Absolute Matrix Research Articles

On absolute matrix summability factors of infinite series and Fourier series

Quite recently, Bor (2021) [22] has proved two main theorems dealing with absolute Riesz summability factors of infinite series and Fourier series by using an almost increasing sequence. In this paper, we have generalized these theorems to the |A,pn|k summability method.

High throughput determination of free biogenic monoamines and their metabolites in urine using thin-film solid phase microextraction

UPLC-MS/MS methods are the gold standard for routine, high-throughput measurements of biogenic monoamines for the diagnosis of catecholamine-producing tumors. However, this cannot be achieved without employing efficient sample pretreatment methods. Therefore, two pretreatment methods, thin-film solid phase microextraction (TF-SPME) and packed fibers solid phase extraction (PFSPE), were developed and evaluated for the analysis of biogenic monoamines and their metabolites in urine. A hydrophilic-lipophilic balance (HLB) coating was chosen for the thin-film blade format SPME method and compared with a Polycrown ether (PCE) composite nanofiber used as an adsorbent for the PFSPE method. Under optimal conditions, the absolute extraction recovery and relative matrix effect of the newly developed TF-SPME method were determined to be 35.7–74.8% and 0.47–3.63%, respectively. The linearity was 0.25–500 ng mL−1 for norepinephrine, epinephrine, dopamine, normetanephrine 3-methoxytyramine, serotonin, histamine, and 0.1–500 ng mL−1 for metanephrine. The intra-and inter-assay coefficients of variation were 0.7–8.7%, and the respective accuracies were calculated to be 90.8–104.7% and 89.5–104.5% for TF-SPME. Compared with the PFSPE method, the TF-SPME method had a higher extraction efficiency, lower matrix effects and a wider linear range for eight target substances, which ensured higher accuracy of simultaneous detection of all compounds of interest. Therefore, the proposed TF-SPME method can be employed for the high throughput screening for neuroendocrine tumors in a routine clinical setting and other relative research by simultaneous quantitation of urine eight biological monoamines in a single run.

$$K_0$$-group of absolute matrix order unit spaces

In this paper, we describe the Grothendieck group $$K_0(V)$$ of an absolute matrix order unit space V. For this purpose, we discuss the direct limit of absolute matrix order unit spaces. We show that $$K_0$$ is a functor from category of absolute matrix order unit spaces with morphisms as unital completely $$\vert \cdot \vert$$ -preserving maps to category of abelian groups. We study order structure in $$K_0(V)$$ and prove that under certain condition, $$K_0(V)$$ is an ordered abelian group. We also show that the functor $$K_0$$ is additive on orthogonal unital completely $$\vert \cdot \vert$$ -preserving maps.

A new note on absolute matrix summability of infinite series

In this paper, absolute matrix summability of an infinite series has been studied. A known theorem dealing with $|\bar{N},p_n|_{k}$ summability factors of an infinite series has been generalized. This new theorem also includes some results.

APPLICATIONS OF MATRIX TRANSFORMATIONS TO ABSOLUTE SUMMABILITY

Rhoades and Sava¸s [6],[11] established necessary for inclusions of the absolute matrix summabilities under additional conditions. In this paper we determine necessary or su¢ cient conditions for some classes of in…nite matrices, and using this get necessary or su¢ cient conditions for more general absolute summabilities applied to all matrices.

Assessment of solid phase microextraction as a sample preparation tool for untargeted analysis of brain tissue using liquid chromatography-mass spectrometry

This work presents an evaluation of solid-phase microextraction (SPME) SPME in combination with liquid chromatography-high resolution mass spectrometry (LC-HRMS) as an analytical approach for untargeted brain analysis. The study included a characterization of the metabolite coverage provided by C18, mixed-mode (MM, with benzene sulfonic acid and C18 functionalities), and hydrophilic lipophilic balanced (HLB) particles as sorbents in SPME coatings after extraction from cow brain homogenate at static conditions. The effects of desorption solvent, extraction time, and chromatographic modes on the metabolite features detected were investigated. Method precision and absolute matrix effects were also assessed. Among the main findings of this work, it was observed that all three tested coating chemistries were able to provide comparable brain tissue information. HLB provided higher responses for polar metabolites; however, as these fibers were prepared in-house, higher inter-fiber relative standard deviations were also observed. C18 and HLB coatings offered similar responses with respect to lipid-related features, whereas MM and C18 provided the best results in terms of method precision. Our results also showed that the use of methanol is essential for effective desorption of non-polar metabolites. Using a reversed-phase chromatographic method, an average of 800 and 1200 brain metabolite features detected in positive and negative modes, respectively, met inter-fibre RSD values below 30% (n=4) after removal of fibre and solvent artefacts from the associated datasets. For features detected using a lipidomics method, a total of 900 and 1800 features detected using C18 fibers in positive and negative mode, respectively, met the same criteria. In terms of absolute matrix effects, the majority of the model metabolites tested showed values between 80 and 120%, which are within the acceptable range. Overall, the findings of this work lay the foundation for further optimization of parameters for SPME-LC-HRMS methods suitable for in vivo and ex vivo brain (and other tissue) untargeted studies, and support the applicability of this approach for non-destructive tissue metabolomics.

On the Unique Solvability of the Generalized Absolute Value Matrix Equation

The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.

A LC-MS3 strategy to determine lamotrigine by Q-Q-trap tandem mass spectrometry coupled with triple stage fragmentation to enhance sensitivity and selectivity.

A high-performance liquid chromatography tandem mass spectrometry cubed (HPLC/MS3) method was developed and validated to quantify lamotrigine in human plasma with carbamazepine as an internal standard. The HPLC/MS/MS system is composed of a Shimadzu UFLC XR high-performance liquid chromatograph coupled with a hybrid linear ion trap triple quadrupole mass spectrometer. Following simple protein precipitation with methanol, the separation of lamotrigine and carbamazepine was performed on an Agilent Poroshell 120 SB-C18 column (4.6 × 50 mm, 2.7 μm) using gradient elution with 0.1% formic acid in water (solvent I) and 0.1% formic acid in methanol (solvent II) at a flow rate of 0.8 mL min-1. The total run time for each sample was 5 min. The method was validated for accuracy, precision, linearity, lower limit of quantification (LLOQ), selectivity, and other parameters. The LC/MS3 method was linear in the concentration range of 0.50-50.0 μg mL-1 (R2 ≥ 0.995). The LLOQ was 0.5 μg mL-1, requiring only 30 μL of human plasma. Intra- and inter-day accuracies were <6.17% and precisions were <11.4% at all concentrations. The absolute recoveries (%) and matrix effect (%) for lamotrigine in human plasma were between 83.8 and 90.7. The developed and validated LC-MS3 assay was successfully applied to monitor the lamotrigine levels in human plasma after the administration of lamotrigine.

ON A NEW APPLICATION OF QUASI POWER INCREASING SEQUENCES

In the present paper, absolute matrix summability of infinite series has been studied. A new theorem concerned with absolute matrix summability factors, which generalizes a known theorem dealing with absolute Riesz summability factors of infinite series, has been proved under weaker conditions by using quasi $\beta$-power increasing sequences. Also, a known result dealing with absolute Riesz summability has been given.

Generalized Almost Increasing Sequences

In [1], Mazhar has proved two theorems on absolute summability of infinite series. In the present paper, these two theorems have been generalized for absolute matrix summability of the series $$\sum a_{n}\lambda_{n}$$ by using almost increasing sequence.

Simultaneous determination and quantitation of hypolipidemic drugs in fingerprints by UPLC-Q-TRAP/MS

An ultra-performance liquid chromatography tandem triple quadrupole compound linear ion trap mass spectrometry (UPLC-Q-TRAP/MS) method was developed and validated for the detection of hypolipidemic drugs in fingerprints. 13 hypolipidemic drugs were well separated by the gradient elution of 0.01% formic acid in water and methanol at a flow rate of 0.4 mL/min within 11 min. The analytes were detected in positive (ESI+) and negative (ESI-) modes and scanned using scheduled multiple reaction monitoring-information dependent acquisition-enhanced product ion (SMRM-IDA-EPI) for best selectivity and sensitivity. The calibration curves showed good linearity in the range of 0.050–50.000 ng/patch with coefficients (r2) higher than 0.9904 for all analytes. Meantime, the LODs and LLOQs were in ranges of 0.001–0.034 and 0.003–0.050 ng/patch. The accuracies, intra-day and inter-day precision ranged from −13.3 to 0.3%, 1.1–10.4% and 3.7–14.5%, respectively. The recoveries ranged from 79.9 to 114.8%, while the absolute and relative matrix effects were in the range of 83.0–107.2% and 2.2–9.7%. By comparing the non-spiked fingerprints from healthy volunteers with the fingerprints obtained from patients, demonstrated that the method was competent for determination and quantitation of hypolipidemic drugs in fingerprints.

A new result on the quasi power increasing sequences

Abstract This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.

Determination of eight environmental phenols in human urine samples by high-throughput solid-phase extraction-ultra-performance liquid chromatography-tandem mass spectrometry

A method combining 96-well plate solid-phase extraction with ultra-performance liquid chromatography-tandem mass spectrometry (96-well SPE LC-MS/MS) was developed for the simultaneous determination of eight environmental phenols in urine samples. The samples included seven bisphenol compounds and triclosan. The urine samples were thawed to room temperature, and the target analytes were deconjugated by β -glucuronidase/aryl-sulfatase in ammonium acetate buffer solution at 37℃ overnight. Then, the effects of three kinds of 96-well solid-phase extraction plates and different elution conditions on the purification of the urine samples and the environmental phenol recoveries were compared. The best purification effect was achieved on Oasis HLB 96-well plate (60 mg) solid phase extraction, using 30% (v/v) acetonitrile aqueous solution as the rinse solution. The target analytes were then eluted by methanol solution and evaporated to dryness using a nitrogen blower. After reconstruction with 0.5 mL methanol/water (1:1, v/v) solution, the target compounds were detected by UPLC-MS/MS. To achieve better chromatographic separation, two kinds of analytical columns (C18 and T3) and different types of mobile phases (methanol and acetonitrile as the organic phase) were also compared. The best chromatographic effect was achieved when the treated samples were separated on a C18 column (100 mm×2.1 mm, 1.7 μm) using acetonitrile/water as the mobile phase at a flow rate of 0.3 mL/min. Mass spectra were recorded by negative electrospray ionization under the multiple reaction monitoring (MRM) mode. The sample matrix effect was also evaluated. The absolute matrix effects of bisphenol A, bisphenol F, bisphenol S, bisphenol B, and bisphenol AF were in the range of 3.47% to 15.32%. Since the above mentioned matrix effect was weak, there was no need for compensation measures. On the contrary, tetrachlorobisphenol A, tetrabromobisphenol A, and triclosan showed an absolute matrix effect of 49.58% (moderate), 71.99% (strong), and 86.93% (strong), thus necessitating compensation measures. Therefore, this strategy uses a one-to-one corresponding isotope internal standard method to offset the matrix effect. Six different urine samples were used to evaluate the relative matrix effect. The relative standard deviations (RSDs) of the eight corresponding internal standard peak areas were 3.63%-9.06%, indicating that the relative matrix effect was stable. Under the optimized conditions, linearity ranges were 0.50-50 μg/L for bisphenol A and bisphenol AF; 0.05-50 μg/L for tetrachlorobisphenol A and bisphenol S; 0.01-50 μg/L for bisphenol F and tetrabromobisphenol A; 1.00-50 μg/L for bisphenol B; and 5.00-200 μg/L for triclosan. The correlation coefficients were all greater than 0.9995. At spiked levels of 2.5, 5, and 25 μg/L, the average recovery ratios of the eight target analytes were 81.01%-118.84%, while the intra-day and inter-day precisions were 0.38%-19.41% and 2.54%-17.83%, respectively. The limits of detection (LOD) were 0.002-1.09 μg/L, and the limits of quantitation (LOQ) were 0.007-3.63 μg/L. This method was successfully applied to the determination of the eight environmental phenols in 64 urine samples collected from Beijing area between 2019 and 2020. All the target environmental phenols were detected, except for bisphenol B and bisphenol AF. Bisphenol A and bisphenol S showed the highest detection rates of 100% and 96.9%, respectively. The detection rates of triclosan, tetrabromobisphenol A, tetrachlorobisphenol A, and bisphenol F were 57.8%, 46.9%, 23.4%, and 21.9%, respectively. The medium values of urinary concentration followed the order 1.44 μg/L(triclosan), 0.69 μg/L(bisphenol A), 0.086 μg/L (bisphenol S), 0.0032 μg/L (tetrabromobisphenol A), 0.00050 μg/L (tetrachlorobisphenol A), 0.00 μg/L (bisphenol F, bisphenol B, and bisphenol AF). The aforementioned results imply that the widespread environmental phenolic exposure of Beijing residents is worthy of attention. Compared with traditional solid-phase extraction methods, the method reported in this paper is time-saving, effective, and suitable for the simultaneous analysis of large quantities of samples; moreover, the small sample and organic solvent consumption make this method more environment- and operator-friendly.

Partial isometries in an absolute order unit space

In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute matrix order unit space. As an application, we describe the comparison of order projections. We also discuss finiteness of order projections.

Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation

We present sufficient conditions for the unique solvability of the matrix equation AXB+C|X|D=E where A,B,C,D and E are given square or rectangular real matrices of appropriate size and X is unknown. We also give sufficient conditions for the non-solvability of the equation in special cases. Our sufficient conditions can be checked with a cubic complexity in terms of the size of the input matrices.

قابلية جمع المتسلسلات المتعامدة بالطريقة المصفوفية المطلقة

ظهرت في مطلع القرن العشرين نظرية المتسلسلات المتعامدة، التي تتعامل مع جمل من الدوال المتعامدة كتعميم طبيعي لنظرية المتسلسلات. وقد تمت دراسة قابلية جمع المتسلسلات المتعامدة بالعديد من الطرائق مثل طرائق سيزارو وهولدر وريمان وبوريل وهاوسدورف ونيورلند ونيورلند المعممة والطريقة المصفوفية. كما تم في هذا البحث دراسة قابلية جمع المتسلسلات المتعامدة البسيطة بطرائق مختلفة نوعاً ما تسمى الطرائق المطلقة والتي تعتمد على الفروق بشكل عام. وذلك من خلال الاعتماد على بعض الأبحاث والمقالات والكتب العلمية في مجال قابلية جمع المتسلسلات. إن الطريقة المصفوفية المطلقة تعد من أهم طرائق قابلية الجمع المطلقة، حيث إن معظم طرائق قابلية الجمع المطلقة، ما هي إلا حالات خاصة من الطريقة المصفوفية المطلقة. ونوصي أخيراً بدراسة الحالة المضاعفة.

Sustainable Development in Block Random Systems

In paper [1], stability of a block random model was studied as a possible model for economic systems. Crisis means significant and quick change in the number of participants of a system. It was proved that a smaller system is more stable than a larger one with the same parameters. Further, the number of participants can significantly alter without any outer interactions resulting in crisis. In paper [2], stability properties of a block random model with fixed number of participants was investigated. It was studied, that how two parameters of the model, density matrix and dispersion influence behavior of the system. It was shown that proportionally smaller in absolute value density matrix results in a shorter cycle time. Also larger dispersion makes the cycle time shorter. It was suggested that a longer cycle time makes it possible the participants to adapt themselves to circumstances and thus to avoid crises. In this case repeated recessions and growths appear which can be called structural cycles. In the present paper we investigate connection between real parameters of economy and parameters of the block random model. We point out that base rate bounded by an appropriate level is useful for working the system without any crisis. As a result of these studies, it has become clear that sustainable development can be defined in terms of avoiding crisis rather than achieving growth.

Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation

The absolute value equation appears in various fields of applied mathematics such as operational research. Here we consider its generalized versionAX+B|X|=C, where A,B,C∈Cn×n are given, |X|=(|xi,j|) and X∈Cn×n is an unknown matrix that must be determined. In this investigation, based on the Picard matrix splitting iteration method, we applied a matrix splitting method for solving it. We will see that under the condition σmin(A)>nσmax(|B|), this method is convergent, where σmax(|B|) denotes the largest singular value of matrix |B| and σmin(A) denotes the smallest singular value of matrix A. Then we give some convergence theorems for our new method and analyze this procedure in detail. Then we consider a p-step iteration method for solving this equation and analyze this procedure. Numerical experiment results show the efficiency of the method.

Preparation of bovine serum albumin restricted access octadecyl/phenyl-mixed-functionalized magnetic silica nanoparticles for magnetic solid phase extraction of antidepressants in aquatic products followed by UHPLC-MS/MS

Pharmaceuticals are widespread in aquatic ecosystem, which may pose a potential threat to fish and human. In the study, a robust and reliable magnetic solid-phase extraction (MSPE) based on bovine serum albumin (BSA) restricted access octadecyl/phenyl-mixed-functionalized magnetic silica nanoparticles (BSA-C18/Ph-Fe3O4@SiO2 NPs) as sorbent was developed for the extraction of venlafaxine, paroxetine, fluoxetine, norfluoxetine, sertraline and diphenhydramine from the muscle extracts of aquatic products followed by ultra-high performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS) detection. The homemade sorbent showed appropriate compatibility in aqueous solution and good performance in reducing matrix interference of snakehead muscle tissue extracts with absolute matrix effect ranging in 95.4%–105.5%. The protocol was validated in analyte-free snakehead muscle with favorable recoveries ranging in 91.6%–103.6% and relative standard deviations (RSDs) less than 9.5%. Limits of detection (LODs) of the drugs were lower than 0.018 μg kg−1. Short-term drug-exposure experiments at low and high doses were conducted on snakeheads, and the measured contents of analytes were in the range 0.029–9.58 μg kg−1 with appropriate recoveries (90.0%–114.0%). The approach was extensively applied for the analysis of twelve species of market-sale aquatic products (total 37 samples), and up to 1.868 and 0.521 μg kg−1 of diphenhydramine and venlafaxine were measured, respectively. The approach shows remarkable potential in biological complex samples.

Quantitative source identification and apportionment of heavy metals under two different land use types: comparison of two receptor models APCS-MLR and PMF.

At present, many researchers are increasingly aware of the importance of using models to identify heavy metal (HM) pollution sources. However, on the performance and application of different source identification models to HMs under different land use types had been studied little. In this study, comparison of absolute principal component scores-multiple linear regression (APCS-MLR) and positive matrix factorization (PMF) models and their application characteristics in identifying pollution sources were carried out by using 11 HMs in Zhongwei City farmland and Shizuishan industrial park, Ningxia. The results indicated that HM pollution in farmland mainly came from pesticides, fertilizers, and deposition of the Yellow River, while the pollution in industrial park mainly originated from atmospheric deposition and various industrial productions. The APCS-MLR model had the problem of less identification sources and the difficulty to explain the complex pollution, while the PMF model not only identified more pollution sources, but also distinguished heavy metal-related sources for two different land use types and different industrial production conditions. It is of great significance the formulation of agricultural-related pesticides' and chemical fertilizers' rational use and various industrial production-related raw materials put in and emission control strategies.