Skew hook Schur functions and the cyclic sieving phenomenon

Fix an integer $t \geq 2$ and a primitive $t^{\text{th}}$ root of unity $\omega$. We consider the specialized skew hook Schur polynomial $\text{hs}_{\lambda/\mu}(X,\omega X,\dots,\omega^{t-1}X/Y,\omega Y,\dots,\omega^{t-1}Y)$, where $\omega^k X=(\omega^k x_1, \dots, \omega^k x_n)$, $\omega^k Y=(\omega^k y_1, \dots, \omega^k y_m)$ for $0 \leq k \leq t-1$. We characterize the skew shapes $\lambda/\mu$ for which the polynomial vanishes and prove that the nonzero polynomial factorizes into smaller skew hook Schur polynomials. Then we give a combinatorial interpretation of $\text{hs}_{\lambda/\mu}(1,\omega^d,\dots,\omega^{d(tn-1)}/1,\omega^d,\dots,\omega^{d(tm-1)})$, for all divisors $d$ of $t$, in terms of ribbon supertableaux. Lastly, we use the combinatorial interpretation to prove the cyclic sieving phenomenon on the set of semistandard supertableaux of shape $\lambda/\mu$ for odd $t$. Using a similar proof strategy, we give a complete generalization of a result of Lee--Oh (arXiv: 2112.12394, 2021) for the cyclic sieving phenomenon on the set of skew SSYT conjectured by Alexandersson--Pfannerer--Rubey--Uhlin (Forum Math. Sigma, 2021).Comment: 13 pages, 2 figure

A Comprehensive Study on Data Science and Its Practical Applications

Data science provides an environment to perform the discoveries like extracting a bit of new knowledge and learning from a large amount of data by using the concepts of statistics, computer science, applied mathematics, and visualization. It's a recently rising field that includes various activities, like data mining and data analysis. Data science can definitely increase value to business

Teaching Differential Equations with Graphics and without Linear Algebra

We present our approach to teaching the Method of Eigenvectors to solve linear systems of ODEs without assuming a prerequisite course in Linear Algebra. Rather we depend heavily on a graphical approach to systems in two dimensions to motivate the eigenvalue equation

Seasonal variations of indoor aerosols (PM2.5) in urban households of Jammu (J&K), India

Indoor pollution is more harmful as people spend more than 90% of their time indoors getting enhanced chances of penetrating aerosols (PM2.5) deeply into the lungs. In the present investigation, an attempt has been made to study seasonal variations of indoor aerosols (PM2.5) in urban households of Jammu(J&K). in the northern region of India. The status of indoor aerosols (PM2.5) and their seasonal variations due to temperature and humidity conditions have been studied for the first time in urban households of Jammu (J&K). The two year study period (2017-2019.) revealed that all types of households of urban areas with non-wood fuel  as well as wood fuel burning practices exhibited significantly (p<0.05) higher values of indoor PM 2.5 during summer season (74.36 µg/m3  and 156.46 µg/m3 ) followed by winter season (62.77 µg/m3   and 143.5µg/m3 ) and lower values during the rainy season (58.47 µg/m3 and 132.52 µg/m3 ). All these values were observed to be above the CPCB prescribed annual limit of 40 µg/m3, thereby exposing the residents to diseases of the respiratory and cardiovascular systems.  The data generated in the present study will act as baseline data for future studies pertaining to indoor aerosols (PM2.5) as well as suggesting mitigation measures

Employees' Knowledge and Skills on Work Productivity at the Manpower Department

The purpose of this research is to evaluate the impact of improving staff knowledge and skills on job productivity. This study employs a descriptive quantitative approach. The findings of this research show that increasing knowledge has a positive and significant impact on job productivity, with tcount = 4.236 > ttable = 1.674 and a significance level of 0.000 0.05. While the employee competence variable has a positive and substantial impact on job production (tcount = 3.143 > ttable = 1.674 with a significant 0.003 0.05

S. cerevisiae Bio-Ethanol Production as a Sustainable Energy Source

We rely on fossil fuels, which will be outdated in a few decades. Many people are looking for solutions to the current energy dilemma in renewable energy, notably biofuels. Among the various biofuels, bioethanol looks to be the most cost- So Saccharomyces cerevisiae is a well-known bioethanol producer. Yeast cells are stressed and inhibited during fermentation, limiting their efficiency for commercial bioethanol generation. Adopt alternative signal transduction mechanisms to defeat these yeast cells. This analysis focuses on common and underutilised carbon feedstocks that can be easily transformed into bioethanol. The several types of protectants, genes, and processes that may be used to design yeast strains are addressed. As a result, we\u27ve proposed techniques for using this profitable option for long-term bioethanol production

Indoor air pollution of PM2.5 in urban households of Jammu, (J&K)

The rising problem of Respirable Particulate Matter i.e. PM2.5 and smaller is catching attention of the policymakers, stakeholders as well as common man. The study of the IndoorPM2.5 of the particular area is very important as it is having direct impact on the human health because PM2.5is absorbed into lung alveolar tissues during breathing and causes respiratory and cardiovascular problems. In present study attempt has been made to assess the status of Indoor PM2.5 in Urban Households of Jammu, (J&K). The average indoor PM2.5 in all the sampled households of Jammu was observed to be 99.49±35.84 µg/m3 which is above the permissible limits of PM 2.5 as prescribed by CPCB. This type of study has been done for the first time in the northern region of India.  The data generated in present study will act as base line data for further studies pertaining to its ionic analysis as well as suggesting mitigation measure

A study of adequacy of informed consent before caesarean section in a tertiary care hospital

Background: Informed consent is an ethical and legal requirement and is practiced before all the surgical procedures. Caesarean section is the commonest obstetric surgery so, this study was aimed to assess the adequacy of informed consent in patients who underwent caesarean section at SMGS Hospital, GMC, Jammu.Methods: A cross-sectional study was done. A total of 230 patients were included in the study. A pre-tested and pre-validated questionnaire was used for the study. The data were expressed as percentage of proportion.Results: 230 patients participated in the study. About 96.95% patients knew the name of the procedure. 91.73% patients were informed about the indication of the surgery. 95.21% of the patients were aware about the benefits of surgery and about 93.41% of the patients were knowing risks of surgery. About 83.04% patients were informed about the procedure of the surgery. About 94.78% and 94.34% of the patients were aware about the need for the blood transfusion and future pregnancy options. Only about 4.35% of the patients were informed about the requirement and type of anaesthesia. 22.18% of the patients knew about the choice for alternate procedure and merely 2.18% of the patients were informed about the right to refuse the procedure.Conclusions: It was found that majority of the patients were well informed about the procedure and the related consequences. Still we can improve some elements of the consent process which can be done by proper awareness and training of health care professionals

Big Data and Its Applications

In times when everything is online, one thing which is common in every application is the use of data. Data is being generated every second, when applications are generating exponentially larger data sets every second it’s the big data which comes into effect. The major objective of this paper is to state the meaning of big data, figure out various ways as how to digest this data. Further this paper will also focus on the applications of Big Data in multiple segments: Finance, Banking and Securities and  Health Care Sector