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pro vyhledávání: '"Pandey, Ram P."'
Given a positive integer $h$ and a nonempty finite set of integers $A=\{a_{1},a_{2},\ldots,a_{k}\}$, the restricted $h$-fold signed sumset of $A$, denoted by $h^{\wedge}_{\pm}A$, is defined as $$h^{\wedge}_{\pm}A=\left\lbrace \sum_{i=1}^{k} \lambda_{
Externí odkaz:
http://arxiv.org/abs/2403.03625
Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is said to be an additive complement of the set $A$ if all sufficiently large natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in B$. This article de
Externí odkaz:
http://arxiv.org/abs/2402.03280
For a nonempty finite set $A$ of integers, let $S(A) = \left\{ \sum_{b\in B} b: \emptyset \not= B\subseteq A\right\}$ be the set of all nonempty subset sums of $A$. In 1995, Nathanson determined the minimum cardinality of $S(A)$ in terms of $|A|$ and
Externí odkaz:
http://arxiv.org/abs/2401.08208
Autor:
Mohan, Pandey, Ram Krishna
Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang and Xing an
Externí odkaz:
http://arxiv.org/abs/2401.04699
Revealing the Underlying Patterns: Investigating Dataset Similarity, Performance, and Generalization
Autor:
Achara, Akshit, Pandey, Ram Krishna
Supervised deep learning models require significant amount of labeled data to achieve an acceptable performance on a specific task. However, when tested on unseen data, the models may not perform well. Therefore, the models need to be trained with ad
Externí odkaz:
http://arxiv.org/abs/2308.03580
Autor:
Pandey, Ram Krishna, Achara, Akshit
Supervised and semi-supervised semantic segmentation algorithms require significant amount of annotated data to achieve a good performance. In many situations, the data is either not available or the annotation is expensive. The objective of this wor
Externí odkaz:
http://arxiv.org/abs/2305.19088
Autor:
Pandey, Ram Krishna, Achara, Akshit
Automatically detecting or segmenting cracks in images can help in reducing the cost of maintenance or operations. Detecting, measuring and quantifying cracks for distress analysis in challenging background scenarios is a difficult task as there is n
Externí odkaz:
http://arxiv.org/abs/2209.04648
Maximal density and the kappa values for the families $\{a,a+1,2a+1,n\}$ and $\{a,a+1,2a+1,3a+1,n\}$
Autor:
Pandey, Ram Krishna, Rai, Neha
Let $M$ be a set of positive integers. We study the maximal density $\mu(M)$ of the sets of nonnegative integers $S$ whose elements do not differ by an element in $M$. In 1973, Cantor and Gordon established a formula for $\mu(M)$ for $|M|\leq 2$. Sin
Externí odkaz:
http://arxiv.org/abs/2204.04731
Autor:
Bhanja, Jagannath, Pandey, Ram Krishna
Publikováno v:
Comptes Rendus Mathematique, Volume 360 (2022), pp. 1099-1111
Let $\mathcal{A}$ be a sequence of $rk$ terms which is made up of $k$ distinct integers each appearing exactly $r$ times in $\mathcal{A}$. The sum of all terms of a subsequence of $\mathcal{A}$ is called a subsequence sum of $\mathcal{A}$. For a nonn
Externí odkaz:
http://arxiv.org/abs/2108.07042
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