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Articles 1861 - 1890 of 10319
Full-Text Articles in Physical Sciences and Mathematics
Epidote - Lawsonite Coexistence In Blueschist-Facies Blockfrom The Tavşanlı Zone - Turkey: Petrological Implications, Mete Çeti̇nkaplan
Epidote - Lawsonite Coexistence In Blueschist-Facies Blockfrom The Tavşanlı Zone - Turkey: Petrological Implications, Mete Çeti̇nkaplan
Turkish Journal of Earth Sciences
Metamorphic evolution of an epidote-lawsonite blueschist sample characterized by the coexistence of lawsonite and epidote from Sivrihisar area (Tavşanlı Zone) was studied herein in terms of petrology and mineral equilibria. Based on the textural evidence and phase composition, 2 prograde stages, defined by assemblage-I and -II, and 1 retrograde stage were recognized. Assemblage-I indicates epidote-blueschist facies conditions (12 ± 1 kbar / 485 ± 10 °C). Assemblage-II is characterized by the coexistence of epidote and lawsonite (17 ± 1 kbar / 515 ± 10 °C) corresponding to the interface of lawsonite blueschist and epidote blueschist facies. Phase diagram calculations and …
Review Of Late Cretaceous Volcanogenic Massive Sulfide Mineralization In The Easternpontides, Ne Turkey, Mustafa Kemal Revan
Review Of Late Cretaceous Volcanogenic Massive Sulfide Mineralization In The Easternpontides, Ne Turkey, Mustafa Kemal Revan
Turkish Journal of Earth Sciences
The production of Cu-Zn from volcanogenic massive sulfide (VMS) deposits in the eastern Pontides began in the early 1900s, with the exploitation of high-grade ores scattered across the district. The district still possesses economically important blind VMS and associated sulfide deposits. Careful descriptive documentation of the typical features of these VMS ores illustrated the geological characteristics that are important in identifying ore localities and can be used to define exploration targets. The eastern Pontide VMS deposits are examples of volcanic-hosted massive sulfide deposits that exhibit many of the characteristics typical of bimodal-felsic-type VMS mineralization. Nearly all known VMS deposits in …
Assessment Of Element Concentrations In Surface Sediment Samples Fromsığacık Bay (Eastern Aegean), Özde Bakak, Fi̇li̇z Küçüksezgi̇n, Fai̇k Erdeni̇z Özel
Assessment Of Element Concentrations In Surface Sediment Samples Fromsığacık Bay (Eastern Aegean), Özde Bakak, Fi̇li̇z Küçüksezgi̇n, Fai̇k Erdeni̇z Özel
Turkish Journal of Earth Sciences
Concentrations of Al, Fe, As, Co, Cr, Cu, Mn, Ni, Pb, Zn, Hg, and organic carbon, and grain size distribution were investigated in the surface sediments of 7 sampling stations in the Sığacık Bay (western Anatolia) in December 2016. At all of the sampling stations, the concentrations of Pb, Ni, Cr, and As were higher than the average shale values. The highest concentrations of Pb, Cu, Zn, As, and Hg were found at stations near Doğanbey Cape. The possible sources of pollution were evaluated using several parameters: the enrichment factor (Ef), contamination factor (Cf), and contamination degree (Cd). The Ef …
Geochemistry, Risk Assessment, And Pb Isotopic Evidence For Sources Of Heavy Metals Instream Sediments Around The Ulukışla Basin, Niğde, Southern Turkey, Abdurrahman Lermi̇, Emmanuel Daanoba Sunkari
Geochemistry, Risk Assessment, And Pb Isotopic Evidence For Sources Of Heavy Metals Instream Sediments Around The Ulukışla Basin, Niğde, Southern Turkey, Abdurrahman Lermi̇, Emmanuel Daanoba Sunkari
Turkish Journal of Earth Sciences
Concentrations of selected elements (Al, Fe, Mn, Mo, As, Cd, Cu, Cr, Ni, Co, Pb, Sb, and Zn) and Pb isotope ratios were determined in 53 sediments from Alihoca, Gümüş, Horoz, and Çakıt streams around the south-central Taurides (Ulukışla Basin), Niğde, which is a known mining province in Turkey. Several pollution and risk assessment indices were used to assess possible heavy metal pollution in the stream sediments and the associated potential ecological risks. Concentrations of As, Cd, Cu, Cr, Ni, Co, Pb, Sb, and Zn were elevated in the streams located near ancient mines, active mines, and slag piles in …
Assessment Of Acid Mine Drainage Formation Using Geochemical And Static Tests In Mutki(Bitlis, Se Turkey) Mineralization Area, Mehmet Ali̇ Gücer, Selçuk Alemdağ, Enver Akaryali
Assessment Of Acid Mine Drainage Formation Using Geochemical And Static Tests In Mutki(Bitlis, Se Turkey) Mineralization Area, Mehmet Ali̇ Gücer, Selçuk Alemdağ, Enver Akaryali
Turkish Journal of Earth Sciences
In this study, geochemical analyses, as well as short-term contact leaching and acid-base accounting tests, were carried out to determine the occurrence of acid mine drainage (AMD) by static tests in the ore stockpile areas at the Mutki Cu-Fe-Cr deposit (Bitlis, SE Turkey). According to the short-term contact leaching tests, the high enrichment in trace element concentrations in ore-bearing samples, especially in potentially toxic metals such as Cr, Cu, Mn, and Zn, were directly related to sulphide and oxide mineralizations. The pH (3.27-4.05) values of water samples, together with the classification of the intracontinental water resources, indicated that the water …
Geochemical, Stable (O, C, And B) And Radiogenic (Sr, Nd, Pb) Isotopic Data From Theeskişehir-Kızılcaören (Nw-Anatolia) And The Malatya-Kuluncak (E-Central Anatolia)F-Ree-Th Deposits, Turkey: Implications For Nature Of Carbonate-Hosted Mineralization, Okay Çi̇men, Loretta Corcoran, Corinne Kuebler, Stefanie Simonetti, Antonio Simonetti
Geochemical, Stable (O, C, And B) And Radiogenic (Sr, Nd, Pb) Isotopic Data From Theeskişehir-Kızılcaören (Nw-Anatolia) And The Malatya-Kuluncak (E-Central Anatolia)F-Ree-Th Deposits, Turkey: Implications For Nature Of Carbonate-Hosted Mineralization, Okay Çi̇men, Loretta Corcoran, Corinne Kuebler, Stefanie Simonetti, Antonio Simonetti
Turkish Journal of Earth Sciences
In Turkey, the largest fluorine (F)-rare earth element (REE)-thorium (Th) deposits are located within the Eskişehir-Kızılcaören (north-western Anatolia) and the Malatya-Kuluncak (east-central Anatolia) regions, and these are associated with Oligocene extensional alkaline volcanic and Late Cretecaous-Early Paleocene postcollisional intrusive rocks, respectively. In the Kızılcaören region, the basement units include the Triassic Karakaya Complex and the Late Cretaceous oceanic units (Neotethyan suture) that are cut and overlain by phonolite and carbonatite intrusions and lava flows. In the Kuluncak region, the plutonic rocks are mainly composed of syenite, quartz syenite, and rare monzonite, and these cut the late-Cretaceous Karapınar limestone, which hosts …
Last Glacial Climate Oscillations And Sudden Environmental Changes Investigated In Stalagmites From Southwest Sulawesi, Western Pacific, Ezgi̇ Ünal İmer, İbrahi̇m Tonguç Uysal, Emma St Pierre, Jian Xin Zhao, James Shulmeister
Last Glacial Climate Oscillations And Sudden Environmental Changes Investigated In Stalagmites From Southwest Sulawesi, Western Pacific, Ezgi̇ Ünal İmer, İbrahi̇m Tonguç Uysal, Emma St Pierre, Jian Xin Zhao, James Shulmeister
Turkish Journal of Earth Sciences
We investigated two stalagmites from the Saripa Cave and Bumi Cave in southern Sulawesi, Indonesia, using high-precision U-series dating and high-resolution trace element and C-O-Sr isotope analysis. The growth record (from 10.4 ± 0.1 ka to 77.4 ± 0.9 ka) of the Saripa Cave stalagmite (SR04-ST3) is fragmented with two major (at the top: 10.4-11.6 ka and middle: 43.8-44.7 ka sections of the stalagmite) and some short (middle and bottom sections) growth phases, interrupted by long-lasting growth hiatuses. Both the timing of the growth phases and the δ18O values for different growth phases are correlated with those of cold/dry (~22 …
Upper Paleocene-Lower Eocene Calcareous Nannofossil Stratigraphy At The Misheiti Section, Central Sinai, Egypt, Atef M. Kasem, Sherwood Wise, Mahmoud Faris, Sherif Farouk, Esam Zahran
Upper Paleocene-Lower Eocene Calcareous Nannofossil Stratigraphy At The Misheiti Section, Central Sinai, Egypt, Atef M. Kasem, Sherwood Wise, Mahmoud Faris, Sherif Farouk, Esam Zahran
Turkish Journal of Earth Sciences
Calcareous nannofossil, δ13C, δ18O, and carbonate content data were used to define and reveal the variations across the latest Paleocene-earliest Eocene interval at the Misheiti Section, Central Sinai, Egypt. The upper part of Tarawan Formation, the Esna Formation, and the lowermost Thebes Formation were included in this study. In this study, the Esna Formation is informally divided into Hanadi/Mahmiya and Abu Had members. Four calcareous nannofossil zones (NP9, NP10, NP11, and NP12) and four subzones (NP9a, NP9b, NP10a, and NP10b) were recognized. The biostratigraphic importance of significant calcareous nannofossil bioevents associated with the P/E boundary was discussed. The LOs of …
Alluvial-Lacustrine Sedimentation And Volcaniclastic Deposition In An Intracontinental Tectonic Graben: Paleoenvironmental Evolution Of The Neogene Sinanpaşa Basin, West-Central Turkey, Eli̇f Akiska, Baki̇ Erdoğan Varol
Alluvial-Lacustrine Sedimentation And Volcaniclastic Deposition In An Intracontinental Tectonic Graben: Paleoenvironmental Evolution Of The Neogene Sinanpaşa Basin, West-Central Turkey, Eli̇f Akiska, Baki̇ Erdoğan Varol
Turkish Journal of Earth Sciences
This study reports on the Sinanpaşa Basin, a typical example of the Miocene tectonic intracontinental grabens formed in West Anatolia, Turkey. The study reconstructs the paleoenvironmental and paleogeographic history of the graben based on a detailed sedimentological analysis of basin-fill deposits exposed mainly near the graben's northern and southern margins. The sedimentary paleoenvironments in the graben range from basin-margin alluvial fan systems and basin-axis fluvial distributary system to an intrabasinal shallow lake environment surrounded by peat-forming mires, changing from carbonate to more clayey, episodically evaporitic, and shifting its shorelines considerably. The spatial distribution and stratigraphic stacking of these paleoenvironments indicate …
Traces Of Mediterranean Origin Holocene Transgression In The Drainage Basin Of Riva-Çayağzı Creek Of The Black Sea (Northeastern İstanbul-Turkey), Bülent Doğan, Ahmet Karakaş, Ati̇ke Nazi̇k, İbrahi̇m Engi̇n Meri̇ç
Traces Of Mediterranean Origin Holocene Transgression In The Drainage Basin Of Riva-Çayağzı Creek Of The Black Sea (Northeastern İstanbul-Turkey), Bülent Doğan, Ahmet Karakaş, Ati̇ke Nazi̇k, İbrahi̇m Engi̇n Meri̇ç
Turkish Journal of Earth Sciences
The Riva-Çayağzı Creek (İstanbul, Black Sea) pours into the Black Sea from the coasts of Turkey. In the drainage basin of this creek, both deep and shallow drillings were undertaken, and the minimum thickness of Holocene stratigraphy was determined as 30 m. The Holocene young deposits are mainly composed of fine-grained sediments and clay, which has the most prominent thickness. The energy of water during the sedimentation process was low and stagnant in the Riva-Çayağzı Creek basin. When the marine mollusc fossils obtained from the shallow boring cores are evaluated, it can be deduced that the sea level in the …
Geochemical And Industrial Properties Of The Kejal Kaolin Deposit, Nw Iran, Tohid Nouri, Rahim Masoumi
Geochemical And Industrial Properties Of The Kejal Kaolin Deposit, Nw Iran, Tohid Nouri, Rahim Masoumi
Turkish Journal of Earth Sciences
The Kejal kaolin deposit, situated in the northwest of Iran, is considered a small part of the Hashtjin hydrothermal zone. The kaolinization process in this deposit has occurred in ignimbritic and volcanic tuff parent rocks in different grades such that severely kaolinized samples can be found in the middle section of the kaolinization profile. Kaolinite is the most abundant clay mineral in the studied samples. Quartz and cristobalite are the main minerals while anatase is the minor mineral of the kaolin samples. Among the major oxides, SiO2, Al2O3, and TiO2 show the highest concentrations in kaolin samples. The mass change …
Geochemistry And Petrography Of Beach Sands Along The Western Coast Of Ghana:Implications For Provenance And Tectonic Settings, Mahamuda Abu, Emmanuel Daanoba Sunkari
Geochemistry And Petrography Of Beach Sands Along The Western Coast Of Ghana:Implications For Provenance And Tectonic Settings, Mahamuda Abu, Emmanuel Daanoba Sunkari
Turkish Journal of Earth Sciences
The paleoweathering, provenance, and tectonic setting of sediments of the western coast of Ghana were unraveled using the geochemistry of 29 beach sands, which are characterized by coarse-, medium-, and fine-grained sizes. The coarse-grained beach sands contain higher SiO2 content (2.9-96 wt.%) than the medium-grained (4.9-94 wt.%) and fine-grained (16.1-90.7 wt.%) sands, implying that the increase in grain size is related to the increase in SiO2 content. Al2O3 and CaO concentrations are higher in the fine- and medium-grained sands than the coarse-grained sands. The beach sands are compositionally immature based on the index of compositional variable values (1.17-141) and Th/Sc …
Excess Lifetime Cancer Risk Due To Natural Radioactivity In Gümüşhane Province, Ne Turkey, Nafiz Maden, Enver Akaryali, Mehmet Ali̇ Gücer
Excess Lifetime Cancer Risk Due To Natural Radioactivity In Gümüşhane Province, Ne Turkey, Nafiz Maden, Enver Akaryali, Mehmet Ali̇ Gücer
Turkish Journal of Earth Sciences
In this study, 162 in situ measurements of 238U, 232Th, and 40K radionuclide concentrations dataset taken by the gamma-ray spectrometer in Gümüşhane, Turkey are presented. The gamma ray measurements were performed by a 512-channel, three-window gamma-ray spectrometry equipment made by GF Instruments. We first observed the radionuclides of the 238U, 232Th, and 40K values in Gümüşhane. We then calculated the hazard indices of gamma radiation such as annual effective dose equivalent (AEDE), internal and external hazard index (Hin, Hex), and excess lifetime cancer risk (ELCR) based on the radionuclide abundances of 238U, 232Th, and 40K for the first time. In …
Mathematical Modeling Of A Continuous-Flow Packed-Bed Reactor With Immobilizedlipase For Kinetic Resolution Of (R,S)-2-Pentanol, Asli Soyer Malyemez, Abdulwahap Giwa, Emi̇ne Bayraktar, Ülkü Mehmetoğlu
Mathematical Modeling Of A Continuous-Flow Packed-Bed Reactor With Immobilizedlipase For Kinetic Resolution Of (R,S)-2-Pentanol, Asli Soyer Malyemez, Abdulwahap Giwa, Emi̇ne Bayraktar, Ülkü Mehmetoğlu
Turkish Journal of Chemistry
In this study, the kinetic resolution of (R,S)-2-pentanol via transesterification to achieve S-2-pentanol, a key intermediate required in the synthesis of anti-Alzheimer drugs, was investigated in continuous-flow packed-bed reactors. The effects of residence time, substrate concentration, and operation time of the enzyme were investigated. Under steady state conditions, 50% conversion and enantiomeric excess of the substrate (ee$_{S}$)>99% were achieved at a residence time of 0.04 min. Productivity of the continuous-flow process (1.341 mmol/min/g)was about 4 times higher than that of the corresponding batch process (0.363 mmol/min/g). In addition, the mathematical modeling of the packed-bed reactor was conductedusing an axial …
Evolution Of Two Overlapping Sand-Rich Clastic Submarine Fans In The Lower Mioceneadana Basin, Southern Turkey: Contribution From A New Palaeocurrent Analysis, Daniel Bayer Da Silva, Bryan Cronin, Hasan Çeli̇k, Karin Goldberg, Benjamin Christopher Kneller, Kemal Gürbüz
Evolution Of Two Overlapping Sand-Rich Clastic Submarine Fans In The Lower Mioceneadana Basin, Southern Turkey: Contribution From A New Palaeocurrent Analysis, Daniel Bayer Da Silva, Bryan Cronin, Hasan Çeli̇k, Karin Goldberg, Benjamin Christopher Kneller, Kemal Gürbüz
Turkish Journal of Earth Sciences
A complete longitudinal profile from the continental shelf break to the basin floor includes a significant and well-exposed turbidite system at the northern edge of the Adana Basin, one of a series of foreland basins in southern Turkey. This study focused on the evolutionary interpretation of 2 coeval submarine fans, the Western Fan and the Eastern Fan, in the Upper Burdigalian-Lower Serravallian Cingöz Formation. The Western Fan was fed by a single major canyonised feeder from the west, and the Eastern Fan was fed by multiple feeder channels to the north. The Western Fan originated as a confined system with …
Latest Priabonian Larger Benthic Foraminiferal Assemblages At The Demise Of Thesoğucak Carbonate Platform (Thrace Basin And Black Sea Shelf, Nw Turkey):Implications For The Shallow Marine Biostratigraphy, Ali̇ Osman Yücel, Ercan Özcan, Ümi̇tcan Erbi̇l
Latest Priabonian Larger Benthic Foraminiferal Assemblages At The Demise Of Thesoğucak Carbonate Platform (Thrace Basin And Black Sea Shelf, Nw Turkey):Implications For The Shallow Marine Biostratigraphy, Ali̇ Osman Yücel, Ercan Özcan, Ümi̇tcan Erbi̇l
Turkish Journal of Earth Sciences
The Eocene-Oligocene transition corresponds to a significant biotic turnover globally. In shallow marine realms, the larger benthic foraminifera (LBF) belonging to most nummulitids and all orthophragminids became extinct at or near the Eocene/Oligocene boundary, reflecting the environmental deterioration. We here record the advanced developmental stages of midlatitude LBF from the Soğucak Carbonate Platform in NW Turkey on the brink of their extinction in the Tethys. The LBF assemblages in the uppermost part of the platform, exposed in Gökçetepe and Karaburun in the Thrace Basin and Black Sea shelf, are represented by the dominant occurrence of Heterostegina d'Orbigny, 1826, Spiroclypeus Douville, …
Late Eocene To Early Oligocene Palynostratigraphy Of The Western Black Sea, Easternparatethys, Recep Hayretti̇n Sancay, Zühtü Bati
Late Eocene To Early Oligocene Palynostratigraphy Of The Western Black Sea, Easternparatethys, Recep Hayretti̇n Sancay, Zühtü Bati
Turkish Journal of Earth Sciences
The Eastern Thrace and Western Black Sea basins provide unique perspectives on the palaeogeographic reconstructions of the Paratethys. Although very thick and extensive Oligocene outcrops and well sections exist in the Thrace Basin, only a few comparable sections are available in the Black Sea onshore areas. In this study, five measured stratigraphic sections of Eocene to Oligocene age from the margins of the Western Black Sea were studied and palynomorph assemblages were identified quantitatively. Index dinoflagellate cyst events and a palynological biozonation as established in the Mediterranean were applied successfully. Priabonian units contain the Aal biozone, whereas Rupelian successions were …
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Weighted Composition Operators From The Bloch Space To Nth Weighted-Typespaces, Ebrahim Abbasi, Songxiao Li, Hamid Vaezi
Turkish Journal of Mathematics
In this work, we characterize the boundedness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces. Some estimates for the essential norm of these operators are also given. As a corollary, we obtain some characterizations for the compactness of weighted composition operators from the Bloch space and the little Bloch space to $n$th weighted-type spaces.
On The Product Of Dilation Of Truncated Toeplitz Operators, Zohra Bendaoud, Nafissa Saouli
On The Product Of Dilation Of Truncated Toeplitz Operators, Zohra Bendaoud, Nafissa Saouli
Turkish Journal of Mathematics
In this paper we study when the product of two dilations of truncated Toeplitz operators gives a dilation of a truncated Toeplitz operator. We will use an approach established in a recent paper written by Ko and Lee. This approach allows us to represent the dilation of the truncated Toeplitz operator via a 2 $\times$ 2 block operator.
On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
On Extensions Of Two Results Due To Ramanujan, Yong Sup Kim, Arjunkumar Rathie, Richard B. Paris
Turkish Journal of Mathematics
The aim in this note is to provide a generalization of an interesting entry in Ramanujan's notebooks that relate sums involving the derivatives of a function $\varphi\left( t\right)$ evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ${}_3F_2$ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ${}_3F_2$(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.
A Generalization Of The Minkowski Distance And New Definitions Of The Central Conics, Harun Bariş Çolakoğlu
A Generalization Of The Minkowski Distance And New Definitions Of The Central Conics, Harun Bariş Çolakoğlu
Turkish Journal of Mathematics
In this paper, we give a generalization of the well-known Minkowski distance family in the $n$-dimensional Cartesian coordinate space. Then we consider three special cases of this family, which are also generalizations of the taxicab, Euclidean, and maximum metrics, respectively, and we determine some circle properties of them in the real plane. While we determine some properties of circles of these generalized distances, we discover a new definition of ellipses, and then we also determine a similar definition of hyperbolas, which will be new members among different metrical definitions of central conics in the Euclidean plane.
Geodesic Motions In So(2,1), İsmet Ayhan
Geodesic Motions In So(2,1), İsmet Ayhan
Turkish Journal of Mathematics
In this study,we have considered the rotational motions of a particle around the origin of the unit 2-sphere $S_2^2$ with constant angular velocity in semi-Euclidean 3-spacewithindextwo $E^3_2$, namely geodesic motions of $SO(2,1)$. Then we have obtained the vector and the matrix representations of the spherical rotations around the origin of a particle on $S_2^2$. Furthermore, we consider some relations between semi-Riemann spaces $SO(2,1)$ and $T_1S_2^2$ such as diffeomorphism and isometry. We have obtained the system of differential equations giving geodesics of Sasaki semi-Riemann manifold $(T_1S_2^2,g^S)$ . Moreover, we consider the stationary motion of a particle on $S_2^2$ corresponding to one …
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Existence And Uniqueness Of Solutions For Nonlinear Caputo Fractional Difference Equations, Churong Chen, Martin Bohner, Baoguo Jia
Turkish Journal of Mathematics
We study two cases of nabla fractional Caputo difference equations. Our main tool used is a Banach fixed pointtheorem, which allows us to give some existence and uniqueness theorems of solutions for discrete fractional Caputo equations. In addition, we develop the existence results for delta fractional Caputo difference equations, which correct ones obtained in Chen and Zhou. We present two examples to illustrate our main results.
Digital Hurewicz Theorem And Digital Homology Theory, Samira Sahar Jamil, Danish Ali
Digital Hurewicz Theorem And Digital Homology Theory, Samira Sahar Jamil, Danish Ali
Turkish Journal of Mathematics
In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we obtain two main results that make this homology different from already existing homologies of digital images. We prove digital analog of Hurewicz theorem for digital cubical singular homology. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.
Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do
Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do
Turkish Journal of Mathematics
In this work, we study max CS, min CS, max-min CS modules and their endomorphism rings. Under certain conditions (e.g., related to nonsingularity and duo-ness), we prove that a module is max CS if and only if it is min CS, and that direct sums of min (max) CS modules is again min (max) CS. Finally, symmetry of max-min CS property on the endomorphism rings of max-min CS modules is investigated.
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green's function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results.
On Geometric Applications Of Quaternions, Burcu Bektaş Demi̇rci̇, Nazim Aghayev
On Geometric Applications Of Quaternions, Burcu Bektaş Demi̇rci̇, Nazim Aghayev
Turkish Journal of Mathematics
Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane}(N)$ and $\mbox{Line}(N)$, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry …
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
On 3-Dimensional Almost Einstein Manifolds With Circulant Structures, Iva Dokuzova
Turkish Journal of Mathematics
A 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e. these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civitaconnection of the metric. Some geometric characteristics of these manifolds are obtained. Examples …
On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda
On Some Sums At The $A$-Points Of The $K$-Th Derivatives Of The Dirichlet $L$-Functions, Mohammed Mekkaoui, Abdallah Derbal, Kamel Mazhouda
Turkish Journal of Mathematics
Let $L^{(k)}(s,\chi)$ be the $k$-th derivative of the Dirichlet L-function associated with a primitive character $\chi$ mod $q$ and $a$ be a complex number. The solutions of $L^{(k)}(s,\chi)=a$ are called $a$-points. In this paper, we give an asymptotic formula for the sums
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Turkish Journal of Mathematics
Let $\mathcal{A}$ be a unital, complex normed $\ast$-algebra with the identity element $\textbf{e}$ such that the set of all algebraic elements of $\mathcal{A}$ is norm dense in the set of all self-adjoint elements of $\mathcal{A}$ and let $\{D_n\}_{n = 0}^{\infty}$ and $\{\Delta_n\}_{n = 0}^{\infty}$ be sequences of continuous linear mappings on $\mathcal{A}$ satisfying \[ \left\lbrace \begin{array}{c l} D_{n + 1}(p) = \sum_{k = 0}^{n}D_{n - k}(p)D_k(p),\\ \\ \Delta_{n + 1}(p) = \sum_{k = 0}^{n}\Delta_{n - k}(p)D_k(p), \end{array} \right. \] for all projections $p$ of $\mathcal{A}$ and all nonnegative integers $n$. Moreover, suppose that $D_0(p) = D_0(p)^2$ holds for all projections …