Solitary Type Research Articles

Solitary wave type solutions of nonlinear improved mKdV equation by modified techniques

In this paper, the improved and modified version of the Sardar sub-equation method (IMSSEM) and the improved generalized Riccati equation mapping method (IGREMM) are manipulated effectively and generously to determine the exact solitary wave soliton solutions of the improved modified KdV (mKdV) equation. The purpose of this study is to provide novel exact solutions to the improved mKdV equation. Specifically, we utilized IMSSEM and IGREMM to study different solutions of the nonlinear improved mKdV equation, focusing on exponential, trigonometric, and trigonometric hyperbolic type solutions. Furthermore, the plotting of various solutions for direct viewing analysis is provided in two and three-dimensional graphs. The new strategies are straightforward, quick, and efficient and have many other advantages, whereas, they provide the most accurate and unique solution to many other types of nonlinear partial differential equations (NPDEs), which usually arise in engineering and applied sciences. It should be noted that these methodologies are novel mathematical instruments that have shown to be the most effective mathematical tools for solving higher-order nonlinear partial differential equations in mathematical physics. Symbolic computation was used to validate all of the solutions that were established. Thus, it is also hoped that these techniques will ultimately reduce the cumbersome workload involved during the process of solutions to complicated NLPDEs.

Ultimate internal pressure bearing capacity of unconstrained and constrained X80 oil and gas pipelines with three typical dents

Three typical dents, denoted as types I, II, and III, encapsulate the prevailing manifestations of mechanical impairment encountered by oil and gas pipelines. Presently, scholarly attention is predominantly directed towards the scrutiny of load-bearing capabilities in pipelines afflicted by a solitary type of dent. To unravel the intricate impact of three typical dents on the performances of dented pipelines, three distinct models of pipeline dents under different constraints were studied in this work. These findings reveal that unconstrained dents consistently exhibit greater plastic strain and deformation zone dimensions compared to their constrained counterparts. The spring-back and rebound performances in unconstrained pipelines were fortified and the external load resistance in constrained pipelines was enhanced by augmenting the indenter diameter and introducing internal pressure. Both unconstrained dents and type I constrained dents failed consistently in the non-dented region, with their ultimate internal pressure resistance unaffected by the constraining factors. In contrast, type II and III constrained dents, featuring smaller indenters, greater dent depths, and reduced diameter-to-thickness ratios, failed within the dented region, which results in a weakened ultimate internal pressure-bearing capacity. Failure occurred in the non-dented region under opposite conditions, leaving the internal pressure resistance unaffected. Finally, dimensionless predictive formulas for the ultimate internal pressures of the type II constrained and type III X80 dented pipelines were obtained through nonlinear fitting. This comprehensive exploration revealed the variations in the ultimate internal pressure-bearing capacities induced by dents, thereby providing valuable insights for pipeline design and safety considerations.

Construction of a Prognostic Prediction Model of Patients with Pathologic N0 in Resected Invasive Mucinous Adenocarcinoma of the Lung

Invasive mucinous adenocarcinoma (IMA) was a rare and specific type of lung adenocarcinoma, which was often characterized by fewer lymphatic metastases. Therefore, it was difficult to evaluate the prognosis of these tumors based on the existing tumor-node-metastasis (TNM) staging. So, this study aimed to develop Nomograms to predict outcomes of patients with pathologic N0 in resected IMA. According to the inclusion criteria and exclusion criteria, IMA patients with pathologic N0 in The Affiliated Lihuili Hospital of Ningbo University (training cohort, n=78) and Ningbo No.2 Hospital (validation cohort, n=66) were reviewed between July 2012 and May 2017. The prognostic value of the clinicopathological features in the training cohort was analyzed and prognostic prediction models were established, and the performances of models were evaluated. Finally, the validation cohort data was put in for external validation. Univariate analysis showed that pneumonic type, larger tumor size, mixed mucinous/non-mucinous component, and higher overall stage were significant influence factors of 5-year progression-free survival (PFS) and overall survival (OS). Multivariate analysis further indicated that type of imaging, tumor size, mucinous component were the independent prognostic factors for poor 5-year PFS and OS. Moreover, the 5-year PFS and OS rates were 62.82% and 75.64%, respectively. In subgroups, the survival analysis also showed that the pneumonic type and mixed mucinous/non-mucinous patients had significantly poorer 5-year PFS and OS compared with solitary type and pure mucinous patients, respectively. The C-index of Nomograms with 5-year PFS and OS were 0.815 (95%CI: 0.741-0.889) and 0.767 (95%CI: 0.669-0.865). The calibration curve and decision curve analysis (DCA) of both models showed good predictive performances in both cohorts. The Nomograms based on clinicopathological characteristics in a certain extent, can be used as an effective prognostic tool for patients with pathologic N0 after IMA resection.

Solitary lung adenocarcinoma: follow-up CT, pathological-molecular characteristics, and surgical prognosis for different morphological classifications

ObjectiveTo investigate the dynamic changes during follow-up computed tomography (CT), histological subtypes, gene mutation status, and surgical prognosis for different morphological presentations of solitary lung adenocarcinomas (SLADC).Materials and methodsThis retrospective study compared dynamic tumor changes and volume doubling time (VDT) in 228 patients with SLADC (morphological types I–IV) who had intermittent growth during follow-ups. The correlation between the morphological classification and histological subtypes, gene mutation status, and surgical prognosis was evaluated.ResultsAmong the 228 patients, 66 (28.9%) were classified as type I, 123 (53.9%) as type II, 16 (7%) as type III, and 23 (10.1%) as type IV. Type I had the shortest VDT (254 days), followed by types IV (381 days) and III (501 days), and then type II (993 days) (p < 0.05 each). Type I had a greater proportion of solid/micropapillary-predominant pattern than type II, and the lepidic-predominant pattern was more common in type II and III than in type I (p < 0.05 each). Furthermore, type II and IV SLADCs were correlated with positive epidermal growth factor receptor mutation (p < 0.05 each). Lastly, the Kaplan–Meier curves showed that the disease-free survival was longest for patients with type II tumors, followed by those with type III and IV tumors, and then those with type I tumors (p < 0.001 each).ConclusionA good understanding of the natural progression and pathological-molecular characteristics of different morphological SLADC types can help make accurate diagnoses, develop individual treatment strategies, and predict patient outcomes.Critical relevance statementA good understanding of the natural progression and pathological-molecular characteristics of different morphological solitary lung adenocarcinoma types can help make accurate diagnoses, develop individual treatment strategies, and predict patient outcomes.Key points• Type I–IV solitary lung adenocarcinomas exhibit varying natural progression on serial CT scans.• Morphological classification of solitary lung adenocarcinomas predicts histological subtype, gene status, and surgical prognosis.• This classification of solitary lung adenocarcinomas may help improve diagnostic, therapeutic, and prognosticating abilities.Graphical

Stepwise progression of invasive mucinous adenocarcinoma based on radiological and biological characteristics

IntroductionInvasive mucinous lung adenocarcinoma (IMA) has unique radiological findings and pathological characteristics. IMA is classified into solitary and pneumonic types; however, it is unclear whether these are biologically identical. MethodsA single-center retrospective analysis was performed for 70 IMA patients (solitary type [n = 38] and pneumonic type [n = 32]) who underwent pulmonary resection between January 2010 and December 2018. We compared clinical and biological characteristics between the two types. ResultsThe frequencies of genetic alternations such as EGFR, KRAS, BRAF, GNAS, ERBB2, TP53, NRG1, and MET were not different. Immunohistochemically, expression of MUC1 was significantly more common in the pneumonic type (5.0% versus 20.0%, p = 0.01) and diffuse MUC6 positive in the solitary type (39.0% versus 13.0%, p = 0.02). We further classified solitary types into those with or without ground-glass opacity (GGO) and pneumonic types into those with or without crazy-paving appearance (CPA), and evaluated their surgical outcomes. Five-year overall survival and relapse free survival rates were 95.8%/86.6%, 64.3%/70.7%, 74.6%/68.9%, and 50.0%/28.6% in patients with solitary type with GGO, solitary type without GGO, pneumonic type without CPA, and pneumonic type with CPA, respectively. ConclusionsThere were no differences in genetic alternations; however, mucin expression pattern was different. Surgical outcomes were different according to the presence of GGO in the solitary type and the presence of CPA in the pneumonic type. These findings suggested a stepwise progression from solitary to pneumonic IMA.

On the dynamics of the (2+1)-dimensional chiral nonlinear Schrödinger model in physics

The nonlinear Schrödinger equation is one of the significant nonlinear complex models describing the optical solitons in dispersive media. In this study, the (2+1)-dimensional chiral nonlinear Schrödinger model has been investigated analytically which is of key importantance in the field of fluid sciences. A variety of exclusive travelling waveform solutions have been established for the complex dynamical model by employing a set of eminent analytical approaches namely the extended modified auxiliary equation mapping method, the improved F-expansion method, and the unified method, respectively. We obtained different forms of solitary types solutions with the help of these technique. The outcomes are a set of bell-shaped, single periodic, optical, and multi-periodic solutions. Finally, the stability of the developed results is also established to validate the computations. The study provides a very spectacular and appropriate way to put together several interesting wave demonstrations for more complex models of current era.

A Comparative Study on Generation and Propagation of Nonlinear Waves in Shallow Waters

This study is concerned with the generation and propagation of strongly nonlinear waves in shallow water. A numerical wave flume is developed where nonlinear waves of solitary and cnoidal types are generated by use of the Level I Green-Naghdi (GN) equations by a piston-type wavemaker. Waves generated by the GN theory enter the domain where the fluid motion is governed by the Navier–Stokes equations to achieve the highest accuracy for wave propagation. The computations are performed in two dimensions, and by an open source computational fluid dynamics package, namely OpenFoam. Comparisons are made between the characteristics of the waves generated in this wave tank and by use of the GN equations and the waves generated by Boussinesq equations, Laitone’s 1st and 2nd order equations, and KdV equations. We also consider a numerical wave tank where waves generated by the GN equations enter a domain in which the fluid motion is governed by the GN equations. Discussion is provided on the limitations and applicability of the GN equations in generating accurate, nonlinear, shallow-water waves. The results, including surface elevation, velocity field, and wave celerity, are compared with laboratory experiments and other theories. It is found that the nonlinear waves generated by the GN equations are highly stable and in close agreement with laboratory measurements.

The Association of Pachydrusen Characteristics with Choroidal Thickness and Patient's Age in Polypoidal Choroidal Vasculopathy versus Central Serous Chorioretinopathy.

We investigated the relationship between pachydrusen and choroidal thickness and age in eyes with polypoidal choroidal vasculopathy (PCV) and fellow eyes, compared to eyes with central serous chorioretinopathy (CSC). This retrospective study included 89 eyes with PCV and 146 eyes with CSC. The number, location, and shape of the pachydrusen and their association with choroidal thickness and age were analyzed. PCV eyes showed pachydrusen more frequently than eyes with CSC (52% vs. 20%, p < 0.001). Large solitary type and clustered type were more frequent in PCV eyes compared to CSC eyes (p = 0.003 and p = 0.001, respectively). Subfoveal choroidal thickness was associated with pachydrusen in eyes with PCV (odds ratio [OR] 1.006, 95% confidence interval [CI] 1.001–1.011, p = 0.027), while age was associated with pachydrusen in CSC eyes (OR 1.137, 95% CI, 1.073–1.205; p < 0.001). Pachydrusen were localized directly over the pachyvessel on optical coherence tomographic findings in approximately two thirds of PCV eyes and fellow eyes (62% and 67%, respectively). Risk factors for pachydrusen differ according to diseases. The presence of pachydrusen was associated with choroidal thickness in PCV, while the association with age was more prominent in CSC.

Abundant variant wave patterns by coupled Boussinesq–Whitham–Broer–Kaup equations

This paper focus on searching for abundant wave patterns to time-fractional coupled Boussinesq–Whitham–Broer–Kaup equations, which plays a crucial role in obtaining the novel insights for propagational dynamics of shallow water. Through the innovative application of complete discrimination system for polynomial method (CDSPM) and conformable fractional transformation, the whole types of solutions for the fractional equations presented in the existing literatures are obtained. In particular, we obtain the solitary wave type solutions and Jacobian elliptic functions type solutions, and the later are initially founded. The existence and applicability of the obtained solutions are proved by concrete examples. Finally, the nature of wave propagation and the fractional characteristics are intuitively revealed by graphical simulations.

Nevus Lipomatosus Cutaneous Superficialis of Hoffmann and Zurhelle: a rare cutaneous hamartoma

Nevus lipomatosus cutaneous superficialis (NLCS) is a rare idiopathic cutaneous hamartoma characterized by ectopic clusters of mature adipose tissues in dermis. It is classified into two types. Classical type presenting as multiple lesions with onset at birth or within third decade of life and solitary type with onset between third to sixth decade of life. Here we present a case of 45 years female with adult onset, asymptomatic, grouped, skin colored, soft sessile growth in zosteriform pattern on left buttock. We here intend to report rare case of classical Nevus Lipomatosus Cutaneous Superficialis.

Constructing new solitary wave solutions to the strain wave model in micro-structured solids

In the present article, the improved modified extended tanh function method is implemented to investigate the strain wave model which governs the wave propagation in micro-structured solids. Solitary and other wave solutions are provided for this model such as singular and bright solitary type solutions. In addition Kink, periodic, Jacobi elliptic, hyperbolic, exponential and Weierstrass elliptic type solutions are constructed. To show the physical characteristics of the raised solutions, graphical illustration of some solutions is presented.

Primary intracranial malignant melanomas in solitary type: a tertiary center experience

PurposeSolitary type primary intracranial malignant melanoma (PIMM) is extremely rare but fatal. The optimal treatment algorithm according to clinical relevance of symptoms and outcomes is unclear. This series emphasized the prognostic factors of solitary PIMM and established the treatment algorithm for this rare disease. MethodsPatients with solitary PIMMs were pathologically verified and treated with neurosurgical tumor resection. All solitary PIMMs recruited at our institute received multidisciplinary team care. We analyzed the clinical findings and prognostic factors. ResultsThe study cohort included 10 patients. PIMMs in solitary type impacted middle-aged populations with male predominance in Taiwan. Most patients (80%) presented a single tumor initially. Six patients had progressed to multiplicity after the initial treatment. Rates of tumor bleeding and leptomeningeal metastasis seeding (LS) are high in solitary PIMMs. Patients who had gross-total resection (GTR) had better survival than those who had incomplete resection, with median overall survival (OS) rates of 170.4 months vs. 5.23 months (p = 0.004). Multiplicity, eloquent area involvement, initial tumor bleeding, LS, hydrocephalus, and Karnofsky Performance Score < 80 at diagnosis were associated with negative outcomes in progression-free survival and OS. Adjuvant radiotherapy for patients who had LS and for those who cannot undergo grossly total tumor removal resulted in a good outcome. ConclusionsGTR demonstrated better outcomes for solitary PIMM. For recurrent tumors, aggressively repeated surgical resection remained beneficial for selected cases. Adjuvant radiotherapy was a treatment option for LS following operation. We proposed a possible treatment algorithm for solitary PIMM.

Drift of elastic floating ice sheets by waves and current: Multiple sheets

A nonlinear theoretical model for deformations, oscillations, and drift motions of multiple elastic ice sheets in shallow waters due to combined nonlinear waves and uniform current is presented. The model is based on the Green–Naghdi theory for the fluid motion and the thin plate theory for the deformation of the ice sheets. In principle, there are N number of the floating sheets with arbitrary lengths, drafts, and rigidities, which may be located at arbitrary distances from each other. Nonlinear waves of solitary and cnoidal types are considered, and there are no restrictions on the wave properties (wave height or wave period). The sheets, located at different positions, are shown to drift with different speeds, but surge in most of the wave conditions with equal amplitudes. It is shown systematically that wavelength and spacing between the sheets are the critical parameters determining the drift response of a set of freely floating ice sheets. When wavelength is equal to the distance between the centers of the sheets, they bend and drift in resonance, causing the largest wave reflection. The ambient current is found to affect the drift motion of the sheets nonlinearly. This work complements the part I paper of the same title, where drift motion of a single ice sheet was investigated.

A new structure of optical solitons to the (n+1)-NLSE

In the current study, the unified technique is employed to produce some new optical solitons for the (n + 1)-dimensional nonlinear Schrödinger equation. Namely, new structures of hyperbolic solitary types explained many complex phenomena’s, which are very important in plasma physics and optical fibers. The proposed technique avoids so many complicated calculations. This technique can be implemented for solving several models arising in applied science. Finally, the wave amplitudes may be controlled by the physical coefficients of dispersion and nonlinearity.

Spatiotemporal nonlinear evolution of the laser pulse and turbulence generation in laser produced plasmas

This study presents a model to understand the behavior of the turbulence generated in the magnetic field of mega gauss order during high-intensity laser interaction with magnetized plasma. The modified nonlinear Schrödinger (MNLS) equation is developed by contemplating the effect of the group velocity dispersion, diffraction, and nonlinearity induced by the relativistic variation of electron mass and the nonlinear ponderomotive force. Numerical simulation is carried out to solve the dimensionless MNLS equation. The simulation results show the generation of the solitary wave type coherent structures in the nonlinear spatiotemporal evolution of the laser pulse at the early stage, but subsequent turbulence generation has also been observed. The ensemble-averaged turbulent power spectrum has been studied and the power-law scaling is approximately ∼ k−1.85(a solid red line of scaling k−1.85 is given for reference). To get insight into the spatiotemporal nonlinear development of the laser pulse, while propagating in the plasma medium, a semi-analytical model has also been presented. The present study could be substantial in replicating astrophysical scenarios by laboratory simulations along with understanding the underlying quintessential physics of magnetic turbulence.

Pelvic Osteochondroma as a Differential Diagnosis for Abdominal Mass: A Case Report

Background: Osteochondroma is the most common benign tumor of the bone. Case Report: In this case, we present a young patient complaining of sensation of a mass in her abdomen since a few weeks ago and abdominal pain, which caused her visit to the clinic. Imaging studies revealed a well-defined lobulated lesion, and pathological examination was correlated with osteochondroma of the iliac bone Conclusion: This site for osteochondroma is very rare, and this case was the solitary type.

Estimated Glomerular Filtration Rate Decline at 1 Year After Minimally Invasive Partial Nephrectomy: A Multimodel Comparison of Predictors

BackgroundLong-term renal function after partial nephrectomy (PN) is difficult to predict as it is influenced by several modifiable and nonmodifiable variables, often intertwined in complex relations. ObjectiveTo identify variables influencing long-term renal function after PN and to assess their relative weight. Design, setting, and participantsA total of 457 patients who underwent either robotic (n = 412) or laparoscopic PN (n = 45) were identified from a multicenter international database. Outcome measurements and statistical analysisThe 1-yr estimated glomerular filtration rate (eGFR) percentage loss (1YPL), defined as the eGFR percentage change from baseline at 1 yr after surgery, was the outcome endpoint. Predictors evaluated included demographic data, tumor features, and operative and postoperative variables. Bayesian multimodel analysis of covariance was used to build all possible models and compare the fit of each model to the data via model Bayes factors. Bayesian model averaging was used to quantify the support for each predictor via the inclusion Bayes factor (BFincl). High-dimensional undirected graph estimation was used for network analysis of conditional independence between predictors. Results and limitationsSeveral models were found to be plausible for estimation of 1YPL. The best model, comprising postoperative eGFR percentage loss (PPL), sex, ischemia technique, and preoperative eGFR, was 207 times more likely than all the other models regarding relative predictive performance. Its components were part of the top 44 models and were the predictors with the highest BFincl. The role of cold ischemia, solitary kidney status, surgeon experience, and type of renorraphy was not assessed. ConclusionsPreoperative eGFR, sex, ischemia technique, and PPL are the best predictors of eGFR percentage loss at 1 yr after minimally invasive PN. Other predictors seem to be irrelevant, as their influence is insignificant or already nested in the effect of these four parameters. Patient summaryKidney function at 1 year after partial removal of a kidney depends on sex, the technique used to halt blood flow to the kidney during surgery, and kidney function at baseline and in the early postoperative period.

Atypical skeletal involvement in patients with Erdheim\u2013Chester disease: CT imaging findings

ObjectivesTo review retrospectively atypical bone findings from computed tomographic (CT) imaging in patients with Erdheim–Chester disease.MethodsAll 28 patients with Erdheim–Chester disease (13 men and 15 women; mean age, 45 years; range, 7–63 years) underwent chest-abdomen-pelvis CT. CT images were reviewed and analyzed for the various features of atypical bone lesions by two radiologists in consensus.ResultsTwenty-one patients had atypical bone involvement. Radiologically, these atypical osseous lesions were categorized into three types: diffuse, nodular and patchy. Eleven (52%) of the 21 patients had spinal lesions, of which four (36%) had the diffuse type, eight (73%) had the nodular pattern, and six (55%) had the patchy pattern. Sixteen (76%) of the 21 patients had pelvic involvement, of which two (13%) were diffuse, nine (56%) were nodular and 11 were (69%) patchy. Ribs were involved in seven (33%) of the 21 patients, with the nodular pattern in one (14%) patient and the patchy type in six (86%) patients. Clavicle involvement was seen in nine (43%) of the 21 patients, of which the diffuse type was found in only one (11%) patient, the nodular type in six (67%) patients, the solitary patchy type in four (44%) patients. Sternum involvement was seen in 10 (48%) of the 21 patients and all were nodular.ConclusionsThis series provides a detailed description of atypical bone involvement in Erdheim–Chester disease which on CT displays three major patterns. Understanding these patterns may help increase the accuracy of diagnosis of this disease.

Clinical and magnetic resonance imaging feature differences between solitary and multiple type Langerhans cell histiocytosis involving the craniofacial bone

PurposeTo investigate the clinical and contrast-enhanced magnetic resonance imaging (MRI) features of craniofacial bone Langerhans cell histiocytosis (LCH) and discuss the differences between a solitary lesion group (SLG) and multiple lesions group (MLG). MethodThis study included 22 consecutive patients with pathologically proven LCH who underwent contrast-enhanced MRI. The clinical data and MRI features were retrospectively assessed. ResultsThe mean patient age was 5 years, and 15 patients were male. The frontal bone was the most frequently affected bone. Ten and 12 patients were classified into the SLG and the MLG, respectively. The following MRI features were observed in >50% cases: T1WI hyperintensity in 15 (68%) cases, T2WI hyperintensity in 16 (73%) cases, bulging sign in 18 (82%) cases, concentric or eccentric soft tissue mass formation in 13 (59%) cases, soft tissue edema in 16 (73%) cases, any grade of bone marrow edema in 16 (73%) cases, surrounding bone enhancement in 17 (77%) cases, and surrounding soft tissue enhancement in 16 (73%) cases. Patient age was significantly higher in the SLG than that in the MLG (P = 0.0014). Perilesional bone marrow edema and enhancement were significantly more prominent in the SLG than in the MLG (P = 0.032, P = 0.040). ConclusionsContrast-enhanced MRI showed additional significant findings of mainly the surrounding details. Older age, extensive bone marrow edema, and enhancement may indicate solitary-type LCH rather than multiple-type LCH. These differences may help distinguish between solitary- and multiple-type LCH, which have different treatment strategies.

Nevus Lipomatosus Cutaneous Superficialis with a Histopathological Appearance Resembling Sclerotic Fibroma: A Rare Case Report

Background: Nevus lipomatosus cutaneous superficialis (NLCS) of Hoffmann–Zurhelle is a benign idiopathic hamartoma. There are two types of NLCS, multiple and solitary. They are found in the abdomen, lower back, buttocks, hips, upper posterior thighs, and pelvis. The diagnosis can be evaluated with a typical histopathological of mature fat cells in the dermis, with 10%–50% of the dermis. Case Report: We reported a case of NLCS with clinical papules and multiple nodules on the buttocks since the age of 6 years with a history of lipoma removal. The dermoscopic examination was conducted to confirm the diagnosis. The histopathological examination showed a dominant sclerotic fibroma with two sessions of biopsy and a few mature fats on the dermis after deeper cuts paraffin block. Cryotherapy with an open spray method is treatment of choice in this patient. Discussion: The appearance of the dermis in NLCS can be normal or an increase in collagen. Interestingly, collagen has sclerosis partially and resembles sclerotic fibroma never been reported. NLCS increases the amount of collagen; however, collagen as sclerosis remains obscure. The features of NLCS histopathological with other morphological abnormalities in the dermis have been reported, such as NLCS with perifollicular fibroma (PF) features. The sclerotic fibroma features are other morphological abnormalities in NLCS, as reported in the PF.