Numerical investigations of shallow water waves via generalized equal width (GEW) equation

In this article, a mathematical model representing solution of the nonlinear generalized equal width (GEW) equation has been considered. Here we aim to investigate solutions of GEW equation using a numerical scheme by using sextic B-spline Subdomain finite element method. At first Galerkin finite element method is proposed and a priori bound has been established. Then a semi-discrete and a Crank-Nicolson Galerkin finite element approximation have been studied respectively. In addition to that a powerful Fourier series analysis has been performed and indicated that our method is unconditionally stable. Finally, proficiency and practicality of the method have been demonstrated by illustrating it on two important problems of the GEW equation including propagation of single solitons and collision of double solitary waves. The performance of the numerical algorithm has been demonstrated for the motion of single soliton by computing L∞ and L2 norms and for the other problem computing three invariant quantities I1, I2 and I3. The presented numerical algorithm has been compared with other established schemes and it is observed that the presented scheme is shown to be effectual and valid

A novel implementation of Petrov-Galerkin method to shallow water solitary wave pattern and superperiodic traveling wave and its multistability: generalized Korteweg-de Vries equation

This work deals with the constitute of numerical solutions of the generalized Korteweg-de Vries (GKdV) equation with Petrov-Galerkin finite element approach utilising a cubic B-spline function as the trial function and a quadratic function as the test function. Accurateness and effectiveness of the submitted methods are shown by employing propagation of single solitary wave. The L2, L∞error norms and I1, I2and I3invariants are used to validate the applicability and durability of our numerical algorithm. Implementing the Von-Neumann theory, it is manifested that the suggested method is marginally stable. Furthermore, supernonlinear traveling wave solution of the GKdV equation is presented using phase plots. It is seen that the GKdV equation supports superperiodic traveling wave solution only and it is significantly affected by velocity and nonlinear parameters. Also, considering a superficial periodic forcing multistability of traveling waves of perturbed GKdV equation is presented. It is found that the perturbed GKdV equation supports coexisting chaotic and various quasiperiodic features with same parametric values at different initial condition

Weighted norm inequalities for the local sharp maximal function

YÖK Tez ID: 444338Bu tez ilk bölümü giriş olmak üzere yedi temel bölümden oluşmaktadır. İkinci bölümde bazı temel tanım ve kavramlar verilmiştir. Üçüncü bölümde ölçülebilir fonksiyonun dağılım fonksiyonlarının ve artmayan yeniden düzenlenmelerinin tanımları ve bazı özellikleri ile bir ölçülebilir fonksiyonun medyanı ile ilgili özellikler verilmiştir. Dördüncü bölümde BMO uzayı ile ilgili önemli özellikler ifade edilmiştir. Beşinci bölümde ise John-Strömberg maksimal fonksiyonu ve onun lokal versiyonu tanımlanmış ve bazı özellikleri incelenmiştir. Altıncı bölümde ağırlıklı John-Strömberg maksimal fonksiyonu ve onun lokal versiyonu tanımlanmış ve fonksiyonun ağırlıklı yeniden düzenlenmesi ile bu fonksiyonun ağırlıklı JohnStrömberg maksimal fonksiyonunun ağırlıklı yeniden düzenlenmesi arasındaki bağıntılar ifade edilmiştir. Son bölümde ise ağırlıklı John-Strömberg maksimal fonksiyonu, Hardy-Littlewood maksimal fonksiyonu ve Calderón-Zygmund singüler integral operatörü üzerine ağırlıklı norm kestirimleri incelenmiştir. Anahtar Kelimeler: Dağılım fonksiyonu, artmayan yeniden düzenlenme, medyan, Hardy-Littlewood maksimal fonksiyonu, Calderón-Zygmund singüler integral operatörü, BMO uzayı.This thesis consists of seven chapters including the introduction part. Some basic definitions and tools are given in the second chapter. The definition and some properties of distribution functions and non-increasing rearrangements of a measurable function, as well as the definition and main properties of median values of any measurable function are presented in the third chapter. BMO space is introduced and some main properties of functions from this space are expressed in the fourth chapter. John-Strömberg maximal function and its local version are defined and some properties of this function are investigated in the fifth chapter. Weighted version of John-Strömberg maximal function and its local version are introduced and relation between weighted non-increasing rearrangements of a function and weighted non-increasing rearrangements of its weighted JohnStrömberg maximal function are studied in the sixth chapter. In the last chapter, weighted norm inequalities related to the weighted John-Strömberg maximal functions, Hardy-Littlewood maximal functions and Calderón-Zygmund singular intergaral operators are expressed and proved. Key Words: Distribution function, non-increasing rearrangement, median, mean oscillation, local maximal function, weight, Hardy-Littlewood maximal function, Calderón-Zygmund singular intergaral operator

Lokal kesin maksimal fonksiyon için ağırlıklı norm eşitsizlikleri

Tez (Yüksek Lisans) -- Kırıkkale Üniversitesi111037

Rate of T alleles and TT genotype at MTHFR 677C->T locus or C alleles and CC genotype at MTHFR 1298A->C locus among healthy subjects in Turkey: Impact on homocysteine and folic acid status and reference intervals

Methylenetetrahydrofolate reductase (MTHFR) is important for folate and homocysteine (Hcy) metabolism. MTHFR 677C->T and 1298A->C MTHFR are two most common mutations which can affect. folate and total homocysteine (tHcy) status This study was designed to determine the rate of,MTHFR 677C->T and 1298A->C mutations. and their Influence Oil serum folate, Hcy and vitamin B12 Status and the reference intervals in 402 healthy Turkish adults. The rate of MTHFR 677C->T or 1298A->C mutations was 50 7% or 54 7%. respectively. The MTHFR 677C->T mutation-specific reference intervals for serum folate and tHcy were characterized by marked shifts in their upper limits In homozygote subjects for MTHFR 677C->T serum folate concentration was lower and serum tHcy concentration was higher than those in the wild genotype. all subjects had lower serum folate and 54% of the subjects had higher tHcy concentration,; than the cutoff Values of = 12 mu mol/L, respectively. Serum vitamin 1312 status was similar in all genotypes Serum tHcy concentrations were inversely correlated with serum folate and vitamin B12 concentrations in all genotypes These data show that the rate of MTHFR 677C->T and 1298A->C mutations is very high in Turks and serum folate and tHcy status are impaired by these mutations

Numerical solutions of kaup-kupershmidt and ıto equations with b-spline collocation method

In this study, it is aimed to obtain the numerical solutions of two types of fifth-order Korteweg-de Vries (KdV) equations namely Kaup-Kupershmidt (K-K) and Ito. For this purpose, collocation finite element method is used. L2 and L error norms are computed for single soliton solutions to demonstrate the proficiency and accuracy of the present method. The method is shown to be unconditionally stable by performing the von-Neumann stability analysis

Numerical solutions of some partial differential equations with B-spline finite element method

Bu tez altı bölüm içermektedir. Birinci bölümde, tezde kullanılan bazı temel kavramlar tanıtılmış, lineer oluşum denklemleri hakkında genel bilgiler verilmiştir. Sonlu farklar ve sonlu elemanlar yöntemleri ile birlikte spline interpolasyon ve B-spline interpolasyon fonksiyonları tanımlanmıştır. Son olarak, nümerik çözümleri hesaplanacak olan dalga denklemleri test problemleri ile birlikte tanıtılmıştır. İkinci bölümde; model problemlerden sınır şartları ile verilen Gilson-Pickering (GP) denklemi septik B-spline kollokasyon metodu kullanılarak nümerik olarak çözülmüştür. Tek solitary dalga hareketinin incelendiği test problemi ile tam çözüm ve nümerik sonuçlar karşılaştırılarak çözülmüştür. Elde edilen sonuçlar tablolaştırılmış ve denklem için kararlılık analizi yapılmıştır. Üçüncü bölümde; Genelleştirilmiş Oskolkov denkleminin yaklaşık çözümünü hesaplamak için kuintik B-spline fonksiyonlara dayalı kollokasyon sonlu elemanlar yöntemi uygulanmıştır. Önerilen yöntem, tek solitary dalga hareketi ve Gaussian ile Undular Bore başlangıç şartları kullanılarak çözülmüştür. Elde edilen sonuçlar tablolaştırılmış ve denklem için kararlılık analizi yapılmıştır. Dördüncü bölümde, Kudryashov-Sinelschkov denkleminin septik B-spline fonksiyonlar kullanılarak sonlu eleman modeli oluşturulmuştur. Kudryashov-Sinelschkov denkleminin şok dalga hareketi, iki solitary dalganın etkileşimi, Gaussian şartı ve Undular bore başlangıç şartı ile ele alınmıştır. Elde edilen sonuçlar tablolaştırılmış ve denklem için kararlılık analizi yapılmıştır. Beşinci bölümde, ilk bölümde tanıtılan fifth order Korteweg de Vries (fKdV) denklemlerinin sayısal çözümleri araştırılmıştır. Sawada-Kotera (SK), Caudrey-Dodd-Gibbon (CDG), Lax, Kaup-Kuperschmit (KK) ve Ito denklemleri için septik B-spline fonksiyonlar kullanılarak nümerik çözümleri elde edilmiştir. Her bir denklem için tek solitary dalga hareketi incelenmiş, sonuçlar tablolaştırılmıştır. Yine her bir denklem için kararlılık analizi yapılmıştır. Altıncı bölümde, her bir denklem için tezde kullanılan kollokasyon sonlu elemanlar yöntemi ile elde edilen sonuçlar ve öneriler verilmiştir.This Ph.D. thesis contains six sections. In the first section, some basic concepts used in the thesis are introduced and general information about linear formation equations is given. Spline interpolation and B-spline interpolation functions are defined together with finite difference and finite element methods. Finally, wave equations, whose numerical solutions are to be calculated, are introduced together with the test problems. In the second section; Gilson-Pickering (GP) equation given with boundary conditions from model problems is solved numerically by using septic B-spline collocation method. The test problem in which single solitary wave motion is examined is solved by comparing the exact solution and numerical results. Obtained results are tabulated and stability analysis is performed for the equation. In the third section; To calculate the approximate solution of the generalized Oskolkov equation, the collocation finite element method based on quintic B-spline functions is applied. The proposed method is solved using single solitary wave motion and Gaussian and Undular Bore initial conditions. Obtained results are tabulated and stability analysis is performed for the equation. In the fourth section, the finite element model of the Kudryashov-Sinelschkov equation is constructed using septic B-spline functions. Shock wave motion of Kudryashov-Sinelschkov equation, interaction of two solitary waves, Gaussian condition and Undular bore initial condition are discussed. Obtained results are tabulated and stability analysis is performed for the equation. In the fifth section, numerical solutions of the fifth order Korteweg de Vries (fKdV) equations introduced in the first section are investigated. Numerical solutions of Sawada-Kotera (SK), Caudrey-Dodd-Gibbon (CDG), Lax, Kaup-Kuperschmit (KK) and Ito equations are obtained by using septic B-spline functions. For each equation, single solitary wave motion is examined and the results are tabulated. Again, stability analysis is performed for each equation. In the sixth section, the results and suggestions obtained by the collocation finite element method used in the thesis for each equation are given

Predictability of lymph node involvement in uterus-confined endometrioid endometrial cancer by tumour size, pattern and location measured with transvaginal ultrasonography: can we save time?

We aimed to investigate whether transvaginal ultrasonography (TVUSG)-measured tumour size, pattern and location were significant predictors for lymph node metastasis in the uterus-confined endometrioid endometrial cancer (EEC) patients. A total of 213 patients with EEC were recruited and 73 of them were considered eligible and were analysed according to lymph node involvement. Tumour size, pattern and location measured by transvaginal ultrasound were recorded. Thereafter, patients were distributed according to their lymph node involvement and were compared with respect to these parameters. The patients’ median age was 56 (27–80). Mean of the resected lymph nodes was 29.68 and 33.5 in lymph-node-negative and positive patients, respectively (p=.525). Tumour diameter was measured >2 cm on transvaginal ultrasound in 28 (48.3%) and 13 (86.7%) cases of the lymph node-negative and positive arms, respectively (p=.008). Transvaginal ultrasound revealed that 18 (31.0%) tumours in lymph node-negative and two (13.3%) in the node positive patients had polypoid pattern (p=.171). Seventeen (54.8%) tumours of the lymph node-negative group and three (42.9%) of the node positive group were determined in the lower uterine segment (p=.250). While tumour diameter measured with TVUSG was predictable for lymph node involvement in the uterus-confined EEC, its pattern and location were not.Impact Statement What is already known on this subject? In clinically early-stage endometrioid endometrial cancer (EEC), it has been recognised for decades that selective lymphadenectomy is a more acceptable strategy than the systematic lymphadenectomy, owing to the low rate of lymph node metastases in the patients. Preoperative imaging, frozen section and recently accepted lymph node concept are the prominent methods in designating appropriate candidates for lymphadenectomy. The measurement of tumour diameter or size obtained intraoperatively by frozen section assessment is one of the parameters used in MAYO criteria for selective lymphadenectomy in endometrial cancer patients. What do the results of this study add? In our study, tumour diameter measured with transvaginal ultrasonography was predictable for lymph node involvement in the uterus-confined EEC. What are the implications of these findings for clinical practice and/or further research? Transvaginal ultrasonography-measured tumour diameter can be considered in deciding to proceed with pelvic lymphadenectomy while waiting for the frozen section result. It should be remembered that this approach could be considered only in clinics using MAYO criteria for selective lymphadenectomy, and it needs to be confirmed with more prospective studies

Five years single institution retrospective analysis of the borderline ovarian tumors'

WOS: 000399391600006Purpose: The aim of this study was to evaluate the borderline ovarian tumor cases who were operated in our clinic Material and Methods: The last 5 years' pathology reports, computer records and archival files of the Cukurova University Medical Faculty Gynecologic Oncology Unit were retrospectively reviewed for the borderline ovarian tumor patients. A total of 41 cases were detected and included in the study. Patients' demographic characteristics, preoperative assessments, operation and pathological features were evaluated Results: Patients' mean age was 41 and 85% of them were premenopausal. Average of the tumor diameter was found to be 10cm in the preoperative ultrasound examination. Mean of the preoperative ca125 value was 120. While total hysterectomy + bilateral salpingo-oophorectomy was applied to 12 cases, unilateral salpingo-oophorectomy was performed in the remaining 29 patients. Lymphadenectomy was carried out in 41.5% of the patients. Serous borderline was the most common histology (70.7%). Majority of the cases was with stage I disease (90.2%). No recurrences were determined among the study population Conclusion: Borderline ovarian tumors have a favorable prognosis and therefore, unilateral salpingo-oophorectomy can be suggested to be a safely treatment approach for patients who desire to protect their fertilit