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Density Functional Theory Calculations Of Equilibrium Oxygen Isotope Fractionation Between Borate Minerals And Aqueous Fluids, Hai-Zhen Wei, Martin Palmer, Jun-Lin Wang, Shao-Yong Jiang, Simon V. Hohl, Yuan-Feng Zhu, Chun Huan, Miao-Miao Zhang, Yeşi̇m Yücel Öztürk
Density Functional Theory Calculations Of Equilibrium Oxygen Isotope Fractionation Between Borate Minerals And Aqueous Fluids, Hai-Zhen Wei, Martin Palmer, Jun-Lin Wang, Shao-Yong Jiang, Simon V. Hohl, Yuan-Feng Zhu, Chun Huan, Miao-Miao Zhang, Yeşi̇m Yücel Öztürk
Turkish Journal of Earth Sciences
Borax, ulexite, and colemanite minerals are by far the most important economic source of boron and occur almost exclusively in nonmarine evaporite deposits. While much is known about the geological setting in which they are found, surprisingly little is known about the chemical and physical properties of the brines from which they are formed. Oxygen isotope studies have the potential to reveal important new information regarding borate formation, but unlike most other common oxygen-bearing salts precipitated from brines, there are no experimental data regarding the oxygen isotope fractionation factors between borates and brines. As a first attempt to address this …
A Review Of The Geothermal System Evolution And Distribution In The Central Anatolian Crystalline Complex (Türkiye), Mehmet Furkan Şener, Muhammed Zeynel Öztürk, Alper Baba
A Review Of The Geothermal System Evolution And Distribution In The Central Anatolian Crystalline Complex (Türkiye), Mehmet Furkan Şener, Muhammed Zeynel Öztürk, Alper Baba
Turkish Journal of Earth Sciences
Türkiye is located in the Mediterranean sector of the Alpine-Himalayan tectonic belt and is among the foremost seven countries in the world having an abundance of geothermal resources. The Central Anatolian Crystalline Complex (CACC) is one of the most important geothermal regions in Türkiye. This study aims to evaluate the geothermal system of CACC using the geological, structural, and hydrogeochemical properties that were obtained from previous studies. The present study investigated and evaluated the hydrogeochemical and isotopic properties of 762 water samples belonging to 45 different localities from 41 scientific studies. The result shows that CACC has different heat sources …
Dynamics Of A Giant Slow Landslide Complex Along The Coast Of The Aral Sea, Central Asia, Gökhan Aslan, Marcello De Michele, Daniel Raucoules, François Renard, John Dehls, Ivanna Penna, Reginald Hermanns, Zi̇yadi̇n Çakir
Dynamics Of A Giant Slow Landslide Complex Along The Coast Of The Aral Sea, Central Asia, Gökhan Aslan, Marcello De Michele, Daniel Raucoules, François Renard, John Dehls, Ivanna Penna, Reginald Hermanns, Zi̇yadi̇n Çakir
Turkish Journal of Earth Sciences
We report here a slow-moving landslide complex of the lateral spreading type revealed by Sentinel-1 interferometric timeseries analysis. Located along the western coast of the Aral Sea, with a >150-km length and 3-km width, a giant active landslide complex, slides with a constant velocity of up to 60 mm/year. Systematic subsidence up to 5 mm/year is also observed along narrow strips of terraces that appear to result from rotations of fault-bounded blocks. The landslide deformation velocity does not correlate with the annual variations of the water level in the southwestern lake of the Aral Sea during the observation period of …
Mineralogical-Petrographical Features, Geochemical Characteristics, And S Isotope Variability Of Pb-Zn Deposits In The Sakarya Fragment Of The Biga Peninsula (Nw Türkiye), Gökhan Demi̇rela, Si̇nan Akiska, Eli̇f Akiska
Mineralogical-Petrographical Features, Geochemical Characteristics, And S Isotope Variability Of Pb-Zn Deposits In The Sakarya Fragment Of The Biga Peninsula (Nw Türkiye), Gökhan Demi̇rela, Si̇nan Akiska, Eli̇f Akiska
Turkish Journal of Earth Sciences
The Biga Peninsula in northwestern Anatolia, a part of the Alpine-Himalayan orogenic belt, has a complex geology that was formed following the closure of the northern branch of the Neotethys. Intense volcanism and plutonism in the area from the Eocene to the Middle Miocene period caused several Pb-Zn-Cu±Ag±Au deposits to form. The geometry of the mineralizations is largely made up of polymetallic veins, manto-chimneys, and irregular replacement bodies. Ore-bearing and host rocks in the mineralization zones and the wall rocks outside the mineralization zones were compiled in this study. The most common minerals in the skarn zones are garnet, pyroxene, …
Using T-Distributed Stochastic Neighbor Embedding For Visualization And Segmentation Of 3d Point Clouds Of Plants, Heli̇n Dutağaci
Using T-Distributed Stochastic Neighbor Embedding For Visualization And Segmentation Of 3d Point Clouds Of Plants, Heli̇n Dutağaci
Turkish Journal of Electrical Engineering and Computer Sciences
In this work, the use of t-SNE is proposed to embed 3D point clouds of plants into 2D space for plant characterization. It is demonstrated that t-SNE operates as a practical tool to flatten and visualize a complete 3D plant model in 2D space. The perplexity parameter of t-SNE allows 2D rendering of plant structures at various organizational levels. Aside from the promise of serving as a visualization tool for plant scientists, t-SNE also provides a gateway for processing 3D point clouds of plants using their embedded counterparts in 2D. In this paper, simple methods were proposed to perform semantic …
Dynamic Deep Neural Network Inference Via Adaptive Channel Skipping, Meixia Zou, Xiuwen Li, Jinzheng Fang, Hong Wen, Weiwei Fang
Dynamic Deep Neural Network Inference Via Adaptive Channel Skipping, Meixia Zou, Xiuwen Li, Jinzheng Fang, Hong Wen, Weiwei Fang
Turkish Journal of Electrical Engineering and Computer Sciences
Deep neural networks have recently made remarkable achievements in computer vision applications. However, the high computational requirements needed to achieve accurate inference results can be a significant barrier to deploying DNNs on resource-constrained computing devices, such as those found in the Internet-of-things. In this work, we propose a fresh approach called adaptive channel skipping (ACS) that prioritizes the identification of the most suitable channels for skipping and implements an efficient skipping mechanism during inference. We begin with the development of a new gating network model, ACS-GN, which employs fine-grained channel-wise skipping to enable input-dependent inference and achieve a desirable balance …
Joint Intent Detection And Slot Filling For Turkish Natural Language Understanding, Osman Büyük
Joint Intent Detection And Slot Filling For Turkish Natural Language Understanding, Osman Büyük
Turkish Journal of Electrical Engineering and Computer Sciences
Intent detection and slot filling are two crucial subtasks of a text-based goal-oriented dialogue system. In a goal-oriented dialogue system, users interact with the system to complete a goal (or to fulfill their intent) and provide the necessary information (slot values) to achieve that goal. Therefore, a user?s text input includes information about the user?s intent and contains required slot values. Recently, joint models that simultaneously detect the intent and extract the slots are proposed to benefit from the interaction between the two tasks. The proposed methods are usually tested using benchmark data sets in English such as ATIS and …
Transforming Temporal-Dynamic Graphs Into Time-Series Data For Solving Event Detection Problems, Kutay Taşci, Fuat Akal
Transforming Temporal-Dynamic Graphs Into Time-Series Data For Solving Event Detection Problems, Kutay Taşci, Fuat Akal
Turkish Journal of Electrical Engineering and Computer Sciences
Event detection on temporal-dynamic graphs aims at detecting significant events based on deviations from the normal behavior of the graphs. With the widespread use of social media, many real-world events manifest as social media interactions, making them suitable for modeling as temporal-dynamic graphs. This paper presents a workflow for event detection on temporal-dynamic graphs using graph representation learning. Our workflow leverages generated embeddings of a temporal-dynamic graph to reframe the problem as an unsupervised time-series anomaly detection task. We evaluated our workflow on four distinct real-world social media datasets and compared our results with the related work. The results show …
Recognizing Handwritten Digits Using Spiking Neural Networks With Learning Algorithms Based On Sliding Mode Control Theory, Yeşi̇m Öni̇z, Mehmet Ayyildiz
Recognizing Handwritten Digits Using Spiking Neural Networks With Learning Algorithms Based On Sliding Mode Control Theory, Yeşi̇m Öni̇z, Mehmet Ayyildiz
Turkish Journal of Electrical Engineering and Computer Sciences
In this paper, a spiking neural network (SNN) has been proposed for recognizing the digits written on the LCD screen of an experimental setup. The convergence of the learning algorithm has been ensured by using sliding mode control (SMC) theory and the Lyapunov stability method for the adaptation of the network parameters. The spike response model (SRM) has been utilized in the design of the SNN. The performance of the proposed learning scheme has been evaluated both on the experimental data and on the MNIST dataset. The simulated and experimental results of the SNN structure have been compared with the …
A Machine Learning Approach For Dyslexia Detection Using Turkish Audio Records, Tuğberk Taş, Muhammed Abdullah Bülbül, Abas Haşi̇moğlu, Yavuz Meral, Yasi̇n Çalişkan, Gunay Budagova, Mücahi̇d Kutlu
A Machine Learning Approach For Dyslexia Detection Using Turkish Audio Records, Tuğberk Taş, Muhammed Abdullah Bülbül, Abas Haşi̇moğlu, Yavuz Meral, Yasi̇n Çalişkan, Gunay Budagova, Mücahi̇d Kutlu
Turkish Journal of Electrical Engineering and Computer Sciences
Dyslexia is a learning disorder, characterized by impairment in the ability to read, spell, and decode letters. It is vital to detect dyslexia in earlier stages to reduce its effects. However, diagnosing dyslexia is a time-consuming and costly process. In this paper, we propose a machine-learning model that predicts whether a Turkish-speaking child has dyslexia using his/her audio records. Therefore, our model can be easily used by smart phones and work as a warning system such that children who are likely to be dyslexic according to our model can seek an examination by experts. In order to train and evaluate, …
Direct Pore-Based Identification For Fingerprint Matching Process, Vedat Delican, Behçet Uğur Töreyi̇n, Ege Çeti̇n, Ayli̇n Yalçin Saribey
Direct Pore-Based Identification For Fingerprint Matching Process, Vedat Delican, Behçet Uğur Töreyi̇n, Ege Çeti̇n, Ayli̇n Yalçin Saribey
Turkish Journal of Electrical Engineering and Computer Sciences
Fingerprints are one of the most important scientific proof instruments in solving forensic cases. Identification in fingerprints consists of three levels based on the flow direction of the papillary lines at the first level, the minutiae points at the second level, and the pores at the third level. The inadequacy of existing imaging systems in detecting fingerprints and the lack of pore details at the desired level limit the widespread use of third-level identification. The fact that fingerprints with images based on pores in the unsolved database are not subjected to any evaluation criteria and remain in the database reveals …
Rank Of Kozlu Formation Coals In The Zonguldak Basin: Implications For Coalbed Gas, Mehmet Namik Yalçin, Cemi̇l Seyi̇s, Sedat İnan
Rank Of Kozlu Formation Coals In The Zonguldak Basin: Implications For Coalbed Gas, Mehmet Namik Yalçin, Cemi̇l Seyi̇s, Sedat İnan
Turkish Journal of Earth Sciences
Carboniferous bituminous coals of the Zonguldak Basin have been mined for over a century. Due to underground mining activity, there have been several fatal incidents related to gas explosions. The gas content of the coals varies greatly in the basin mainly based on coal maturity (rank), increasing with increasing coal depth. In this study, we report a map for coal depth and coal rank in the Kozlu-Üzülmez-Karadon districts of Zonguldak Basin with hope the that it would aid coal gas exploration/exploitation and also coal gas degassing efforts for safer underground mining production in the Zonguldak Basin.
Zircon Grain Shape Parameters From Ignimbrites Of The Central Anatolian Volcanic Province (Cavp) With Implications For Petrogenetic Processes, Lütfi̇ye Akin
Turkish Journal of Earth Sciences
Zircon morphology parameters reflect the physicochemical conditions during crystallization and can be modified by different processes. Zircon populations from Miocene-Pliocene ignimbrites of the Central Anatolian Volcanic Province (CAVP) were studied to reveal relations between the external morphology of zircons and petrogenetic processes. Descriptive grain shape parameters (e.g., minor and major axes, area, perimeter, aspect ratio, roundness, and circularity) were automatically measured from transmitted light images of zircons by a graphical application called AnalyZr. Principal component and cluster analysis were used to determine potential shape descriptors (perimeter, major and minor axis length, and maximum and minimum Feret) for characterizing grains from …
Stepwise Dynamic Nearest Neighbor (Sdnn): A New Algorithm For Classification, Deni̇z Karabaş, Derya Bi̇rant, Peli̇n Yildirim Taşer
Stepwise Dynamic Nearest Neighbor (Sdnn): A New Algorithm For Classification, Deni̇z Karabaş, Derya Bi̇rant, Peli̇n Yildirim Taşer
Turkish Journal of Electrical Engineering and Computer Sciences
Although the standard k-nearest neighbor (KNN) algorithm has been used widely for classification in many different fields, it suffers from various limitations that abate its classification ability, such as being influenced by the distribution of instances, ignoring distances between the test instance and its neighbors during classification, and building a single/weak learner. This paper proposes a novel algorithm, called stepwise dynamic nearest neighbor (SDNN), which can effectively handle these problems. Instead of using a fixed parameter k like KNN, it uses a dynamic neighborhood strategy according to the data distribution and implements a new voting mechanism, called stepwise voting. Experimental …
Cognitive Load Detection Using Ci-Ssa For Eeg Signal Decomposition And Nature-Inspired Feature Selection, Jammisetty Yedukondalu, Lakhan Dev Sharma
Cognitive Load Detection Using Ci-Ssa For Eeg Signal Decomposition And Nature-Inspired Feature Selection, Jammisetty Yedukondalu, Lakhan Dev Sharma
Turkish Journal of Electrical Engineering and Computer Sciences
Cognitive load detection is eminent during the mental assignment of neural activity because it indicates how the brain reacts to stimuli. The level of cognitive load experienced during mental arithmetic tasks can be determined using an electroencephalogram (EEG). The EEG data were collected from publicly available datasets, namely, mental arithmetic task (MAT) and simultaneous task workload (STEW). The first phase comprises decomposing the electroencephalogram (EEG) signal into intrinsic mode functions (IMFs) using circulant singular spectrum analysis (Ci-SSA). In the second phase, entropy-based features were evaluated using IMFs. After that, the extracted features were fed to nature-inspired feature selection algorithms: genetic …
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834--2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup $S$ an ordered hypersemigroup $V$ having a greatest element ($poe$-hypersemigroup) can be constructed in such a way that there exists a pseudoideal $T$ of $S$ such that $S$ is isomorphic to $T$. If $S$ does not have a greatest element, then this can be regarded …
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz
Turkish Journal of Mathematics
The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{\infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{\infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.
Higher Topological Complexity Of A Map, Cesar Augusto Ipanaque Zapata, Jesús González
Higher Topological Complexity Of A Map, Cesar Augusto Ipanaque Zapata, Jesús González
Turkish Journal of Mathematics
The higher topological complexity of a space $X$, $\text{TC}_r(X)$, $r=2,3,\ldots$, and the topological complexity of a map $f$, $\text{TC}(f)$, have been introduced by Rudyak and Pavesiç, respectively, as natural extensions of Farber's topological complexity of a space. In this paper we introduce a notion of higher topological complexity of a map $f$, $\text{TC}_{r,s}(f)$, for $1\leq s\leq r\geq2$, which simultaneously extends Rudyak's and Pavesiç notions. Our unified concept is relevant in the $r$-multitasking motion planning problem associated to a robot devise when the forward kinematics map plays a role in $s$ prescribed stages of the motion task. We study the homotopy …
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^\ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem …
Extended Calculus On ${\Cal O}({\Mathbb C}_{H}^{1\Vert1})$, Sali̇h Çeli̇k
Extended Calculus On ${\Cal O}({\Mathbb C}_{H}^{1\Vert1})$, Sali̇h Çeli̇k
Turkish Journal of Mathematics
We give an extended calculus over the function algebra on $h$-deformed superplane. For this, we extend the $(h_1,h_2)$-deformed differential calculus on the $h$-deformed superplane by adding inner derivations. We reformulate the results with an $R$-matrix and present the tensor product realization of the wedge product. We also discuss Cartan calculus via a contraction.
On The Monoid Of Partial Isometries Of A Cycle Graph, Vitor H. Fernandes, Tania Paulista
On The Monoid Of Partial Isometries Of A Cycle Graph, Vitor H. Fernandes, Tania Paulista
Turkish Journal of Mathematics
In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.
The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari
The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari
Turkish Journal of Mathematics
Using the Brzdek fixed point theorem, we establish the Hyers?Ulam stability problem of Drygas functional equations \begin{equation} \delta(x+y-z)+\delta(x-y)+\delta(-y-z)+\delta(y)=\delta(x-y-z)+\delta(y-z)+\delta(x+y)+\delta(-y)\nonumber \end{equation} for all $x,y,z\in A$.
Modification Of The Sector Theorem Of Kondo-Tanaka, Eric Choi
Modification Of The Sector Theorem Of Kondo-Tanaka, Eric Choi
Turkish Journal of Mathematics
Kondo-Tanaka proved that if a rotationally symmetric plane $M_m$ is von Mangoldt or Cartan-Hadamard outside a compact set and has finite total curvature, then it has a sector with no pair of cut points. We show that the condition of finite total curvature can be removed. %The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations.
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.
Identities Involving Special Functions From Hypergeometric Solution Of Algebraic Equations, Juan Luis Gonzalez-Santander
Identities Involving Special Functions From Hypergeometric Solution Of Algebraic Equations, Juan Luis Gonzalez-Santander
Turkish Journal of Mathematics
From the algebraic solution of $x^{m}-x+t=0$ for $m=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these results, and applying other known reduction formulas of hypergeometric functions, we derive new reduction formulas of special functions as well as the calculation of some definite integrals in terms of elementary functions.
Fractional Semilinear Neumann Problem With Critical Nonlinearity, Zhenfeng Jin, Hongrui Sun
Fractional Semilinear Neumann Problem With Critical Nonlinearity, Zhenfeng Jin, Hongrui Sun
Turkish Journal of Mathematics
In this paper, we consider the following critical fractional semilinear Neumann problem \begin{equation*} \begin{cases} (-\Delta)^{1/2}u+\lambda u=u^{\frac{n+1}{n-1}},~u>0\quad&\, \mathrm{in}\ \Omega,\\ \partial_\nu{u}=0 &\mathrm{on}\ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^n~(n\geq5)$ is a smooth bounded domain, $\lambda>0$ and $\nu$ is the outward unit normal to $\partial\Omega$. We prove that there exists a constant $\lambda_0>0$ such that the above problem admits a minimal energy solution for $\lambda<\lambda_0$. Moreover, if $\Omega$ is convex, we show that this solution is constant for sufficiently small $\lambda$.
Liouville-Type Theorem For One-Dimensional Porous Medium Systems With Sources, Anh Tuan Duong
Liouville-Type Theorem For One-Dimensional Porous Medium Systems With Sources, Anh Tuan Duong
Turkish Journal of Mathematics
In this paper, we are concerned with the one-dimensional porous medium system with sources \begin{align*} \begin{cases}u_t-( u^m)_{xx} =a_{11}u^{p}+a_{12} u^rv^{r+m}, (x,t)\in J\times I\subset\mathbb{R}\times \mathbb{R}\\ v_t-(v^m)_{xx} =a_{21} u^{r+m}v^{r}+a_{22}v^{p},\;(x,t)\in J\times I\subset \mathbb{R}\times \mathbb{R}, \end{cases} \end{align*} where $p=2r+m$, $m>1$, $r>0$. Under the conditions $a_{12}\geq 0, a_{21}\geq 0$, $a_{11}>0$, and $a_{22}>0$, we prove that the system does not possess any nontrivial nonnegative weak solution.
A Short Note On A New Approach To Rayleigh-Bénard-Chandrasekhar Convection In Weakly Electrically Conducting Viscoelastic Liquids, Hati̇ce Muti̇
A Short Note On A New Approach To Rayleigh-Bénard-Chandrasekhar Convection In Weakly Electrically Conducting Viscoelastic Liquids, Hati̇ce Muti̇
Turkish Journal of Mathematics
The onset of magnetoconvection (known as Rayleigh-Bénard-Chandrasekhar convection) in two relaxation time viscoelastic liquids is studied here without seeking explicit recourse to a normal stress formulation as is usually done in these studies. Magnetoconvection refers to the flow of fluid in the presence of both thermal gradients (Rayleigh-Bénard convection) and a magnetic field. When these two effects are combined, they can lead to interesting and complex patterns of fluid motion. Understanding magnetoconvection in viscoelastic liquids is crucial for various industrial and scientific applications. The hyperbolic-type of linear momentum equation is decomposed into two first-order equations in time by cleverly separating …
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya
Turkish Journal of Mathematics
In this work, we consider a velocity-vorticity formulation for the $g$-Navier-Stokes equations. The system is constructed by combining the velocity-pressure system which is included by using the rotational formulation of the nonlinearity and the vorticity equation for the $g$ -Navier-Stokes equations. We prove the existence and uniqueness of weak and strong solutions of this system with the periodic boundary conditions.