The well-known formulas for Divided differences in the case of one and two dimensional with multiple knots have played an important role in applied mathematics, particularly in numerical analysis, polynomial and lagrange interpolations. In this article we obtain a new formula for two dimensional Divided differences in the case of multiple knots. This formula has a simpler form than the known formula given in literature. It is friendly using for computations and analysis.  

Background and Aim: Noise pollution is one of the urban problems that can affect the exposed individuals’,cognitive function. This study set to investigate the impact of traffic noise on drivers’,cognitive variables including perceptual capacity, speed of perception, and Divided attention concerning the role of individual orientation and neuroticism. Methods: This study recruited 35 male student participants. The Eysenck personality questionnaire was used to evaluate the participants’,personalities (neuroticism and extroversion). Participants were then exposed to traffic noise, and the Adaptive Tachistoscopic Traffic Perception Test (ATTPT) was performed to assess their capacity and speed of perception. The Peripheral Perception Test (PPT) was also conducted to evaluate the Divided attention using the Vienna test system software. Results: Introverted and stable individuals had better performance in perceptual capacity and speed of perception tasks after exposure to traffic noise. However, these effects were not observed in extrovert and unstable individuals. This study also showed no significant alterations in variables in extroverted (introverted/extroverted) subjects with neuroticism (unstable/stable) concerning Divided attention tasks after traffic noise exposure. Conclusion: This study showed that Divided attention in extrovert individuals with neuroticism was not influenced by traffic noise exposure. But perceptual capacity and perception speed was influenced by traffic noise in introverts and unstable subjects.

Trigeminal neuralgia (TN) is "a sudden, usually unilateral, severe, brief, stabbing, recurrent pain in the distribution of one or more branches of the fifth cranial nerve" according to the international association for the study of pain. It is a debilitating condition of clinical importance not just because recent British and Dutch epidemiological studies show it to be more common than previously thought, affecting close to 30 per 100, 000 people, but also because it is commonly misdiagnosed by dental and medical professionals.

The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to intro duce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the Divided differences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method.

This paper draws attention to some of the consequences of the decline and possible slump of the liberal world order, while focusing predominantly on factors that have Divided the Western world, most notably the toxic rise of nationalism, nativism, populism, authoritarianism, anti-institutionalism, anti-immigrant, and anti-globalization sentiments. We argue, that as the United States further embraces economic nationalism and protectionism under the Trump administration, the support for multilateral institutions, rooted in the liberal order, is likely to significantly retreat. The dissolution of the liberal order will arguably pave the way for political disorder across the globe, while at the same time dividing the Western world at a time when an economically resurgent China, in a strategic alliance with a more assertive Russia under Putin, is likely to pose new challenges to the West. Their rivalries notwithstanding, both Beijing and Moscow are likely to seek ways to improve their bilateral relations with Washington in order to curtail and better manage regional and global tensions. It is worth noting that the risks of abandoning a liberal world order, which for more than seven decades has espoused relative prosperity, as well as a legal and institutional framework for conflict resolution, may prove to be enormously damaging and consequential.

Introduction: Subclinical hypothyroidism is an endocrine disorder that can adversely affect cognitive performance. In this regard, patients with subclinical hypothyroidism may develop poor attention. However, the effects of this endocrine disorder on auditory attention is unclear. This study aims to evaluate the impact of subclinical hypothyroidism on auditory Divided attention. Materials and Methods: This cross-sectional, case control study was performed on 30 adult patients, aged 20-40 years, who met the study inclusion criteria. Based on their Thyroid Stimulating Hormone (TSH) level, the subjects were Divided into two case groups (each with 15 patients) with a TSH level of 5˂ TSH≤ 10 and 10˂ TSH≤ 15. A healthy control group was recruited with matched age, sex, and education with the case groups. The participants were evaluated by the Persian version of the Bergen dichotic listening test. Among different experimental situations that included non-forced attention, forced right, and forced left, we chose the non-forced attention. Statistical analysis was done in SPSS V. 25. Results: There was a significant difference between the subclinical hypothyroid (5˂ TSH≤ 10 group) and controls in the scores of the right and left ear. However, there was no significant difference between scores of right and left ear in subclinical hypothyroid (10˂ TSH≤ 15 group). No significant difference in scores of the right and left ear was found between men and women in three groups. Conclusion: Subclinical hypothyroidism had no effect on auditory Divided attention.

Certain stratified charge Divided chamber engines have a very small pre-chamber, equipped with a spark plug and a main chamber connected to the pre-chamber through nozzles. A theoretical model is presented in this research to predict ignition delay and initiation of combustion in the pre-chamber. It considers ame progress in the pre-chamber up to the point where the ame penetrates the main chamber through the connecting nozzles. Step by step calculations then continue in the main chamber and the mass fraction burned and the energy release rate is calculated. The process continues to the point where all the fuel is burned. At each step, due to a one degree rotation of the crank shaft, there is a change in the cylinder volume, due to the movement of the piston and, also, a change in the mole fraction burned, due to the burning of a fraction of the mixture. Considering heat transfer from the cylinder contents to its surrounding area, some important operating parameters, such as indicated power, indicated thermal efficiency, indicated septic fuel consumption, indicated mean elective pressure and volumetric efficiency, are predicted. Stepwise calculations also provide in-cylinder pressure-volume and pressure-crank angle diagrams, as well as the in-cylinder contents temperature variation with the crank position and concentration of species existing in the combustion products. Predicted values obtained by the present model are compared with corresponding experimental values available in the literature to evaluate the accuracy of the model. The comparison shows reasonable agreement between theoretical and measured values.

Three questions have occupied my mind and many others no doubt-- for some time and this paper tries to answer these three questions. The first question is about the identity of the person who Divided Sa'di's ghazals into four parts of Tayyebat, Badaye', Khavatimand Ghadim. The second question is about the reasons for this division and my last question concerns those weak and problematic ghazals which have not been excluded.