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Adaptive Two-Derivative Runge–Kutta–Nyström Method With Trigonometric Fitting Approach, Nur Nabila Huda, Khai Chien Lee, Nurul Huda Abdul Aziz

Turkish Journal of Mathematics

A fifth-order trigonometrically-fitted explicit two-derivative Runge–Kutta–Nyström method with an adaptive step size strategy, denoted as ATFRKN5, is proposed for efficiently solving second-order ordinary differential equations of the form u^″(x) = f(x, u(x)) that exhibit oscillatory behavior. The order conditions of the method are derived using Taylor series expansion, enabling the construction of two-derivative Runge–Kutta–Nyström schemes up to orders four and five. Trigonometric fitting is applied by incorporating the basis functions e^iλx and e^−iλx, λ ∈ ℝ, allowing the method to adapt naturally to problems with dominant frequencies. …

On Sequences Arising From The Action Of Modular Group, Tuncay Köroğlu, Bahadir Özgür Güler

Turkish Journal of Mathematics

This paper examines the sequences produced by the natural action of specific elements of the modular group on extended rational numbers. The polynomial sequences Pr(c) and Qr(c) are derived from the orbit of the point at infinity under a specific modular transformation. These sequences satisfy linear recurrence relations, which are analyzed using generating functions. The polynomials encode k-Fibonacci numbers, and studying their behavior modulo a fixed integer m reveals notable arithmetic and combinatorial properties. We also explore the connection between these modular actions and Farey graphs, illustrating the hyperbolic transformations as nested geodesic paths in the upper half-plane.

A Module Theoretic Approach To (B,C)-Invertibility, Tuğba Pakel, Burcu Üngör, Handan Köse, Sai̇t Halicioğlu, Abdullah Harmanci

Turkish Journal of Mathematics

In this paper, we introduce and investigate the concept of an (r, f)-inverse in the context of modules, drawing inspiration from the (b, c)-inverse, which is the analogous notion in ring theory. We demonstrate the uniqueness of (r, f)-inverses in modules whenever they exist. We provide some necessary and sufficient conditions for the existence of (r, f)-inverses in modules.

Existence Results And Uniqueness For Some Caputo-Hadamard Fractional Differential Equations Via The Measures Of Noncompactness, Manochehr Kazemi, Mohammad Esmael Samei, Hamid Reza Sahebi, Osman Tunç

Turkish Journal of Mathematics

In this paper, the existence of solutions to Caputo–Hadamard fractional differential equations is investigated using measures of noncompactness and the Petryshyn fixed point theorem. Several new results are established, recovering certain earlier results under weaker conditions. Finally, two illustrative examples are presented.

Proportion Of Nilpotent Subgroups In Finite Groups And Their Properties, João Victor Monteiros De Andrade, Leonardo Santos Da Cruz

Turkish Journal of Mathematics

​This work introduces and investigates the function J(G) = Nil(G) / L(G) , where Nil(G) denotes the number of nilpotent subgroups and L(G) the total number of subgroups of a finite group G. The function J(G), defined on the interval (0,1], represents the proportion of nilpotent subgroups relative to the total number of subgroups, including trivial ones. It serves as a tool for analyzing structural patterns in finite groups, particularly in nonnilpotent families such as supersolvable and dihedral groups. Analytical results reveal the distribution of J(G) values across products of dihedral groups, emphasizing its density over (0,1]. Additionally, a probabilistic …

Optimal Control Of An Inverse Two-Point Boundary Value Problem For A Pseudoparabolic Equation With Samarskii–Ionkin-Type Boundary Conditions, Khanlar R. Mamedov, Tursun K. Yuldashev, Zholdoshbek Zh. Shermamatov

Turkish Journal of Mathematics

This paper investigates an inverse optimal control problem for a pseudoparabolic equation governed by nonlinear control function in a two-point boundary condition. The differential equation is considered under Samarskii Ionkin-type boundary value conditions with respect to the spatial variable x. Necessary optimality conditions are derived, and the associated nonlinear functional equations are analyzed. Using the contraction mapping principle, the existence and uniqueness of the control function are established. Subsequently, the redefinition function and the state function are determined. The convergence of their respective Fourier series representations is rigorously proven.

Close-To-Convexity Properties Of Inverse Hypergeometric Functions, Ijlal Hussain, Wasim Ul Haq, Janusz Sokol

Turkish Journal of Mathematics

The normalized inverse hypergeometric function zF_ν⁻¹(d, e, f; z) = ∑_s=0^∞ A_sz^s+1 is considered, where A_s = (f)_s(ν + 1)_s / (d)_s(e)_s. We aim to provide constraints on d, e, f, and ν under which zF_ν⁻¹(d, e, f; z) belongs to various subclasses of the class of close-to-convex functions. Coefficient characterizations of these families are derived under additional conditions. Some associated operators …

Ricci Solitons On Manifolds With Norden Golden Structure, Bang-Yen Chen, Foued Aloui, Mohammed Nisar, Majid Ali Choudhary

Turkish Journal of Mathematics

​The concept of golden structure is a compelling area with wide-ranging applications. In this paper, we introduce and investigate the notion of Norden golden Ricci solitons. In particular, we investigate Ricci solitons on a Norden golden Riemannian manifold of constant sectional curvature. Furthermore, we explore Ricci solitons and Norden golden Ricci solitons on Norden golden Riemannian manifolds whose potential vector fields are killing, conformal killing, concurrent, or homothetic.

Comparisons Of Some Weighted Mixed Biased Estimators For The Linear Regression Model, Dünya Karapinar, Murat Polat, Ni̇met Özbay, Selahatti̇n Kaçiranlar

Turkish Journal of Mathematics

This paper presents comparative results on the two-parameter weighted mixed estimator, which is a distinct class of estimator defined to address the problem of multicollinearity. The two-parameter weighted mixed estimator is a general estimator that includes the weighted mixed estimator, the weighted mixed Liu estimator, and the weighted mixed ridge estimator. Detailed comparisons among the mentioned estimators are carried out based on the matrix mean square error. Theoretical findings are supported by two numerical examples in addition to a Monte Carlo simulation study.

Improved Oscillation Criteria For A Class Of Neutral Differential Equations In The Canonical Case, Abdulaziz Khalid Alsharidi, Ali Muhib

Turkish Journal of Mathematics

This paper develops an analytical framework based on comparison with first-order equations to derive new oscillation criteria for all solutions of a class of second-order differential equations with multiple delays. These criteria extend and improve upon previously published results. Illustrative examples are provided to validate the theoretical findings and to demonstrate the significance and applicability of the proposed criteria.

Oscillation Properties Of First-Order Difference Equations With Nonmonotone Delays: New Insights And Criteria, Emad Attia, George Chatzarakis

Turkish Journal of Mathematics

In this paper, we examine the oscillatory behavior of the first-order linear delay difference equation Δy(n) + p(n) y(τ(n)) = 0, n ∈ ℕ₀. It is known in the literature that, for any C > 0, the condition lim sup_n→∞ ∑_i=τ(n)ⁿ p(i) > C, with τ(n) nonmonotone, is not, in general, sufficient to establish the oscillation of the difference equation. We prove that, for certain classes of difference equations, the aforementioned condition is sufficient to ensure the …

On The Number Of Exact Factorization Of Finite Groups, Jesus Alonso Ochoa Arango, Maria Angelica Umbarila Martin

Turkish Journal of Mathematics

In this work, the function f2(G), which counts the number of exact factorizations of a finite group G, is studied. The value of  f2(G) is computed for several well-known families of finite groups, and an asymptotic expression is derived for the number of exact factorizations of the alternating group A2n .

Synthesis Of Werner- And Werner-Like-Type Clathrates, Their Characterization, And Theoretical Calculation Of Their Properties, Zari̇fe Si̇bel Şahi̇n, Zeki̇ Kartal

Turkish Journal of Chemistry

In this paper, the synthesis and structural characterization of three new coordination compounds in crystal structure consisting of a nickel atom, varying numbers of 3-aminopyridine molecules, and two isothiocyanate ion ligands are presented. The crystal structures of these compounds were determined by single crystal X-ray diffraction. Consequently, the explicit formulas and shorthand notations of the compounds are [Ni(NCS)2(C5H6N2)2(H2O)]·(H2O) (1), [Ni(NCS)2(C5H6N2)3]·(C2H6) (2), and [Ni(NCS)2(C5H6N2)4]·2(C5H6N2) (3). The consistency of the crystal structure data was confirmed by elemental analysis and infrared spectroscopy. These coordination compounds are Werner-like-type clathrates containing water, ethane, and 3-aminopyridine molecules as guest molecules in their structures, respectively. According to …

Deep Learning Technology In Multimodal Remote Sensing Data Fusion To Analyze Crop Growth And Economic Forecast, Tianlong Jiang, Ziyang Liu, Li Sun

Turkish Journal of Agriculture and Forestry

This paper integrated multimodal remote sensing (RS) data with deep learning to develop a maize growth analysis and income prediction model based on CNN (Convolutional Neural Network)-Attention and Bi-LSTM (Bidirectional Long Short-Term Memory). Utilsing Landsat 8, Sentinel-2, and Sentinel-1 satellite data, the CNN-Attention network extracts vegetation features such as NDVI (Normalised Difference Vegetation Index), EVI (Enhanced Vegetation Index), and canopy density for corn growth stage identification and prediction. The study combined these features with meteorological, soil, and market data and fed them into a Bi-LSTM model for time series analysis to forecast corn income. The method achieved 98.3% accuracy in …

Analysis Of Agricultural Remote Sensing Data Driven By Artificial Intelligence On Crop Growth Patterns And Economic Benefits Of Grain, Yang Wang

Turkish Journal of Agriculture and Forestry

To address the shortcomings of conventional agricultural statistical and monitoring methods on a regional scale, this paper proposes the use of artificial intelligence-driven remote sensing data for analysing crop growth patterns and the economic benefits of grain. Winter wheat data from three stations in a single province from 2011 to 2020 was used, with the leaf area index (LAI) used as the key crop growth indicator value. The simulated annealing algorithm was used to assimilate the LAI and remote sensing leaf area index (MODIS-LAI), simulated by the World Food Study (WOFOST) simulation model, to carry out simulation analysis of winter …

Computational And Experimental Analysis Of Oleanolic Acid As An Allosteric Activator Of Sirt1, Emrah Sariyer, Eda Dokumacioğlu, Hati̇ce İskender

Turkish Journal of Chemistry

Sirtuin 1 (SIRT1) is a member of the sirtuin protein family and the biological effects of SIRT1 encompass various areas such as the ageing process, metabolism regulation, and cellular stress response. SIRT1 activators are compounds that enhance the activity of SIRT1 enzyme. These activators can be natural or synthetic compounds and have the potential to provide health benefits by augmenting the biological effects of SIRT1. Oleanolic acid (OA) is a triterpenoid compound that has antiinflammatory, antioxidant, and glucose and lipid metabolism-regulating properties naturally found in many plants. The aim of the present study was to investigate the effect of OA …

Investigation Of The Enzyme-Inhibitory, Antibacterial, And Anticancer Properties Of Metal Phthalocyanines, Meryem Topal, Fevzi̇ Topal, Firat Yilmaz, Esra Bulut Atalay, Ümi̇t Muhammet Koçyi̇ği̇t, Emre Güzel

Turkish Journal of Chemistry

In this study, the enzyme inhibitory, antibacterial, and anticancer activities of a phthalonitrile derivative and its metal phthalocyanines (Pcs; indium, zinc, copper, cobalt, and manganese; 1–6) were investigated. The cobalt and manganese Pcs were synthesized for the first time in this study. The inhibitory activities of the symmetric Pcs, which were expected to interact with acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) via their 4-(isopropylbenzyl)oxy substituents through host–guest interactions, were investigated. More selective inhibition of AChE than BChE was observed for these compounds. For AChE, CoPc was identified as the most potent inhibitor (IC50 = 14.81 nM), whereas for BChE, InPc was …

Nucleophilic Cyclization Of N-Propargylated Pyrazole-5-Carboxylates: Synthesis Of Pyrazolo[1,5-A]Pyrazin-4(5h)-One Derivatives, Meli̇k Firat Mengeş, Meltem Tan Uygun

Turkish Journal of Chemistry

Cyclization reactions are among the most important and widely used methods for synthesizing biologically active fused heterocyclic compounds. In the present study, pyrazolopyrazinone derivatives (10a–i) were synthesized from N-propargylated pyrazoles via nucleophilic cyclization with hydrazine hydrate under a nitrogen atmosphere. Nuclear magnetic resonance (NMR) spectral analyses confirmed that ring closure proceeded in a manner consistent with the formation of a six-membered pyrazinone moiety. In addition, the pyrazolotriazepinone derivative 15c was synthesized using an alternative approach. In this method, substitution with chloroacetone was first carried out, followed by ring closure with hydrazine hydrate, affording a seven-membered triazepinone system. Comparison of the …

Sensitive Stripping Voltammetric Determination Of An Anthracene–Isatin Schiff Base In Biological Samples, Gökçe Öztürk, İrem Gökgöz, Emi̇ne Arslan, Eli̇f Şi̇şman, İnci̇ Seli̇n Doğan, Di̇lek Kul, Fatma Ağin

Turkish Journal of Chemistry

​In the present study, the electrochemical behavior and quantitative determination of the Schiff base 3-[(anthracen-2-yl)imino]-5-nitro-1,3-dihydro-2H-indol-2-one (ANT) were investigated for the first time using voltammetric techniques at a glassy carbon electrode. The effects of solvent composition, pH, and scan rate on the redox behavior of ANT were systematically evaluated. The compound exhibited an irreversible oxidation process governed by adsorption-controlled kinetics. Quantitative analysis was conducted using differential pulse stripping voltammetry (AdS-DPV) and square-wave stripping voltammetry (AdS-SWV) under optimized conditions. Both methods exhibited linear responses over the concentration range of 0.2–8.0 μM, with limits of detection of 0.0366 μM and 0.0433 μM for …

Influence Of Precursor Synthesis Temperature And Hydrothermal Alkaline Medium On Agglomeration And Crystal Phase Of Barium Titanate Nanoparticles, Murat Özen

Turkish Journal of Chemistry

Phase‑pure, cube‑like barium titanate (BaTiO3) nanoparticles were synthesized via hydrothermal treatment of a single‑source barium-titanium peroxo-hydroxide precursor. Precursor solutions prepared at room temperature, 0 °C, and –10 °C with various storage times exhibited Ba/Ti molar ratios ranging from 0.66 to 1.05 as determined by X-ray fluorescence. Cooling the precursor solution to –10 °C effectively suppressed the polymerization of Ti-O-Ti, yielding near‑ideal stoichiometry and finer precursor particles. Subsequent hydrothermal processing in NH4OH, KOH, and NaOH (0.5–10 M, 100–200 °C) revealed the strong dependence of agglomeration and morphology on the alkaline medium. While NH4OH and KOH resulted in severe agglomeration and the …

Templating Effect Of Neutral Dithiane Ligands On The Self-Assembly Of Cationic Au(I)-Phosphine Units, Farzane Osanlou, Abdollah Neshat, Mohammad Reza Yousefshahi, Vaclav Eigner, Michal Dusek, Shahram Seidi

Turkish Journal of Chemistry

The interactions between the dinuclear Au(I) precursor (dppm)Au2Cl2 and neutral sulfur-containing dithianes (specifically 1,3- and 1,4-dithiane) were examined in the presence of NH₄PF₆. Although these sulfur-based ligands were initially employed to facilitate the formation of mixed phosphine/sulfur Au(I) complexes, single-crystal X-ray diffraction analysis revealed the unexpected generation of multinuclear Au(I) assemblies exclusively coordinated by phosphine ligands. When 1,3-dithiane was present, a trinuclear Au(I) complex was isolated, characterized by a central four-coordinate Au(I) center exhibiting a distorted see-saw geometry, flanked by two terminal Au(I) centers with T-shaped coordination environments. Importantly, the dithiane ligand did not coordinate directly to the gold centers …

Vanadium’S Journey From Essential Trace Metal To Emerging Environmental Pollutant In The Anthropocene Era, Tanu Arora, Nivedita Agnihotri, Mohammad Azam

Turkish Journal of Chemistry

Vanadium, previously considered a minor trace element, is gaining global environmental attention due to its expanding applications in metallurgy, energy storage, catalysis, and agriculture. With this rise in its industrial and technological uses, however, anthropogenic emissions of vanadium into the atmosphere, soils, and water bodies have also escalated. Unlike many heavy metals, vanadium exhibits complex redox behavior, primarily existing as V(IV) and V(V) species, which significantly impacts its environmental mobility, bioavailability, and toxicity. Vanadium exhibits complex behavior that necessitates an integrated research approach to better understand its various roles in scientific fields. This review summarizes the current knowledge on vanadium’s …

Biomechanical Analysis Of Skeletal Open Bite Treatment Methods: A Comparative Finite Element Study ​, Ömer Faruk Sari, Muhammed Hi̇lmi̇ Buyukcavus

Turkish Journal of Medical Sciences

Background/aim: The biomechanical effects of zygomatic anchorage plates, vertical chin-caps, and occipital headgear on dentofacial structures in patients with skeletal anterior open bite malocclusion were compared using three-dimensional finite element analysis.

Materials and methods: Three-dimensional finite element models were constructed based on computed tomography data obtained from a patient with skeletal anterior open bite. Simulation models representing zygomatic anchorage-supported intrusion, vertical chin-cap, and occipital headgear were generated under fixed orthodontic conditions. In each scenario, a unilateral force of 200 g (1.96 N) was applied along clinically relevant force vectors. Stress distributions in craniofacial bones, sutural structures, teeth, roots, and temporomandibular …

Res-Mnd: Motor Neuron Disease Detection Using Res4net–Convolutional Block Attention Module ​, Shuriya Balusamy, Rakesh Sivalingam, Shobana Rooben, Sony Helen

Turkish Journal of Medical Sciences

Background/aim: Motor neuron diseases (MNDs) are progressive neurological disorders that cause muscle weakness and wasting as a result of ongoing neurodegeneration. MNDs require comprehensive diagnostic approaches that integrate clinical symptoms, laboratory findings, and multimodal imaging data.

Materials and methods: In this study, a novel residual network for motor neuron disease detection (RES-MND) framework is proposed for detecting MNDs using multimodal imaging data. Initially, the input multimodal images, including MRI, CT, PET, and DTI, are preprocessed using adaptive dynamic histogram equalization and the total variation bilateral filter. The preprocessed multimodal images are processed through Res4Net-CBAM for feature extraction to enhance image …

Two-Dimensional Inverse Scattering Solution Using Nurbs Expansion And A Deep Learning Method, Meisam Shafaee

Turkish Journal of Physics

This paper presents a novel framework for solving two-dimensional (2D) inverse scattering problems by integrating nonuniform rational B-spline (NURBS) parameterization with convolutional neural networks (CNNs). Tra ditional pixel/voxel-based deep learning methods often suffer from high dimensionality and discretization artifacts, while purely geometric approaches lack robust inversion mechanisms. To address these limitations, we propose a hybrid frame work where the relative permittivity profile of an unknown scatterer is compactly represented as a NURBS surface, parameterized by a sparse set of control points and weights. This approach reduces the problem dimensionality over 16 times. On the other hand, using NURBS expansion ensures …

From Stability To Spintronics: A Comprehensive High-Throughput Investigation Of 2d Mf4 Lieb Lattices, Uğur Yorulmaz

Turkish Journal of Physics

The research on two-dimensional (2D) materials which have intrinsic magnetism and exotic electronic struc tures is an important quest in condensed matter physics. The Lieb lattice offers a unique platform for studying strongly correlated electron phenomena. In this work, we systematically investigated the structural, dynamical, mechanical, electronic, and magnetic properties of monolayer transition metal tetrafluorides (MF4, where M = Ag, Cd, Cr, Cu, Fe, Hf, Mn, Mo, Nb, Ni, Pd, Pt, Rh, Ru, Sc, Ta, Ti, V, W, and Y) arranged in a 2D Lieb lattice, using first-principles calculations based on density functional theory (DFT) with Hubbard (U) corrections. Our …

Analytical Solution Of The Green’S Functions For The Poisson Problem Outside A Disk, Mohammad Khorrami

Turkish Journal of Physics

The Poisson problem in the space outside of a disk is investigated. Specifically, the Green’s function corresponding to the problem is calculated. The Green’s function equation is separable in terms of (oblate) ellipsoidal coordinates. Therefore, these coordinates are used to obtain a series expression for the Green’s function. This is done for both the Dirichlet and Neumann problems. The result is used to calculate the electric potential for some examples, with specific boundary conditions on a disk.

Long-Term Measurements Of Global Solar Radiation In Osmaniye, Türkiye (2014–2023), Muhi̇tti̇n Şahan, Hali̇de Şahan, Ramazan Kaya

Turkish Journal of Physics

This paper presents the horizontal solar radiation data for Osmaniye (37◦04′N, 36◦22′E), located in Mediterranean region of Türkiye, over the period 2014–2023. Solar radiation variability, recorded at 1-min intervals, was evaluated in terms of hourly, daily, monthly, seasonal, and annual averages. Over the 10-year periods, the mean daily total and daily average global radiations received on a horizontal surface were 1,360,000 W/m2 and 371.47 W/m2, respectively. The monthly averaged daily global radiation (averaged over the 10-year period) ranged from 202.94 W/m2 in December to 496.86 W/m2 in July. The seasonal average values of solar radiations were 452.14 W/m2 in summer, …

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Turkish Journal of Physics

No abstract provided.

Species Identification Using Otolith Morphometry Of Four Gurnards (Family: Triglidae) From  Edremit Bay (Aegean Sea), Ahmet Mert Şenbahar, Di̇lek İlhan, Aydin Ünlüoğlu, Sencer Akalin

Turkish Journal of Zoology

Shape and size analyses of otoliths are widely considered appropriate tools for distinguishing between fish species and for assessing populations and stocks.  The present study aims to distinguish four gurnard species collected from Edremit  Bay (Aegean Sea) based on variations in their otolith shape morphology. A total of 60  specimens of Eutrigla gurnardus, 64 of Chelidonichthys lastoviza, 60 of  Chelidonichthys lucerna, and 60 of Lepidotrigla cavillone were analyzed. No  significant intraspecific differences were noted in the morphology of the left and right  otoliths, and so only the left sagittal otoliths were subjected to further analysis. Otolith  shape was quantified using …