Minimum number of additive tuples in groups of prime order

For a prime number $p$ and a sequence of integers $a_0,\dots,a_k\in \{0,1,\dots,p\}$, let $s(a_0,\dots,a_k)$ be the minimum number of $(k+1)$-tuples $(x_0,\dots,x_k)\in A_0\times\dots\times A_k$ with $x_0=x_1+\dots + x_k$, over subsets $A_0,\dots,A_k\subseteq\mathbb{Z}_p$ of sizes $a_0,\dots,a_k$ respectively. An elegant argument of Lev (independently rediscovered by Samotij and Sudakov) shows that there exists an extremal configuration with all sets $A_i$ being intervals of appropriate length, and that the same conclusion also holds for the related problem, reposed by Bajnok, when $a_0=\dots=a_k=:a$ and $A_0=\dots=A_k$, provided $k$ is not equal 1 modulo $p$. By applying basic Fourier analysis, we show for Bajnok's problem that if $p\ge 13$ and $a\in\{3,\dots,p-3\}$ are fixed while $k\equiv 1\pmod p$ tends to infinity, then the extremal configuration alternates between at least two affine non-equivalent sets.Comment: This version is the same as the published version except for modifications to reflect Reference [5], that was brought to our attention after publicatio

DOTS Awareness and the Myths and Misconceptions about DOTS among Medical Practitioners in Mysore

Background: Annually 2 million people in India develop Tuberculosis and 330,000 die. WHO-recommended DOTS strategy was pilot-tested in 1993 and launched as Revised National Tuberculosis Control Program (RNTCP) in 1997. Awareness of DOTS among the doctors in the private sector was appalling although nationwide coverage was attained by 2006. OBJECTIVE: To study awareness of DOTS among Medical Practitioners of urban and rural Mysore. Methodology: 401 Medical practitioners in hospitals and nursing homes of urban and rural areas of Mysore who treated Tuberculosis patients (private and public sector) were approached. They were grouped under different specialties as per the year of graduation (before or after introduction of DOTS). Results: 38 % doctors who graduated before the introduction of DOTS didn’t follow DOTS compared to 14.9% doctors who graduated later. 100% doctors working in Government sector felt that DOTS was better than daily regimen while 85% from the private sector felt so. Only 47.9% of the doctors in the private sector practiced DOTS compared to 95.1 % in the Govt. Sector. Hence, the number of doctors practicing DOTS in Private Sector was less than 50 % of that in the Govt. Sector. Both of these comparisons were found to be statistically highly significant (p<0.001). Awareness of DOTS was alarmingly low among Orthopedic Surgeons, Gynecologists and Pediatricians when compared to Physicians and General Practitioners. Conclusions: DOTS awareness is still low among doctors who graduated before the introduction of DOTS. Private practitioners harbored myths and misconceptions about DOTS

The Effects of Post-Thermal Annealing on the Emission Spectra of GaAs/AlGaAs Quantum Dots grown by Droplet Epitaxy

We fabricated GaAs/AlGaAs quantum dots by droplet epitaxy method, and obtained the geometries of the dots from scanning transmission electron microscopy data. Post-thermal annealing is essential for the optical activation of quantum dots grown by droplet epitaxy. We investigated the emission energy shifts of the dots and underlying superlattice by post-thermal annealing with photoluminescence and cathodoluminescence measurements, and specified the emissions from the dots by selectively etching the structure down to a lower layer of quantum dots. We studied the influences of the degree of annealing on the optical properties of the dots from the peak shifts of the superlattice, which has the same composition as the dots, since the superlattice has uniform and well-defined geometry. Theoretical analysis provided the diffusion length dependence of the peak shifts of the emission spectra

Electronic structure of self-assembled InAs/InP quantum dots: A Comparison with self-assembled InAs/GaAs quantum dots

We investigate the electronic structure of the InAs/InP quantum dots using an atomistic pseudopotential method and compare them to those of the InAs/GaAs QDs. We show that even though the InAs/InP and InAs/GaAs dots have the same dot material, their electronic structure differ significantly in certain aspects, especially for holes: (i) The hole levels have a much larger energy spacing in the InAs/InP dots than in the InAs/GaAs dots of corresponding size. (ii) Furthermore, in contrast with the InAs/GaAs dots, where the sizeable hole $p$, $d$ intra-shell level splitting smashes the energy level shell structure, the InAs/InP QDs have a well defined energy level shell structure with small $p$, $d$ level splitting, for holes. (iii) The fundamental exciton energies of the InAs/InP dots are calculated to be around 0.8 eV ($\sim$ 1.55 $\mu$m), about 200 meV lower than those of typical InAs/GaAs QDs, mainly due to the smaller lattice mismatch in the InAs/InP dots. (iii) The widths of the exciton $P$ shell and $D$ shell are much narrower in the InAs/InP dots than in the InAs/GaAs dots. (iv) The InAs/GaAs and InAs/InP dots have a reversed light polarization anisotropy along the [100] and [1$\bar{1}$0] directions

Coping with tuberculosis and directly observed treatment : a qualitative study among patients from South India

Background: In India, the Revised National TB control programme (RNTCP) offers free diagnosis and treatment for tuberculosis (TB), based on the Directly Observed Treatment Short course (DOTS) strategy. We conducted a qualitative study to explore the experience and consequences of having TB on patients enrolled in DOTS and their caretakers in Tumkur district, located in a southern state of India, Karnataka. Methods: We conducted 33 in-depth interviews on a purposive sample of TB patients from three groups: (1) patients who reached RNTCP directly on their own and took DOTS at RNTCP; (2) patients who were referred by private practitioners (PPs) to RNTCP and took DOTS at RNTCP; and (3) patients diagnosed by RNTCP and took DOTS from PPs. Data was analyzed using a thematic approach with the support of NVivo9. Results: The study revealed that TB and DOTS have a large impact on patient's lives, which is often extended to the family and caretakers. The most vulnerable patients faced the most difficulty in accessing and completing DOTS. The family was the main source of support during patient's recovery. Patients residing in rural areas and, taking DOTS from the government facilities had to overcome many barriers to adhere to the DOTS therapy, such as long travelling distance to DOTS centers, inconvenient timings and unfavorable attitude of the RNTCP staff, when compared to patients who took DOTS from PPs. Advantages of taking DOTS from PPs cited by the patients were privacy, flexibility in timings, proximity and more immediate access to care. Patients and their family had to cope with stigmatization and fear and financial hardships that surfaced from TB and DOTS. Young patients living in urban areas were more worried about stigmatisation, than elderly patients living in rural areas. Patients who were referred by PPs experienced more financial problems compared to those who reached RNTCP services directly. Conclusion: Our study provided useful information about patient's needs and expectations while taking DOTS. The development of mechanisms within RNTCP towards patient centered care is needed to enable patients and caretakers cope with disease condition and adhere to DOTS