Conca and Varbaro (2020) [7] showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free. In this paper, we give some beautiful applications of this fact ...

The invariant v-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J. Combin. Theory Ser. A 177:105310, 2021) initiated the study of the v-number of edge ideals. Inspired ...

We establish Lyapunov-type inequality for equations concerning general class of second-order non-symmetric elliptic operators with singular coefficients. Our approach is based on the probabilistic representation of solutions ...

The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [G. Ambartsoumian, M. J. Latifi, and R. K. Mishra, Inverse Problems, 36 (2020), ...

In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in R2. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, ...

If the Krull dimension of the semigroup ring is greater than one, then affine semigroups of maximal projective dimension (MPD) are not Cohen–Macaulay, but they may be Buchsbaum. We give a necessary and sufficient condition ...