How large can the first eigenvalue be on a surface of genus two?

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture.Comment: 20 pages; 4 figure

Refugee Children: Education in Emergencies for Empowerment

A famous Nigerian proverb says, “It takes an entire village to raise a child.” Today, when the world is facing one of the greatest migration crisis it has encountered, as a global village, the world as a whole would have to get together to solve the issue and ensure that children who are the most vulnerable victims of forced migration do not get impacted immeasurably. The United Nations High Commissioner for Refugees (UNHCR) report 2015, hints at an alarming status, that of the world's total refugee population, about 51 percent are children below 18. The United Nations Children's Fund (UNICEF) has already launched a campaign ‘No Lost Generation' that is focused on providing access to quality education to refugee children. Lebanon which is encountering a great rush of Syrian refugees had started in 2014, a program called ‘Reaching All Children with Education' (RACE). The British Council has even gone a step further in providing online support to aspirants of higher education. They have started a program called ‘Language and Academic Skills and E-Learning Resource' (LASER). It aims at providing entry level competence to people from 18–25 to enrol in tertiary education. The Bolivarian Republic of Venezuela has provided unrestricted access to education, to migrants at all levels and given a right to free education to all refugee children. However, the gravity of the problem is so very huge that a major gap in providing access to education and receiving it still exists for the refugee children. DOI: 10.5281/zenodo.337218

Can the possibility of some linkage of monsoonal precipitation with solar variability be ignored? Indications from foraminiferal proxy records

Foraminiferal studies on a shallow water sediment core off Karwar, central west coast of India have revealed significant changes in the monsoonal precipitation during the last around 720 years. The results hint towards some possibility of linkage of monsoonal precipitation with solar variability during this period

Weak Interactions in Binary Mixtures of Chlorobenzene & Bromobenzene with o-, m- & p-Xylenes

605-60

Role of Ni-Mn hybridization in magnetism of martensitic state of Ni-Mn-In shape memory alloys

Extended X-ray Absorption Fine Structure (EXAFS) studies on Ni$_{50}$Mn$_{25+x}$In$_{25-x}$ have been carried out at Ni and Mn K edge as a function of temperature. Thermal evolution of nearest neighbor Ni-Mn and Mn-Mn bond distances in the martensitic phase give a clear evidence of a close relation between structural and magnetic degrees of freedom in these alloys. In particular, the study highlights the role of Ni 3d - Mn 3d hybridization in the magnetism of martensitic phase of these alloys.Comment: Accepted for publication in EP

Monitoring of ambient air quality in relation to traffic density in Bareilly City (U.P.), India

An ambient air quality study was undertaken in Bareilly city, U.P., India during the year 2010 and 2011. The seasonal air quality data was obtained from ten monitoring sites across the city considering sampling site of Cantt as control site. The maximum (713.06±55.64 µg/m3) suspended particulate matter (SPM), sulphur dioxide (SO2) (80.08±4.77 µg/m3) and nitrogen oxides (NOx) (64.98±3.53 µg/m3) level was found at Choupla during the winter 2011. Among the annual mean values of air pollutants were analyzed, SPM level was found to be above the National Ambient Air Quality Standards (NAAQS) (200 µg/m3) at all the polluted sites. SO2 and NOx levels were below the threshold limits (80 µg/m3) as per NAAQS. The ambient air quality was correlated with the traffic density in the city. The pollution level was observed to be positively correlated with traffic density which is the major source of air pollution in the city. The ambient air quality at different monitoring sites was categorized into different pollution level on the basis of Oak ridge air quality index (ORAQI). Light to moderate air pollution conditions were present at different sites. Sampling site of Choupla (SVII) observe maximum ORAQI of 64.48 and 70.81 and falls under category of moderate pollution