Elementary Characterization Research Articles

Characterization of the Jaccard dissimilarity metric and a generalization

The Jaccard dissimilarity metric identifies the distance between two finite sets by the number of their unique elements as a proportion of their joint cardinality. This note gives an elementary characterization of the Jaccard metric by means of three simple axioms. Relaxing the most substantial one allows for a general family of new dissimilarity quasi-metrics to emerge that encompasses Jaccard’s metric.

On planarity of graphs in homotopy type theory

AbstractIn this paper, we present a constructive and proof-relevant development of graph theory, including the notion of maps, their faces and maps of graphs embedded in the sphere, in homotopy type theory (HoTT). This allows us to provide an elementary characterisation of planarity for locally directed finite and connected multigraphs that takes inspiration from topological graph theory, particularly from combinatorial embeddings of graphs into surfaces. A graph is planar if it has a map and an outer face with which any walk in the embedded graph is walk-homotopic to another. A result is that this type of planar maps forms a homotopy set for a graph. As a way to construct examples of planar graphs inductively, extensions of planar maps are introduced. We formalise the essential parts of this work in the proof assistant Agda with support for HoTT.

AN Elementary Characterization of the Galois Group of a Doubly Even Octic Polynomial

AN Elementary Characterization of the Galois Group of a Doubly Even Octic Polynomial

Uncovering the structural and photoelectric properties of perovskite crystals by joint multifaceted characterization and theoretical analysis

The potential of organic-inorganic hybrid perovskites, owing to their distinct photoelectric attributes and boosted photoluminescence stability, has garnered substantial attention. Despite comprehensive examinations of the synthesis and optical characteristics of FAPbBr3 crystals, the understanding of their microstructure's implication on photoelectric applications, their electronic configuration, and electron-phonon interplay remains vague. In this study, we detailed the electronic configuration, phonon dispersion, and vibrational properties using density functional theory. We further calculated the formation enthalpy stability diagram. Characterization and calculation of the crystalline structure were accomplished via Rietveld refinement. Phonon dispersion curves, as well as total and partial phonon densities of states, were also calculated. The theoretical results align well with experimental Fourier infrared and Raman spectra. Beyond elementary characterization, we explored the photoelectric qualities of FAPbBr3 crystals, thereby reaffirming the outstanding photoelectric attributes and extensive application potential. A non-contact fixed-point lighting device was designed based on the principle of electromagnetic induction coils, which proved the uniformity of crystal luminescence. According to the first principle, FAPbBr3 possesses a Poisson ratio of 0.32, indicative of high flexibility, emphasizing their superb photoelectric characteristics and vast application scope.

GALOIS GROUPS OF RECIPROCAL SEXTIC POLYNOMIALS

AbstractLet F be a subfield of the complex numbers and $f(x)=x^6+ax^5+bx^4+cx^3+bx^2+ax+1 \in F[x]$ an irreducible polynomial. We give an elementary characterisation of the Galois group of $f(x)$ as a transitive subgroup of $S_6$ . The method involves determining whether three expressions involving a, b and c are perfect squares in F and whether a related quartic polynomial has a linear factor. As an application, we produce one-parameter families of reciprocal sextic polynomials with a specified Galois group.

Bi-utility representable orderings on a countable set

An elementary characterization of the existence of a bi-utility representation for a partial order on a countable set is presented. The approach followed allows us to develop an algorithm for obtaining all such kind of representations in the finite case.

Elementary characterization of essential $${\mathscr {F}}$$-sets and its combinatorial consequences

Elementary characterization of essential $${\mathscr {F}}$$-sets and its combinatorial consequences

Elementary characterization of metals in lipsticks by EDXRF

Usually classified as cosmetic consumer products, makeups usually contain significant quantities of colorants, which may contain toxic and heavy metals, such as Hg, Cd, As, Cr, Tl, and Pb. According the Health Regulatory Agency (ANVISA), lipsticks are classified as low health risk, grade 1. However, similar makeups for the children are classified as grade 2, high risk, and within this category there is no cosmetic product for embellishment. Many metals, present in the colorants, can cross the mucous membranes and skin barrier and could be absorbed into the blood system, which can cause systemic damage to internal organs. Many chemical components present in the lipsticks, such as Al, Pb, Cd, Br, Cu, Zr, Cr, Hg, TiO2 in nanoparticulate form, could be considered as potentially toxic. Present work was undertaken in order to study the presence of mentioned above metals in the samples of commercial lipsticks. The metals characterization and elementary identification was performed using EDXRF technique. This method allows to perform the qualitative and quantitative analysis by means of the characteristic X-rays spectra emitted by the elements present in studied samples. The experimental setup was based on mini X-ray tube with Ag target and detector (AMPTEK). The partial results of the study revealed that the lipstick samples revealed the presence of Mg, Al, Si, P, S, Cl, K, Ca, Ti, Cr, Mn, Fe, Ni, Zn, Br, Rb, which suggest that prolonged and constant use of such cosmetics may constitute a potential threat to the health especially in the case of children.

On Hua semigroups

A semigroup is called a Hua semigroup if any mapping satisfying is either a homomorphism or an anti-homomorphism. We use this name for such a semigroup since it is relevant to a well-known result in ring theory, which is established by L. K. Hua in 1949. C. M. Reis and H. J. Shyr first translated Hua’s result from rings to semigroups in 1977. In this paper, elementary characterizations, a hierarchy and closure properties of the class of Hua semigroups and its four subclasses are given. We show that every cancellative semigroup is a Hua semigroup, which generalizes Reis and Shyr’s result.

Elementary preservation of the Noetherian condition and the potential applications in computational physics

We give an elementary proof of the preservation of the Noetherian condition for commutative rings with unity R having at least one finitely generated ideal I such that the quotient ring is again finitely generated, and R is I—adically complete. Moreover, we offer as a direct corollary a new elementary proof of the fact that if a ring is Noetherian then the corresponding ring of formal power series in finitely many variables is Noetherian. Furthermore, we discuss the potential applications that this new elementary proof possesses regarding the simplification of conceptual generations in mathematics and computational physics based on the new computational paradigm of Artificial Mathematical Intelligence. In addition, we give a counterexample showing that the ‘completion’ condition cannot be avoided on the former theorem. Lastly, we give an elementary characterization of Noetherian commutative rings that can be decomposed as a finite direct product of fields.

Pit lakes from Southern Sweden: natural radioactivity and elementary characterization

Natural radioactivity in the environment is a field gaining more attention in last decades. This work is focused on the study of natural radioactivity complemented with elementary characterization at former non-uraniferous mining areas in Sweden. This aim is addressed through the study of mining lakes, called pit lakes, which are water bodies generated after opencast mining. Environmental matrices (water, sediments and rocks) from 32 Swedish pit lakes, commonly used for recreational purposes were radiometrically characterized via alpha (238U, 234U, 232Th, 230Th, 210Po isotopes) and gamma spectrometry (238U and 232Th series radionuclides). Additionally, ambient dose rate equivalent in the immediate surrounding of each pit lake was quantified. Physico-chemical parameters (pH, specific conductivity, dissolved oxygen, oxidation–reduction potential) and elemental composition (major and trace elements by ICP-MS) were analysed in water samples and elementary composition of sediments/rocks was measured by XRF and SEM–EDX in some specific cases. A non-negligible number of pit lakes (26%) with enhanced U levels in water was found. At some sites, rocks contained up to 4% of U in areas with high degree of interaction with local population. Concerning the elementary perspective, another popular site (due to its turquoise water) was found to have elevated dissolved heavy metal levels. Results obtained in this work prove that measurement of natural radioactivity is another component that should be included in routine analysis of characterization in mining areas, especially if restauration of post-mining sites is intended for human recreational.

Elementary characterization of smoke tunnel using flow over a circular cylinder

The utilization of the smoke tunnel for flow visualization of aerodynamics studies needs calibration of the tunnel. This paper aims to describe the characterization of the smoke tunnel using the smoke injection technique. The main phenomenon considered is the wake behaviour occurring at the downstream side of the cylinder. The experiment is conducted by injecting the smoke perpendicular to a circular cylinder placed in the tunnel. The visualized smoke flow lines resemble the streamline patterns which will reveal the wake behaviour. The procedure of smoke based visualization was carried out for various Reynolds numbers and the corresponding physics is described with the limitations of the tunnel.

Approach to modelling uniform transmission lines for broadband high‐frequency applications

A novel high-frequency lossy uniform transmission line model is presented in this study. Novel features include a compactness of form and a level of simplicity that confers enhanced simulation efficiency in practical applications. Although specifically developed to target implementation in generic versions of SPICE, the compact high-frequency model can be implemented using only four lines of netlist syntax in the case of circuit simulators that offer native Laplace equation support. Featuring a broadband frequency response characteristic that is defined by only four parameters, the compact HF model is based on a novel theoretical approach that elegantly connects the four model parameters to physical line parameters using only elementary line characterisation data. Important and perhaps surprising differences between the new model theory and classical textbook theory are highlighted and discussed. The lessons learned are then incorporated into a second hybrid model featuring a higher level of complexity that combines both new and classical theoretical approaches into a single set of model equations that are better suited for atypically small controlled impedance structures such as silicon interposers and on-chip clock and data distribution schemes.

Innovative amplifiers for muon spectroscopy experiments at RAL

The high intensity pulsed muon beam of ISIS facility at Rutherford Appleton Laboratory (RAL, U.K.) allows to perform high precision muonic X-ray spectroscopy experiments. In particular, FAMU and CHNET_TANDEM projects at RAL are dedicated, respectively, to a precise measurement of the Zemach radius of the proton through the measure of the hyperfine splitting of the ground state of the muonic hydrogen atom and to the optimization of analytical methods based on the muonic atom spectroscopy for non-destructive elementary characterization of archaeological samples. Custom electronic boards dedicated to the detector amplification stages have been designed and prototypized to provide fast high resolution for both experiments. The main features and performance of these custom boards are described in details in this work.

Compatible Ag+ Complex-Assisted Ultrafine Copper Pattern Deposition on Poly(ethylene terephtalate) Film with Micro Inkjet Printing.

Firm immobilization of catalysts on the predesigned position over substrates is an essential process for producing flexible circuits by the electroless deposition (ELD) process. In this work, a compatible Ag+ complex was developed and directly printed on the poly(ethylene terephtalate) (PET) film through a micro inkjet printing instrument to trigger the deposition of ultrafine copper patterns with approximately 20 μm in width. Morphological and elementary characterization verified that the nanosized silver catalyst was uniformly distributed in the bridge layer, which could enhance the adhesion between the PET film and deposited copper patterns. Moreover, after 30 min of ELD, the copper patterns exhibited a low resistivity of 2.68 × 10-6 Ω·cm and maintained considerable conductivity even after 2000 times of cyclical bending. These interesting conductive and mechanical features demonstrate the tremendous potential of this Ag+ complex-assisted copper deposition in the interconnection of high-density integrated flexible electronics.

Invariant automatic continuity for compact connected simple Lie groups

In this note we prove that a homomorphism from a compact connected simple Lie group with the norm topology to any separable SIN group is automatically continuous. This generalizes a result by Dowerk and Thom. Further, we prove some elementary characterizations of invariant automatic continuity.

Spatial and seasonal dynamics of elemental composition and mineralogy of intertidal and subtidal sediments in the Lima estuary (NW Portugal)

In estuaries, the mineral distribution in the top sediment layer results from the combined effect of fluvial and coastal inputs and may present seasonal patterns owing to forcing, e.g., floods, storms, waves, and tides. Our main goal was to study the estuarine sedimentological components, including textural and geochemical parameters, in order to characterize the seasonal and spatial dynamics of subtidal and intertidal sediments in a highly energetic temperate estuary (River Lima, NW Portugal). Subtidal sediments were usually anoxic within the middle estuary and presented higher amounts of clay and silt than intertidal sediments. Oxygen, silicon, carbon, aluminum, and potassium were the most abundant elements. The amount of silicon and carbon was related to the clay and silt content of the sediments. The mineralogical composition of sediments reflected the lithology of the watershed, with the most representative minerals being quartz, microcline (k-alkaloid feldspar), and albite (plagioclase), in line with the results obtained in the elementary characterization. The lower stretches were particularly rich in iron silicates and anatase. No clear seasonal variation was found for sediment elemental and mineralogical compositions. Factor analysis explained 80% of the elemental origin, being 33% related to terrigenous origin, 24% to marine sediments, and 15% to anthropogenic inputs.

Elementary characterization of samples of Portland cement, natural gypsum and phosphogypsum mortars from Brazil

Portland cement, the basic ingredient of concrete and is manufactured by crushing, milling and proportioning limestone, sand, clay, iron ore and secondary materials such as shells, chalk or marl combined with shale slate or blast furnace slag, fly ash, gypsum, phosphogypsum, and some others. Evaluating the physical and mineralogical characteristics of the cement and its chemical composition is essential to establish the quality of the product. Therefore, the objective of this work was to characterize and quantify the most common chemical elements in the samples of Brazilian Portland cement, natural gypsum, and phosphogypsum mortars by means of X-ray dispersive energy spectroscopy (EDXRF), as well as to evaluate the strength of these mortars. For analysis of the compressive strength, initially prepared samples were submitted to a destructive mechanical test. Subsequently samples were milled and compacted to form thin tablets, which were submitted to the EDXRF analysis. The qualitative and quantitative analyzes showed that for phosphogypsum mortar the largest mass fractions were found of 49.8±2.5% (Si), 24.66±0.96% (S) and 22.10±0.42% (Ca). For gypsum mortar those values were found of 43.41±0.45% (Ca), 33.8 ± 0.8% (S) and 18.9±1.2% (Si), respectively; and for Portland cement mortar, the predominant elements in those samples have the mass fractions of 64.20±0.52% (Ca) and 27.3±1.5% (Si). The results showed that obtained values of mass fraction of the elements Si, S, K, Ca, Ti, Fe are in rather good agreement with quantities indicated for manufacture. Besides, gypsum and phosphogypsum presented almost the same composition and compressive strength.

Elementary characterization of Ti metal alloys used in implant dentistry

The main goal of present work is analytical characterization of standard dental implants broadly used by Brazilian dentists. An ideal biological alloy for dental implants must have very high biocompatibility, which means that such material should not provoke any serious adverse tissue response. Dental implants are generally marketed as commercially pure titanium (TiCP) due to their excellent mechanical and physical properties. However, sometimes other alloys are employed and consequently it is essential to study the chemical elements present in those alloys that could bring prejudice for the health. Present work investigated TiCP metal alloys used for dental implant manufacturing and evaluated the presence of elements. For alloy characterization and identification of elements it was used EDXRF technique. This method allows to perform the qualitative and quantitative analysis of the materials using the spectra of the characteristic X-rays emitted by the elements present in the metal samples. The experimental setup was based on two X- ray tubes, Mini X model with Ag and Au targets and X-123SDD detector (AMPTEK) and a 0.5 mm Cu collimator, developed due to specific sample geometrical and topography characteristics. Obtained results showed that implant alloys are not exactly TiCP but were manufactured using Ti-Al-V alloy, which contained Fe, Ni, Cu and Zn. The presence of such metals as Al and V in all studied samples shows very clear that studied implants were not manufactured from TiCP alloy. Moreover, according to the American Society for Testing and Materials (ASTM), these elements should not be present in TiCP.

Spectroscopic and elementary characterization of humic substances in organic substrates

The humic substances, major constituents of the organic matter of the substrates, play an important role in plant development, including: the availability of nutrients, the generation of negative charges (CEC) and the buffering effect. Based on this, this study aimed to use the molecular absorption spectroscopy in the ultraviolet-visible region (UV-VIS), the vibrational spectroscopy Fourier transform infrared (FTIR) and the elementary analysis CHN/O techniques to characterize the humic acid (HA) and fulvic acid (FA) fractions of the humic substances of five organic substrates, named as T1, T2, T3, T4, and T5, which were produced at the Federal University of Tocantins – Campus Gurupi. The molecular absorption spectra in UV-VIS and FTIR on the T1, T2, T3, T4 and T5 substrates showed humification, the formation of negative charges, which is related to the cation exchange capacity (CEC) and the complexation of metal ions that are considered nutrients. The biggest humification was shown for the T4 substrate, in function of its higher cabon-acid humic/carbon-acid fulvic ratio and the lower C/N ratio, allied to a negative charge generation, the low E4/E6 ratio found in the humic acid fraction. The complexation of metal nutrient ions indicates the greatest potencial of its use for seedlings production and the conservation of the chemical and physical properties of the organic substrate.