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Introduction- Body's musculoskeletal system depends on vitamin D, and a lack of it is a widespread health issue worldwide. In terms of reduced quality of life, diminished productivity, and the expense of diagnosis and treatment, low back pain (LBP)and radiculopathy in lumbar degenerative disease is a significant health issue. The present study was conducted to investigate the relationship between vitamin D level and correlation with lowback pain and radiculopathy in lumbar degenerative disease in a medical college of Eastern India. Material and methods- The institution based descriptive observational cross-sectional study was conducted at Department of Neurosurgery, NRS Medical College and Hospital, Kolkata for a study period of one year. Complete history was taken and physical examination was done. Values of serum Vitamin D level and VAS was examined. Results were analysed using SPSS version 25.0. Results- Out of all the 150 patients selected 120 (80%) had vitamin D insufficiency (group A) and 30 (20%) had vitamin D sufficiency. No significant relation was found w.r.t. age, gender, BMI, education, occupation and marital status. The mean±SD value of vitamin D in group A was 15.48±3.12 and in group B was 38.79±6.2 and on comparison results were statistically significant with p value <0.001. The mean±SD value of VAS among low back pain in group A was 5.67±2.67 and in group B was 4.35±1.23, on comparison results were statistically significant with p value <0.001. The mean±SD value of VAS in patients of radiculopathy in group A was 5.23±2.51 and in group B was 4.13±1.04, on comparison results were statistically significant with p value <0.001. Negative correlation (-0.556; -0.558) was found between pain score and vitamin D level with statistically significant association (p<0.001) among low back pain and radiculopathy patients. Conclusion –Significant association was found between vitamin D insufficiency and pain scores of LDD. Most patients of LDD had vitamin d insufficiency in our study. So vitamin D insufficiency can be one of the risk factor for development of LDD. So widespread screening of vitamin D level should be done in all patients of LDD so that we can treat vitamin d insufficiency if present along with other treatment of LDD for overall better management.

Lack of appropriate donors, non-utilization of high throughput phenotyping and genotyping platforms with high genotype × environment interaction restrained identification of robust QTLs for grain protein content (GPC) in rice. In the present investigation a  BC 3 F 4 mapping population was developed using grain protein donor, ARC10075 and high-yielding cultivar Naveen and 190 lines were genotyped using 40 K Affimetrix custom SNP array with the objective to identify stable QTLs for protein content. Three of the identified QTLs, one for GPC ( qGPC1 . 1 ) and the other two for single grain protein content ( qSGPC 2. 1 , qSGPC7 . 1 ) were stable over the environments explaining  13%, 14% and 7.8% of the phenotypic variances, respectively. Stability and repeatability of these additive QTLs were supported by the synergistic additive effects of multi-environmental-QTLs. One epistatic-QTL, independent of  the  main effect QTL was detected over the environment for SGPC. A few functional genes governing seed storage protein were hypothesised inside these identified QTLs. The qGPC1 . 1 was validated by NIR Spectroscopy-based high throughput phenotyping in BC 3 F 5 population. Higher glutelin content was estimated in high-protein lines with the introgression of qGPC1 . 1 in telomeric region of short arm of chromosome 1. This was supported by the postulation of probable candidate gene inside this QTL region encoding glutelin family proteins.

In this paper, first we consider that the conformal vector field X is identical with the Reeb vector field ς and next, assume that X is pointwise collinear with the Reeb vector field ς ; in both cases it is shown that the manifold N 2 m + 1 becomes a Kenmotsu manifold and N 2 m + 1 is locally a warped product N ′ × f M 2 m , in which M 2 m indicate an almost Kähler manifold, with coordinate t , N ′ being the open interval and f = c e t for some c ( positive constant). Beside these, we establish that if a ( k , μ ) ′ -almost Kenmotsu manifold admits a Killing vector field X , then either it is locally a warped product of an open interval and an almost Kähler manifold or X is a strict infinitesimal contact transformation. Furthermore, we also investigate η -Ricci-Yamabe soliton with conformal vector fields on ( k , μ ) ′ -almost Kenmotsu manifolds and finally, we construct two examples.

Let ℍ be the division ring of real quaternions. Let SL(2, ℍ) be the group of 2 × 2 quaternionic matrices $A={\\scriptsize{(\\begin{array}{l@{\\quad}l} a & b \\\ c & d \\end{array})}}$ with quaternionic determinant det A = |ad − aca−1b| = 1. This group acts by the orientation-preserving isometries of the five-dimensional real hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, ℍ).

While the developing world is approaching towards food security, nutritional aspects must be addressed properly to combat malnutrition. As the staple food of half of the world’s population, rice is a major source of nutrition and needs to be nutritionally enriched with proteins, micronutrients, etc. With the objective of quantitative and qualitative improvement of grain protein content (GPC) in a popular high-yielding background, ‘Naveen’, we developed backcross population using high GPC (11%–13%) donor, ARC 10075. The range of GPC in BC3F4 lines was 7.13%–13.6%, estimated through calibrated NIR spectroscopy. Among the population lines, seven having phenotypic similarity with the recurrent parent, Naveen were identified based on high yield coupled with high protein content (10%–12%). Further, elevated levels of glutelin and some of the essential amino acids such as lysine and threonine also indicated the qualitative improvement of grain protein of these lines. Based on higher GPC and protein yield in multilocational testing two high-yielding lines, viz. CR2829-PLN-37 (CR Dhan 310), and CR 2829-PLN-100 (CR Dhan 311/Mukul) in the genetic background of cv. Naveen with an average 10.2% and 10.1% GPC respectively, in polished rice were released at the national and state level respectively. These high-yielding varieties with high GPC can significantly contribute towards better nourishment of millions of underprivileged children depending mainly on rice for their nutrition.

In this paper, first we consider that the conformal vector field \\(X\\) is identical with the Reeb vector field \\(\\) and next, assume that \\(X\\) is pointwise collinear with %the Reeb vector field \\(\\), in both cases it is shown that the manifold \\(N^2m+1\\) becomes a Kenmotsu manifold and \\(N^2m+1\\) is locally a warped product \\(N' _f M^2m\\), where \\(M^2m\\) is an almost Kähler manifold, \\(N'\\) is an open interval with coordinate t, and \\(f = ce^t\\) for some positive constant c. Beside these, we prove that if a \\((\"k\",)'\\)-almost Kenmotsu manifold admits a Killing vector field \\(X\\), then either it is locally a warped product of an almost Kähler manifold and an open interval or \\(X\\) is a strict infinitesimal contact transformation. Furthermore, we also investigate \\(\\)-Ricci-Yamabe soliton with conformal vector fields on \\((\"k\",)'\\)-almost Kenmotsu manifolds and finally, we construct an example.

Let SL(2, \\( H\\)) be the group of \\(2 2\\) quaternionic matrices \\(A=pmatrix a & b \\\ c & d pmatrix\\) with quaternionic determinant \\( A=|ad-aca^-1 b|=1\\). This group acts by the orientation-preserving isometries of the five dimensional (real) hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, \\( H\\)) using test maps.

Let \\(\\) be a field with a non-trivial involution \\(c: ^c\\). An element \\(g ın GL_n()\\) is called \\(c\\)-real if it is conjugate to \\((g^c)^-1\\). We prove that for \\(n 2\\), \\(g ın GL_n()\\) is \\(c\\)-real if and only if it has a representation in some unitary group of degree \\(n\\) over \\(\\).