Mohamed A. El-Beltagy

On the oscillation of third order neutral delay dynamic equations on time scales

Han et al. [Z. Han, T. Li, S. Sun, C. Zhang, Oscillation behavior of third order neutral Emden-Fowler delay dynamic equations on time-scales, Adv. Differential Equations 2010 (2010). Article ID 586312, 23 pages] gave some criteria for the oscillation and asymptotic behavior of solutions of the third order neutral delay dynamic equation (r(t)(x(t)-a(t)x(@t(t)))^@D^@D)^@D+p(t)x^@c(@d(t))=0 on a time scale T, where @c>0 is the quotient of odd positive integers. In this paper, the authors establish some new criteria for the oscillation of this equation that improve and unify those of Han et al.

Intraspinal neuroblastoma: Treatment options and neurological outcome of spinal cord compression

Malignant spinal cord compression (MSCC) is a common complication of cancer. Paraspinal neuroblastoma (NB) in the thoracic, abdominal and pelvic regions may extend into the neural foramina causing compression of nerve roots and even the spinal cord. The prompt initiation of specific treatment can improve the neurological outcome. The aim of the present study was to review the clinical features, the management received and the factors that may affect the outcome of patients with MSCC caused by paraspinal NB. During a period between July 2007 and December 2012, a total of 576 NB patients were treated at the Children’s Cancer Hospital (Cairo, Egypt). Intraspinal disease extension was present in 51 patients (9%). The children with intraspinal disease extension were reviewed for disease pattern, neurological manifestations and treatment outcome. Children with intraspinal disease extension had an equal male to female ratio (1:1), and approximately two-thirds of patients (34/51) had a clinically manifested cord compression. The duration of neurological manifestations was >4 weeks in 58.8% (20/34) of symptomatic patients and ≤4 weeks in 41.2% (14/34). Subsequent to starting treatment, neurological manifestations showed a complete recovery in 16 patients (47.1%), partial in 11 (32.4%), and stationary course was found in 7 (20.6%). Manifestations of ≤4 weeks in duration carried an improved outcome compared with longer time compression, with a complete recovery in 78.6%, versus 25% for patients with a longer symptom duration (P=0.008). The upfront treatment, patient age and site of the primary tumor did not significantly affect the neurological outcome. Spinal cord compression in NB can be effectively managed with upfront chemotherapy. Initial surgical decompression should be reserved for benign variants only, including ganglioneuroma. Neurological manifestations of <4 weeks duration upon presentation are usually reversible.

Numerical Approximation of Higher-Order Solutions of the Quadratic Nonlinear Stochastic Oscillatory Equation Using WHEP Technique

This paper introduces higher-order solutions of the stochastic nonlinear differential equations with the Wiener-Hermite expansion and perturbation (WHEP) technique. The technique is used to study the quadratic nonlinear stochastic oscillatory equation with different orders, different number of corrections, and different strengths of the nonlinear term. The equivalent deterministic equations are derived up to third order and fourth correction. A model numerical integral solver is developed to solve the resulting set of equations. The numerical solver is tested and validated and then used in simulating the stochastic quadratic nonlinear oscillatory motion with different parameters. The solution ensemble average and variance are computed and compared in all cases. The current work extends the use of WHEP technique in solving stochastic nonlinear differential equations.

Incidence of kiaa1549-braf fusion gene in Egyptian pediatric low grade glioma

BackgroundLow grade gliomas are the most common brain tumor in children. Tandem duplication involving the KIAA1549 and the BRAF kinase genes results in a gene fusion that has been recently characterized in a subset of low grade glioma While there is no clear evidence that the KIAA1549-BRAF gene fusion has an effect on prognosis, it is an attractive target for therapy development and as a diagnostic tool.MethodsIn the current study we examine the prevalence of KIAA1549-BRAF gene fusion in pediatric patients diagnosed with low grade glioma in the Egyptian population and its relationship to clinical and histological subtypes. Sixty patients between the ages of 1 to 18 years were analyzed for the presence of KIAA1549-BRAF fusion gene products using reverse transcription-PCR and sequencing. The clinicopathologic tumor characteristics were then analyzed in relation to the different fusion genes.ResultsKIAA1549-BRAF fusion genes were detected in 56.6% of patients. They were primarily associated with pilocytic astrocytoma (74.2%) and pilomyxoid astrocytoma (60%). Translocation 15–9 was the most common, representing (55.8%) of all positive samples followed by 16–9 (26.4%) and 16–11 (8.8%). Pilocytic astrocytomas presented primarily with 15–9 (32.2%), 16–9 (25.8%) and 16–11 (6.4%) while pilomyxoid astrocytomas presented with 15–9 (46.6%), 16–9 (6.6%) and 16–11 (6.6%) translocations.ConclusionGene fusion is found to be significantly increased in cerebellar pilocytic astrocytoma tumors. Furthermore, 15–9 was found to have a higher incidence among our cohort compared to previous studies. While most of the gene fusion positive pilomyxoid astrocytomas were 15–9, we find the association none significant.

Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation

A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.

Solution of the Stochastic Heat Equation with Nonlinear Losses Using Wiener-Hermite Expansion

In the current work, the Wiener-Hermite expansion (WHE) is used to solve the stochastic heat equation with nonlinear losses. WHE is used to deduce the equivalent deterministic system up to third order accuracy. The solution of the equivalent deterministic system is obtained using different techniques numerically and analytically. The finite-volume method (FVM) with Pickard iteration is used to solve the equivalent system iteratively. The WHE with perturbation technique (WHEP) is applied to deduce more simple and decoupled equivalent deterministic system that can be solved numerically without iterations. The system resulting from WHEP technique is solved also analytically using the eigenfunction expansion technique. The Monte-Carlo simulations (MCS) are performed to get the statistical properties of the stochastic solution and to verify other solution techniques. The results show that higher-order solutions are essential especially in case of nonlinearities where non-Gaussian effects cannot be neglected. The comparisons show the efficiency of the numerical WHE and WHEP techniques in solving stochastic nonlinear PDEs compared with the analytical solution and MCS.

Uncertainty Quantification of a 1‐D Beam Deflection Due to Stochastic Parameters

In this paper the uncertainty quantification of a 1‐D beam deflection subjected to stochastic excitation, stochastic material property and mixed stochastic parameters is considered. A stochastic finite‐volume solver based on the polynomial chaos expansion is developed and used to quantify the deflection in all cases. Monte Carlo simulations accelerated by a RBF neural network were used to verify the results. The RBF neural‐network is trained with the dominant eigenpairs of the covariance kernel to reduce the dimensionality of the neural network. The mean and variance of the beam maximum deflection is quantified, compared and verified in all cases.

Efficiency estimation of type-I censored sample from the weibull distribution based on sup-entropy

ABSTRACT On the basis of Awad sup-entropy, the efficiency function for type-I censored sample from the Weibull distribution is numerically introduced. The properties of the derived efficiency are discussed. Furthermore, for a given efficiency, the termination time of the experiment, and the maximum likelihood estimates for the Weibull parameters, are proposed. Simulation results are tabulated and discussed. Censored and complete samples are compared for a wide range of the efficiency. The comparisons show the quality of the developed algorithms and the effectiveness of using censoring in estimating with the Weibull distribution.

Oscillation Criteria for Some Higher Order Integrodynamic Equations on Timescales

We study the oscillation behavior for some higher order integrodynamic equations on timescales. We establish some new sufficient conditions guaranteeing that all solutions of theses equations are oscillatory. Some numerical examples in the continuous case are given to validate the theoretical results.

Optimal selection of energy storage systems

Given the variability of the demand on energy (electricity) from end consumers and the variability of supply from the renewable energy sources, the smart grid can suffer from the gap caused by the mismatch of these two variables. The energy storage techniques are required in order to minimize the impact of the mismatch between the supply and the demand. However, the selection of the storage technique and the specific storage device are very critical aspects to the success of the integration of renewable energy sources into the smart grid since this requires careful evaluation of available techniques and effective scheduling of their operations. The model we propose in this paper is based on mathematical modeling (specifically linear programming) which allows the evaluation of various storage systems such as Pumped Hydro Storage and different types of batteries from economic and performance aspects. The case of Saudi Arabia is used to show how the model can help the engineers and the decision makers in selecting the most efficient storage systems and how they can integrate the operations such that the interruption of the power supply is minimized.