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Articles 31 - 60 of 404
Full-Text Articles in Physical Sciences and Mathematics
Geochemistry Of The Lake Sediments On Robert Island, South Shetland Islands, Antarctica: Implications For Weathering Processes In Polar Areas, Merve Özyurt, Yilmaz Demi̇r, Korhan Özkan, Rai̇f Kandemi̇r
Geochemistry Of The Lake Sediments On Robert Island, South Shetland Islands, Antarctica: Implications For Weathering Processes In Polar Areas, Merve Özyurt, Yilmaz Demi̇r, Korhan Özkan, Rai̇f Kandemi̇r
Turkish Journal of Earth Sciences
The preliminary results of geochemical analyses of the surface sediments from 4 lakes on Robert Island, South Shetland, Antarctica, are presented herein. The samples were collected during the Turkish Antarctic Expedition (TAE-II) in 2018. Sediment samples were obtained from the littoral zone (approximately 20 cm) of 4 different lakes exposed on the glacier-free land area on Robert Island. The lake sediments predominantly consist of fine-grained sand, clay, and silt particles. These particles include Fe-shale and graywacke geochemical characteristics. Their plagioclase index of alteration, chemical index of weathering, chemical index of alteration, and other weathering index values, suggest that the studied …
Accuracy Investigation Of Gnss-Reflectometry For Sea Level Monitoring On Horseshoe Island, Antarctica: Preliminary Results Of The Turkish Permanent Gnss Station (Tur1), Mahmut Oğuz Selbesoğlu, Hasan Hakan Yavaşoğlu, Mustafa Fahri̇ Karabulut, Özgün Oktar, Vahap Engi̇n Gülal, Hi̇mmet Karaman, Mustafa Ersel Kamaşak
Accuracy Investigation Of Gnss-Reflectometry For Sea Level Monitoring On Horseshoe Island, Antarctica: Preliminary Results Of The Turkish Permanent Gnss Station (Tur1), Mahmut Oğuz Selbesoğlu, Hasan Hakan Yavaşoğlu, Mustafa Fahri̇ Karabulut, Özgün Oktar, Vahap Engi̇n Gülal, Hi̇mmet Karaman, Mustafa Ersel Kamaşak
Turkish Journal of Earth Sciences
Antarctica is called a natural laboratory and is highly important for investigating climate change and its evolution over time. Sustainability is a critical concern due to the challenges posed by glacier melting and rising sea levels due to global warming. According to the Intergovernmental Panel on Climate Change, since the industrial age, the global mean sea level has risen by about 20 cm as a result of the increase in the average world temperature by 1 °C. Therefore, long-term observations by satellite-based techniques in and around Antarctica are of great importance for monitoring the impacts of climate change. In the …
Applicability Of Real-Time Ppp Technique In Polar Regions As An Accurate And Efficient Real-Time Positioning System, Reha Meti̇n Alkan, Serdar Erol, Bi̇lal Mutlu
Applicability Of Real-Time Ppp Technique In Polar Regions As An Accurate And Efficient Real-Time Positioning System, Reha Meti̇n Alkan, Serdar Erol, Bi̇lal Mutlu
Turkish Journal of Earth Sciences
The polar regions, which include the Arctic and Antarctic areas, attract the attention of people every day, and issues that are closely related to the future of humanity make these regions even more important. Accurate and reliable positioning in polar regions is very critical for scientific research projects and also for commercial, touristic, and other human activities. In this study, the usability and the accuracy performance of the real-time precise point positioning (RT-PPP) technique in high-latitude polar regions with harsh environmental and extreme atmospheric conditions were investigated. Within that framework, the GNSS dataset of six IGS multi-GNSS stations located at …
The Petrogenesis Of Analcime In The Coppermine Formation On Robert Island, South Shetland Islands, Antarctica, Rai̇f Kandemi̇r, Yilmaz Demi̇r, Cüneyt Şen, Ufuk Celal Yağcioğlu
The Petrogenesis Of Analcime In The Coppermine Formation On Robert Island, South Shetland Islands, Antarctica, Rai̇f Kandemi̇r, Yilmaz Demi̇r, Cüneyt Şen, Ufuk Celal Yağcioğlu
Turkish Journal of Earth Sciences
The South Shetland Islands were shaped by island arc volcanism that occurred from the Jurassic to the Quaternary. Robert Island is located in the center of this archipelago, and Coppermine Peninsula, located on the southwestern part of Robert Island, exposures significant rock outcrops of basalts and andesitic-basaltic agglomerates of the Coppermine Formation. The investigated samples were collected during Turkish Antarctic Expedition 2 (TAE-II), in March-April 2018, from the area northeast of Triplet Hill. The volcanic rocks exhibited an amygdaloidal microlithic-porphyritic texture. Subhedral to anhedral phenocrysts of labradorite, augite, and olivine were observed with holocrystalline groundmass composed of plagioclase, pyroxene, and …
Webgis-Based Data Center Design For Polar Science Studies: Simulation Of Türkiye, Müge Şenel, Hasan Hakan Yavaşoğlu, Burcu Özsoy, Hi̇mmet Karaman, Mustafa Ümi̇t Gümüşay
Webgis-Based Data Center Design For Polar Science Studies: Simulation Of Türkiye, Müge Şenel, Hasan Hakan Yavaşoğlu, Burcu Özsoy, Hi̇mmet Karaman, Mustafa Ümi̇t Gümüşay
Turkish Journal of Earth Sciences
Scientific studies concentrated in Antarctica hold great value and importance for humanity. Research projects are conducted in various disciplines on the continent, where nearly 100 research stations from 30 countries are established. Despite the challenges posed by Antarctica's natural structure, unique environment, difficult working conditions, and limited logistics opportunities, scientific research conducted there is indispensable due to the valuable information it offers. In pursuit of accessing this information, Turkish Antarctic expeditions have been organized since 2017. In this study, a polar data center was established through a web-based geographic information system (WebGIS), a significant infrastructure for the continuity of scientific …
Exploring Crowdsourcing Accountability For Mapping Antarctica: A Case Study Using 5 Years Of Social Media Data, Ayşe Gi̇z Gülnerman Gengeç
Exploring Crowdsourcing Accountability For Mapping Antarctica: A Case Study Using 5 Years Of Social Media Data, Ayşe Gi̇z Gülnerman Gengeç
Turkish Journal of Earth Sciences
The continent of Antarctica is one of the most challenging regions in terms of generating and updating geodata. Extensive research has been conducted on geodata acquisition, primarily focusing on earth observation satellites and local surveys in polar regions. Earth observation satellites offer limited spatial, temporal, and semantic data, while local surveys are constrained by polar regions' size and challenging conditions. This article delves into the crowdsourced data, aiming to significantly enhance geodata contribution in polar regions beyond current methods. To our knowledge, this study is the first of its kind to address social media data, a form of crowdsourcing, specifically …
Water Chemistry And Pigment Composition Of 13 Lakes And Ponds In Maritime Antarctica, Korhan Özkan
Water Chemistry And Pigment Composition Of 13 Lakes And Ponds In Maritime Antarctica, Korhan Özkan
Turkish Journal of Earth Sciences
The Antarctic Peninsula has been rapidly warming, resulting in changes to the abundance and surface cover of terrestrial aquatic ecosystems, as well as their ecosystem structure and function. Therefore, comparative studies of aquatic ecosystems across large latitudinal gradients can be useful in better understanding these changes and making more reliable predictions regarding the consequences of climate change. During Turkish Antarctic Expeditions in 2018 and 2019, samples were collected from 10 lakes and 3 ponds across Maritime Antarctica (north-western coasts of the Antarctic Peninsula). These lakes and ponds were located on Ardley, Robert, Livingstone, Galindez, and Horseshoe islands, covering a latitudinal …
Accuracy Assessment Of Glacier Depth Monitoring Based On Uav-Gpr On Horseshoe Island, Antarctica, Mahmut Oğuz Selbesoğlu, Mustafa Fahri̇ Karabulut, Özgün Oktar, Burak Akpinar, Oleg Vassilev, Mehmet Arkali, Şeyma Nur Tufan, Alptuğ Şeref Ayyildiz, Esra Günaydin, Ati̇lla Yilmaz, Doğaç Baybars Işiler, Burcu Özsoy
Accuracy Assessment Of Glacier Depth Monitoring Based On Uav-Gpr On Horseshoe Island, Antarctica, Mahmut Oğuz Selbesoğlu, Mustafa Fahri̇ Karabulut, Özgün Oktar, Burak Akpinar, Oleg Vassilev, Mehmet Arkali, Şeyma Nur Tufan, Alptuğ Şeref Ayyildiz, Esra Günaydin, Ati̇lla Yilmaz, Doğaç Baybars Işiler, Burcu Özsoy
Turkish Journal of Earth Sciences
Unmanned aerial systems have a wide range of uses in studying the impacts of climate change over several fields. Recently, its combination with a ground-penetrating radar (GPR) technology has been demonstrated to be highly effective for surveying glaciers, especially in difficult and inaccessible terrains like Antarctica. In this context, this study focused on exploring the potential of using an unmanned aerial vehicle (UAV)-GPR to measure the depth of glaciers on Horseshoe Island, West Antarctica. The data were collected during the seventh Turkish Antarctic Expedition (TAE-VII) in February and March 2023, within the scope of the international project titled "Glacier monitoring …
The Geo/Thermochronology Of Dismal Island (Marguerite Bay, Antarctic Peninsula), Fati̇h Karaoğlan, Burcu Karataş, Yavuz Özdemi̇r, Erhan Gülyüz, Oleg Vassilev, Mahmut Oğuz Selbesoğlu, Semi̇h Gi̇ldi̇r
The Geo/Thermochronology Of Dismal Island (Marguerite Bay, Antarctic Peninsula), Fati̇h Karaoğlan, Burcu Karataş, Yavuz Özdemi̇r, Erhan Gülyüz, Oleg Vassilev, Mahmut Oğuz Selbesoğlu, Semi̇h Gi̇ldi̇r
Turkish Journal of Earth Sciences
Dismal Island is located at the entrance of Marguerite Bay between Adelaide Island to the northeast and Alexander Island to the southwest within the Antarctic Peninsula (AP). Its unique position between Alexander and Adelaide islands provides the opportunity to perform testing and link these regions through Cenozoic magmatism and tectonics due to the subduction of the Pacific plate beneath the AP along the northern margin. Dismal Island was visited in February 2021 within the framework of the sixth Turkish Antarctic Expedition (TAE-VI). Thirteen samples were collected for petrography, geochronology, and low-temperature thermochronology (LTT). Of the samples, 3 were dated using …
Almacık Complex-An Exhumed Lower To Middle Crust In Northwest Anatolia, Aral Okay, Andrew R.C. Kylander-Clark, Sarah Sherlock
Almacık Complex-An Exhumed Lower To Middle Crust In Northwest Anatolia, Aral Okay, Andrew R.C. Kylander-Clark, Sarah Sherlock
Turkish Journal of Earth Sciences
The Almacık Complex is a tectonic unit of high-grade metamorphic rocks in the Intra-Pontide Suture Zone in northwest Turkey. It consists mainly of amphibolite, metaultramafic rock, and gneiss, which are intruded by numerous pre-, syn-, and posttectonic felsic veins. The Almacık Complex is variously interpreted as a Cretaceous or Neoproterozoic ophiolite, or a Permian mafic-ultramafic complex representing the middle to lower crust of the Sakarya Zone. Herein, new petrological and geochronological data were presented from the Almacık Complex. Two-pyroxene geothermometry in the metawebsterites indicated that the Almacık Complex has undergone upper amphibolite-facies metamorphism at 750 ± 30 °C and 8 …
More Evidence Of Tropical Conditions In The Middle Eocene Climatic Optimum (Meco) With New Fossil Woods From North-Central Türkiye, Ünal Akkemi̇k, Fi̇kret Koçbulut, Özlem Toprak, Umut Tunç
More Evidence Of Tropical Conditions In The Middle Eocene Climatic Optimum (Meco) With New Fossil Woods From North-Central Türkiye, Ünal Akkemi̇k, Fi̇kret Koçbulut, Özlem Toprak, Umut Tunç
Turkish Journal of Earth Sciences
Fossil wood descriptions are among the most important indicators in understanding forest structures across geological ages. This study was carried out to obtain new findings about the Middle Eocene Climate Optimum (MECO) period of Anatolia with new samples collected from the Middle Eocene-aged fossil area near Amasya-Göynücek. The fossil area falls into the Göynücek Volcanics in the region. Transverse, radial, and tangential microscopic sections were taken from three new fossil wood samples, and all identifications were performed on these microscopic sections. As a result, the fossil species were identified as Pinuxylon cf. P. tarnocziense, cf. Dichrostachyoxylon zirkelii, and Laurinoxylon perseamimatus …
Middle Eocene Alveolina-Dominated Benthic Foraminiferal Assemblages Of The Western Flank Of The Isparta Angle (Sw Türkiye): Taxonomy, Biostratigraphy, Microfacies Analysis, And Paleoenvironmental Implications, Alper Bozkurt, Muhi̇tti̇n Görmüş, Banu Türkmen Bozkurt
Middle Eocene Alveolina-Dominated Benthic Foraminiferal Assemblages Of The Western Flank Of The Isparta Angle (Sw Türkiye): Taxonomy, Biostratigraphy, Microfacies Analysis, And Paleoenvironmental Implications, Alper Bozkurt, Muhi̇tti̇n Görmüş, Banu Türkmen Bozkurt
Turkish Journal of Earth Sciences
Middle Eocene formations of the western part of the Isparta Angle contain abundant larger benthic foraminifera (LBF). Twelve species belonging to the genus Alveolina, including A. callosa, A. fragilis, A. aff. fusiformis, A. gigantea, A. cf. gigantea, A. hottingeri, A. kieli, A. levantina, A. nuttalli, A. cf. obtusa, A. stipes, and A. tenuis have been identified throughout the two measured sections from Dinar and Çardak (SW Türkiye). The investigated assemblages, consisting also of nummulitids, orthophragminids, textulariids, rotaliids, and miliolids, allow us to assign the Suçıkan section to shallow benthic zone 13 (SBZ13) and the Karabayır section to SBZ17. Based on …
Mapping Crustal Structure And Deformation Using Gravity Data In The Bursa Basin And Surroundings, Türkiye, Bülent Oruç, Emi̇r Balkan
Mapping Crustal Structure And Deformation Using Gravity Data In The Bursa Basin And Surroundings, Türkiye, Bülent Oruç, Emi̇r Balkan
Turkish Journal of Earth Sciences
The structure and deformation of the Bursa Basin and surroundings was carried out through the interpretation of Bouguer gravity and isostatic residual gravity anomalies. The spectral analysis was carried out on Bouguer anomalies to obtain the average depths of the crustal structure under the Bursa Basin and surroundings. Parker-Oldenburg algorithm was used to estimate the depths of the interface between upper and lower crust with respect to an average depth and density contrast. We used Mallick-Sharma algorithm to separate the regional gravity anomalies from Bouguer anomalies to estimate the isostatic residual gravity anomalies. Euler deconvolution and two-dimensional density contrast distribution …
Interpreting Structural Configuration Of The Sengkang Basin Of Indonesia Using Edge Detection And 3-D Euler Deconvolution To Satellite Gravity Data, Jamhir Safani, Khalil Ibrahim, Wa Deni, Al Rubaiyn, Firdaus Firdaus, Harisma Harisma
Interpreting Structural Configuration Of The Sengkang Basin Of Indonesia Using Edge Detection And 3-D Euler Deconvolution To Satellite Gravity Data, Jamhir Safani, Khalil Ibrahim, Wa Deni, Al Rubaiyn, Firdaus Firdaus, Harisma Harisma
Turkish Journal of Earth Sciences
The East Walanae Fault Zone and the West Walanae Fault Zone are the two active fault segments in the south arm of Sulawesi. These fault segments are responsible for the formation of the Sengkang Basin. This geological complexity makes the Sengkang Basin a very interesting area to study. This research aims to (1) identify basin boundaries and lithological contacts; (2) estimate the positions of fault segments; and (3) model the basement beneath the Sengkang Basin. The free-air gravity anomaly from the GGMPlus dataset is employed and then corrected using Bouguer and terrain corrections to provide the complete Bouguer gravity anomaly …
A Study On The Magnetite Skarn Mineralization (Gümüşhane, Türkiye): A Magnetic Survey, Ferkan Si̇pahi̇, Münür Burhan Sadiklar, Mehmet Ali̇ Gücer, Ali̇ Aydin, Rasi̇m Taylan Kara
A Study On The Magnetite Skarn Mineralization (Gümüşhane, Türkiye): A Magnetic Survey, Ferkan Si̇pahi̇, Münür Burhan Sadiklar, Mehmet Ali̇ Gücer, Ali̇ Aydin, Rasi̇m Taylan Kara
Turkish Journal of Earth Sciences
Iron (Fe)-skarn mineralizations (Çambaşı, Dereli, Eğrikar, Karadağ, Kopuz, Sekü, Donguldere, Arnastal, Özdil, Ögene, İkizdere, Ovit Dağı, Kartiba, etc.) in the eastern part of the Pontides (NE Türkiye) are accommodated in the Pontide paleomagmatic arc and the eastern part of the Pontides Metallogenic Belt containing numerous various deposits. Fe-skarn mineralization around the Arnastal Plateau (Gümüşhane-Türkiye) is fragmentary in this area, which is covered with plants (grasses, flowers, etc.). Thus, it was attempted to describe the subsurface structures and Fe mineralization using an interpretation of the available geological and existing magnetic data in this area. Granitoid and volcano-sedimentary series (Upper Cretaceous) outcrop …
An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak
An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak
Turkish Journal of Mathematics
In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.
Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying
Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying
Turkish Journal of Mathematics
In this paper, we introduce the fibonomial sequence spaces $b_{p}^{r,s,F}$ and $b_{\infty}^{r,s,F},$ and show that these are BK-spaces. Also, we prove that these new spaces are linearly isomorphic to $\ell_{p}$ and $\ell_{\infty}.$ Moreover, we determine the $\alpha$-, $\beta$-, $\gamma$-duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space $b_{p}^{r,s,F}.$
Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu
Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu
Turkish Journal of Mathematics
The paper presents existence results of $(\phi,\varphi)$ best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory.
Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória
Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória
Turkish Journal of Mathematics
Motivated by circular complex interval arithmetic, some operations on closed balls in $\mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $\mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n \in \{3, 7\}$, are studied. In addition, certain equations involving the defined multiplications are solved.
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic
Turkish Journal of Mathematics
This paper presents a generalization of the concepts of partial-$A$-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial-$A$-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left $p$-partial-$A$-isometry as a broader class of operators, including partial-$A$-isometry and left polynomially partial isometry. Some basic properties of a left $p$-partial-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation …
Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?
Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?
Turkish Journal of Mathematics
In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on $\theta$-continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every $\theta$-continuous function is continuous if topologies are generated by $\theta$-open sets and we will give an example of a weakly continuous function which is not $\tau_\theta$-continuous. This will complete the diagram of relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous, weakly continuous, and faintly continuous functions.
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
A New Approaching Method For Linear Neutral Delay Differential Equations By Using Clique Polynomials, Şuayi̇p Yüzbaşi, Mehmet Emi̇n Tamar
Turkish Journal of Mathematics
This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating $y^{\prime}(u)$ using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to …
Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman
Involutive Automorphisms And Derivations Of The Quaternions, Eyüp Kizil, Adriano Da Silva, Okan Duman
Turkish Journal of Mathematics
Let $Q=(\frac{a,b}{{\Bbb R}})$ denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra $H$ of Hamilton's quaternions. We have presented explicitly in \cite{Kizil-Alagoz} the matrix of a typical derivation of $Q$. Given a derivation $d\in Der(H)$, we show that the matrix $D\in M_{3}({\Bbb R})$ that represents $d$ on the linear subspace $% H_{0}\simeq {\Bbb R}^{3}$ of pure quaternions provides a pair of idempotent matrices $AdjD$ and $-D^{2}$ that correspond bijectively to the involutary matrix $\Sigma $ of a quaternion involution $\sigma $ and present several equations involving these matrices. In particular, …
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev
Invariant Subspaces Of Operators Via Berezin Symbols And Duhamel Product, Mübari̇z T. Garayev
Turkish Journal of Mathematics
The Berezin symbol $\tilde{A}$ of an operator $A$ on the reproducing kernel Hilbert space $\mathcal{H}\left( \Omega\right) $ over some set $\Omega$ with the reproducing kernel $k_{\lambda}$ is defined by \[ \tilde{A}(\lambda)=\left\langle {A\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}}\right\Vert }},\frac{{k_{\lambda}}}{{\left\Vert {k_{\lambda}% }\right\Vert }}}\right\rangle ,\ \lambda\in\Omega. \] We study the existence of invariant subspaces for Bergman space operators in terms of Berezin symbols.
Generalized Pell Graphs, Vesna Irsi̇c, Sandi Klavzar, Eli̇f Tan
Generalized Pell Graphs, Vesna Irsi̇c, Sandi Klavzar, Eli̇f Tan
Turkish Journal of Mathematics
In this paper, generalized Pell graphs $\Pi _{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi _{n,k}$ is a median graph, and that $\Pi _{n,k}$ embeds into a Fibonacci cube.
Interpolation Polynomials Associated To Linear Recurrences, Muhammad Syifa'ul Mufid, Laszlo Szalay
Interpolation Polynomials Associated To Linear Recurrences, Muhammad Syifa'ul Mufid, Laszlo Szalay
Turkish Journal of Mathematics
Assume that $(G_n)_{n\in\mathbb{Z}}$ is an arbitrary real linear recurrence of order $k$. In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by $(t,G_t)$ ($n_0\le t\le n_1$). The main result is an explicit formula depends on the explicit formula of $G_n$ and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of $(G_n)$. During the investigations, we developed certain formulae related to the finite differences.
Free Ordered Products-Ordered Semigroup Amalgams-Ordered Dominions, Michael Tsingelis
Free Ordered Products-Ordered Semigroup Amalgams-Ordered Dominions, Michael Tsingelis
Turkish Journal of Mathematics
Given an indexed family $\left\{ \left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right),i\in I \right\}$ of disjoint ordered semigroups, we construct an ordered semigroup having $\left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right)$, $i\in I$ as subsemigroups (with respect to the operation and order relation of each $\left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right)$, $i\in I$). This ordered semigroup is the free ordered product ${{\underset{i\in I}{\mathop{\Pi }}\,}^{*}}{{S}_{i}}$ of the family $\left\{ {{S}_{i}},i\in I \right\}$ and we give the crucial property which essentially characterizes the free products. Next we study the same problem in the case that the family $\left\{ \left( {{S}_{i}},{{\cdot }_{i}},{{\le }_{i}} \right),i\in I \right\}$ of ordered …
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves, Karol Gryszka
Proximality And Transitivity In Relation To Points That Are Asymptotic To Themselves, Karol Gryszka
Turkish Journal of Mathematics
We discuss dynamical systems that exhibit at least one weakly asymptotically periodic point. In the general case we prove that the system becomes trivial (it is either a periodic point or a fixed point) provided it is equicontinuous and transitive. This result can be used to provide a simple characterization of periodic points in transitive systems. We also discuss systems whose orbits are both proximal and weakly asymptotically periodic. As a result, we obtain a more general tool to detect mutual dynamics between two close orbits which need not be bounded (or have the empty limit set).
Some Congruences With $Q-$Binomial Sums, Neşe Ömür, Zehra Betül Gür, Si̇bel Koparal, Lai̇d Elkhiri
Some Congruences With $Q-$Binomial Sums, Neşe Ömür, Zehra Betül Gür, Si̇bel Koparal, Lai̇d Elkhiri
Turkish Journal of Mathematics
In this paper, using some combinatorial identities and congruences involving $q-$harmonic numbers, we establish congruences that for any odd prime $p$ and any positive integer $\alpha$,% \begin{equation*} \text{ }\sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}\frac{% q^{-\alpha npk+ n\tbinom{k+1}{2}+2k}}{[k]_{q}}{\alpha p-1 \brack k}_{q}^{n} \pmod{[p]_{q}^{2}} , \end{equation*}% and \begin{equation*} \sum\limits_{k=1 \pmod{2}}^{p-1}(-1)^{nk}q^{-\alpha npk+ n\tbinom{k+1}{2}+k}{\alpha p-1 \brack k}_{q}^{n}% \widetilde{H}_{k}(q)\pmod{[p]_{q}^{2}} ,\text{ } \end{equation*}% where $n$ is any integer.
Operator Index Of A Nonsingular Algebraic Curve, Anar Dosi̇
Operator Index Of A Nonsingular Algebraic Curve, Anar Dosi̇
Turkish Journal of Mathematics
The present paper is devoted to a scheme-theoretic analog of the Fredholm theory. The continuity of the index function over the coordinate ring of an algebraic variety is investigated. It turns out that the index is closely related to the filtered topology given by finite products of maximal ideals. We prove that a variety over a field possesses the index function on nonzero elements of its coordinate ring iff it is an algebraic curve. In this case, the index is obtained by means of the multiplicity function from its normalization if the ground field is algebraically closed.