Research
Research
Research
Research
189+ open-access research outputs.
We develop a measure and integration theory for random normed modules. Given a probability space $({\rm X},\Sigma,\mathfrak m)$, we introduce and study measures taking values into the space $L^0(\math…
In this paper, our main aim is to extend a classical theorem of Phelps on norm-attaining functionals from the space of scalar-valued continuous functions $C(\Omega)$ to its vector-valued counterpart $…
Let $X$ be a Banach space. For $x \in X$ with $\|x\| = 1$, we denote the state space by $S_x = \{x^* \in X^* : \|x^*\| = x^*(x) = 1\}.$ In this paper, we study weak$^*$-weak and weak$^*$-$\|\cdot\|$ p…
We review recent results on Radon-Nikod\'ymification of abstract measure spaces, the particular case of integral geometric measure, and applications to the dual of SBV.…
We study the planar Nikod\'ym maximal operator $\mathcal{N}_{\Theta;\delta}$ associated to a direction set $\Theta \subset \mathbb{S}^{1}$. We show that the quasi-Assouad dimension $s := \dim_{\mathrm…
We reexamine the classical subset sum problem: given a set $X$ of $n$ positive integers and a number $t$, decide whether there exists a subset of $X$ that sums to $t$; or more generally, compute the s…
We introduce and study equivariant versions of the Radon-Nikod\'ym property for Banach spaces, together with the closely related notions such as dentability, the Bishop-Phelps and Krein-Milman propert…
In this paper we introduce the notion of an almost preserved extreme point (APEP) of a set as a weakening of the concept of preserved extreme points, and we systematically study such points. As a main…
We demonstrate that the best $k$-sparse approximation of a length-$n$ vector can be recovered within a $(1+\epsilon)$-factor approximation in $O((k/\epsilon) \log n)$ time using a non-adaptive linear …
We study maximal monotone operators $A : X \rightrightarrows X^*$ whose Fitzpatrick family reduces to a singleton; such operators will be called uniquely representable. We show that every such operato…
In a large database system, upper-bounding the cardinality of a join query is a crucial task called $\textit{pessimistic cardinality estimation}$. Recently, Abo Khamis, Nakos, Olteanu, and Suciu unifi…
Multimodal relation extraction (MRE) is a crucial task in the fields of Knowledge Graph and Multimedia, playing a pivotal role in multimodal knowledge graph construction. However, existing methods are…
We define the speed measure $\nu$ for mappings $\gamma:I\to X$ from an interval to a metric space that are locally of bounded variation. We characterize continuity and absolute continuity of $\gamma$ …
We study classes of Banach spaces where the points of weak$^*$-weak continuity for the identity mapping on the dual unit ball form a weak$^*$-dense and weak$^*$-$G_{\delta}$ set. We also discuss how t…
The classical Chain Rule formula $(f\circ g)'(x;u)=f'(g(x);g'(x;u))$ gives the (partial, or directional) derivative of the composition of mappings $f$ and $g$. We show how to get rid of the unnecessar…
A compact space $K$ is Radon-Nikod\'{y}m if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $\diamondsuit (\mathrm{non}{\mathcal{M}})$, there is a Radon-Niko…
We introduce the super alternative Daugavet property (super ADP) which lies strictly between the Daugavet property and the Alternative Daugavet property as follows. A Banach space $X$ has the super AD…
We introduce a new class of bounded linear operators, called range strongly exposing (RSE) operators, which form a natural intermediate class: weaker than Bourgain's absolutely strongly exposing opera…
A regular separable first-countable countably compact space is called a Nyikos space. In this paper, we give a partial solution to an old problem of Nyikos by showing that each locally compact Nyikos …
Which principle underpins the design of an effective anomaly detection loss function? The answer lies in the concept of Radon-Nikod\'ym theorem, a fundamental concept in measure theory. The key insigh…
Free open-access publishing with Google Scholar indexing.
Submission Guide →