Linear Dependence Research Articles

Large Angular Momentum States in a Graphene Film

At energy lower than 2 eV, the dispersion law of the electrons in a graphene sheet presents a linear dependence of the energy on the kinetic momentum, which is typical of photons and permits the description of the electrons as massless particles by means of the Dirac equation and the study of massless particles acted upon by forces. We analytically solve the Dirac equation of an electron in a graphene disk with radius of 10,000 atomic units pierced by a magnetic field and find the eigenenergies and eigenstates of the particles for spin up and down. The magnetic field ranges within three orders of magnitude and is found to confine the electron in the disk. States with a relatively large total angular momentum exist and can be considered in a vorticose condition; these states are seen to peak at different distances from the disk centre and can be used to store few bit of information.

Scattering by a biisotropic obstacle and the properties of the Beltrami spherical vector waves

In this paper, we take a fresh look at the determination of the transition matrix for a homogeneous, biisotropic particle employing the Null‐field approach. The condition for passivity of the material is discussed. In particular, we focus on some previously unproved properties of the Beltrami spherical vector waves, such as completeness, orthogonality, and linear independence, which are all instrumental in the analysis of the scattering problem with the Null‐field approach. Some numerical examples illustrate the approach.

Cross-Correlation among Seismic Events, Rainfalls, and Carbon Dioxide Anomalies in Spring Water: Insights from Geochemical Monitoring in Northern Tuscany, Italy

Variations in the CO2 dissolved in water springs have long been observed near the epicenters of moderate and strong earthquakes. In a recent work focused on data collected during the 2017–2021 period from a monitoring site in the Northern Apennines, Italy, we noticed a significant correlation between CO2 anomalies and moderate-to-weak seismic activity. Here, we extended this analysis by focusing on data collected from the same site during a different period (2010–2013) and by integrating the CENSUS method with an artificial neural network (ANN) in the already-tested protocol. As in our previous work, a fit of the computed residual CO2 distributions allowed us to evidence statistically relevant CO2 anomalies. Thus, we extended a test of the linear dependence of these anomalies to seismic events over a longer period by means of binary correlations. This new analysis also included strong seismic events. Depending on the method applied, we observed different time lags. Specifically, using the CENSUS methodology, we detected a CO2 anomaly one day ahead of the earthquake and another anomaly eleven days ahead. However, no anomaly was observed with the ANN methodology. We also investigated possible correlations between CO2 concentrations and rain events and between rain events and earthquakes, highlighting the occurrence of a CO2 anomaly one day after a rain event of at least 10 mm and no linear dependence of seismic and rain events. Similar to our previous work, we achieved a probability gain of around 4, which is the probably of earthquake increases after CO2 anomaly observations.

An Inquiry-Oriented Approach to Determinants

In introductory linear algebra classrooms, determinants are often taught in a formulaic way that obscures their rich connections to graphical interpretations of linear transformations. As an alternative, in this paper, we introduce an innovative task sequence exploring the determinant conceptualized as a measure of the distortion of space. The task sequence is part of the Inquiry-Oriented Linear Algebra (IOLA) curricular materials, which build from experientially real tasks that allow for active student engagement in the guided reinvention of key mathematical ideas through student and instructor inquiry. The task sequence begins with students developing a conceptualization of the 2 × 2 matrix determinant as a ratio between the (signed) area of an image object and the area of its pre-image object transformed by the associated linear transformation. They then use this conceptualization to construct for themselves the 2 × 2 determinant formula and the determinant of a matrix inverse. Finally, students explore 2D and 3D GeoGebra applets to reinvent and explain core theorems related to the determinant involving linear dependence and switching/scaling rows and columns. Student work examples are provided throughout the paper.

Parallel flows as a key component to interpret Super-X divertor experiments

The Super-X Divertor (SXD) is an alternative divertor configuration leveraging total flux expansion at the Outer Strike Point (OSP). While the extended 2-Point Model (2PM) predicts facilitated detachment access and control in the SXD configuration, these attractive features are not always retrieved experimentally. These discrepancies are at least partially explained by the effect of parallel flows which, when self-consistently included in the 2PM, reveal the role of total flux expansion on the pressure balance and weaken the total flux expansion effect on detachment access and control, compared to the original predictions. This new model can partially explain the discrepancies between the 2PM and experiments performed on tokamak à configuration variable (TCV), in ohmic L-mode scenarios, which are particularly apparent when scanning the OSP major radius Rt. In core density ramps in lower Single-Null (SN) configuration, the impact of Rt on the CIII emission front movement in the divertor outer leg—used as a proxy for the plasma temperature in the divertor—is substantially weaker than 2PM predictions. Furthermore, in OSP radial sweeps in lower and upper SN configurations, in ohmic L-mode scenarios with a constant core density, the peak parallel particle flux density at the OSP is almost independent of Rt, while the 2PM predicts a linear dependence. Finally, analytical and numerical modeling of parallel flows in the divertor is presented. It is shown that an increase in total flux expansion can favour supersonic flows at the OSP. Parallel flows are also shown to be relevant by analysing SOLPS-ITER simulations of TCV.

High‐pressure and high‐temperature Raman spectroscopic study of zircon as a pressure scale in hydrothermal DACs

AbstractRaman spectra of zircon have recently been used as a pressure scale for studies of geological fluids at high temperatures and high pressures using diamond anvil cells (DACs). The zircon scale is advantageous in high chemical stability and the large pressure response of the B1g mode. Despite its excellent applicability, the calibration of the scale has been carried out only in a narrow pressure–temperature range, especially under limited high‐temperature and high‐pressure conditions. In this study, the pressure and temperature dependence of the Raman modes of synthetic zircon was investigated up to 9.5 GPa and from room temperature to 776 K using an externally heated diamond anvil cell. Ruby and gold were used as the reference pressure scales. The Raman shift of the B1g mode for the antisymmetric stretching of the SiO4 structure in zircon showed a linear pressure dependence of 5.48(4) cm−1/GPa up to 8 GPa at room temperature, in agreement with the previous studies. Measurements under high‐pressure and high‐temperature conditions confirmed that the pressure dependence up to 9.5 GPa along the isotherms from 373 to 675 K was consistent with the room‐temperature value; the wavenumbers can be well deduced from the sum of the individual effects of pressure and temperature, obtained at ambient temperature and pressure, respectively. A comparison of the zircon scale with the c‐BN Raman spectroscopic scale confirmed that the pressures determined with these scales were in reasonable agreement. The present results provide a confident use of the zircon Raman spectroscopic scale in a wider pressure–temperature range than previous studies for the internally consistent pressure determination.

Augmented LT codes over binary extension fields with increased ratio of full‐degree columns

AbstractThis letter proposes an augmented scheme of LT codes to improve the decoding success rate. The method involves substituting the 1‐s in full‐degree columns of the generator matrix of conventional LT codes with binary extension field elements and simultaneously increasing the ratio of full‐degree columns in the ideal soliton distribution. For non‐full‐degree columns, we retain the nonzero elements as 1‐s in the conventional LT codes generator matrix to preserve computational efficiency. Compared to conventional LT codes, the proposed method enhances the linear independence of the generator matrix, leading to a higher decoding success rate with minimal data packets. Experimental results demonstrate the effectiveness of the method at improving the performance of LT codes, with close to 100% decoding success rate achieved with around 5% data redundancy.

Reservoir-triggered seismicity: case study of the Dnister Hydro Power Complex (Ukraine)

The work considers the seismic activity around the Dnister Hydro Power Complex in the Dnister Reservoir area from 2012 to 2021. Maximum local magnitude of earthquakes for the studied period is ML=3.4. Hypocenters of earthquakes are at the depth of 1—3 km. They are located nearby to previously established faults and contacts of structures with a different lithological composition. Artificial water level regulation in the reservoir is related to the operation of the Dnister Hydro Power Plant and, according to our results, probably affects the occurrence of seismic events. Although the maximum water level changes only by 8.7 m, the region has increased natural seismicity and is located in the transition zone between 6th and 7th isoseims according to the seismic zoning map of Ukraine. Accumulated natural stresses can be triggered into earthquakes when there is a sudden change in water pressure. The seismicity of the region around the Dnister Reservoir was investigated for 10 years, taking into account the water level data in the reservoir, as well as comparing the location of earthquakes with the State Geological Map of the Crystalline Foundation. The profile of the State Geological Map of the Crystalline Foundation with the projected earthquakes hypocenters allowed to indicate that a significant number of earthquakes are located between different lithological structures. In order to assess the interrelationship between seismicity and water level changes in the reservoir, 111 periods of lowering or filling of the reservoir were selected. Parameters of seismic activity within the periods were calculated and analysed. Correlation between the sum of logarithms of energy with water volume changes and pressure changes in the Dnister Reservoir was established. Considering linear dependence it is possible to predict potential intensity of local seismicity caused by water level changes in the Dnister Reservoir.

Solution processed self-powered broadband flower-like Zn(Al)O-mixed metal oxide dye sensitized photodetector

This article elucidates a solution-based framework through which a novel self-powered broadband Zn(Al)O-mixed metal oxide (MMO) photodetector treated with organic 535-bisTBA dye (N719) was reported. The deposited MMO layer exhibited flower-like morphology with sheet thickness of 19.4 nm alongside optical bandgap of 3.11 eV, while MMO treated with N719 delivered broad absorbance (450–600 nm). Further, pristine MMO and N719-treated photodetectors responded coherently to the utilized wavelengths with photocurrent of 35.7 and 56.2 μA at 405 and 530 nm, respectively. In conjunction, the spectral-response (Rλ) of pristine MMO device revealed visible blind feature wherein N719-treated photodetector exhibited broad Rλ throughout 375-625nm. The time-resolved characteristics demonstrated response time of 0.85 and 0.80 sec. for pristine MMO and N719-treated devices, respectively. The fabricated photodetectors expressed considerable linear power dependency (R20.99) at 0 bias evidencing self-power feature of the proposed geometry.

On Universality of Some Beurling Zeta-Functions

Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the number of generalized integers and the mean of the generalized von Mangoldt function, the linear independence of the set {logp:p∈P}, and the existence of a bounded mean square for ζP(s). Under the above hypotheses, we obtain the universality of the function ζP(s). This means that the set of shifts ζP(s+iτ) approximating a given analytic function defined on a certain strip σ^<σ<1 has a positive lower density. This result opens a new chapter in the theory of Beurling zeta functions. Moreover, it supports the Linnik–Ibragimov conjecture on the universality of Dirichlet series. For the proof, a probabilistic approach is applied.

An accurate model for the solubilities of anhydrite in H2O–NaCl solutions at temperatures up to 1073 K, pressures up to 14,000 bar, and mole fractions of NaCl up to 0.3

An accurate density-based solubility model is established for anhydrite in H2O–NaCl solutions, which is valid for temperatures up to 1073 K, pressures up to 14,000 bar, and mole fractions of NaCl (xNaCl) up to 0.3. The isobaric linear dependence of the mineral solubility logarithm on the solvent density logarithm should be a common phenomenon similar to isothermal linear dependence, particularly at relatively high pressures. The terms about P in the equations of the density-based model are rational and necessary to elevate the accuracy of mineral solubility models. This model reproduces the complicated changing trends of anhydrite solubility with temperature, pressure, and xNaCl. Compared to numerous experimental data, the average relative deviations of calculated anhydrite solubilities in water and the aqueous NaCl solution are 3.52% and 9.64%, respectively, which are within experimental uncertainties. According to this model, the anhydrite deposition would result from any salinity variation departing from the specified xNaCl in skarn- or porphyrite-type iron ore-forming hydrothermal fluids.

Synthesis and characterization of Al-doped ZnO/CdO heterostructured nanocomposites for enhancing NO2 gas sensing performance

In this study, both petal-shaped Al-doped (1 at%) ZnO (Al-ZnO) and Al-ZnO/CdO heterostructured nanomaterials were successfully designed and synthesized via a facile two-step hydrothermal method. Characterizations of crystallinity, morphology and composition were performed by XRD, HR-TEM, FE-SEM, EDS, XPS, and Raman. The results of XRD, HR-TEM, and XPS reveal that Al-ZnO/CdO materials grew well together and coexisted. The petal shaped Al-ZnO/CdO heterostructured nanocomposite with 2 mol% of CdO was exposed to NO2, NH3, CH3COCH3, C2H5OH, and H2 at an optimal operating temperature of 200 °C. Compared with pure ZnO and Al-ZnO, the petal-shaped Al-ZnO/CdO heterostructured nanocomposite exhibited specifically high enhanced performances in response and selectivity for the NO2 gas sensing. Moreover, the sensitivity to NO2 displayed excellent linear dependence in the range of 0.5 ∼ 5 ppm, which shows promise in the detection of NO2 using a petal-shaped Al-ZnO/CdO heterostructured nanocomposite-based sensor.

An ideal candidate for observing anomalous Hall effect induced by the in-plane magnetic field

The anomalous Hall effect induced by the in-plane magnetic field (anomalous planar Hall effect) has recently attracted a lot of interests due to its numerous advantages. Although several schemes have been put forward in theory, experimental observations in many materials so far are often accompanied by planar Hall effects due to other mechanisms, rather than the pure anomalous planar Hall effect (APHE). We propose the surface state of the strained topological insulator as an ideal candidate to observe this effect. The surface state exhibits a pure APHE, characterized by a linear dependence on the magnetic field and a 2π periodicity, which remains robust against the scattering of non-magnetic and various magnetic impurities, as long as the uniaxial strain preserves mirror symmetry. Although a general strain that breaks the mirror symmetry can induce the conventional Drude Hall effect, the anomalous contribution remains dominant. Furthermore, we present a feasible scheme to distinguish between the two contributions based on their distinct magnetic field dependencies. Our work is of great significance for promoting experimental observation of the APHE and provides reference value in the search for other realistic materials.

Validation of the Quantitative Determination Method of the active substance in Angiolin eye drops by spectrophotometry

Today, cataracts are the main cause of vision loss. Therefore, the creation of new ophthalmic medicines (drugs), namely eye drops, based on the active substance angiolin ((S)-2,6-diaminohexanoic acid 3-methyl-1,2,4-triazolyl-5-thioacetate) is an urgent task. Previously, we developed a method of standardization of the active substance – by the spectrophotometry. According to the requirements of the SPhU, the next step was the validation of the developed methods. That became the purpose of our work. Validation of the method of quantitative determination of active substances was carried out according to the following indicators: specificity, linearity, range of application, accuracy, correctness and robustness. In the course of the conducted studies, it was established that the method is characterized by sufficient convergence and correctness, as the criterion of insignificance of the systematic error of the method is fulfilled. The systematic error of the method satisfies the requirements of statistical and practical insignificance. The high value of the correlation coefficient r = 1.0000 and 0.99994 satisfies the requirements of the acceptance criterion (r = 0.9998) and confirms the linearity of the dependence between the amount of Angiolin taken and found in the range from 80% to 120%, according to its nominal content in the drug. The requirements for the linear dependence parameters (a, SD0/b, r) of the Angiolin determination method are met in the entire concentration range from 80% to 120% of the nominal value. Thus, the developed method of standardization of active substances in Angiolin eye drops is valid and can be introduced into the project of QCM (quality control methods).

Manganese (II) Halides for X‐Ray Imaging and Moisture Detection

AbstractOrganic–inorganic hybrid metal halides are widely used in X‐ray detection and imaging due to their high X‐ray absorption efficiency, ease of synthesis, and efficient luminescence. However, the issue of lead toxicity remains a concern. In this study, non‐toxic, 0D 2,2′‐(Ethylenedioxy)bis(ethylamine) manganese (II) bromide (EDBEMnBr4) is synthesized using the simple mechanical grinding method and the solution method that exhibits intense green emission at ≈525 nm. Moreover, the change of structure under the influence of temperature and water significantly affects its fluorescence color under UV light. Scintillator materials with and without moisture exposure showed spatial resolutions of 7 and 4 lp mm−1, and low detection limits of 4.62 and 5.25 µGyair s−1, respectively, meeting medical industry standards (<5.5 µGyair s−1). Furthermore, based on the apparent change in luminescence color triggered by moisture for EDBEMnBr4, a preliminary attempt is made to apply it to humidity monitoring showing that the boundary of color change has a good linear dependence on humidity and time. This work provides new opportunities for Mn‐based metal halides in both X‐ray detection as well as moisture detection.

Linear dependence of the equatorial electrojet component of X-class-triggered solar flare effects with respect to the maximum flare X-ray flux

Solar flares effects (SFE) are short geomagnetic disturbances (mainly in the horizontal component) observed during the development of solar flares. SFE are caused by current enhancements in multiple layers of the ionosphere induced by the flare ionizing radiation. Despite their origin, very few research studies have focused on the connection between the horizontal SFE amplitude and the maximum flare X-ray flux. By analyzing measurements from the magnetic station at Huancayo, Peru, located in the American sector of the equatorial electrojet (EEJ) current, we computed the horizontal SFE amplitudes triggered by X-class solar flares of Solar Cycle 24 by using a novel method. The EEJ contribution to the horizontal SFE amplitude was calculated using data from the geomagnetic observatory at Pilar, Argentina, located outside the EEJ belt. We found that the EEJ contribution to the horizontal SFE amplitude is linearly dependent on the perpendicular component of the maximum flare X-ray flux for two states of the EEJ current. We also found that the flare X-ray ionizing effect is around three times stronger in the EEJ current than in the solar quiet current, being the EEJ current the most important contributor to the horizontal SFE amplitude. In addition, our results suggest that the weak linear relationship between the pre-flare horizontal geomagnetic variation and the EEJ component of the horizontal SFE amplitude found by a previous study might be only a coincidence, instead of a real connection between both parameters. Exceptional SFE were studied separately.

Polarity of Organic Solvent/Water Mixtures Measured with Reichardt’s B30 and Related Solvatochromic Probes—A Critical Review

The UV/Vis absorption energies (νmax) of different solvatochromic probes measured in co-solvent/water mixtures are re-analyzed as a function of the average molar concentration (Nav) of the solvent composition compared to the use of the mole fraction. The empirical ET(30) parameter of Reichardt’s dye B30 is the focus of the analysis. The Marcus classification of aqueous solvent mixtures is a useful guide for co-solvent selection. Methanol, ethanol, 1,2-ethanediol, 2-propanol, 2-methyl-2-propanol, 2-butoxyethanol, formamide, N-methylformamide (NMF), N,N-dimethylformamide (DMF), N-formylmorpholine (NFM), 1,4-dioxane and DMSO were considered as co-solvents. The ET(30) values of the binary solvent mixtures are discussed in relation to the physical properties of the co-solvent/water mixtures in terms of quantitative composition, refractive index, thermodynamics of the mixture and the non-uniformity of the mixture. Significant linear dependencies of ET(30) as a function of Nav can be demonstrated for formamide/water, 1,2-ethanediol/water, NMF/water and DMSO/water mixtures over the entire compositional range. These mixtures belong to the group of solvents that do not enhance the water structure according to the Marcus classification. The influence of the solvent microstructure on the non-linearity ET(30) as a function of Nav is particularly clear for alcohol/water mixtures with an enhanced water structure.

Advanced spectroscopic investigation of colour centres in LiF crystals irradiated with monochromatic hard x-rays

Nominally-pure lithium fluoride (LiF) crystals were irradiated with monochromatic hard x-rays of energy 5, 7, 9 and 12 keV at the METROLOGIE beamline of the SOLEIL synchrotron facility, in order to understand the role of the selected x-ray energy on their visible photoluminescence (PL) response, which is used for high spatial resolution 2D x-ray imaging detectors characterized by a wide dynamic range. At the energies of 7 and 12 keV the irradiations were performed at five different doses corresponding to five uniformly irradiated areas, while at 5 and 9 keV only two irradiations at two different doses were carried out. The doses were planned in a range between 4 and 1.4 × 103 Gy (10.5 mJ cm−3 to 3.7 J cm−3), depending on the x-ray energy. After irradiation at the energies of 7 and 12 keV, the spectrally-integrated visible PL intensity of the F2 and F3 + colour centres (CCs) generated in the LiF crystals, carefully measured by fluorescence microscopy under blue excitation, exhibits a linear dependence on the irradiation dose in the investigated dose range. This linear behaviour was confirmed by the optical absorption spectra of the irradiated spots, which shows a similar linear behaviour for both the F2 and F3 + CCs, as derived from their overlapping absorption band at around 450 nm. At the highest x-ray energy, the average concentrations of the radiation-induced F, F2 and F3 + CCs were also estimated. The volume distributions of F2 defects in the crystals irradiated with 5 and 9 keV x-rays were reconstructed in 3D by measuring their PL signal using a confocal laser scanning microscope operating in fluorescence mode. On-going investigations are focusing on the results obtained through this z-scanning technique to explore the potential impact of absorption effects at the excitation laser wavelength.

Reversible Thiyl Radical Addition−Fragmentation Chain Transfer Polymerization

AbstractDeveloping reversible‐deactivation radical polymerization (RDRP) methods that could directly control the thiyl radical propagation is highly desirable yet remains challenging in modern polymer chemistry. Here, we reported the first reversible thiyl radical addition‐fragmentation chain transfer (SRAFT) polymerization strategy, which utilizes allyl sulfides as chain transfer agents for reversibly deactivating the propagating thiyl radicals, thus allowing us to directly control a challenging thiyl radical chain polymerization to afford polymers with well‐defined architectures. A linear dependence of molecular weight on conversion, high chain‐end fidelity, and efficient chain extension proved good controllability of the polymerization. In addition, density functional theory calculations provided insight into the reversible deactivation ability of allyl sulfides. The SRAFT strategy developed in this work represents a promising platform for discovering new controlled polymerizations based on thiyl radical chemistry.

Effect of Partial Doping with La Atoms on Some Superconducting and Electrotransport Characteristics of Y1-x LaxBa2Cu3Oy Polycrystals

The effect of the location with different concentrations of La atoms (x = 0; 0.02; 0.028; 0.11) on some superconducting and electrotransport characteristics of Y1−xLaxBa2Cu3Oy polycrystalline compounds was studied by recording the temperature dependence ρ(T) curves of resistivity in the case of direct current in the range of temperatures (77K - 300K). The temperatures at the onset (Τcon) and offset (Tc0) of the transition, as well as the width of the transition - ΔΤc = Τcon-Tc0, were considered as the superconducting characteristics. The absolute values of ρ(300K) and ρ(100K) and their ratio a = ρ(300K)/ρ(100K) were considered as electric transport characteristics, as well as the temperature coefficient of resistivity dρ/dT, which was determined by ρ(T) in the range of linear dependence with the slope of the curve. From the comparison of these characteristics, it was concluded that there is a certain correlation between the superconducting and electrotransport properties of the studied compounds depending on the concentration x of the partial location of Y atoms with La. Type: