Mathematical and Numerical Analysis of a Pair of Coupled Cahn-Hilliard Equations with a Logarithmic Potential

Mathematical and numerical analysis has been undertaken for a pair of coupled Cahn-Hilliard equations with a logarithmic potential and with homogeneous Neumann boundary conditions. This pair of coupled equations arises in a phase separation model of thin film of binary liquid mixture. Global existence and uniqueness of a weak solution to the problem is proved using Faedo-Galerkin method. Higher regularity results of the weak solution are established under further regular requirements on the initial data. Further, continuous dependence on the initial data is presented. Numerically, semi-discrete and fully-discrete piecewise linear finite element approximations to the continuous problem are proposed for which existence, uniqueness and various stability estimates of the approximate solutions are proved. Semi-discrete and fully-discrete error bounds are derived where the time discretisation error is optimal. An iterative method for solving the resulting nonlinear algebraic system is introduced and linear stability analysis in one space dimension is studied. Finally, numerical experiments illustrating some of the theoretical results are performed in one and two space dimensions

The Effect of Mediated Glosses on Vocabulary Retention and Reading Comprehension with English Language Learners in Saudi Arabia

This study investigated the effectiveness of mediated glosses for understanding technical terms with foreign language learners. Previous research has found that online glosses improve information access, comprehension, vocabulary retention, and efficiency. Pavio's dual coding theory and Mayer's generative theory both posit that learning should improve when multiple coding systems are engaged through different media representations. An expert panel in petroleum engineering identified critical technical terms (e.g. compress, velocity, and permeable). The designers then used an iterative process to refine definitions, pictures, and animations in developing three gloss conditions. For condition 1 (audio and text), the term was written in English and Arabic, pronounced in English and defined in English. Condition 2 (audio, text and picture) had condition 1 features with a picture. Condition 3 (audio, text and animation) had condition 1 features with an animation. Participants were 222, 18-24 year-old male native Arabic speakers enrolled in petroleum engineering courses. Three groups under three gloss conditions read an online story in English with 50 glossed words, and completed a 22-item multiple-choice comprehension test. The three groups then reviewed 59 glossed terms without the story, and completed a vocabulary test immediately following and two weeks later. Demographic and attitude questionnaires were administered. Results found that, when controlling for language ability, those who received audio, text, and picture glosses (M=9.72) had higher comprehension scores than the text-based group (M=8.35), F (2,218) =3.07, p<.05. Those who received the audio, text, and picture gloss (M=3.88) agreed that "Online texts are better than paper-based texts," more than the audio and text group (M=3.41); F (2,216) =3.10, p<.05. There was a positive relationship between students' language-learning anxiety and reading comprehension (r=.203, p<.05), immediate vocabulary test (r=.229, p<.05), and delayed vocabulary test (r=.207, p<.05). Moderate anxiety levels facilitated language learning. Online glosses with dynamic pictures were found to be more effective in supporting comprehension and were rated higher than text-based glosses. The design process revealed that pictorial and animated representations should include negative and positive examples. Dynamic pictures may often be as effective as animations. Further mediated gloss research with more advanced language learners is warranted

Rescue Of Embryonic Dysmorphogenesis in Diabetic Rats by Using the Antioxidant α- Lipoic Acid

Background: The risk of congenital anomalies in children of diabetic mothers is three to four times that in offspring of non-diabetic mothers. The exact mechanisms of these birth defects are not known. Of the several factors suggested to contribute to embryonic maldevelopment in diabetic pregnancy, the formation of reactive oxygen species (ROS) and subsequent disturbances to cellar defenses appears to be a plausible hypothesis. Antioxidants have been reported to rescue the embryos from being malformed in animal experiments. This study was aimed to determine if the ideal antioxidant lipoic acid would ameliorate the embryos from maternal diabetes-induced anomalies. Methods: Female Wistar rats (200-250 gm) were assigned to five different treatment groups. Non-treated control rats, streptozotocin (STZ) (60 mg/kg)-induced diabetes mellitus, STZ diabetic rats treated with lipoic acid (STZ+LA), lipoic acid and Tris buffer treated rats (LA control), and Tris buffer alone treated rats. LA control and STZ+LA groups were treated with daily intraperitoneal injection of 20 mg/kg LA from GD 6 through GD 19. Morphological and skeletal malformations of the embryos were recorded. Results: Diabetic rats showed a significant incidence of resorption, growth retardation and malformation of fetuses. Lipoic acid and Tris buffer treatments showed no significant differences when compared with non-treated control data. Diabetic rats supplemented with lipoic acid had a significant decrease in fetal resorption/death, and improvement in fetal body weight. Lipoic also significantly reduced the incidence of various external and skeletal malformations in the diabetic group. Conclusion: Lipoic acid exerts a potent protective effect against diabetes-related resorption, intrauterine growth retardation and malformations. Prospective studies should aim at evaluating the exact mechanism by which LA acts to rescue embryos of growth retardation and malformations in this model

A Comprehensive Exploration of Chemical Inventory: Multifaceted Challenges and Profound Insights

This paper provides a comprehensive exploration of the multifaceted challenges and profound insights associated with chemical inventory. It highlights the critical findings and contributions in the areas of safety, efficiency, and compliance within chemical inventory facilities. By emphasizing the importance of robust risk assessments, implementation of safety measures, adherence to regulatory frameworks, and development of comprehensive emergency response plans, this paper aims to foster safer, more efficient, and compliant chemical inventory environments. Drawing attention to the tragic Beirut port explosion in 2020, this paper underscores the urgent need to address the challenges inherent in chemical inventory and presents valuable insights to mitigate potential hazards

Start-up delay Estimation at Signalized Intersections: Impact of Left-Turn Phasing Sequences

This paper aims to investigate the start-up delay at signalized intersections in Abu Dhabi (AD) city, UAE. Impact of external factors that may affect the start-up delay is examined including left turn phasing sequences (split/lead/lag), movement turning (through/left), intersection location (CBD/non-CBD) and day time (peak/off-peak). A new technique of data collection was applied based on the automate records of license plate of vehicles and a comparison with the traditional video recorded technique was carried out. Data covered 66 approaches of 36 signalized intersections. The analysis showed that overall estimated mean value of the start-up delay is 2.201 sec. with a standard deviation of 1.823 sec. The t-test shows significant statistical difference in start-up delay between observations at through and left movements, at CDB and non-CDB area and at split and lead/lag phasing. However, no significant differences were found between peak and off-peak periods and between split and lead phasing. In general, lead/lag phasing sequences not only improved the overall delay at signalized intersection but also improved the start-up delay.nbsp nbs

The Effectiveness of a Program Based on Montessori Activities in Developing Practical Life Skills for Pre-school Children

The study aimed to measure the impact of a program based on Montessori activities in developing practical life skills for pre-school children.The study sample consisted of (80) children enrolled in kindergarten, divided equally into two groups: experimental and control in the age group (5-6) years, and the study followed the quasi-experimental approach and the following tools: the practical life skills scale, and the training program Based on Montessori activities prepared by the study team, and the results of the study concluded: There are statistically significant differences at the level of significance (0.01) between the mean scores of the children of the experimental and control groups in the post-measurement of life skills, and their totality is in favor of the children of the experimental group. The results also showed that there were statistically significant differences at the level of significance (0.01) between the mean scores of the children of the experimental group in the two measurements of practical life skills, and their total sum in favor of the post measurement, in addition to that there were no statistically significant differences between the mean scores of the children of the experimental group in the two post measurements. The traceability of practical life skills, and their totality. Finally, the results showed that there are no statistically significant differences at the level of significance (0.05) between the mean scores of the children of the experimental group in the dimensional measurement of my skills: (personal care, dealing with others) according to the gender variable (male / female), while significant differences were found. A statistic at the level of significance (0.05) between the mean scores of the children of the experimental group in the dimensional measurement of sensory focus and accuracy skill, and the total sum of practical life skills according to the gender variable (male / female) in favor of females

An Inverse Eigenvalue Problem for the Schrödinger Equation on the Unit Ball of R\u3csup\u3e3\u3c/sup\u3e

The inverse eigenvalue problem for a given operator is to determine the coefficients by using knowledge of its eigenfunctions and eigenvalues. These are determined by the behavior of the solutions on the domain boundaries. In our problem, the Schrödinger operator acting on functions defined on the unit ball of $\mathbb{R}^3$ has a radial potential taken from $L^2_{\mathbb{R}}[0,1].$ Hence the set of the eigenvalues of this problem is the union of the eigenvalues of infinitely many Sturm-Liouville operators on $[0,1]$ with the Dirichlet boundary conditions. Each Sturm-Liouville operator corresponds to an angular momentum $l =0,1,2....$. In this research we focus on the uniqueness property. This is, if two potentials $p,q \in L^2_{\mathbb{R}}[0,1]$ have the same set of eigenvalues then $p=q.$ An early result of P\ oschel and Trubowitz is that the uniqueness of the potential holds when the potentials are restricted to the subspace of the even functions of $L_{\mathbb{R}}^2[0,1]$ in the $l=0$ case. Similarly when $l=0$, by using their method we proved that two potentials $p,q \in L^2_{\mathbb{R}}[0,1]$ are equal if their even extension on $[-1,1]$ have the same eigenvalues. Also we expect to prove the uniqueness if $p$ and $q$ have the same eigenvalues for finitely many $l.$ For this idea we handle the problem by focusing on some geometric properties of the isospectral sets and trying to use these properties to prove the uniqueness of the radial potential by using finitely many of the angular momentum

Nontuberculous Mycobacteria in Saudi Arabia and Gulf Countries: A Review

Nontuberculous Mycobacteria (NTM) are causing growing health problems worldwide. This is indicated by an increasing amount of scientific reports showing not only well-identified species reemerging but also emergence of new species. The emergence and reemergence of NTM are particularly worrying in developing countries due to scarce published data and improper identification. Here we aimed to examine the main epidemiological aspects and diagnostic challenges associated with NTM in countries of the Gulf Cooperation Council (GCC) and compare these findings to the international arena findings. Data revealed that countries of the GCC are largely dominated by rapidly growing mycobacteria species such as M. fortuitum (29%) and M. abscessus (17%) with high rate of definitive respiratory diseases. On the other hand, most of the developed countries are dominated by slowly growing mycobacteria such as MAC, M. kansasii, and M. gordonae. More efforts are needed, however, to gain insights into NTM issues in countries of the GCC