Combinatorial identities associated with a bivariate generating function for overpartition pairs

We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler\u27s pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate a certain double series with a weight 7/2 theta series

Health seeking behavior of the mothers for the special care new-born unit discharged children: A comparative study

Establishment of special care new-born units (SCNU) in hospitals not only serves to provide the intensive care to sick neonates, but presents with opportunities to enhance knowledge and modify attitude and practices of their parents through behavior change communication (BCC). A cross-sectional study was conducted in Dibrugarh District, Assam from January to June, 2011 to assess differences in health-care seeking behavior of these mothers from mothers of newborns who were born at home and mothers who had normal uneventful institutional deliveries. Mothers of 29 SCNU discharged, 34 institutions delivered and 26 home delivered children were interviewed using a semi-structured interview schedule and a knowledge, attitude and practice (KAP) survey tool. Mothers of children admitted to SCNU scored better in questions related to vaccination, contraception, protection of child from infections and cold and perceptions about traditional healers, but overall KAP scores in the three groups were not found significantly different

A study of lab satisfaction of MCA and MSc. (IT) students of department computer science of Saurashtra University, Rajkot

For the last few years, development in Information and Communication Technology is remarkable and still the development is under progress which can be easily observed in the current trend and the market is the evidence for it. Universities are the main source provider for IT Skilled personals to fulfill the demands of IT People in the Market. This situation arise a clear question in our mind that whether the current Lab facilities are satisfactory up to which level especially to the students who are the actual users and beneficiary of the Lab Resources. To answer this question, we conduct a survey type of research by conducting some test on the Lab Users and after analyzing few parameters like Infrastructure, Arrangement, Timings, Internet facility, laboratory practical literature, Updated version of all software, User rights, Assistant teacher's availability, all practical in parallel with theory class, faculty response for the practical and important of all, the benefit of the lab subject syllabus design to the student career. From the data obtained, we came to know about results which are present in this paper to throw the light upon current practice by the Department of Computer Science and also suggested the solutions for the issues which came up during the research study.</p

White Light Induced E/Z-Photoisomerization of Diphenylamine-Tethered Fluorescent Stilbene Derivatives: Synthesis, Photophysical, and Electrochemical Investigation

A facile synthesis and detailed photophysical investigation of E/Z-isomerization of fluorescent diphenylamine tethered stilbene derivatives (DPASs) under white light exposure have been carried out to understand the effect on fluorescence, electrochemical properties, and photostability under various activation/deactivation pathways. In solution state, in the dark, the E-isomer of DPASs (<b>6a</b>–<b>d</b>) exhibited high fluorescence quantum yields (Φ_fl ≈ 53% to 60% in DMSO). However, on white light exposure, ¹H NMR and HPLC studies revealed that pure E-isomer of the DPAS <b>6a</b> (∼9.5 mM) started converting into its Z-form by photoisomerization until it reaches to nearly equilibrium. At low concentrations (∼10 μM), the absorption band of the pure E-isomer in the range of 350–450 nm gradually decreased to adopt Z-conformation <b>6a′</b> until a photostationary state was reached. The structure of the E-isomer <b>6a</b> was unequivocally confirmed by X-ray diffraction analysis. The synthesized DPAS compounds <b>6a</b>–<b>d</b> possessed positive solvatochromic properties, two photon absorption properties, and good thermal stability. The electrochemical investigations using DPASs showed reversible oxidation resulting in formation of a stable radical cation. Owing to useful photophysical, electrochemical and thermal properties, these DPAS derivatives are suitable for their application in biomedical imaging as well as in fabrication of electroluminescent materials