We provide the solutions of Linear Left-invariant 2nd-order Evolution Equations on the 2D-Euclidean motion group. These solutions are given by group convolution with the corresponding Green’s functions which we derive in explicit form. A particular case coincides with the Forward Kolmogorov equation of the direction process, the exact solution of which was strongly required in the field of imag...

Likelihood-based Imprecise Regression (LIR) is a recently introduced approach to regression with imprecise data. Here we consider a robust regression method derived from the general LIR approach and we establish an exact algorithm to determine the set-valued result of the LIR analysis in the special case of simple linear regression with interval data.

objective: whole-mouth examination is generally considered as a gold standard for exact periodontal disease assessment. partial mouth examination also has sometimes been used for this purpose, but its efficacy has been questioned. with regard to symmetric destruction hypothesis of periodontal disease, the present study investigated the efficacy of partial- mouth examination as an alternative fo...

This paper addresses the maintenance of discovered frequent patterns when a batch of transactions are removed from the original dataset. We conduct an in-depth investigation on how the frequent pattern space evolves under transaction removal updates using the concept of equivalence classes. Inspired by the evolution analysis, an effective and exact algorithm TRUM is proposed to maintain frequen...

We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existential elementary doctrines has a left biadjoint that can be obtained as a composite of two others. Finally, we conclude how this notion encompasses both that of the exact completion of a regular category as well as that ...

Background The relationship between handedness and digital dermatoglyphic patterns has never been investigated in the Sinhalese population. The goal of this study is to establish the above mentioned relationship, which would positively aid personal identification.  Findings One hundred forty Sinhalese students (70 right-handed and 70 left-handed) were studied for their digital dermatoglyphic pa...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

Let $$M$$ be a closed manifold and $$L$$ an exact magnetic Lagrangian. In this paper we prove that there exists residual set $$\mathcal{G}$$ of $$H^{1}\left(M;\mathbb{R}\right)$$ such the property $${\widetilde{\mathcal{M}}}\left(c\right)={\widetilde{\mathcal{A}}}\left(c\right)={\widetilde{\mathcal{N}}}\left(c\right),\forall c\in\mathcal{G},$$ with $${\widetilde{\mathcal{M}}}\left(c\right)$$ su...