On Walsh Spectrum of Cryptographic Boolean Function

Walsh transformation of a Boolean function ascertains a number of cryptographic properties of the Boolean function viz, non-linearity, bentness, regularity, correlation immunity and many more. The functions, for which the numerical value of Walsh spectrum is fixed, constitute a class of Boolean functions known as bent functions. Bent functions possess maximum possible non-linearity and therefore have a significant role in design of cryptographic systems. A number of generalisations of bent function in different domains have been proposed in the literature. General expression for Walsh transformation of generalised bent function (GBF) is derived. Using this condition, a set of Diophantine equations whose solvability is a necessary condition for the existence of GBF is also derived. Examples to demonstrate how these equations can be utilised to establish non-existence and regularity of GBFs is presented

Theoretical Study of Physisorption of Nucleobases on Boron Nitride Nanotubes: A New Class of Hybrid Nano-Bio Materials

We investigate the adsorption of the nucleic acid bases, adenine (A), guanine (G), cytosine (C), thymine (T) and uracil (U) on the outer wall of a high curvature semiconducting single-walled boron nitride nanotube (BNNT) by first principles density functional theory calculations. The calculated binding energy shows the order: G>A\approxC\approxT\approxU implying that the interaction strength of the (high-curvature) BNNT with the nucleobases, G being an exception, is nearly the same. A higher binding energy for the G-BNNT conjugate appears to result from a stronger hybridization of the molecular orbitals of G and BNNT, since the charge transfer involved in the physisorption process is insignificant. A smaller energy gap predicted for the G-BNNT conjugate relative to that of the pristine BNNT may be useful in application of this class of biofunctional materials to the design of the next generation sensing devices.Comment: 17 pages 6 figure

A Maiorana-McFarland Construction of a GBF on Galois ring

Bent functions shows some vital properties among all combinatorial objects. Its links in combinatorics, cryptography and coding theory attract the scientific community to construct new class of bent functions. Since the entire characterisation of bent functions is still unexplored but several construction on different algebraic structure is in progress. In this paper we proposed a generalized Maiorana-McFarland construction of bent function from Galois ring

Tale of GRB 171010A/SN 2017htp and GRB 171205A/SN 2017iuk: Magnetar origin?

We present late-time optical follow-up observations of GRB 171010A/SN 2017htp ($z$ = 0.33) and low-luminosity GRB 171205A/SN 2017iuk ($z$ = 0.037) acquired using the 4K$\times$4K CCD Imager mounted at the 3.6m Devasthal Optical Telescope (3.6m DOT) along with the prompt emission data analysis of these two interesting bursts. The prompt characteristics (other than brightness) such as spectral hardness, T$_{90}$, and minimum variability time-scale are comparable for both the bursts. The isotropic $X$-ray and kinetic energies of the plateau phase of GRB 171205A are found to be less than the maximum energy budget of magnetars, supporting magnetar as a central engine powering source. The new optical data of SN 2017htp and SN 2017iuk presented here, along with published ones, indicate that SN 2017htp is one of the brightest and SN 21017iuk is among the faintest GRB associated SNe (GRB-SNe). Semi-analytical light-curve modelling of SN 2017htp, SN 2017iuk and only known GRB associated superluminous supernova (SLSN 2011kl) are performed using the $\texttt{MINIM}$ code. The model with a spin-down millisecond magnetar as a central engine powering source nicely reproduced the bolometric light curves of all three GRB-SNe mentioned above. The magnetar central engines for SN 2017htp, SN 2017iuk, and SLSN 2011kl exhibit values of initial spin periods higher and magnetic fields closer to those observed for long GRBs and H-deficient SLSNe. Detection of these rare events at such late epochs also demonstrates the capabilities of the 3.6m DOT for deep imaging considering longitudinal advantage in the era of time-domain astronomy.Comment: Accepted for publication in New Astronomy; Received 21 April 2022, Revised 13 June 2022, Accepted 1 July 202

Study the antimicrobial agents sensitivity of methicillin resistant Staphylococcus aureus isolated from patients admitted in RIMS, Ranchi

Background: Methicillin-resistant Staphylococcus aureus (MRSA) is a major cause of hospital-acquired infections that are becoming increasingly difficult to combat because of emerging resistance to all current antibiotic classes. For this, study of MRSA isolated from admitted patients were carried out. These strains were separately tested for their sensitivity to different antibiotics to know which group of antibiotics are most effective particularly for cases of RIMS, Ranchi. Material & Methods: The present study was carried out in the Department of Microbiology, Rajendra Institute of Medical Sciences (RIMS), Ranchi clinical isolates of MRSA strains were obtained from admitted patients of RIMS, Ranchi. The sources of isolate included pus from infected surgical wounds, infected burn wounds, conjunctival swab, aural swab, throat swab, vaginal swab, urine etc for microbiological analysis and antimicrobial sensitivity of MRSA. Disc diffusion method was employed. Results: All the 264 cases of staphylococcal species isolated from different clinical specimens were subjected to coagulase test. It was observed that out of 264 strains of staphylococci isolated from different sites 165 strains (62.5%) were coagulase positive and 99 strains (37.5%) were coagulase negative by tube method. It was observed that out of 165 strains of staph. aureus isolated from different clinical samples 64 strains of staph. aureus were resistant to methicillin (38.78%). Maximum isolation of MRSA were from pus 38 (51.35%), followed by throat swab 19 (36.36%), aural swab (14.28%) and conjunctival swab (44.44%). It was observed that out of 165 strains of s. aureus isolated only 64 strains were resistant to methicillin. All strains of MRSA were 100% sensitive to Vancomycin & linezolid. Similarly 92.3% were sensitive to netilmicin, 89.7% to clindamycin, 82.1% to ciprofloxacin, 74.4% to cephotaxime, 69.2% to azithromycin, 56.4% to roxithromycin & clarithromycin, 17.9% to piperacillin/tazobactam. The most effective antibiotic against MRSA was vancomycin, linezolid, netilmicin & clindamycin. Conclusion: After comparing the effectiveness of antibiotics against MRSA infection it can be concluded that piperacillin/tazobactam, clarithromycin, roxithromycin azithromycin, cefotaxime & ciprofloxacin are of little value in treating the MRSA infection. They should not be used indiscriminately and in a haphazard manner otherwise increment in emergence of resistant strains may not be checked

The new 130-cm optical telescope at Devasthal, Nainital

A modern Ritchey-Chretien Cassegrain 130-cm diameter optical telescope has been successfully installed at Devasthal, Nainital in the central Himalayan region. This location was chosen after carrying out extensive site surveys. The first images obtained with the telescope indicate that atmospheric seeing and sky darkness at Devasthal are nearly at values as measured during the site survey. The values of seeing and sky darkness are comparable to some of the best astronomical sites in the world. The 130-cm telescope is functional and observations can be carried out from the control centre at Devasthal or from the Manora Peak in Nainital. This telescope has started providing valuable data for a number of research projects and is expected to help meet part of the national requirement in optical observational astronomy from small-aperture ground-based telescopes

Faint high-energy gamma-ray photon emission of GRB 081006A from Fermi observations

Since the launch of the Fermi gamma - ray Space Telescope on June 11, 2008, the LAT instrument has solidly detected more than 20 GRBs with high energy photon emission above 100 MeV. Using the matched filter technique, 3 more GRBs have also shown evidence of correlation with high energy photon emission as demonstrated by Akerlof et al. In this paper, we present another GRB unambiguously detected by the matched filter technique, GRB 081006A. This event is associated with more than 13 high energy photons above 100 MeV. The likelihood analysis code provided by the $Fermi$ Science Support Center (FSSC) generated an independent verification of this detection by comparison of the Test Statistics (TS) value with similar calculations for random LAT data fields. We have performed detailed temporal and spectral analysis of photons from 8 keV up to 0.8 GeV from the GBM and the LAT. The properties of GRB 081006A can be compared to the other two long duration GRBs detected at similar significance, GRB 080825C and GRB 090217A. We find that GRB 081006A is more similar to GRB 080825C with comparable appearances of late high energy photon emission. As demonstrated previously, there appears to be a surprising dearth of faint LAT GRBs, with only one additional GRB identified in a sample of 74 GRBs. In this unique period when both $Swift$ and $Fermi$ are operational, there is some urgency to explore this aspect of GRBs as fully as possible.Comment: ApJ, 745, 7