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Yeryüzü canlılar için yaşama elverişli bir biçimde tanzim edilmiştir. Dünyanın imtihan yurdu olması hasebiyle de insanlar zaman zaman farklı türden musibet veya doğal afetler ile sınanmaktadır. Bu hadiselerden birisi Kur’ân’da başta zelzele olmak üzere çeşitli kavramlarla ifade edilen depremlerdir. Yeryüzünün canlı bir organizma olduğu dikkate alındığında onun sarsıntılarla değişime maruz kalması gayet tabiidir. Ancak bu depremlerin tek müsebbibi ne dünyanın olağan hareketleri ne de diğer canlı varlıklardır. Yeryüzünde cereyan eden bu olayların gerçekleşmesinde Yüce Allah’ın irade, kudret ve hikmeti tecelli etmekle birlikte kusur ve ihmalkârlıktan dolayı oluşan zararda da insanoğlunun payına düşmektedir. İslâm âlimleri Kur’ân ve sünnetten ilgili nasları göz önünde bulundurarak depremlerin oluş hikmetleri konusunda farklı görüşler beyan etmişlerdir. Kimisi bu olayların ceza, kimisi ikaz, kimisi ibret ve kimisi de imtihan maksatlı olduğunu söylese de depremin ceza amaçlı olduğu düşüncesi hariç diğer hususlarda çoğunlukla aynı veya benzer meyanda kanaatler ileri sürülmüştür. Depremin işlenen suçların bir cezası olup-olmadığına dair ihtilaf olmakla birlikte bu olayın, Allah’ın takdir ettiği yasalar çerçevesinde gerçekleştiği, bunda mutlak etkin ve yetkin gücün Allah (c.c.) olduğu konusunda ittifak sağlanmıştır. Ancak bu farklı görüşlerin Kur’ân, sünnet ve aklî delillerle uzlaştırılması mümkündür. Bu minvalde toptancı bir bakış açısıyla meseleye yaklaşmak yanlış inanç ve anlayışların ortaya çıkmasına sebebiyet vermektedir. Zira Kur’ân ve sünnette yer alan hakikatler, akla ve mantığa tezat teşkil etmez. Bu itibarla Kur’ân, depremi doğal bir afet olarak adlandırmakla birlikte kendisinden ders ve ibretler çıkarılması gereken bir ikaz aracı, çarpıcı mesajlar ihtiva eden bir imtihan olarak da söz etmiştir. Yüce Allah, hikmetinin bir gereği olarak zahiri sebepleri yaptıklarına birer perde kıldığı için Onun (c.c.) hikmetine tam olarak vakıf olmak neredeyse imkânsızdır. Çünkü dünya hikmet ve imtihan yurdudur, ceza ve mükâfat yeri değildir. Aksi bir durum söz konusu olmuş olsaydı yeryüzünde günah işleyen, zulmeden her bir insan derhal cezalandırılır ya da helak olurdu. Bu sebeple insan, sınırlı kapasitesiyle ilgili naslar çerçevesinde ancak bazı hikmetleri kısmen kavrayabilir ki bu durum onun dârü’l-hikmette yaşam sürmesinden kaynaklanmaktadır. Bu çalışmada; deprem manasında geçen kelimelerin Kur’ân’daki kullanımlarına yer verilmekte, deprem ve benzeri hadiselere maruz kalan önceki ümmetlerin hangi sebepler yüzünden helak oldukları, depremlerin hangi dini kavramlarla ilişkilendirildiği İslâm âlimlerinin yorumları ile izah edilmektedir. Ayrıca konu hakkında yapılan anket çalışmaları de dikkate alınarak aklî ve naklî delillerden hareketle en sahih değerlendirmeler yapılmaktadır. Dolayısıyla çalışmanın amacı depremlerin doğal birer afet mi, ilahî birer ceza mı, ibret alınması gereken bir hadise mi veya varsa başka nedenler mi olduklarına cevap bulmaya çalışmak ve ulaşılan sonuçları doküman analizi yöntemiyle uzlaştırmaya çaba sarf etmektir.

Kur’ân tüm insanlığa hitap eden beliğ bir kitaptır. O, herhangi bir iddianın ispatında insan aklının anlayamayacağı ifadeleri, metotları kullanmaz. Âyetleri üzerinde düşünen birisi, Kur’ân’ın muhataplarına çeşitli metotlarla yaklaştığını görür. Bu bağlamda Kur’ân; bazen muhataplarını korkutur, bazen verdiği cevaplarla münkirleri susturur, bazen de istifham cümleleri ile onları çaresiz bırakır. Kimi zaman yumuşak, kimi zaman sert, kimi zaman tehdit içerikli olsa da Kur’ân, insanları hidayete kavuşturma amacı güder ve akılları harekete geçirerek muhataplarını ikna etmeye çalışır. Her bilim dalının kendine özgü konuları olduğu gibi sıkça kullandığı bazı araştırma metotları da vardır. Kur’ân, akıl yürütme biçimlerinden olan bazı diyalektik metotlar kullanır. Bunlardan biri de taḥliye’den önce taḫliye metodudur. Bu metot, herhangi bir varlığın her türlü kusurdan arındırılması, ardından güzel meziyetlerle donatılması esasına dayanır. Bu çalışmada taḫliye, yasaklardan sakınarak her türlü terk etme eylemi; taḥliye ise emredilen fiilleri yaparak gerçekleşen iyilikler biçiminde ele alınacak, başta âyet ve hadisler olmak üzere klasik dönemde ve günümüzde yapılan çalışmalardan da yararlanarak Kur’ân mesajının anlaşılmasındaki rolü değerlendirilecektir.

Introduction: Understanding the variations of abdominal vascular structures is important for preventing complications of abdominal surgical procedures for gastrointestinal disease such as necrotizing enterocolitis or others that may arise in patients with congenital cardiac disease. We analysed the coeliac trunk and its branches in children with congenital heart disease to determine whether there is a greater prevalence of associated vascular abnormalities. Methods: We retrospectively analysed thoracic computed tomography (CT) angiograms performed in our hospital in paediatric patients with congenital heart disease. We documented the anatomical variations observed in abdominal sections in which the coeliac trunk and hepatic arteries were included in the field of view. We used the Uflacker classification to describe anatomical variants of the coeliac trunk, and the Michels classification and its modified version (Hiatt classification) to describe the anatomy of the hepatic artery system. Results: Our study included 178 patients with congenital heart disease. We identified coeliac trunk variants in 10.7% of the patients. Gastrosplenic trunk was to the most prevalent variant, amounting to 5.6% of total cases. We found hepatic artery variations in 19.1% of the patients. According to the Michels classification, the prevalence of accessory left hepatic artery arising from the left gastric artery as 4.5%, compared to 6.7% based on the Hiatt classification. Conclusion: The prevalence of coeliac trunk and hepatic artery variations in patients with congenital heart disease was not greater in our study compared to other series in the literature. Clinicians must be vigilant about the variations detected in multislice CT scans to avoid complications resulting from vascular abnormalities, especially in patients who undergo abdominal surgery. Resumen: Introducción: Comprender las variaciones de las estructuras vasculares abdominales es importante para prevenir complicaciones de procedimientos quirúrgicos abdominales por enfermedades gastrointestinales, como la enterocolitis necrotizante u otras que pueden desarrollarse en pacientes con cardiopatías congénitas. Se examinará el tronco celíaco y sus ramas en niños con cardiopatía congénita para determinar si hay una mayor prevalencia de anomalías concomitantes. Métodos: Exploración retrospectiva de pacientes pediátricos con cardiopatías congénitas sometidos a una angiotomografía computarizada (angio-TC) en nuestro hospital. Se registraron las variaciones anatómicas en secciones abdominales en las que el plano de adquisición incluía el tronco celíaco y las arterias hepáticas. Se utilizó el método de Uflacker para describir las variantes anatómicas del tronco celíaco. Las variaciones en el sistema de la arteria hepática se caracterizaron mediante la clasificación de Michels y la versión modificada de Hiatt. Resultados: La muestra incluyó a 178 pacientes pediátricos con cardiopatías congénitas. Se encontraron variaciones de la arteria celíaca en el 10,7% de los pacientes. La variante más prevalente era el tronco gastroesplénico, que representaba el 5,6% de todos los casos. La prevalencia de variaciones de la arteria hepática fue del 19,1%. La prevalencia observada de arteria hepática izquierda accesoria con origen en la arteria gástrica izquierda fue del 4,5%, según la clasificación de Michels y del 6,7% según la clasificación de Hiatt. Conclusión: En nuestro estudio, no se observó una prevalencia mayor de variaciones del tronco celíaco y de la arteria hepática en pacientes con cardiopatías congénitas en comparación con lo descrito en series previas. Los médicos deben prestar atención a las variaciones detectadas en las tomografías computarizadas multicorte para evitar complicaciones derivadas de variaciones vasculares, especialmente en pacientes sometidos a cirugía abdominal.

In this study, two fractional differential equations describing the characteristics of three-dimensional nonlinear ion-acoustic waves (IAWs) in plasmas are considered with the conformable fractional derivative (CFD). 3+1-dimensional space–time fractional Jimbo–Miwa (JM) equation and 3+1-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV-ZK) equation are reduced into ordinary differential equations and an investigation into the exact solutions is carried out through the modified exponential function method (MEFM). These exact wave solutions are beneficial in interpreting the interior structure and characteristics of physical phenomena modeled by the aforementioned nonlinear evolution equations (NLEEs) arising in magnetized plasma. Various analytical methods were applied to such equations. Therefore, it is vital to determine the proper technique for the present problem. The proposed scheme has demonstrated a different spectrum of wave structures. The portrait of the exact solutions permits the exploration of plasmas, plasma models, and optics. The software system Mathematica is employed and the rational, exponential, trigonometric, and hyperbolic function solutions are acquired. The graphical results are presented for the physical nature of the solutions. The results are compared with the integer-order models.

Introduction and Objective: The aim of this study was to evaluate the coronary arteries in patients undergoing thoracic CT angiography for congenital heart disease, to determine the frequency of detection of coronary artery anomalies in congenital heart diseases, and to determine which type of anomaly is more common in which disease. Materials and Methods: In our investigation, a 128-detector multidetector computed tomography machine was used to perform thorax CT angiography. The acquisition parameters were set to 80–100 kVp based on the patient’s age and mAs that the device automatically determined based on the patient’s weight. During the examination, an intravenous (IV) nonionic contrast material dose of 1–1.5 mL/kg was employed. An automated injector was used to inject contrast material at a rate of 1.5–2 mL/s. In the axial plane, 2.5 mm sections were extracted, and they were rebuilt with 0.625 mm section thickness. Results: Between October 2022 and May 2024, 132 patients who were diagnosed with congenital heart disease by echocardiography and underwent Thorax CT angiography in our department were retrospectively evaluated. Of the evaluated patients, 32 were excluded with exclusion criteria such as patients being younger than 3 months, older than 18 years, insufficient contrast enhancement in imaging and contrast-enhanced imaging, thin vascular structure, and motion and contrast artifacts; the remaining 100 patients were included in this study. The age range of these patients was 3 months to 18 years (mean age 4.4 years). Conclusion: In congenital heart diseases, attention to the coronary arteries on thoracic CT angiography examination in the presence of possible coronary anomalies may provide useful information.

The Hotelling T2 statistic is used to compare the mean vectors of two independent multivariate Gaussian distributions. Nevertheless, this statistic is highly sensitive to outliers and is not suitable for high-dimensional datasets where the number of variables exceeds the sample size. This study introduces a robust permutation test based on the minimum regularized covariance determinant (MRCD) estimator to address these limitations of the two-sample Hotelling T2 statistic. Simulation studies were performed to evaluate the proposed test’s empirical size, power, and robustness. Additionally, the test was applied to both uncontaminated and contaminated Alzheimer’s Disease datasets. The findings from the simulations and real data examples provide clues that the proposed test can be effectively used with high-dimensional data without being impacted by outliers. Finally, an R function within the “MVTests” package was developed to implement the proposed test statistic on real-world data.

Every word of the Qur'an ensures the understanding of the divine will. The foundation signs in it were created for this purpose. Just like the punctuation marks that ensure the correct understanding of a Turkish sentence, the foundation marks in the Qur'an have assumed the same function. The signs of foundation, which give the opportunity to breathe by interrupting the recitation at the places where the mana is completed, and the signs of ibtida, which provides the recitation starting from the appropriate place for the integrity of the meaning, have a significant importance in the authentic interpretation of the Qur'an. The scholar, who wrote very important works related to the field and brought an independent topic under the name of "Secâvend" to the science of recitation, undoubtedly Muhammad b. Tayfur es-Secavendi. According to him, it is considered obligatory to dwell on the foundation denoted by the remzi (م) in the mushafs. Because when vasl is performed in these places, the nature and meaning of the verse changes. Based on these reasons, a foundation is different from other types of foundations. In this study, the signs of the need for foundation were examined within the framework of the verse integrity, and it was analyzed why Secavendi considered it necessary to make a foundation, taking into account the possible meanings that may occur in the case of vasl.

The Boussinesq equation describes water with small amplitudes and long waves, which is one of the most famous nonlinear evolution equations. Boussinesq-type equations have become crucial for predicting wave transformations in coastal areas since dispersion, time dependence, and weak nonlinearity terms are included in the equation. Here, the Boussinesq-like equations by using the m+1/G′-expansion approach are investigated. In this work, we try to offer complexiton solutions to the studied types of Boussinesq equations and reveal the efficiency of this method to construct soliton solutions. The exact solutions for the Boussinesq-like equations, including spatiotemporal dispersion, are computed using this method. Complexiton traveling wave solutions in the forms of kink, singular, periodic, and periodic-lump are obtained through calculations. The graphs of these solutions are drawn and analyzed to better understand and analyze these gained solutions. Moreover, the existence of all solutions is verified, and to our knowledge, the solutions are novel.

This study analyzes the Hirota–Satsuma–Ito equation, which discusses the propagation of unidirectional shallow-water waves and the interactions between two long waves with different dispersion forms. For the proposed equation, the sine-Gordon expansion method has been considered. This method is derived from the sine-Gordon equation. Different types of solutions, namely, bright, periodic, and dark-bright soliton solutions, are derived. When these solutions are compared to other previously published research, to our knowledge, the study concludes that they are innovative, and this method was not applied to this equation. The validation of the obtained solutions is verified and plotted as three-dimensional figures to comprehend physical phenomena. With the proper parameter values, distinct graphs are created to convey the physical representation of specific solutions. The results of this paper show that the method effectively improves a system’s nonlinear dynamical behavior. This study will be useful to a wide range of engineers who specialize in engineering models. The findings show that the computational approach is successful, simple, and even applicable to complex systems.

Introduction:In this retrospective study, our purpose was to research the usefulness of apparent diffusion coefficient (ADC) histogram graphics for the preoperative diagnosis of parotis tumors with heterogeneous signal distribution.Methods:Our patient group included 50 patients with total 52 parotid gland masses who had diffusion-weighted imaging and ADC maps before operation or biopsy, which were archived in our instutional Picture Archiving and Communications System. Free-hand region of interest-based ADC histogram parameters were minimum (ADC min), maximum (ADC max), mean (ADC mean) and standard deviation (SD) (ADC SD). Statistical analyses were performed with the SPSS 17.0 using Kruskal-Wallis, Mann-Whitney U tests, Spearmans’ rho correlation and receiver operating characteristic (ROC) curve.Results:ADC min, ADC max and especially the ADC mean were statistically significant in differentiating pleomorphic adenoma (PA) from Warthin tumor (WT). ADC min and ADC max values were also significant in differentiating PA from malignant tumor (MT) (p0.05).Conclusion:Our results support the assumption that ADC histogram parameters can help discriminate PA from WT and PA from MTs preoperatively. However, they are unhelpful in the differential diagnosis of malignant masses from WT.

The purpose of this research paper is to investigate the (3+1)-dimensional Hirota bilinear equation that arises in nonlinear waves in fluid dynamics, plasma physics and shallow water waves. We use Hirota’s bilinear approach and a long-wave method to explore the dynamical features of the suggested equation. Multiple M-lump waves mixed with soliton solutions are constructed. Also, the breather wave and its interaction with one-soliton and M-lump waves are derived. These solutions are believed to play a role in understanding the dynamical aspects of the (3+1)-dimensional Hirota bilinear equation.

In this study, we investigate the (2 + 1)-dimensional Korteweg-De Vries (KdV) equation with the extension of time-dependent coefficients. A symbolic computational method, the simplified Hirota’s method, and a long-wave method are utilized to create various exact solutions to the suggested equation. The symbolic computational method is applied to create the Lump solutions and periodic lump waves. Hirota’s method and a long-wave method are implemented to explore single-, double- and triple-M-lump waves, and interaction physical phenomena such as an interaction of single-M-lump with one-, two-soliton solutions, as well as a collision of double-M-lump with single-soliton waves. Furthermore, the simplified Hirota’s method is employed to explore complex multi-soliton solutions. To realize dynamics, the gained solutions are drawn via utilizing different arbitrary variable coefficients.

In this study, the m+1G′-expansion technique and the extended rational sine–cosine approach are applied to investigate the (2+1)-dimensional integrodifferential equation, namely the Jaulent–Miodek evolution equation (JMEE). Via these powerful approaches, some wave solutions to the JMEE evolution equation are successfully constructed. Using suitable values of the parameters, we plot the 2- and 3-dimensional graphs of the reported solutions. The two utilized approaches are powerful and efficient mathematical tools that secure important wave solutions. The reported solutions in this study may be used in explaining the physical features of various nonlinear physical models.

The aim of this work, is to construct some novel solutions for a new extension of the shallow water model in (3+1)-dimensions. Based on two methods namely; simplified Hirota’s method and a long-wave method a class of solutions are reported. Multiple soliton solutions in complex form, breather wave, and mixed breather–soliton solutions are constructed by using simplified Hirota’s method. To explore rational solutions and construct a class of physical interaction phenomena, a long-wave method is applied to N-soliton solutions. To our knowledge, the addressed solutions in this article are novel. Moreover, to better realize the physical meaning of obtained solutions, all solutions are plotted in three-dimension. The obtained solutions may be used in a wide variety of physical scenarios relevant to the environment, including modeling of floods and tsunamis as well as flow in rivers and open channels.

In this paper, we find new travelling wave solutions to the nonlinear electrical transmission line model. Exponential function method is applied. This model is used to the voltage behaviors in electrical transmission lines. Under a suitable choice of control parameters, we plot the figures along with contour surfaces of new solutions by using computational programs such as Mathematica, Maple and Matlab. Some information about the behavior of voltage on the electrical lines is extracted. The hyperbolic, periodic or singular properties are reported.

Kur’ân ve sünnet, Müslümanların hayatını düzenleyen en önemli iki şer’î delildir. Onların belirlediği ya da sınırlarını çizdiği hükümler, her Müslümanı bağlayıcı niteliktedir. Bu bağlamda Kur’ân ve sünnet, bireyin dine bağlılık derecesini tayin eden birtakım ölçüler koymuştur. Bu ölçülerin en önemlilerinden biri de itidaldir. Her yer ve her şartta dengeyi sağlayan itidal, yerine göre insanı iffet sahibi kılar, yerine göre hikmet ehli yapar ve yerine göre ise cesaret sembolü kılar. İffetin olmadığı yerlerde ya hiçbir şeye iştah duymayan ya da helal-haram demeden her namusa göz diken insan tipleri belirir. Hikmetin olmadığı yerlerde ya hiçbir şeyden anlamayan ya da hakkı batıl, batılı da hak suretinde gösteren kimseler ortaya çıkar. Cesaretin olmadığı yerlerde de ya aşırı korkak bireyler ya da hiçbir şeyden korkmayan zalim diktatörler yetişir. İşte bu çalışmada, ifrat ve tefrit arasında yer alan orta halli bir duruş olarak gösterilen itidalin inanç, ibadet ve ahlâk boyutları dindarlık ölçeğinde ele alınacaktır. Ayrıca itidalin fert ve toplum hayatındaki lüzumuna, etkilerine yer verilecektir.

In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrödinger-Boussinesq system that includes beta derivative. The new exact solution is obtained have a hyperbolic function, trigonometric function, exponential function, and rational function. These solutions might appreciate in laser and plasma sciences. It is shown that this method, provides a straightforward and powerful mathematical tool for solving the nonlinear problems. Moreover, the linear stability of this nonlinear system is analyzed.

Assistive devices can significantly improve caregivers’ ability to help disabled people with their daily activities. Existing assistive devices are not fully capable of safe transfer and are still in their early stages of development. In this research, a body-transfer system is designed and developed to ensure that the posture and body angle of the person in the sagittal plane remains unaltered while transferring from bed to wheelchair and vice versa. Two independently controlled conveyor belts (2-DOF) mounted on the indigenously developed bed are employed to transfer the disabled person using a sliding approach. Additionally, a wheelchair with conveyor belts that are fully automated is used to carry and transfer the user to and from the wheelchair. Furthermore, an integrated control architecture has been developed for safely operating the entire body-transfer system (from an indigenously developed bed and wheelchair). Finally, an experimental assessment of the body-transfer system’s performance has been conducted. The experimental findings demonstrate that the system can transfer up to 120 kg of body weight while the user’s posture remains unaltered in the sagittal plane. Users perceive a reduction in wrist and shoulder pain index using the body-transfer system. The system has great potential for relocating disabled persons safely while reducing the load on caregivers.

The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this paper, an efficient mathematical technique, namely; the sine-Gordon expansion method is employed to construct the traveling wave solutions to the (3 + 1)-dimensional Kadomtsev–Petviashvili and (3 + 1)-dimensional nonlinear Schrödinger equations. Using suitable values of the parameters, the two- and three-dimensional figures of the obtained solutions are plotted. Keywords: Sine-Gordon expansion method, Kadomtsev–Petviashvili equation, Schrödinger equation, wave solutions

This manuscript aims to construct a family of travelling wave solutions to the high nonlinearity differential equation for obtaining new hyperbolic function solutions by using an analytical method, which is based on the exponential function. A number of new hyperbolic solutions for the model have been newly derived by using the method. We take advantage of some computer programming for all numerical calculations, and surfaces of solutions obtained in this paper. Keywords: Benjamin-Bona-Mahony-Peregrine-Burgers equation, The modified exponential function method, Hyperbolic function solution

The studies of the dynamics behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. This study investigates the nonlinear fractional modified Boussinesq equation and the fractional bad Boussinesq equation using the extended sinh-Gordon equation expansion method. Several travelling wave solutions are successfully constructed. By choosing suitable values of parameters, the 2D and 3D graphs of the reported solutions are successfully plotted. The convergence analysis of the applied method is also discussed. Keywords: The Sinh-Gordon equation, Boussinesq equations, Solitons, M-fractional derivative, Convergence analysis

In this work, N-soliton waves, fusion solutions, mutiple M-lump solutions and the collision phenomena between one-M-lump and one-, two-soliton solutions to the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation are successfully revealed. A class of one-, two-, three-soliton, one-, two-fusion solutions are derived via the Hirota bilinear method and 1-M-lump, 2-M-lump solutions are constructed via the long-wave method. Moreover, physical collision phenomenon of 1-M-lump with one-, two-soliton solutions and also, with fusion solutions are successfully presented. The velocity of the 1-M-lump wave in x- and y-direction are also studied.

In this paper, we use the modified exponential function method in terms of Kf(x) instead of ef(x)and the extended sinh-Gordon method to find some new family solution of the M-fractional paraxial non-linear Schrödinger equation. The novel complex and real optical soliton solutions are plotted in 2-D, 3-D with a contour plot. Moreover, the dark exact solutions, singular soliton solutions, kink-type soliton solution, and periodic dark-singular soliton solutions for M-fractional paraxial non-linear Schrödinger equation are constructed. We guarantee that all solutions are new and verified the main equation of the M-fractional paraxial wave equation. For existence, the constraint condition is also added.

The analytical solution of the longitudinal wave equation in the MEE circular rod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordon expansion is based on the well-known wave transformation and sine - Gordon equation. In the longitudinal wave equation in mathematical physics, the transverse Poisson MEE circular rod is caused by the dispersion. Some solutions with complex, hyperbolic and trigonometric functions have been successfully implemented. Numerical simulations of all solutions are given by selecting the appropriate parameter values. The physical meaning of the analytical solution explaining some practical physical problems is given.

This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM), which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.

In this paper, we apply the sine-Gordon expansion method which is one of the powerful methods to the generalized-Zakharov equation with complex structure. This algorithm yields new complex hyperbolic function solutions to the generalized-Zakharov equation with complex structure. Wolfram Mathematica 9 has been used throughout the paper for plotting two- and three-dimensional surface of travelling wave solutions obtained.

Firmalar, özellikle e-ticaret firmaları, öneri sistemleri kullanarak müşteri memnuniyetini, dolayısı ile karlılıklarını artırmayı hedeflemektedirler. Günümüzde Öneri Sistemleri yaygın olarak kullanılmakta ve bunları kullanan firmalara stratejik avantajlar sağlamaktadır. Bu sistemler farklı aşamalardan oluşurlar. İlk aşamada kullanıcı-ürün değerlendirme matrisi kullanılarak aktif kullanıcı ile diğer kullanıcılar arasındaki benzerlikler bulunur. Daha sonra bu benzerliklerden yola çıkılarak aktif kullanıcının yakın komşuları belirlenir. Tahmin hesaplama aşamasında, ilk adımda bulunan benzerlikler kullanılarak aktif kullanıcının yakın komşularının ağırlık vektörü oluşturulur. Komşular tahmin hesaplamasına bu ağırlıklar oranında etki ederler. Bu çalışmamızda işbirlikçi filtreleme algoritmalarının son basamağı olan tahmin hesaplama adımı için yeni yöntemler geliştirilmiştir. Bu yöntemlerin başarımı literatürde kullanılan değerlendirme metrikleri ile ölçülüp bu alanda yapılan çalışmalar ile karşılaştırılmıştır.

Companies, in particular e-commerce companies, aims to increase customer satisfaction, hence in turn increase their profits, using recommender systems. Recommender Systems are widely used nowadays and they provide strategic advantages to the companies that use them. These systems consist of different stages. In the first stage, the similarities between the active user and other users are computed using the user-product ratings matrix. Then, the neighbors of the active user are found from these similarities. In prediction calculation stage, the similarities computed at the first stage are used to generate the weight vector of the closer neighbors. Neighbors affect the prediction value by the corresponding value of the weight vector. In this study, we developed two new methods for the prediction calculation stage which is the last stage of collaborative filtering. The performance of these methods are measured with evaluation metrics used in the literature and compared with other studies in this field.

This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the considered model are derived. Various figures such as 3D and 2D surfaces with the selecting the suitable of parameter values are plotted.

Müminler için asıl amaç, Allah’ın (cc) hoşnutluğunu elde ederek dünya ve ahiret saadetine nail olmaktır. Bu hedefe en doğru ve en kısa yoldan ulaşmak elzemdir. Genel manada insanları, özelde ise müminleri, ilâhî rızaya ve asıl saadete namzet kılan Yüce Allah, Peygamberleri aracılığıyla en sağlam ve doğru yolu bildirmiştir. Kuşkusuz bu, sırât-ı müstakîm yoludur. Hak Teâlâ bu yolu, saadete kavuşmak isteyenler için bir vasıta kılmış ve buna tabi olmak gerektiğini birçok ayette belirtmiştir. Bu ilâhî davet doğrultusunda istikâmet üzere olmak, doğrusu çok büyük bir lütuftur. Böyle bir lütuftan mahrum kalmak ise, dünya ve ahiret açısından nasipsizlik ve ciddi bir kayıp demektir. İşte bu çalışma ile dil, fiil (amel) ve kalpte istikâmetin nasıl, ne şekilde tezahür ettiği Kur’ân ve sünnet doğrultusunda izah edilecektir.

In this study, by using the finite difference method (FDM for short) and operators, the discretized Cahn-Allen equation is obtained. New initial condition for the Cahn-Allen equation is introduced, considering the analytical solution given in Application of the modified exponential function method to the Cahn-Allen equation, AIP Conference Proceedings 1798, 020033 [1]. It is shown that the FDM is stable for the usage of the Fourier-Von Neumann technique. Accuracy of the method is analyzed in terms of the errors in and Furthermore, the FDM is treated in order to obtain the numerical results and to construct a table including numerical and exact solutions as well as absolute measuring error. A comparison between the numerical and the exact solutions is supported with two and three dimensional graphics via Wolfram Mathematica 11.

In this study, we have applied the modified exp(−Ω(ξ))-expansion function method to the (2 + 1)-dimensional Boussinesq water equation. We have obtained some new analytical solutions such as exponential function, complex function and hyperbolic function solutions. It has been observed that all analytical solutions have been verified to the (2 + 1)-dimensional Boussinesq water equation by using Wolfram Mathematica 9. We have constructed the two- and three-dimensional surfaces for all analytical solutions obtained in this paper using the same computer program.

In this paper, a fractional order economic system is studied. An active control technique is applied to control chaos in this system. The stabilization of equilibria is obtained by both theoretical analysis and the simulation result. The numerical simulations, via the improved Adams–Bashforth algorithm, show the effectiveness of the proposed controller.

In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation. Primarily, we seek some exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using ETEM. Then, we research dark soliton solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation by using GKM. Lastly, according to the values of some parameters, we draw two and three dimensional graphics of imaginary and real values of certain solutions found by utilizing both methods.

Objective: In this study, we reviewed the reproductive outcomes following ICSI in 5 couples where the male partners had undergone renal transplantations. Chronic renal failure and dialysis may adversely affect male reproductive function resulting in severely depressed semen parameters or even azoospermia, which maybe further adversely affected by the immunosuppression taken from after transplantation. Study design: Case report. Setting: A private fertility clinic. Patients: The study included five infertile couples where the male partners were the recipients of renal transplants, 3–15 years prior to having ICSI treatment. All couples suffered from male factor infertility, with diagnoses of; azoospermia, asthenoteratozoospermia, oligoasthenoteratozoopsermia. Results: In the 5 case reports 5 ICSI and 3 FET treatment procedures were completed. In all but one of the cases grade 1 quality embryos were obtained and transferred. From the 8 embryo transfers performed 4 pregnancies were obtained, one miscarried at 8 weeks and 3 resulted in live births. Conclusions: In this study, we showed that pregnancy and normal live birth were possible following ICSI treatment for male factor infertility, where male partners had had renal transplants and were under immunosuppressive therapy.

In this study, we investigate some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation and the (2 + 1)-dimensional cubic Klein–Gordon equation by using the generalized Kudryashov method. After we submitted the general properties of the generalized Kudryashov method in Section 2, we applied this method to these problems to obtain some new analytical solutions, such as rational function solutions, exponential function solutions and hyperbolic function solutions in Section 3. Afterwards, we draw two- and three-dimensional surfaces of analytical solutions by using Wolfram Mathematica 9.

Objective: To investigate the use of an oocyte M-Index as a measure of the reproductive competence of oocyte cohorts collected following COS for ICSI. Design: A retrospective analysis of 3135 autologous ICSI cycles. Setting: A private IVF clinic. Materials and methods: Oocytes were denuded immediately after oocyte collection and the in vivo oocyte M-Index was calculated for the oocyte cohort collected (number of normal metaphase II oocytes per total number of normal oocytes collected). The measured outcomes were analyzed according to the M-Index (0–20%, 21–40%, 41–60%, 61–80%, and 81–100%) and female age (20–30, 31–40 years). Main outcomes: Clinical pregnancy. Results: 60,955 oocytes were collected from the 3135 ICSI cycles, 57,214 (93.9%) were normal and 39,364 (68.8%) of these were metaphase II oocytes. 71.6% of metaphase I oocytes reached nuclear maturity by the time of the ICSI procedure. Trend analyses of fertilization and clinical pregnancy to M-Index showed that fertilization increased significantly (p 40%. Conclusion: Our analysis shows that a simple maturation index calculated at the time of oocyte collection in a given ICSI cycle provides important prognostic information with regard to potential pregnancy outcomes and may reflect the importance of cytoplasmic maturation in oocyte competence.

In the last decade, it has been proven in several research papers that, mathematical tools are rather power in describing real world problem in all fields of science, technology and engineering. Various mathematical models that examine real world problems have been studied and developed with the aim of predicting the future. Due to the wider applicability of these tools, research observes that the field of applied sciences is a rapidly growing discipline and has engaged the minds of researchers. The recently developed mathematical models bear certain kinds of complexities. Therefore new methods have been elaborated for observing the properties of intricated models accurately. Moreover, comprehensive information about the models have been found by modifiying the existing methods in literature. By means of the outstanding increase in information, such findings uncover new aspects and properties of real world problems. In addition, structural changes of models and technical improvements in practices brought out novel challenging issues. Such challenges have resulted in new and modified methods. Therefore, the studies in such fields are essential and meaningful in understanding the diverse aspects of the models. This special issue aims at addressing these interesting research matters in the field of applied and engineering sicences. The main source of the articles in this special issue were the selected papers from those presented at the Second International Conference on Computational Mathematics and Engineering Sciences (CMES2017), which was held on May 20-22, 2017, in Istanbul, Turkey. During CMES2017, several various papers related to applied and engineering sicence have been presented. In this special issue, we have received 12 manuscripts based on rigorous reviews. This special issue has greatly benefited from the cooperation among the authors, reviewers, and editors. We would like to express our sincere gratitude to Moulay Ismail University and Firat University for organizing CMES2017 Conference and all the authors for their contributions, which has made this special issue possible.

This study bases attention on new analytical solutions of Phi-four equation. The modified exp -expansion function method (MEFM) has been used to obtain analytical solutions of the Phi-four equation. By using this method, dark soliton solutions and trigonometric function solution of the Phi-four equation have been found.

In this study, a new approach that assumes and is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-cosh-Gordon equations. Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions. According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.

We put into operation a moderately original analytical modus operandi, the Homotopy decomposition method, for getting to the bottom of coupled nonlinear van der Pol type’s equations arising in chaotic synchronization dynamics of coupled non-linear oscillators. Numerical solutions are given, and some properties show signs of physically reasonable reliance on the parameter values. The trustworthiness of HDM and the lessening in calculation bestow HDM a wider applicability. On top, the calculations concerned in HDM are especially trouble-free and undemanding. It is verified that HDM is a controlling and capable utensil for nonlinear ODEs. It was also established that HDM is further professional than the PEM, ADM, VIM, HAM and HPM. We can without difficulty bring to a close that the Homotopy decomposition method is an efficient tool to solve approximate solution of nonlinear partial differential equations.

In this paper, the cubic-quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation in parabolic law media are investigated to obtain the dark, singular, bright-singular combo and periodic soliton solutions. Two powerful methods, the m + G ′ G improved expansion method and the exp − φ ξ expansion method are utilized to construct some novel solutions of the governing equations. The obtained optical soliton solutions are presented graphically to clarify their physical parameters. Moreover, to verify the existence solutions, the constraint conditions are utilized.

The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions.

In this study, the generalized Kudryashov method (GKM) is handled to find exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. These time-fractional equations can be turned into another nonlinear ordinary differantial equation by travelling wave transformation. Then, GKM has been implemented to attain exact solutions of time-fractional Burgers equation, time-fractional Cahn-Hilliard equation, and time-fractional generalized third-order KdV equation. Also, some new hyperbolic function solutions have been obtained by using this method. It can be said that this method is a generalized form of the classical Kudryashov method.

The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM) to some interesting nonhomogeneous fractional ordinary differential equations (FODEs). Finally, we use the solutions to form two-dimensional (2D) graphs, by using the symbolic algebra package Mathematica Program 7.

A new method with a different auxiliary equation from the Riccati equation is used for constructing exact travelling wave solutions of nonlinear partial differential equations. The main idea of this method is to take full advantage of a different auxilliary equation from the Riccati equation which has more new solutions. More new solitary solutions are obtained for the RLW Burgers and Hirota Satsuma coupled equations.

The classification of exact solutions, including solitons and elliptic solutions, to the generalized equation by the complete discrimination system for polynomial method has been obtained. From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.

By considering an improved tanh function method, we found some exact solutions of Boussinesq and Burgers-like equations. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. We found some exact solutions of the Boussinesq equation and the Burgers-like equation.