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2021

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Classification Of P300 Based Brain Computer Interface Systems Using Longshort-Term Memory (Lstm) Neural Networks With Feature Fusion, Ali̇ Osman Selvi̇, Abdullah Feri̇koğlu, Derya Güzel Jan 2021

Classification Of P300 Based Brain Computer Interface Systems Using Longshort-Term Memory (Lstm) Neural Networks With Feature Fusion, Ali̇ Osman Selvi̇, Abdullah Feri̇koğlu, Derya Güzel

Turkish Journal of Electrical Engineering and Computer Sciences

Enabling to obtain brain activation signs, electroencephalography is currently used in many applications as a medical diagnostic method. Brain-computer interface (BCI) applications are developed to facilitate the lives of individuals who have not lost their brain functions yet have lost their motor and communication abilities. In this study, a BCI system is proposed to make classification using Bi-directional long short term memory (Bi-LSTM) neural networks. In the designed system, spectral entropy method including instantaneous frequency change of signal is used as feature fusion. In the study, electroencephalography (EEG) data of 10 participants are collected with Emotiv EPOC+ device using 2x2 …

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Mri Based Genomic Analysis Of Glioma Using Three Pathway Deep Convolutionalneural Network For Idh Classification, Sonal Gore, Jayant Jagtap Jan 2021

Mri Based Genomic Analysis Of Glioma Using Three Pathway Deep Convolutionalneural Network For Idh Classification, Sonal Gore, Jayant Jagtap

Turkish Journal of Electrical Engineering and Computer Sciences

As per 2016 updates by World Health Organization (WHO) on cancer disease, gliomas are categorized and further treated based on genomic mutations. The imaging modalities support a complimentary but immediate noninvasive diagnosis of cancer based on genetic mutations. Our aim is to train a deep convolutional neural network for isocitrate dehydrogenase (IDH) genotyping of glioma by auto-extracting the most discriminative features from magnetic resonance imaging (MRI) volumes. MR imaging data of total 217 patients were obtained from The Cancer Imaging Archives (TCIA) of high and low-grade gliomas. A 3-pathway convolutional neural network was trained for IDH classification. The multipath neural …

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Leukocyte Classification Based On Feature Selection Using Extra Trees Classifier: Atransfer Learning Approach, Diana Baby, Sujitha Juliet Devaraj, Jude Hemanth, Anishin Raj M M Jan 2021

Leukocyte Classification Based On Feature Selection Using Extra Trees Classifier: Atransfer Learning Approach, Diana Baby, Sujitha Juliet Devaraj, Jude Hemanth, Anishin Raj M M

Turkish Journal of Electrical Engineering and Computer Sciences

The criticality of investigating the white blood cell (WBC) count cannot be underestimated, as white blood cells are an important component of the body's defence system. From helping to diagnose hidden infections to insinuating the presence of comorbidities like immunodeficiency, an accurate white blood cell count can contribute significantly to shape a physician?s assessment. The manual process performed by the pathologists for the classification of WBCs is a time consuming and tedious task, which is further disadvantaged by a lack of accuracy. This study concentrates on the automatic detection and classification of WBC without data augmentation into four subtypes such …

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Improved Cell Segmentation Using Deep Learning In Label-Free Optical Microscopyimages, Aydin Ayanzadeh, Özden Yalçin Özuysal, Devri̇m Pesen Okvur, Sevgi̇ Önal, Behçet Uğur Töreyi̇n, Devri̇m Ünay Jan 2021

Improved Cell Segmentation Using Deep Learning In Label-Free Optical Microscopyimages, Aydin Ayanzadeh, Özden Yalçin Özuysal, Devri̇m Pesen Okvur, Sevgi̇ Önal, Behçet Uğur Töreyi̇n, Devri̇m Ünay

Turkish Journal of Electrical Engineering and Computer Sciences

The recently popular deep neural networks (DNNs) have a significant effect on the improvement of segmentation accuracy from various perspectives, including robustness and completeness in comparison to conventional methods. We determined that the naive U-Net has some lacks in specific perspectives and there is high potential for further enhancements on the model. Therefore, we employed some modifications in different folds of the U-Net to overcome this problem. Based on the probable opportunity for improvement, we develop a novel architecture by using an alternative feature extractor in the encoder of U-Net and replacing the plain blocks with residual blocks in the …

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Diagnosis Of Paroxysmal Atrial Fibrillation From Thirty-Minute Heart Ratevariability Data Using Convolutional Neural Networks, Murat Sürücü, Yalçin İşler, Resul Kara Jan 2021

Diagnosis Of Paroxysmal Atrial Fibrillation From Thirty-Minute Heart Ratevariability Data Using Convolutional Neural Networks, Murat Sürücü, Yalçin İşler, Resul Kara

Turkish Journal of Electrical Engineering and Computer Sciences

Paroxysmal atrial fibrillation (PAF) is the initial stage of atrial fibrillation, one of the most common arrhythmia types. PAF worsens with time and affects the patient?s life quality negatively. In this study, we aimed to diagnose PAF early, so patients can start taking precautions before this disease gets worse. We used the atrial fibrillation prediction database, an open data from Physionet and constructed our approach using convolutional neural networks. Heart rate variability (HRV) features are calculated from time-domain measures, frequency-domain measures using power spectral density estimations (fast Fourier transform, Lomb-Scargle, and Welch periodogram), time-frequencydomain measures using wavelet transform, and nonlinear …

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Macro-And Micromechanical Modelling Of Ha-Elastin Scaffold Fabricated Using Freeze Drying Technique, Matin Mohammadzadeh Rad, Saeed Saber-Samandari, Mojtaba Sadighi, Lobat Tayebi, Mohammad Mohammadi Aghdam, Amirsalar Khandan Jan 2021

Macro-And Micromechanical Modelling Of Ha-Elastin Scaffold Fabricated Using Freeze Drying Technique, Matin Mohammadzadeh Rad, Saeed Saber-Samandari, Mojtaba Sadighi, Lobat Tayebi, Mohammad Mohammadi Aghdam, Amirsalar Khandan

School of Dentistry Faculty Research and Publications

No abstract provided.

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Covid-19 Detection On Ibm Quantum Computer With Classical-Quantum Transferlearning, Erdi̇ Acar, İhsan Yilmaz Jan 2021

Covid-19 Detection On Ibm Quantum Computer With Classical-Quantum Transferlearning, Erdi̇ Acar, İhsan Yilmaz

Turkish Journal of Electrical Engineering and Computer Sciences

Diagnose the infected patient as soon as possible in the coronavirus 2019 (COVID-19) outbreak which is declared as a pandemic by the world health organization (WHO) is extremely important. Experts recommend CT imaging as a diagnostic tool because of the weak points of the nucleic acid amplification test (NAAT). In this study, the detection of COVID-19 from CT images, which give the most accurate response in a short time, was investigated in the classical computer and firstly in quantum computers. Using the quantum transfer learning method, we experimentally perform COVID-19 detection in different quantum real processors (IBMQx2, IBMQ-London and IBMQ-Rome) …

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Deep-Learning-Based Spraying Area Recognition System Forunmanned-Aerial-Vehicle-Based Sprayers, Shahbaz Khan, Muhammad Tufail, Muhammad Tahir Khan, Zubair Ahmed Khan, Shahzad Anwer Jan 2021

Deep-Learning-Based Spraying Area Recognition System Forunmanned-Aerial-Vehicle-Based Sprayers, Shahbaz Khan, Muhammad Tufail, Muhammad Tahir Khan, Zubair Ahmed Khan, Shahzad Anwer

Turkish Journal of Electrical Engineering and Computer Sciences

Unmanned aerial vehicle (UAV)-based spraying system employing machine learning techniques is a recent advancement in precision agriculture for precise spraying, promoting saving chemicals (pesticide/herbicide), and enhancing their effectiveness. This study aims to develop an efficient deep learning system for UAV-based sprayers, which has the capability to accurately recognize spraying areas. A deep learning system is proposed and developed incorporating a faster region-based convolutional neural network (R-CNN) for the imagery collected. In order to develop a classifier for identifying spraying areas from nonspraying areas, four different agriculture croplands and orchards were considered. All the experiments were performed in agriculture fields through …

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Analyzing The Performances Of Evolutionary Multi-Objective Optimizers On Designoptimization Of Robot Gripper Configurations, Murat Dörterler, Ümi̇t Ati̇la, Rafet Durgut, İsmai̇l Şahi̇n Jan 2021

Analyzing The Performances Of Evolutionary Multi-Objective Optimizers On Designoptimization Of Robot Gripper Configurations, Murat Dörterler, Ümi̇t Ati̇la, Rafet Durgut, İsmai̇l Şahi̇n

Turkish Journal of Electrical Engineering and Computer Sciences

Robot grippers are widely used in a variety of areas requiring automation, precision, and safety. The performance of the grippers is directly associated with their design. In this study, four different multiobjective metaheuristic algorithms including particle swarm optimization (MOPSO), artificial algae algorithm (MOAAA), grey wolf optimizer (MOGWO) and nondominated sorting genetic algorithm (NSGA-II) were applied to two different configurations of highly nonlinear and multimodal robot gripper design problem including two objective functions and a certain number of constraints. The first objective is to minimize the difference between minimum and maximum forces for the assumed range in which the gripper ends …

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A Novel Fibonacci Hash Method For Protein Family Identification By Usingrecurrent Neural Networks, Talha Burak Alakuş, İbrahi̇m Türkoğlu Jan 2021

A Novel Fibonacci Hash Method For Protein Family Identification By Usingrecurrent Neural Networks, Talha Burak Alakuş, İbrahi̇m Türkoğlu

Turkish Journal of Electrical Engineering and Computer Sciences

Identification and classification of protein families are one of the most significant problem in bioinformatics and protein studies. It is essential to specify the family of a protein since proteins are highly used in smart drug therapies, protein functions, and, in some cases, phylogenetic trees. Some sequencing techniques provide researchers to identify the biological similarities of protein families and functions. Yet, determining these families with sequencing applications requires huge amount of time. Thus, a computer and artificial intelligence based classification system is needed to save time and avoid complexity in protein classification process. In order to designate the protein families …

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Development Of An Intelligent Controller For Robot-Aided Assessment Andtreatment Guidance In Physical Medicine And Rehabilitation, Mehmet Emi̇n Aktan, Erhan Akdoğan Jan 2021

Development Of An Intelligent Controller For Robot-Aided Assessment Andtreatment Guidance In Physical Medicine And Rehabilitation, Mehmet Emi̇n Aktan, Erhan Akdoğan

Turkish Journal of Electrical Engineering and Computer Sciences

In this study, an intelligent controller was developed for a rehabilitation robot called DIAGNOBOT, which can be used for assessment and treatment in the rehabilitation of wrist and forearm. The controller has a decision support system structure strengthened with conventional statistical methods and databases. The controller uses the patient's biomechanical parameters to make an assessment and proposes a treatment in line with this. In accordance with the recommended treatment, it produces the control parameters, torque, and position information for the control of the rehabilitation robot. The system's ability of assessment and treatment was tested with voluntary patients. Through these test …

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Swft: Subbands Wavelet For Local Features Transform Descriptor For Cornealdiseases Diagnosis, Samer Al-Salihi, Sezgi̇n Aydin, Nebras Hussein Jan 2021

Swft: Subbands Wavelet For Local Features Transform Descriptor For Cornealdiseases Diagnosis, Samer Al-Salihi, Sezgi̇n Aydin, Nebras Hussein

Turkish Journal of Electrical Engineering and Computer Sciences

Human cornea is the front see-through shield of the eye. It refracts light onto the retina to induce vision.Therefore, any defect in the cornea may lead to vision disturbance. This deficiency is estimated by sets of topographicalimages measured, and assessed by an ophthalmologist. Consequently, an important priority is the early and accuratediagnosis of diseases that may affect corneal integrity through the use of machine learning algorithms. Images producedby a Pentacam device can be subjected to rotation or some distortion during acquisition; therefore, accurate diagnosisrequires the use of local features in the image. Accordingly, a new algorithm called subbands wavelet for …

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Heuristic Based Binary Grasshopper Optimization Algorithm To Solve Unitcommitment Problem, Muhammad Shahid, Tahir Nadeem Malik, Ahsan Said Jan 2021

Heuristic Based Binary Grasshopper Optimization Algorithm To Solve Unitcommitment Problem, Muhammad Shahid, Tahir Nadeem Malik, Ahsan Said

Turkish Journal of Electrical Engineering and Computer Sciences

The unit commitment problem in power system is a highly nonlinear, nonconvex, multiconstrained, complex,highly dimensional, mixed integer and combinatorial generation selection problem. The phenomenon of committing anddecommitting represents a discrete problem that requires binary/discrete optimization techniques to tackle with unitcommitment optimization problem. The key functions of the unit commitment optimization problem involve decidingwhich units to commit and then to decide their optimum power (economic dispatch). This paper confers a binarygrasshopper optimization algorithm to solve the unit commitment optimization problem under multiple constraints.The grasshopper optimization algorithm is a metaheuristic, multiple solutions-based algorithm inspired by the naturalswarming behavior of grasshopper towards food. …

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A Novel Pulse Plethysmograph Signal Analysis Method For Identification Of Myocardial Infarction, Dilated Cardiomyopathy, And Hypertension, Muhammad Umar Khan, Sumair Aziz Jan 2021

A Novel Pulse Plethysmograph Signal Analysis Method For Identification Of Myocardial Infarction, Dilated Cardiomyopathy, And Hypertension, Muhammad Umar Khan, Sumair Aziz

Turkish Journal of Electrical Engineering and Computer Sciences

Cardiac diseases (CDs) are one of the leading causes of the growing global mortality rate. Early detectionof CDs is necessary to avoid a high increase in the mortality rate. Machine learning-based computer-aided diagnosisof CDs using various physiological signals has recently been used by researchers. Since pulse plethysmograph (PuPG)signal contains a wealth of information about cardiac pathologies, therefore, this paper presents an expert system designfor the automatic diagnosis of cardiac disorders like hypertension, dilated cardiomyopathy and myocardial infarctionusing a novel fingertip PuPG signal analysis. The proposed system first performs signal denoising of raw PuPG sensordata using discrete wavelet transform (DWT). After …

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Neural Relation Extraction: A Review, Mehmet Aydar, Özge Bozal, Furkan Özbay Jan 2021

Neural Relation Extraction: A Review, Mehmet Aydar, Özge Bozal, Furkan Özbay

Turkish Journal of Electrical Engineering and Computer Sciences

Neural relation extraction discovers semantic relations between entities from unstructured text using deeplearning methods. In this study, we make a clear categorization of the existing relation extraction methods in termsof data expressiveness and data supervision, and present a comprehensive and comparative review. We describe theevaluation methodologies and the datasets used for model assessment. We explicitly state the common challenges inrelation extraction task and point out the potential of the pretrained models to solve them. Accordingly, we investigateadditional research directions and improvement ideas in this field.

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Chaos In Metaheuristic Based Artificial Intelligence Algorithms:A Short Review, Gökhan Atali, İhsan Pehli̇van, Bi̇lal Gürevi̇n, Hali̇l İbrahi̇m Şeker Jan 2021

Chaos In Metaheuristic Based Artificial Intelligence Algorithms:A Short Review, Gökhan Atali, İhsan Pehli̇van, Bi̇lal Gürevi̇n, Hali̇l İbrahi̇m Şeker

Turkish Journal of Electrical Engineering and Computer Sciences

Metaheuristic based artificial intelligence algorithms are commonly used in the solution of optimization problems. Another area -besides engineering systems- where chaos theory is widely employed is optimization problems. Being applied easily and not trapping in local optima, chaos-based search algorithms have attracted great attention. For example, it has been reported that when random number sequences generated from different chaotic systems are replaced with parameter values in bioinspired and swarm intelligence algorithms, an increase in the performance of metaheuristic algorithms is observed. Many scientific studies on developing hybrid algorithms in which metaheuristic algorithms and chaos theory are used together are already …

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Using Eeg To Detect Driving Fatigue Based On Common Spatial Pattern Andsupport Vector Machine, Li Wang, David Johnson, Yingzi Lin Jan 2021

Using Eeg To Detect Driving Fatigue Based On Common Spatial Pattern Andsupport Vector Machine, Li Wang, David Johnson, Yingzi Lin

Turkish Journal of Electrical Engineering and Computer Sciences

To investigate the correlation between electroencephalogram (EEG) and driving fatigue states, this study used machine learning algorithms to detect driving fatigue based on EEG. 14 channels of EEG data were collected from thirty-four healthy subjects in this research at Northeastern University. Each subject participated in two scenarios (baseline and fatigue scenarios). Subjective ratings of fatigue levels were also obtained from the subjects using the NASA-Task Load Index (TLX). The common spatial pattern (CSP) algorithm was used to extract features from the raw EEG data. The support vector machine (SVM) was used as the classifier in the design of the machine …

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Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam Jan 2021

Ideal Triangulation And Disc Unfolding Of A Singular Flat Surface, İsmai̇l Sağlam

Turkish Journal of Mathematics

An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of geodesics having length $\leq L$ connecting them, where $L$ is any positive number, we prove that each singular flat surface has an ideal triangulation provided that the surface has singular points when it has no boundary components, or each of its boundary components has a singular point. Also, we prove that such a surface contains a …

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On The Local And Global Stability Of An Sirs Epidemic Model With Logistic Growth And Information Intervention, İrem Çay Jan 2021

On The Local And Global Stability Of An Sirs Epidemic Model With Logistic Growth And Information Intervention, İrem Çay

Turkish Journal of Mathematics

In this study, we investigate an susceptible-infected-recovered-susceptible (SIRS) epidemic model with logistic growth and information intervention. Firstly, the basic reproduction number $R_0$ is defined and the main results are given in terms of local stability. Then, sufficient conditions for the global stability of endemic equilibrium are obtained. Finally, some numerical simulations are given to validate our theoretical conclusions.

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On Some Nonlocal Inverse Boundary Problem For Partial Differential Equations Of Third Order, Ziyatkhan S. Aliyev, Yashar T. Mehraliyev, Elmira H. Yusifova Jan 2021

On Some Nonlocal Inverse Boundary Problem For Partial Differential Equations Of Third Order, Ziyatkhan S. Aliyev, Yashar T. Mehraliyev, Elmira H. Yusifova

Turkish Journal of Mathematics

In this paper, we consider the inverse boundary value problem for a partial differential equation of third order with nonlocal boundary conditions, including an integral condition. Using analytical and operator-theoretic methods, as well as the Fourier method, the existence and uniqueness of the classical solution of this problem is proved.

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Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales, Hali̇s Can Koyuncuoğlu Jan 2021

Some Qualitative Results For Functional Delay Dynamic Equations On Time Scales, Hali̇s Can Koyuncuoğlu

Turkish Journal of Mathematics

Let $\mathbb{T}$ be a nonempty, closed, and arbitrary set of real numbers, namely a time scale, and consider the following delay dynamical equation% \[ x^{\Delta}\left( t\right) =a\left( t\right) x\left( t\right) +f\left( t,x\left( \mathbb{\vartheta}\left( t\right) \right) \right) ,\text{ }t\in\mathbb{T}, \] where $\mathbb{\vartheta}$ stands for the abstract delay function. The main goal of this study is three-fold: obtaining the existence of an equi-bounded solution, proving the asymptotic stability of the zero solution, and showing the existence of a periodic solution based on new periodicity concept on time scales for the given delayed equation under certain conditions. In our analysis, we propose an …

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A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan Jan 2021

A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan

Turkish Journal of Mathematics

In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integro-differential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present …

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Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim Jan 2021

Global Existence And Blow-Up Of Solutions For Parabolic Equations Involving The Laplacian Under Nonlinear Boundary Conditions., Anass Lamaizi, Abdellah Zerouali, Omar Chakrone, Belhadj Karim

Turkish Journal of Mathematics

This paper is concerned with the existence and blow-up of solutions to the following linear parabolic equation: $ ~~ u_t - \Delta u +u = 0 \quad \text{ in } \Omega \times (0,T) $, under nonlinear boundary condition in a bounded domain $ \Omega \subset \mathbb{R}^n $, $n \geq 1$, with smooth boundary. We obtain a threshold result for the global existence of solutions, next we shall prove the existence time $T$ of solution is finite when the initial energy satisfies certain condition.

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On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş Jan 2021

On Lyapunov-Type Inequalities For $(N+1)$St Order Nonlinear Differential Equations With The Anti-Periodic Boundary Conditions, Mustafa Fahri̇ Aktaş

Turkish Journal of Mathematics

In this paper, we establish new Lyapunov-type inequalities for $\left(n+1\right)$st order nonlinear differential equation including $p$-relativistic operator and $q$-prescribed curvature operator under the antiperiodic boundary conditions.

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An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe Jan 2021

An Exponential Equation Involving $K$-Fibonacci Numbers, Alioune Gueye, Salah Eddine Rihane, Alain Togbe

Turkish Journal of Mathematics

For $k\geq 2$, consider the $k$-Fibonacci sequence $(F_n^{(k)})_{n\geq 2-k}$ having initial conditions $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the preceding $k$ terms. Some well-known sequences are special cases of this generalization. The Fibonacci sequence is a special case of $(F_n^{(k)})_{n\geq 2-k}$ with $k=2$ and Tribonacci sequence is $(F_n^{(k)})_{n\geq 2-k}$ with $k=3$. In this paper, we use Baker's method to show that 4, 16, 64, 208, 976, and 1936 are all $k$-Fibonacci numbers of the form $(3^a\pm 1)(3^b\pm 1)$, where $a$ and $b$ are nonnegative integers.

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On Some Topological Properties In The Class Of Alexandroff Spaces, Sami Lazaar, Houssem Sabri, Randa Tahri Jan 2021

On Some Topological Properties In The Class Of Alexandroff Spaces, Sami Lazaar, Houssem Sabri, Randa Tahri

Turkish Journal of Mathematics

In the class of Alexandroff spaces we study the properties of being a submaximal, door, Whyburn and weakly Whyburn space. We provide characterizations in order theoretical terms. Connections with posets, counting formulas and numerical results in the class of finite spaces are also given.

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On A Coupled Caputo Conformable System Of Pantograph Problems, Sabri T. M. Thabet, Sina Etemad, Shahram Rezapour Jan 2021

On A Coupled Caputo Conformable System Of Pantograph Problems, Sabri T. M. Thabet, Sina Etemad, Shahram Rezapour

Turkish Journal of Mathematics

Our fundamental purpose in the present manuscript is to explore existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems in which for the first time, the given boundary conditions are formulated in the Riemann-Liouville conformable framework. To reach the mentioned aims, we utilize different analytical techniques in which some fixed point results play a vital role. In the final part, a simulative example is designed to cover the applicability aspects of theoretical findings available in this research manuscript from a numerical point of view.

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Infinitesimal Bending Of Dna Helices, Miroslav Maksimovic, Ljubica Velimirovic, Marija Najdanovic Jan 2021

Infinitesimal Bending Of Dna Helices, Miroslav Maksimovic, Ljubica Velimirovic, Marija Najdanovic

Turkish Journal of Mathematics

The mathematics of DNA molecules is often studied as a double helix model. This paper focuses on the modelling of infinitesimal bending of DNA helices. The paper checks the flexibility of DNA molecule, i.e. the flexibility of double helix in infinitesimal bending theory. Actually, first, we find infinitesimal bending field of an arbitrary curve on the helicoid, that leaves bent curves on the helicoid, and show that helix bending on the helicoid is not possible. Finally, we deal with the infinitesimal bending of helicoid, using PDEs. Visualization of infinitesimal bending was done in Mathematica.

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A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter, Turhan Köprübaşi Jan 2021

A Study Of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter, Turhan Köprübaşi

Turkish Journal of Mathematics

Let $L$ denote the discrete Dirac operator generated in $\ell _{2}\left( %TCIMACRO{\U{2115} }% %BeginExpansion \mathbb{N} %EndExpansion ,% %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion ^{2}\right) $ by the difference operators of first order% \begin{equation*} \left\{ \begin{array}{cc} {\bigtriangleup y_{n}^{\left( 2\right) }+p_{n}y_{n}^{\left( 1\right) }=\lambda y_{n}^{(1)}} & \\ {\bigtriangleup y_{n-1}^{\left( 1\right) }+q_{n}y_{n}^{\left( 2\right) }=\lambda y_{n}^{(2)}}, \end{array} \text{ }n\in \mathbb{N} \setminus \left\{ k-1,k,k+1\right\} \right. \end{equation*} with boundary and impulsive conditions% \begin{equation*} \begin{array}{c} y_{0}^{(1)}=0\text{ }, \\ \\ \left( \begin{array}{c} y_{k+1}^{(1)} \\ y_{k+2}^{(2)}% \end{array}% \right) =\theta \left( \begin{array}{c} y_{k-1}^{(2)} \\ y_{k-2}^{(1)}% \end{array}% \right) ;\text{ }\theta =\left( \begin{array}{cc} \theta _{1} & \theta _{2} \\ \theta _{3} & \theta _{4}% …

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A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari Jan 2021

A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari

Turkish Journal of Mathematics

In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM …

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