (USSL), permeability index (PI), Kelly's ratio (KR), and Residual Sodium Carbonate (RSC).

Surface waters are important for the environmental ecosystem. The aim of the study is to find the highest explanatory value among the quantitative variables, depending on the chemical content of the surface waters flowing from the Goynuk canyon creek (Kemer, Antalya). Therefore, regression analysis was performed with SPSS26 statistical software, considering two different quantitative variables. In particular, a strong and positive correlation was found between Na-Ni (0.656**) and Na-Sr (0.857**). For this reason, the explanatory rate is very high in multivariate statistical analyzes to be conducted in the study area.

Earthquakes are natural events and it is quite easy and beneficial to convert them to wealth (national asset) rather than catastrophe. The earthquakes exert their catastrophe on the buildings/structures founded in soil grounds. There is not even a single case study of an earthquake that caused a catastrophe where structures/buildings are founded on/in a rocky ground that is not proper for agriculture. However, almost all inland earthquakes, particularly strike-slip and normal fault zones ultimately create larger and thicker soil mantle, which is heated by (a) kinetic energy created by particle movements and (b) higher geothermal gradient peculiar to active fault zones. So, people should use fertile soil plains for agriculture and surrounding rocky lands for settlement in accordance with the recommendations of Mother Nature and State Laws and in accordance with the maxim "Love the nature, never challenge it”.

An earthquake is a natural event and it is quite easy and beneficial to convert it to wealth rather than disaster. A strong earthquake exerts its catastrophe on the buildings/structures found in the soil grounds. There is not even a single case study that creates catastrophe where structures/buildings are erected on/in the rocky ground whose extensive planar discontinuities are free of expansive clay minerals. Every strong earthquake has proven this reality. The last earthquake with a magnitude of 7.7 hit Pazarcik/Kahramanmaras/Turkey on the 6th of February. The epicenter is at the fertile soil plain of the township Çigdemtepe (Crocushill)/Pazarcik which has been erected on the weak rock of clayey limestone. Despite that, casualty (the number of dead and injured) is zero in the township of Crocushill) whereas a very severe disaster has occurred in (a) Battalgazi and (b) Harran soil plains which are orderly 160 and 200 km away from the epicenter. The reasons behind this fact are “the seismic energy attenuates in strong rock over a thousand times more than that in thick (t>20 m) soil mantle” and “wave velocity in rock is practically 30 times higher than that in saturated soil”. It should also be noted that there is no liquefaction in the rock. If the locations of engineering structures are chosen other than irrigable agricultural areas, fertile soils and possible landslide areas, no problems will be encountered. It is not important where and when the earthquake will occur, but where it will collapse. These hazardous areas also overlap with agricultural areas.

Red soil is formed by weathering due to the effect of bedrock and various fluids in subtropical and tropical climate zones. The major and trace element geochemistry of red soil are important for understanding its environmental conditions and interpreting its genesis. This study aims to determine how red soil is formed in the study area, where magmatic rocks are located, and to determine their relationship with magmatic fluids. In this context, geochemical analyses were conducted, and index values, spatial distributions, and multivariate statistics of the samples were calculated. Methods: A total of 49 red soil samples collected from the Sutlegen Village in the Kas district of Antalya were subjected to geochemical analysis. The following major elements were found in the red soil samples: Al2O3, SiO2, Fe2O3, TiO2, CaO, MgO, K2O, P2O5, and SO3. The Al2O3–SiO2–Fe2O3 triangular diagram revealed that the samples underwent moderate laterization. Multivariate statistical analyses indicated that major element oxides of Al2O3, Fe2O3, and SiO2 behaved differently from other components and revealed that red soil formations were associated with magmatic fluids. The region is a potential area for economic bauxite resources. Detailed investigations should be conducted on mineral exploration for bauxite ore.

The purpose of this paper is to use multivariate statistical methods with asymmetric distributions approach, chemical analysis, and inductively coupled plasma–mass spectrometry (ICP-MS) device. We investigate data of heavy metal content from Akcay Riverwater to the Mediterranean involving Finike sea coast at Turkey. We determine the chemical content, origin of heavy metals of the surface water in Akcay River, which flows into the Mediterranean realted to the above-mentioned region by multivariate statistical analysis, pollution indices, and density maps involving numerical comments by numbers. With the help of special numbers represented by special chemical components and simmetric statistical methods given above, in this paper, we obtain many new relations and results. Furhermore, we give some comments, observations, and remarks about the results of this paper. These results have a high potential to be used not only in engineering fields and health sciences, but also in applied mathematics, statistics, and other fields.

Over 60% of the countries just like Turkey have suffered from earthquakes. The observations have revealed that the buildings/civil engineering structures in/on the rocky grounds did not get damaged by the earthquakes. The major reason behind it is that the modulus of elasticity of saturated rocks is million times greater than that of saturated soil units. Furthermore, while the saturated soil units are susceptible to liquefaction (shear strength approaches to zero) at varying degrees, rock units do not get liquefied. None of the structures on the rocky ground has been affected by the recent destructive earthquakes studied by the authors and/or their colleagues in Turkey and abroad. As also has been highlighted by Marmara (17 August 1999) and Van (23 October 2011) earthquakes, the civil engineering structures in/on rocky grounds, even adjacent to the epicenter, have not been affected by the destructive earthquakes in respective regions that are seismically active. It is quite explicit that the number of casualties in the settlements in/on rocky grounds is zero. In Turkey, the land required for housing is 1% of the country. However, 57% of the area is available for construction. The remaining 43% consists of forest, restricted zones, and the lands of fertile soil which are composed of soil plains and landslides. Thus, the earthquake disasters can be overwhelmed by effective land use planning.

Bu çalışmanın amacı, Türkiye, Taşucu Körfezi (Mersin) sahili boyunca 33 lokasyondan toplanan güncel çökeltilerde ağır metal içeriklerini ve olası kökenlerini incelemektir. Tüm örneklerdeki sedimanter dokusu, ana (Fe, Mg, Al, Si, Ca, Na, K, Ti) ve eser (Pb, Zn, Mn, Sn, As, Sb, Co, Cr, Cu, Hg, Ag, Cd, Ni, Mo, V, W) element içerikleri ölçülmüştür. Ana ve eser elementlerin genel konsantrasyonu Al'a normalize edildi ve zenginleştirme faktörü hesaplanmıştır. Çok değişkenli istatistiksel analizler, ağır metal içerikleri arasında anlamlı bir korelasyon ilişkisini göstermesi ve eser metallerin yakın ilişkisinin olduğunu göstermesi bunların aynı kaynaktan olduğunu göstermektedir. Ana ve eser elementlerin dağılımı üç farklı faktöre işaret etmektedir; birinci faktör antropojenik aktiviteleri, ikinci faktör doğal süreci ve üçüncüsü ise çalışma alanındaki kaynaklar arasında (antropojenik) önemli bir fark olduğunu gösteren ara faktördür. Elementlerin diğer alanlarla karşılaştırılması neticesinde Sb, Mo, As, Cr, W, Ni, Sn ve Co’ın zengin olduğu gözlenmiştir. Taşucu körfezinin özellikle kıyı çökellerinde normal koşulların yeniden sağlanması için iyileştirici önlemler alınmalıdır.

The trinity of the water-discontinuity-clay is the main cause behind most geotechnical problems involving rock slopes. The water molecule is unique to have a dipole property and is a common reactant in numerous chemical reactions. Discontinuity controls the slope stability. The planarity, continuity, and clay mineral infill are particularly important in the areas where outslope bedding dominates. The shear strength of clay mineral approaches zero upon saturation. The discontinuity nomenclature reduces the volume of the geomodel (GM) works, which comprise geology, hydrogeology, engineering geology, geoenvironment, and the geotechnics over 80%. The smectite-group clay minerals have a unit cell with net negative charge. Hence the water is readily captured by the electrically unbalanced mineral causing it to swell by more than 10% of its dry volume and then its shear strength approaches zero. The outsloping bedding, layering, or the basically imbricated thrust faults in places are the common examples of large-scale landslides. The discontinuity survey with the proposed nomenclature and approach is especially important in locating and orienting linear engineering structures. Consequently, this approach enhances the researchers and designers considerably in conducting projects conveniently in terms of timing, environment, safety/security and the cost.

The cities are also expanding with growth in construction rapidly, depending on the population growth. This development causes a lot of environmental problems. Pollution in water is one of the main problems and the aim of this paper is to evaluate water pollution in the study area. There are some statistical methods developed for the measurement and evaluation of water pollution; heavy metal pollution index (HPI) is one of them. Antalya is, one of the big cities in Turkey, also growing fast; population and settlement in this city are increasing quickly. That is why two streams, Duden and Goksu, are selected to measure the heavy metal pollution. The 24 water samples from Duden Stream and 18 water samples from Goksu Stream were taken systematically in June 2018 and were analyzed by using HPI. The heavy metals, from the highest value to the lowest one, were Sr > Fe > Al > Mn > As > Ni > Cu > Pb > Cr > Se in Duden Stream; and Sr > Fe > Al > Ni > As > Cu > Mn > Pb > Cr > Se in Goksu Stream. The Sr and Al values have exceeded the standard permissible values in both of the streams. The heavy metal pollution index (HPI) was used to evaluate the potential risk. Regarding quality the water samples have been classified as "good" and "poor", generally. On the other hand, some water samples had heavy metal pollution above standards Especially, the water of D15 - D19 - D20 and G13 samples were determined as "very poor" according to the standards As a conclusion, the anthropogenic factors and urbanization may be the cause of the pollution. Living creatures that use water may have health problems and ecological equilibrium may be hampered in these stations. Groundwater may be contaminated in these areas. So, the urbanization needs to be done more carefully.

Purpose. Isparta Angle occurs along the Mesozoic carbonate axis. Carbonated rocks forming the Taurus belt are continuous with allochthonous and autochthonous features. The rocks in the region are abnormally contacted with each other and can be found as allochthons on each other. The contacts between the tectono-stratigraphic units are commonly tectonic with the carbonate platforms forming the autochthonous basement to the west and east. For this reason, the initial relations between the rock masses and their initial geographical locations are not known. Methods. Some of the carbonated rocks show similar characteristics to each other in terms of sedimentation environment, stratigraphic relations and some other characteristics; but they are separated from each other by different characteristics throughout the belt. Findings. In this study, relationships between mass and material properties of marbles, which are produced in the allochthonous and autochthonous parts of the carbonated rocks in the western part of the Taurus belt, were investigated. Originality. As a result of this study, it has been determined that the mass and material characteristics of autochthonous limestones are better in quality than those of allochthonous limestones. Practical implications. Marble production qualities and block efficiency of allochthonous and autochthonous rocks have been evaluated.

The importance of getting the clean water has increased due topopulation growth. This requirement is not limited to drinking and irrigationwater; it is also important in energy production and industry development.Antalya is one of the provinces with the highest water demand due to itsmigration, agriculture and industry growth. Kumluca is one of the importantdistricts of Antalya with its growing population, important agricultural areasand hydroelectric power plants just north of it. Agricultural is performed inall season. In this study, in order to understand the effects of increasingpopulation and agriculture, heavy metal anomalies were investigated in surfacewaters that passes throughout the plain. In May 2018, a systematic sampling wastaken from 48 locations between Alakir Dam and Alakir Bridge. The data obtainedin the results of chemical analysis was interpreted using HPI statisticalanalysis. HPI value anomalies wereconcentrated in two regions. These grouping were considered that because of thedam in the upper region; because of the agricultural activities in the lowerregion.

The protection of the existing resources has become much more important than getting fresh water. The traditional methods, like well and pump, can reduce the groundwater level and dry up the reservoirs. On the other hand, there are some environmentally friendly methods like "qanat". Qanat is a water management system which has been used to supply water in semi-arid and arid regions for a long time; for example, in Iran, Iraq, Morocco, Oman etc. The system consists of many vertical well connected by gently sloping tunnel with tapping into the groundwater table. The main idea is to reduce the evaporation and leakage, keep the natural balance of the groundwater without pumping. The main idea in this study is to find suitable places for qanats in terms of geology and hydrology and to create a model for new water projects in Antalya. A "pilot area" near to Elmali, which is one of the districts of Antalya, is selected. The geological units in the area are permeable - highly permeable micritic limestone and impermeable - poor permeable claystone - siltstone. The surface waters in the area are generally seasonal. The physical and chemical properties of surface waters were determined. The water in the area was classified "as very good quality water for drinking" and "very good for irrigations". Besides that, the study showed that "the geological model is very appropriate for "qanat" and to get water by gravitation without decreasing the groundwater table and damaging natural balance".

The Trans-European Motorway (TEM) Project is a sub-regional cooperation among Central, Eastern and South Eastern European countries. Turkey is one of them with a motorway section has 3,600 km length. Sarisih landslide is located between Km 37+800 and Km 38+500 stations in Pozanti - Tarsus - Mersin section of Turkish segment. This was a fossil landslide before the construction of motorway and the safety factor was 1. There are a lot of huge landslides in the area like that because of the water-discontinuity-clay trinity (WDC). However, after the construction of the road over toe of the landslide, the balance of the mass has changed, the safety factor decreased below 1 and the landslide has reactivated. The wrong alignment selection causes a lot of geotechnical and environmental problems with increasing cost and consuming time. However, there was a more economic and environmentally friendly solution which is a short tunnel on the other side of the valley. In this study, this solution has been investigated and also back analysis of the Sarisih landslide has been made. This study showed that "to take precautions is much more engineering approach than remediation works" in terms of safety, time, cost and environment.

The right site selection for a linear engineering project like motorway or pipeline depends on geological, engineering geological and geotechnical properties of the region. The detailed investigation of them will reduce the cost and also extend the economic life of the projects. The motorway which has 140 km length among Tekir-Tarsus and Mersin is one of the examples. The study area is located at the northwest of Adana with 24 km between Km 36+000 - 60+000 of Pozanti -Tarsus - Mersin motorway. There is an active fault zone which is called Ecemis in the area. The motorway has been extended parallel to this active fault, occasionally. The fault zone is characterized by numerous huge landslides with several billions of cubic meters. The water-discontinuity-clay trinity (WDC) is well developed in this trough and plays a significant role in the formation of these landslides. Additionally, the zone includes fertile valleys and is highly rich in terms of flora and fauna. So, any engineering project causes a lot of geotechnical and environmental problems. In this study, three route alternatives have been investigated to minimize these problems and also the cost of the project. The study showed that it is possible to construct an engineering structure without damaging the nature with low cost "if we can understand the language of the nature".

Numerous huge landslides and a lot of springs are located in Ecemis Fault Zone between Adana and Nigde, in the south of Turkey. The waterdiscontinuity-clay trinity plays a significant role in the formation of these landslides and morphology of the area. A large-scale dam and a highway were planned in this valley where is highly rich in terms of flora and fauna and composed by huge slopes. This study showed that the water in the area is meteoric and one of the main cause of landslides. Any big project can cause many geotechnical problems with remedial works. Because, the safety coefficient of huge landslides is 1 which means their stability is critical and any operation will disrupt this balance. Because of this and/or similar geotechnical problems; the projects were canceled. Besides, water is potable and suitable for irrigation and the valley stands as national wealth.