On generalized eigenvalue problems of fractional (p,q)(p,q)-Laplace operator with two parameters

For $s_1,s_2\in(0,1)$ and $p,q \in (1, \infty)$, we study the following nonlinear Dirichlet eigenvalue problem with parameters $\alpha, \beta \in \mathbb{R}$ driven by the sum of two nonlocal operators: \begin{equation*} (-\Delta)^{s_1}_p u+(-\Delta)^{s_2}_q u=\alpha|u|^{p-2}u+\beta|u|^{q-2}u\;\;\text{in }\Omega, \quad u=0\;\;\text{in } \mathbb{R}^d \setminus \Omega, \end{equation*} where $\Omega \subset \mathbb{R}^d$ is a bounded open set. Depending on the values of $\alpha,\beta$, we investigate the existence and non-existence of positive solutions to the above problem. A continuous curve in the two-dimensional $(\alpha,\beta)$-plane is constructed, which separates the regions of the existence and non-existence of positive solutions. In addition, we prove that the first Dirichlet eigenfunctions of the fractional $p$-Laplace and fractional $q$-Laplace operators are linearly independent.Comment: 30 page

Collapse of a Bose gas: kinetic approach

We have analytically explored temperature dependence of critical number of particles for the collapse of a harmonically trapped attractively interacting Bose gas below the condensation point by introducing a kinetic approach within the Hartree-Fock approximation. The temperature dependence obtained by this easy approach is consisted with that obtained from the scaling theory.Comment: Brief Report, 4 pages, 1 figure, Accepted in Pramana-Journal of Physic

Effect of Progressive Muscle Relaxation on the Adverse Cardiovascular Profile in Women with Polycystic Ovarian Syndrome

Background: The altered stress reactivity in polycystic ovarian syndrome (PCOS) may constitute a link between depression, overweight, and cardiovascular risk factors. Aims: To study the effects of progressive muscle relaxation (PMR) on the stress levels of PCOS patients and their influence on the cardiovascular risk factors. Subjects and Methods: This prospective pilot project was conducted on 100 PCOS patients in a tertiary care hospital of West Bengal, after receiving approval from the Institutional Ethical Committee and informed consent of the subjects. The stress levels were assessed and conventional autonomic function tests and the lipid profi les were analyzed. The subjects were divided into two groups using an online randomizer. One group received medication, while the other group received medication and practiced progressive muscle relaxation (PMR) for three months. All parameters were re‑evaluated at the end of three months. Results: The perceived stress scale was significantly less in subjects practicing relaxation exercises, as compared to subjects only on medication. The waist/hip ratio, pulse rate, and systolic blood pressure were significantly lower, while there was no difference in the body mass index (BMI) and diastolic blood pressure. Results of the autonomic function tests showed a significant parasympathetic tilt in subjects practicing PMR. In patients with PCOS, who were on PMR, cholesterol, triglycerides, and low‑density cholesterol (LDL) were significantly lower and high‑density cholesterol HDL was significantly higher. Conclusions: PCOS patients are a high‑risk group for developing the metabolic syndrome and relaxation therapies may be recommended as an adjuvant therapy, to tilt the autonomic balance to parasympathetic dominance, to improve the cardiovascular profile.Keywords: Autonomic functions, cardiovascular system, polycystic ovarian syndrome, stres

Disparities in the contraceptive use among currently married women in Muslim densely populated States of India: An evidence from the nationally representative survey.

Background: The rationalizations for low use of contraception and high fertility among Muslims compared to other religious group in India are highly controversial. The study was aimed to explain to what extent differences in the use of contraception exist among the religious groups and also examine its associated factors in the Muslim populated States in the country. Methods: The third round of District Level Household and Facility Survey (DLHS-3) was used to accomplish our objectives. Bivariate analysis was used to show the religion wise distribution of limiting, spacing and traditional methods of contraceptive use in relation to socio-economic characteristics. The multivariate logistic regression was also employed to estimate the odds ratio (95% CI) for contraceptive use. SPSS 20.0 version and Arc GIS 10.0 software were employed to carry out the analyses. Results: The study found that the prevalence of limiting contraceptive use was comparatively much lower among Muslims (19.9%) than Non-Muslims (39.3%). In comparison to Non-Muslims, Muslims used 3.5 percentage points and 2.6 percentage points spacing and traditional methods of contraception respectively. The Muslims women from Assam (3.4%), Uttar Pradesh (4.4%) and Bihar (8.3%) reported low use of limiting contraceptive methods as compared to other Muslim populated States. The highest difference in the limiting method was observed in Bihar (21 percentage points) and followed by West Bengal (19 percentage points) between Muslim and Non-Muslim. The level of education and place of residence appeared as the main explaining factors of family planning in the study. Conclusion: The study concluded that the significant inequalities exist among Muslims and Non-Muslims concerning the current use of limiting methods. The policy design and programmes should make on rural, uneducated women to take into account the inequalities in the contraceptive use. &nbsp

Application of probiotics and prebiotics for promoting growth of Tiger shrimp (Penaeus monodon): an approach to eco-friendly shrimp aquaculture

The current study has been conducted to evaluate the growth performance of shrimp (Penaeus monodon) by applying eco-friendly culture mechanism like prebiotics and probiotics. The experiment was carried out for 95 days in different shrimp farms at coastal district of Bagerhat, Bangladesh. Three different treatments viz., probiotic treated as T1, prebiotics treated as T2 and both probiotics and prebiotics as T3 with a control group were designed to conduct the experiment. The size of the experimental ponds was five acre and the stocking density was 4/m2 in each treatment. CP NASA shrimp feed (32% protein) was given thrice in a day during the study period. After 95 days of culture period, the maximum weight gain was observed at T3 (33.78±0.18 g) whereas the minimum weight gain was observed at control group (25.69±0.10 g). The survival rate was the highest in T3 (89.01%) followed by T2 (75.51%) and T1 (53.44%) and the lowest rate was observed in control group (50.88%). Overall production was higher in T3 (833.78 kg ha-1) compared to T2 (553.40 kg ha-1), T1 (447.84 kg ha-1) and Control group (310.57 kg ha-1). pH value was found to maximum in T3 (7.71±0.08) and it was minimum in T1 (7.41±0.10). In addition, the maximum TAN value was found to be 2.22±0.19 mg L-1 in C pond and it was minimum in T3 (0.32±0.06 mg L-1). Therefore, it could be concluded that combine application of probiotics and prebiotics might be the reliable media to enhance production of shrimp by maintaining eco-friendly environment in aquaculture. Int. J. Agril. Res. Innov. Tech. 10(2): 15-20, December 202

Wire EDM Parameters for Surface Roughness in Straight Gear Manufacturing: An Experimental Study

The gears are an essential component of any system. A gear is a spinning circular machine part with cut teeth, or inserted teeth (called cogs) in the case of a cogwheel or gearwheel, which mesh with another toothed part to convey torque. A gear is sometimes referred as a cog colloquially. Geared devices can adjust a power source's speed, torque, and direction. To eliminate backlash, high precision is required while making gears. Wire cut EDM is a high-precision machining technology that may manufacture high-precision straight gear. The goal of this research is to use the WEDM Process on an EMS 45 to determine the surface roughness of the workpiece and to optimise the influence of current and wire speed on the surface roughness of the straight gear. Wire cut machining parameters employed were 4, 6, and 8 amperes of current and 9, 11, and 13 mm/min of wire speed. Wire has a diameter of 0.25 mm, and the cutting material is brass. It has been demonstrated that as current and wire speed increase, surface roughness decreases, and vice versa. As a result, reduced machine settings can be used to generate a smoother and better workpiece surface

On the curvature of vortex moduli spaces

We use algebraic topology to investigate local curvature properties of the moduli spaces of gauged vortices on a closed Riemann surface. After computing the homotopy type of the universal cover of the moduli spaces (which are symmetric powers of the surface), we prove that, for genus g>1, the holomorphic bisectional curvature of the vortex metrics cannot always be nonnegative in the multivortex case, and this property extends to all Kaehler metrics on certain symmetric powers. Our result rules out an established and natural conjecture on the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.

Author Identification from Literary Articles with Visual Features: A Case Study with Bangla Documents

Author identification is an important aspect of literary analysis, studied in natural language processing (NLP). It aids identify the most probable author of articles, news texts or social media comments and tweets, for example. It can be applied to other domains such as criminal and civil cases, cybersecurity, forensics, identification of plagiarizer, and many more. An automated system in this context can thus be very beneficial for society. In this paper, we propose a convolutional neural network (CNN)-based author identification system from literary articles. This system uses visual features along with a five-layer convolutional neural network for the identification of authors. The prime motivation behind this approach was the feasibility to identify distinct writing styles through a visualization of the writing patterns. Experiments were performed on 1200 articles from 50 authors achieving a maximum accuracy of 93.58%. Furthermore, to see how the system performed on different volumes of data, the experiments were performed on partitions of the dataset. The system outperformed standard handcrafted feature-based techniques as well as established works on publicly available datasets