in this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. following this, we establish the minkowski and brunn-minkowski inequalities for volumes difference function of the projection and intersection bodies.

One of the fundamental results regarding intersection bodies is Busemann’s theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is natural to ask how much of convexity is guaranteed under the intersection body operation. In this paper we provide several results about the (strict) improvement of convexity for intersection bodies of symmetric bodies of r...

In this paper, we first introduce a new concept of dual quermassintegral sum function of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the Aleksandrov– Fenchel inequality and the Brunn–Minkowski inequality for mixed intersection...

It is a well-known result due to Busemann that the intersection body of an origin-symmetric convex body is also convex. Koldobsky introduced the notion of k-intersection bodies. We show that the k-intersection body of an origin-symmetric convex body is not necessarily convex if k > 1.

This study was carried out to analyze the variations of Benzene, Toluene, and para- Xylene (BTp-X) present in the urban air of Delhi. These pollutants can enter into the human body through various pathways like inhalation, oral and dermal exposure posing adverse effects on human health. Keeping in view of the above facts, six different locations of Delhi were selected for the study during summe...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

The intersection body of a ball is again a ball. So, the unit ball Bd ⊂Rd is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach– Mazur distance. E. Lutwak asked if there is any other star-shaped body that satisfies this property. We show that this fixed point is a local attractor, i.e., that the iterations of th...

This study was carried out to analyze the variations of Benzene, Toluene, and para- Xylene (BTp-X) present in the urban air of Delhi. These pollutants can enter into the human body through various pathways like inhalation, oral and dermal exposure posing adverse effects on human health. Keeping in view of the above facts, six different locations of Delhi were selected for the study during summe...