Real Matrices Research Articles

Application of catalytic hydrodechlorination for the fast removal of chlorinated azole pesticides in drinking water

Catalytic hydrodechlorination (HDC) is regarded as a promising purifying technology for drinking water treatment. So far, it has proved to be highly effective for the removal of different groups of chlorinated micropollutants including pharmaceuticals, neonicotinoid pesticides, personal care products or chloroacetic acids. The azole pesticides, recently included in the EU Watch Lists (Decisions 2020/1161 and 2022/1307), are a group of micropollutants of particular concern for drinking water given their high toxicity, persistence, and bioaccumulation potential. In this work, the feasibility of HDC for the removal of a representative group of chlorinated azole pesticides tebuconazole (TEB), tetraconazole (TET), prochloraz (PCZ), penconazole (PEN), metconazole (MET) and imazalil (IMZ)) is demonstrated, and their reactivity is compared with that observed for other halogenated micropollutant groups. Notably, all the pesticides investigated in this work (100 μg L−1) were completely dechlorinated within 30 min under ambient conditions using a 1 wt% Pd/Al2O3 catalyst concentration of 0.25 g L−1 and a H2 feeding of 50 mL N min−1. The experimental data were accurately described by a pseudo-first order kinetic equation and rate constant values in the range from 1.08 to 2.60 L gcat−1 min−1 were obtained. These values are quite close to those achieved for the most reactive neonicotinoid pesticides and significantly higher than the obtained for chloroacetic acids and most pharmaceuticals (e.g. diclofenac, sertraline or chlorpromazine). From the identification of the generated reaction intermediates and the final non-chlorinated products, sequential reaction pathways were proposed for each pollutant. Remarkably, despite the high toxicity exhibited by the azole pesticides tested, with LC50 values within the 0.4–7.0 mg L−1 range using A. salina, HDC effluents were non-toxic in all cases. Furthermore, the catalyst showed a remarkable stability upon three consecutive runs. Finally, the versatility of the process was demonstrated in the treatment of real aqueous matrices such as DWTP and tap water, where no significant differences were found either in terms of activity or stability.

Generalized Quaternions and Matrix Algebra

In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained real and complex matrices corresponding to the real and complex basis of the generalized quaternions. Also, we investigated the basis features of real and complex matrices. We get Pauli matrices corresponding to generalized quaternions. Then, we have shown that the algebra produced by these matrices is isomorphic to the Clifford algebra Cl(E_αβ^3) produced by generalized space E_αβ^3.
 Finally, we studied the relations among the symplectic matrices group corresponding to generalized unit quaternions, generalized unitary matrices group, and generalized orthogonal matrices group.

Flavor-food ingredient interactions in fortified or reformulated novel food: Binding behaviors, manipulation strategies, sensory impacts, and future trends in delicious and healthy food design.

With consumers gaining prominent awareness of health and well-being, a diverse range of fortified or reformulated novel food is developed to achieve personalized or tailored nutrition using protein, carbohydrates, or fat as building blocks. Flavor property is a critical factor in the acceptability and marketability of fortified or reformulated food. Major food ingredients are able to interact with flavor compounds, leading to a significant change in flavor release from the food matrix and, ultimately, altering flavor perception. Although many efforts have been made to elucidate how food matrix components change flavor binding capacities, the influences on flavor perception and their implications for the innovation of fortified or reformulated novel food have not been systematically summarized up to now. Thus, this review provides detailed knowledge about the binding behaviors of flavors to major food ingredients, as well as their influences on flavor retention, release, and perception. Practical approaches for manipulating these interactions and the resulting flavor quality are also reviewed, from the scope of their intrinsic and extrinsic influencing factors with technologies available, which is helpful for future food innovation. Evaluation of food-ingredient interactions using real food matrices while considering multisensory flavor perception is also prospected, to well motivate food industries to investigate new strategies for tasteful and healthy food design in response to consumers' unwillingness to compromise on flavor for health.

Fate of sulfamerazine by synchronous adsorption and photocatalysis dependent on natural organic matter properties

ABSTRACT Natural organic matter (NOM) can impede the removal of organic micro-pollutants (OMPs) through several mechanisms, including inner filter effect, competition with the target OMP, and radical scavenging, during synchronous adsorption/photocatalysis of multi-functional composites. In this study, the fate and inhibitory mechanisms of sulfamerazine (SMZ, a model OMP) that occurred in presence of seven different NOM samples (i.e. three standard NOM surrogates, a river water sample, a carbon filter effluent and two different sand filter effluents) during the adsorption/photocatalysis by a composite of Bi2O3-TiO2 supported on powdered activated carbon (Bi2O3-TiO2/PAC, abbreviated as BTP) when exposed to visible light irradiation were revealed. The results indicated that adsorption played a greater attribution than photocatalysis on SMZ removal. The primary impediment to the adsorption and photocatalytic degradation of SMZ was attributed to the presence of terrestrial-derived, humic-like NOM fractions with high aromaticity. The adsorption efficacy of SMZ was weakened by the absorption of NOM and its degradation products onto the BTP surface. The inner filter effect, competition between NOM and SMZ, and radical scavenging were responsible for the reduced photocatalysis of SMZ. In the cases of real water matrices, the presence of inorganic anion and co-existed NOM reduced the removal of SMZ. In summary, the findings of this work offer a comprehensive comprehension of the impact of NOM fractions on photocatalysis, emphasizing the necessity to examine the interplay between NOM and background inorganic constituents in the degradation of OMP via adsorption/photocatalysis.

A note on complex conference matrices

Let Fq be the Galois field of order q=pm, p a prime number and m a positive integer. We prove in this article that for any nontrivial multiplicative character ϰ of Fq⁎ and for any b∈Fq⁎ we have∑a∈Fq⁎ϰ(a)ϰ(a+b)‾=−1. Whenever q is odd and ϰ is the Legendre symbol this formula reduces to the well-known Jacobsthal's formula. A complex conference matrix is a square matrix of order n with zero diagonal and unimodular complex numbers elsewhere such that C⁎C=(n−1)I. Paley used finite fields with odd orders q=pm, p prime and the real Legendre symbol to construct real symmetric conference matrices of orders q+1 whenever q≡1(mod4) and real skew-symmetric conference matrices of orders q+1 whenever q≡−1(mod4). In this article we extend Paley construction to the complex setting. We extend Jacobsthal's formula to all other nontrivial characters to produce a complex symmetric conference matrix of order q+1 whenever q≥4 is any prime power as well as a complex skew-symmetric conference matrix of order q+1 whenever q is any odd prime power. These matrices were constructed very recently in connection with harmonic Grassmannian codes, by use of finite fields and the character table of their additive characters. We propose here a new proof of their construction by use of the above generalized formula similarly as was done by Paley in the real case. We also classify, up to equivalence, the complex conference matrices constructed with some nontrivial characters. In particular, we prove that the complex conference matrix constructed with any nontrivial multiplicative character ϰ and that one constructed with ϰpk for any integer k=1,...m−1 are permutation equivalent. Moreover, we determine the spectrum of any complex conference matrix obtained from this construction.

Sunflower meal ethanol solute powder as an upcycled value-product to prolong food shelf life

In this study the potential of sunflower meal ethanol-wash powder (SEWP) to be used as antimicrobial agent in liquid foods was investigated. SEWP represents the waste of the main process of protein isolation from industrially produced sunflower meal. The washing liquids remaining after treatment of the sunflower meal with 75% aqueous ethanol solution were collected and turned into powder rich in bioactive compounds. Due to its recognized properties, different concentrations (2.5 and 5% w/v) of SEWP were first tested in vitro against Alicyclobacillus acidoterrestris and a cocktail of Pseudomonas putida and Pseudomonas fluorescens strains, using appropriate culture media. Then, the SEWP antimicrobial efficacy was tested on two real food matrices differing in their composition. Soymilk, rich in proteins, and apple juice, composed mainly of carbohydrates, were used as food models. Concentrations equal to 1%, 1.5%, 2%, 2.5%, 5% and 7.5% (w/v) SEWP were tested in the juice, whereas the sole three highest concentrations were tested in the soymilk. Both beverages were pre-inoculated with different spoilage bacteria. The same mix of Pseudomonas spp. and A. acidoterrestris strain used for the in vitro test were employed to contaminate the soymilk and the apple juice, respectively. In vitro results showed moderate effects of SEWP against selected target microorganisms. On the contrary, two completely different microbial evolutions were recorded in the soymilk and apple juice. The three concentrations of SEWP were slightly effective against spoilage of soymilk, whereas all the concentrations used in the juice were sufficient to completely inhibit microbial growth of A. acidoterrestris. The shelf life of the apple juice supplemented with 1% SEWP was extended for more than 21 days. Considering both the antimicrobial efficacy and the sensory properties of the juice, the lowest SEWP concentration (1% w/v) demonstrated the best result as a bioprotectant. Overall results imply dependence of SEWP antimicrobial efficiency on food composition and a need of preliminary evaluation of the product if used as an antimicrobial agent in the food industry.

The liberation set in the inverse eigenvalue problem of a graph

The inverse eigenvalue problem of a graph G is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of G. The strong spectral property is a powerful tool in this problem, which identifies matrices whose entries can be perturbed while controlling the pattern and preserving the eigenvalues. The Matrix Liberation Lemma introduced by Barrett et al. in 2020 advances the notion to a more general setting. In this paper we revisit the Matrix Liberation Lemma and prove an equivalent statement, that reduces some of the technical difficulties in applying the result.We test our method on matrices of the form M=A⊕B and show how this new approach supplements the results that can be obtained from the strong spectral property only. While extending this notion to the direct sums of graphs, we discover a surprising connection with the zero forcing game on Cartesian products of graphs.Throughout the paper we apply our results to resolve a selection of open cases for the inverse eigenvalue problem of a graph on six vertices.

Evaluating the catalytic effect of Fe@Fe2O3-modified granulated cork as an innovative heterogeneous catalyst in electro-fenton degradation of benzoquinone in different aqueous matrices

This study investigated the potential of a novel biomass-derived cork as a suitable catalyst after its modification with Fe@Fe2O3 for in-situ application in heterogeneous electro-Fenton (HEF) process for benzoquinone (BQ) elimination from water. No attempts on the application of modified granulated cork (GC) as a suspended heterogeneous catalyst in the HEF process for water treatment have been published yet. GC was modified by sonification approach in a FeCl3 + NaBH4 solution to reduce the ferric ions to metallic iron in order to obtain Fe@Fe2O3-modified GC (Fe@Fe2O3/GC). Results clearly demonstrated that this catalyst exhibited excellent electrocatalytic properties, such as a high conductivity as well as relatively high redox current and possessed several active sites for water depollution applications. Using Fe@Fe2O3/GC as catalyst in HEF, 100% of BQ removal was achieved in synthetic solutions by applying 33.3 mA cm−2 after 120 min. Different experimental conditions were tested to determine that best possible conditions can be as follow: 50 mmol L−1 Na2SO4 and 10 mg L−1 of Fe@Fe2O3/GC catalyst using Pt/carbon-PTFE air diffusion cell by applying 33.3 mA cm−2. Nevertheless, when Fe@Fe2O3/GC was used in the HEF approach to depollute real water matrices, no complete BQ concentration was removal achieved after 300 min of treatment, achieving between 80 and 95% of effectiveness.

Singular matrices whose Moore-Penrose inverse is tridiagonal

A variety of characterizations of nonsingular matrices whose inverse is tridiagonal (irreducible or not) have been widely investigated in the literature. One well-known such characterization is stated in terms of semiseparable matrices. In this paper, we consider singular matrices A and give necessary and sufficient conditions for the Moore-Penrose inverse of A to be tridiagonal. Our approach is based on bordering techniques, as given by Bapat and Zheng (2003). In addition, we obtain necessary conditions on A analogous to the semiseparability conditions in the nonsingular case, though in the singular case they are not sufficient, as illustrated with examples. We apply our results to give an explicit description of all the 3×3 real singular matrices and 3×3 Hermitian matrices whose Moore-Penrose inverse is irreducible and tridiagonal.

The effect of cold storage and cooking on the viability of Clostridioides difficile spores in consumer foods.

The increased detection of clinical cases of Clostridioides difficile coupled with the persistence of clostridial spores at various stages along the food chain suggest that this pathogen may be foodborne. This study examined C. difficile (ribotypes 078 and 126) spore viability in chicken breast, beef steak, spinach leaves and cottage cheese during refrigerated (4°C) and frozen (-20°C) storage with and without a subsequent sous vide mild cooking (60°C, 1h). Spore inactivation at 80°C in phosphate buffer solution, beef and chicken were also investigated to provide D80°C values and determine if PBS was a suitable model system for real food matrices. There was no decrease in spore concentration after chilled or frozen storage and/or sous vide cooking at 60°C. Non-log-linear thermal inactivation was observed for both C. difficile ribotypes at 80°C in phosphate buffer solution (PBS), beef and chicken. The predicted PBS D80°C values of 5.72±[2.90, 8.55] min and 7.50±[6.61, 8.39] min for RT078 and RT126, respectively, were in agreement with the food matrices D80°C values of 5.65min (95% CI range from 4.29 to 8.89min) for RT078 and 7.35min (95% CI range from 6.81 to 7.01min) for RT126. It was concluded that C. difficile spores survive chilled and frozen storage and mild cooking at 60°C but may be inactivated at 80°C. Moreover thermal inactivation in PBS was representative of that observed in real food matrices (beef and chicken).

On the existence of Luenberger reduced order observer

Abstract In this paper the explicit necessary and sufficient conditions for the existence of Luenberger reduced order observer are established. In particular, it is proven that for the given linear time-invariant system of order n, having p linearly independent outputs and m inputs, a Luenberger observer of order (n − p) can be constructed if and only if the given system is detectable. Furthermore, a procedure is given for the construction of the observer. Our approach is based on the properties of real and polynomial matrices.

Sensitive riboflavin sensing using silver nanoparticles deposited onto screen-printed electrodes via controlled-energy spark discharges

In this work, we elaborated the graphite screen-printed electrodes (SPEs) modification with metal nanoparticles formed as a result of spark discharges produced between a metal wire electrode and SPE that are connected to an Arduino board-based DC high voltage power supply. This sparking device allows, on the one hand, the toposelective formation of NPs of controlled dimensions through a direct and liquid-free approach, and on the other hand, controls the number and energy of the discharges delivered to the electrode surface during a single spark event. This way, the potential damage to the SPE surface by the action of heat evolved during the sparking process is considerably minimized compared with the standard setup in which each spark event consists of multiple electrical discharges. Data demonstrated that the sensing properties of the resulting electrodes are significantly improved compared with those achieved when conventional spark generators are employed, as demonstrated for silver-sparked SPEs that exhibit enhanced sensitivity to riboflavin. Sparked AgNp-SPEs were characterized using scanning electron microscopy and voltammetric measurements in alkaline conditions. The analytical performance of sparked AgNP-SPEs was evaluated by various electrochemical techniques. Under optimum conditions, the detection range for DPV was from 1.9 (LOQ) to 100nM riboflavin (R2=0.997), while a limit of detection (LOD, S/N 3) of 0.56nM was achieved. The analytical utility is demonstrated for the determination of riboflavin in the real matrices of B-complex pharmaceutical preparation and an energy drink.

STATISTICAL CONVERGENCE OF MATRIX SEQUENCES

This paper extends the statistical convergence of real or complex numbers to the real square matrices sequences . In this context, we investigate the relation between the statistical convergence, statistical Cauchy condition, strong Ces\`{a}ro summability of matrices sequences. This leads us to an initial analysis of the Tauberian conditions for the statistical convergence of matrix sequences.

Magnetic MnFe2O4 nanoparticles anchored on sludge-derived biochar in activating peroxydisulfate for levofloxacin degradation: Mechanism, degradation pathways and cost analysis

The sludge-derived biochar (SBC) was prepared by a low-cost microwave pyrolysis process, and then MnFe2O4 nanoparticles were anchored onto the surface of SBC through a hydrothermal route to construct a magnetic MnFe2O4/SBC composite catalyst. As-obtained MnFe2O4/SBC catalysts were characterized by XRD, FT-IR, Raman, FE-SEM, BET surface area and XPS. The optimized MnFe2O4/SBC(1:3) catalyst showed a higher catalytic activity to activate peroxydisulfate (PDS) for levofloxacin (LVF) degradation than that of SBC, MnFe2O4 and reported magnetic composite catalysts. After 80 min of reaction, 79.5% of LVF in water (10 mg/L) was degraded by MnFe2O4/SBC(1:3) in the presence of PDS (1.5 g/L), and LVF degradation followed the pseudo-second-order kinetics. Calcium carbonate (CaCO3) in SBC participates in PDS activation. XPS analysis, oxidative species capture experiments, EPR and linear sweep voltammetry (LSV) tests confirmed that LVF degradation in MnFe2O4/SBC-PDS oxidation system was achieved through the non-radical (electron transfer, 1O2) and radical (SO4•−, ∙OH and O2•−) pathways, with the former playing a dominant role. The degradation routes of LVF were established based on the degradation intermediates. LVF removal efficiency from real water matrices was improved by means of increasing catalyst dosage and reaction temperature. Cost analysis indicates that MnFe2O4/SBC-PDS oxidation process is a cost-effective method to eliminate the antibiotics in water.

The Double Dyson Index β Effect in Non-Hermitian Tridiagonal Matrices.

The Dyson index, β, plays an essential role in random matrix theory, as it labels the so-called "three-fold way" that refers to the symmetries satisfied by ensembles under unitary transformations. As is known, its 1, 2, and 4 values denote the orthogonal, unitary, and symplectic classes, whose matrix elements are real, complex, and quaternion numbers, respectively. It functions, therefore, as a measure of the number of independent non-diagonal variables. On the other hand, in the case of β ensembles, which represent the tridiagonal form of the theory, it can assume any real positive value, thus losing that function. Our purpose, however, is to show that, when the Hermitian condition of the real matrices generated with a given value of β is removed, and, as a consequence, the number of non-diagonal independent variables doubles, non-Hermitian matrices exist that asymptotically behave as if they had been generated with a value 2β. Therefore, it is as if the β index were, in this way, again operative. It is shown that this effect happens for the three tridiagonal ensembles, namely, the β-Hermite, the β-Laguerre, and the β-Jacobi ensembles.

On the Moore-Penrose pseudo-inversion of block symmetric matrices and its application in the graph theory

The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion of symmetric real matrices with application in the graph theory. We introduce a novel concept of positively and negatively pseudo-inverse matrices and graphs. We also give sufficient conditions on the elements of a block symmetric matrix yielding an explicit form of its Moore-Penrose pseudo-inversion. Using the explicit form of the pseudo-inverse matrix we can construct pseudo-inverse graphs for a class of graphs which are constructed from the original graph by adding pendent vertices or pendant paths.

Transformation of Mytella falcata residual shell into CaAl/LDH adsorbent: Removal of methyl orange and methylene blue dyes

AbstractThis study analyzed the viability of using malacoculture residue (Mytella falcata) to produce layered double hydroxides (LDHs) and for its subsequent use as an adsorbent. The CaAl/LDH‐RE material was produced with calcium oxide from the residue and the CaAl/LDH‐AP was produced with a commercial reagent. Both were used to remove methyl orange (MO) and methylene blue (MB) dyes. The CaAl/LDH‐RE presented a surface area of 28.54 m2 g−1, being 65.62% larger than the CaAl/LDH‐AP material (17.23 m2 g−1). The adsorbents showed mesopores distributed on a surface formed by plates in the form of hexagonal sheets arranged in an overlapping manner. The dosage of 0.05 g L−1 obtained the removal of 95% and 97% for MO, while for MB it was 94% and 93% using the adsorbents LDH/CaAl‐AP and LDH/CaAl‐RE, respectively. The system reached equilibrium at 90 min for MO and 120 min for MB. The pseudo‐second order model well represented the kinetic data reaching 11.36 mg g−1 (CaAl/LDH‐RE) and 8.42 mg g−1 (CaAl/LDH‐AP) for MO, and 4.47 mg g−1 (CaAl/LDH‐RE) and 4.14 mg g−1 (CaAl/LDH‐AP) for MB. The Freundlich model better represented the isothermal data, where the temperature exerted little influence. Adsorbents showed similar removal percentages in real and synthetic matrices. The LDH/CaAl‐RE can be applied in up to 3 cycles, maintaining its adsorption capacity. These results corroborate the use of MFW to produce CaAl/LDH‐RE, which can be used for the efficient removal of organic pollutants in an aqueous solution.

INSTINCT: Inception-based Symbolic Time Intervals series classification

Symbolic Time Intervals (STIs) describe events having a non-zero time duration, which occur in a wide range of application domains. In this paper, we target the challenge of STIs series classification (STIC), which refers to the categorization of series of STIs. Over the recent years several advancements have been made in STIC, all of which are based on either distance-metrics or feature-based traditional classifiers, mostly relying on hand-engineering of features. Due to the high computational cost of either distance calculation or feature extraction, most methods also have quite little potential to scale. We introduce INSTINCT – a novel deep learning-based framework for STIC, which 1) proposes an almost fully information-preserving transformation of raw STIs series into real matrices, and 2) presents a novel ensemble of deep inception-based convolutional neural networks for their classification. The evaluation is applied to the six real-world STIC benchmark datasets and demonstrates that INSTINCT significantly improves accuracy over seven state-of-the-art methods, as well as over three deep learning-based baselines. In addition, a comprehensive architecture study of INSTINCT is conducted as well as a scalability analysis, reporting an overall time complexity which is linear in each of the main properties of the input STIs series.

Advanced oxidation and a metrological strategy based on CLC-MS for the removal of pharmaceuticals from pore & surface water

In this work, it is studied the photolysis, electrolysis, and photo-electrolysis of a mixture of pharmaceutics (sulfadiazine, naproxen, diclofenac, ketoprofen and ibuprofen) contained in two very different types of real water matrices (obtained from surface and porewater reservoirs), trying to clarify the role of the matrix on the degradation of the pollutants. To do this, a new metrological approach was also developed for screening of pharmaceuticals in waters by capillary liquid chromatography mass spectrometry (CLC-MS). This allows the detection at concentrations lower than 10 ng mL−1. Results obtained in the degradation tests demonstrate that inorganic composition of the water matrix directly influences on the efficiency of the drugs removal by the different EAOPs and better degradation results were obtained for experiments carried out with surface water. The most recalcitrant drug studied was ibuprofen for all processes evaluated, while diclofenac and ketoprofen were found to be the easiest drugs for being degraded. Photo-electrolysis was found to be more efficient than photolysis and electrolysis, and the increase in the current density was found to attain a slight improvement in the removal although with an associated huge increase in the energy consumption. The main reaction pathways for each drug and technology were also proposed.

Real Schur norms and Hadamard matrices

We present a preliminary study of Schur norms ‖ M ‖ S = max { ‖ M ∘ C ‖ : ‖ C ‖ = 1 } , where M is a matrix whose entries are ± 1 , and ∘ denotes the entrywise (i.e. Schur or Hadamard) product of the matrices. We recover a result of Johnsen that says that, if such a matrix M is n × n , then its Schur norm is bounded by n , and equality holds if and only if it is a Hadamard matrix. We develop a numerically efficient method of computing Schur norms, and as an application of our results we present several almost Hadamard matrices that are better than were previously known.