Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case

The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form $-d^2/dx^2+V(g;x)$, where the potential is an elliptic function depending on a coupling vector $g\in{\mathbb R}^4$. Alternatively, this operator arises from the $BC_1$ specialization of the $BC_N$ elliptic nonrelativistic Calogero-Moser system (a.k.a. the Inozemtsev system). Under suitable restrictions on the elliptic periods and on $g$, we associate to this operator a self-adjoint operator $H(g)$ on the Hilbert space ${\mathcal H}=L^2([0,\omega_1],dx)$, where $2\omega_1$ is the real period of $V(g;x)$. For this association and a further analysis of $H(g)$, a certain Hilbert-Schmidt operator ${\mathcal I}(g)$ on ${\mathcal H}$ plays a critical role. In particular, using the intimate relation of $H(g)$ and ${\mathcal I}(g)$, we obtain a remarkable spectral invariance: In terms of a coupling vector $c\in{\mathbb R}^4$ that depends linearly on $g$, the spectrum of $H(g(c))$ is invariant under arbitrary permutations $\sigma(c)$, $\sigma\in S_4$

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

Analysis of hydrogen diffusion in the three stage electro-permeation test

The presence of hydrogen traps within a metallic alloy influences the rate of hydrogen diffusion. The electro-permeation (EP) test can be used to assess this: the permeation of hydrogen through a thin metallic sheet is measured by suitable control of hydrogen concentration on the front face and by recording the flux of hydrogen that exits the rear face. Additional insight is achieved by the more sophisticated three stage EP test: the concentration of free lattice hydrogen on the front face is set to an initial level, is then dropped to a lower intermediate value and is then restored to the initial level. The flux of hydrogen exiting the rear face is measured in all three stages of the test. In the present study, a transient analysis is performed of hydrogen permeation in a three stage EP test, assuming that lattice diffusion is accompanied by trapping and de-trapping. The sensitivity of the three stage EP response to the depth and density of hydrogen traps is quantified. A significant difference in permeation response can exist between the first and third stages of the EP test when the alloy contains a high number density of deep traps

Distinguishing Lightweight Block Ciphers in Encrypted Images

Modern day lightweight block ciphers provide powerful encryption methods for securing IoT communication data. Tiny digital devices exchange private data which the individual users might not be willing to get disclosed. On the other hand, the adversaries try their level best to capture this private data. The first step towards this is to identify the encryption scheme. This work is an effort to construct a distinguisher to identify the cipher used in encrypting the traffic data. We try to establish a deep learning based method to identify the encryption scheme used from a set of three lightweight block ciphers viz. LBlock, PRESENT and SPECK. We make use of images from MNIST and fashion MNIST data sets for establishing the cryptographic distinguisher. Our results show that the overall classification accuracy depends firstly on the type of key used in encryption and secondly on how frequently the pixel values change in original input image

Use of Sleeve Nets to Improve Survival of the Boisduval Silkworm, Anaphe panda, in the Kakamega Forest of Western Kenya

Prospects for development of a wild silk industry in Africa would be improved if silkworm survival during mass production could be improved. A study on the survival of the Boisduval silkworm, Anaphe panda (Boisduval) (Lepidoptera: Thaumetopoeidae) was conducted with and without protection by net sleeves in two different forest habitats (natural and modified) in the Kakamega forest of western Kenya. Overall, cohort survival was significantly higher (P < 0.001) in the natural than in the modified forest, but larval survival was improved over three-fold by protection with net sleeves in both habitat types. In the modified forest, only 16.8% of unprotected larvae survived to the pupal stage and formed cocoons, whereas 62.3% survived in the same environment when they were protected with net sleeves. In the natural forest, 20.4% of unprotected larvae survived, whereas 67.7% survived in net sleeves. There was also a significant effect of season; cohorts of larvae that eclosed in the wet season had significantly lower survival than those eclosing in the dry season (P = 0.02). Sources of mortality appeared to be natural enemies (parasites, predators and diseases) and climatic factors

New limit for the half-life of double beta decay of 94^{94}Zr to the first excited state of 94^{94}Mo

Neutrinoless Double Beta Decay is a phenomenon of fundamental interest in particle physics. The decay rates of double beta decay transitions to the excited states can provide input for Nuclear Transition Matrix Element calculations for the relevant two neutrino double beta decay process. It can be useful as supplementary information for the calculation of Nuclear Transition Matrix Element for the neutrinoless double beta decay process. In the present work, double beta decay of $^{94}$Zr to the $2^{+}_{1}$ excited state of $^{94}$Mo at 871.1 keV is studied using a low background $\sim$ 230 cm$^3$ HPGe detector. No evidence of this decay was found with a 232 g.y exposure of natural Zirconium. The lower half-life limit obtained for the double beta decay of $\rm^{94}Zr$ to the $2^{+}_{1}$ excited state of $\rm^{94}Mo$ is $T_{1/2} (0\nu + 2\nu)> 3.4 \times 10^{19}$ y at 90% C.L., an improvement by a factor of $\sim$ 4 over the existing experimental limit at 90\% C.L. The sensitivity is estimated to be $T_{1/2} (0\nu + 2\nu) > 2.0\times10^{19}$ y at 90% C.L. using the Feldman-Cousins method.Comment: 11 pages, 7 figures, Accepted in Eur. Phys. J.

An indigenous cluster beam apparatus with a reflectron time-of-flight mass spectrometer

The design and fabrication of a Smalley-type cluster source in combination with a reflectron based time-of-flight (TOF) mass spectrometer are reported. The generation of clusters is based on supersonic jet expansion of the sampling plume. Sample cells for both liquid and solid targets developed for this purpose are described. Two pulsed Nd-YAG lasers are used in tandem, one (532 nm) for target vapourization and the other (355 nm) for cluster ionization. Methanol clusters of nuclearity up to 14 (mass 500 amu) were produced from liquid methanol as the test sample. The clusters were detected with a mass resolution of ~2500 in the R-TOF geometry. Carbon clusters up to a nuclearity of 28 were obtained using a polyimide target. The utility of the instrument is demonstrated by carrying out experiments to generate mixed clusters from alcohol mixtures

Antibiotics Resistance of Vibrio spp. Isolated from Diseased Seabass and Tilapia in Cage Culture

Vibriosis has become one of the most important bacterial diseases in marine cultured organisms in recent years. This study was focusing on isolation and identification of Vibrio spp. isolated from diseased seabass (Lates calcarifer), tilapia (Oreochromis niloticus) and seawater from Sri Tujuh lagoon in East Coast of Malaysia; also determination of antibiotic resistance patterns among Vibrio spp. Vibrio species isolated from diseased seabass in Pantai Sri Tujuh, Tumpat, Kelantan were screened for their antibiotic sensitivity patterns by Kirby-Bauer method. A total of 47 isolates belonging to three different species were identified which are V. parahaemolyticus, V. vulnificus, and V. alginolyticus. In this study, high incidence of erythromycin, chloramphenicol and sulfamethoxazole resistance was observed among the Vibrio isolates, whereas all isolates were susceptible to oxytetracycline. Vibrio isolates were 96% resistant to one or more different classes of antibiotic, and 17 different resistance patterns were identified. The MAR index of 0.4 indicating the Vibrio spp. in these farmed fish might have been indiscriminately and continuously exposed to those antibiotics during culturing stages of the fish. This study showed that multidrug-resistant Vibrio spp. were common in diseased seabass and tilapia cultured at Sri Tujuh lagoon. These essential findings suggested involvement of seafood in transmission of these pathogen to human. In addition, oxytetracycline can be used as a treatment to combat vibriosis in diseased seabass and tilapia

ETHNO-BOTANICAL STUDY OF MEDICINAL PLANTS OF PADDAR VALLEY OF JAMMU AND KASHMIR, INDIA

The Paddar Valley, historically known as Sapphire Valley situated in Kishtwar district, is a prime landmark in the Jammu region of J&K state and is known for its rich cultural and plant diversity because of diverse habitats such as rivers, streams, meadows and steep mountain slopes. The area located in the dry temperate region comprising typical vegetation which disappears completely on the eastern slopes, dominated by a variety of economical species which play an important role in the rural life. The inhabitants are dependent on plant resources for food, fuel, timber, shelter, fodder/forage, household articles and traditional medicines in treating diseases like malaria, cancer, gastro-intestinal ailments, etc. This paper deals with the observations on traditional therapeutic application by the inhabitants of Paddar Valley. The ethno-botanical information on medicinal plants would not only be useful in conservation of traditional cultures and biodiversity but also community health care and drug development. Exploration survey in Paddar Valley has revealed that people collect and sell these medicinal species through local intermediaries / contractors to earn their livelihood. But the scientific cultivation and appropriate post-harvest management would improve employment opportunity and income of local farmers in the region