Search results for "analyysi"
showing 10 items of 1950 documents
Optimization of spodumene identification by statistical approach for laser-induced breakdown spectroscopy data of lithium pegmatite ores
2021
Mapping with laser-induced breakdown spectroscopy (LIBS) can offer more than just the spatial distribution of elements: the rich spectral information also enables mineral recognition. In the present study, statistical approaches were used for the recognition of the spodumene from lithium pegmatite ores. A broad spectral range (280–820 nm) with multiple lines was first used to establish the methods based on vertex component analysis (VCA) and K-means and DBSCAN clusterings. However, with a view to potential on-site applications, the dimensions of the datasets must be reduced in order to accomplish fast analysis. Therefore, the capability of the methods in mineral identification was tested wi…
Development of two-color resonance ionization scheme for Th using an automated wide-range tunable Ti:sapphire laser system
2018
Two-color resonance ionization schemes of Th were investigated by an automated wide-range tunable, grating-assisted Ti:Sa laser system with intracavity SHG option. A two-color ionization scheme via autoionizing state (1st step: 372.049 nm and 2nd step: 401.031 nm) was developed and its relative efficiency was lower by factor of three compared to a known three color scheme. peerReviewed
Laser-induced time-resolved luminescence in analysis of rare earth elements in apatite and calcite
2021
Laser-induced time-resolved luminescence was used to study rare earth element (REE) containing natural apatite and calcite minerals. The luminescence from 400 nm to 700 nm in the minerals was analyzed with excitation ranges 210–340 nm and 405–535 nm. As an outcome, several useful excitation wavelengths to detect one or more REE from apatite and calcite are reported. The feasibility of selected excitations in e.g. avoiding the disturbance of intense Mn2+ luminescence band, results was demonstrated with a non-gated detector. peerReviewed
Singular value decomposition approach to the yttrium occurrence in mineral maps of rare earth element ores using laser-induced breakdown spectroscopy
2017
Laser-induced breakdown spectroscopy (LIBS) has been used in analysis of rare earth element (REE) ores from the geological formation of Norra Kärr Alkaline Complex in southern Sweden. Yttrium has been detected in eudialyte (Na15 Ca6(Fe,Mn)3 Zr3Si(Si25O73)(O,OH,H2O)3 (OH,Cl)2) and catapleiite (Ca/Na2ZrSi3O9·2H2O). Singular value decomposition (SVD) has been employed in classification of the minerals in the rock samples and maps representing the mineralogy in the sampled area have been constructed. Based on the SVD classification the percentage of the yttrium-bearing ore minerals can be calculated even in fine-grained rock samples. peerReviewed
Complementary Judgment Matrix Method with Imprecise Information for Multicriteria Decision-Making
2018
The complementary judgment matrix (CJM) method is an MCDA (multicriteria decision aiding) method based on pairwise comparisons. As in AHP, the decision-maker (DM) can specify his/her preferences using pairwise comparisons, both between different criteria and between different alternatives with respect to each criterion. The DM specifies his/her preferences by allocating two nonnegative comparison values so that their sum is 1. We measure and pinpoint possible inconsistency by inconsistency errors. We also compare the consistency of CJM and AHP trough simulation. Because preference judgments are always more or less imprecise or uncertain, we introduce a way to represent the uncertainty throu…
The squared symmetric FastICA estimator
2017
In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches…
Loomis-Whitney inequalities in Heisenberg groups
2021
This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…
X-ray Tomography of One-forms with Partial Data
2021
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
A Cornucopia of Carnot groups in Low Dimensions
2022
Abstract Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous with respect to the automorphisms induced by the derivation, this metric space is known as Carnot group. Carnot groups appear in several mathematical contexts. To understand their algebraic structure, it is useful to study some examples explicitly. In this work, we provide a list of low-dimensional stratified groups, express their Lie product, and present a basis of left-invariant vector fields, together with their respective left-invaria…
Approximation by mappings with singular Hessian minors
2018
Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.