Asymptotic normality of quadratic forms of martingale differences

We establish the asymptotic normality of a quadratic form \(Q_n\) in martingale difference random variables \(\eta _t\) when the weight matrix A of the quadratic form has an asymptotically vanishing diagonal. Such a result has numerous potential applications in time series analysis. While for i.i.d. random variables \(\eta _t\), asymptotic normality holds under condition \(||A||_{sp}=o(||A||) \), where \(||A||_{sp}\) and ||A|| are the spectral and Euclidean norms of the matrix A, respectively, finding corresponding sufficient conditions in the case of martingale differences \(\eta _t\) has been an important open problem. We provide such sufficient conditions in this paper.     

Development of an HPLC post-column antioxidant assay for Solidago canadensis radical scavengers

The aim of this work was to modify and validate the post-column high-performance liquid chromatography (HPLC)-ABTS and DPPH methods for evaluating the antioxidant activity of the methanolic extracts of Solidago canadensis (Canadian goldenrod) leaves and flowers. Separation of the analytes was performed via the HPLC-PDA method on a YMC analytical column using a gradient elution program. Three compounds with antioxidant properties – chlorogenic acid, rutin and isoquercitrin – and two unidentified antioxidants were established. The research showed that the coil temperature regimes and loop length combinations influence the optimised post-column assay method for detecting the antioxidant activity of goldenrod radical scavengers. Investigations established that the temperature in the reaction coil was a substantial factor contributing to the signal strength of the analytes after reacting with the DPPH and ABTS radicals.     

Pharmacological Potential and Chemical Composition of Crocus sativus Leaf Extracts

Crocus sativus L. (saffron) has been traditionally used as a food coloring or flavoring agent, but recent research has shown its potent pharmacological activity to tackle several health-related conditions. Crocus sp. leaves, and petals are the by-products of saffron production and are not usually used in the medicine or food industries. The present study was designed to determine the chemical composition of the water and ethanolic extracts of C. sativus leaves and test their cytotoxic activity against melanoma (IGR39) and triple-negative breast cancer (MDA-MB-231) cell lines by MTT assay. We also determined their anti-allergic, anti-inflammatory, and anti-viral activities. HPLC fingerprint analysis showed the presence of 16 compounds, including hydroxycinnamic acids, xanthones, flavonoids, and isoflavonoids, which could contribute to the extracts’ biological activities. For the first time, compounds such as tectoridin, iristectorigenin B, nigricin, and irigenin were identified in Crocus leaf extracts. The results showed that mangiferin (up to 2 mg/g dry weight) and isoorientin (8.5 mg/g dry weight) were the major active ingredients in the leaf extracts. The ethanolic extract reduced the viability of IGR39 and MDA-MB-231 cancer cells with EC₅₀ = 410 ± 100 and 330 ± 40 µg/mL, respectively. It was more active than the aqueous extract. Kaempferol and quercetin were identified as the most active compounds. Our results showed that Crocus leaves contain secondary metabolites with potent cytotoxic and antioxidant activities.     

Ultrasonic method for the whole blood coagulation analysis

The developed ultrasonic method is based on the experimentally established fact that the ultrasound velocity in a blood sample is changing in a specific way during the blood clotting process. For ultrasound velocity measurements pulse echo method was selected. Implementation of this approach has a few problems caused by small dimensions of the measurement cell. All elements of the cell contacting with the blood are made of biologically compatible materials. The length of Pd coated chamber is 5 mm, volume 0.2 ml. Data of measurements are stored and processed by PC. The ultrasound velocity in a sample is displayed as it changes in time during the experiment; the temperature is monitored as well. Application of the digital filtering allows to smooth the coagulation curve and reach the sensitivity up to +/-3 cm/s. The coagulation curves were obtained at frequency 5 MHz and they represent peculiar stages of blood clotting characterised by their duration and ultrasound velocity differences. Fine structure of ultrasonic velocity changes is registered from the very beginning of the clotting to lysis. Such experiments were carried out using blood samples taken from a few hundred volunteers. For dynamic calibration and periodic checking of the measuring system the liquid medium in which acrylamide polymerisation reaction takes place is proposed as a reference liquid. Such a liquid mimics clotting blood from the point of view of ultrasonic velocity changes.     

Effective Isolation of Picrocrocin and Crocins from Saffron: From HPTLC to Working Standard Obtaining

Saffron is widely cultivated and used as a spice. Recently published data on the chemical composition and pharmacological potential of saffron determine its use in pharmacy and medicine. The proposed high-performance thin-layer chromatography (HPTLC) method allows good separation of 11 analytes. The saffron quality (Iran, Ukraine, Spain, Morocco samples) assessment was based on the European Pharmacopoeia monograph and ISO 3632. The HPTLC method for the safranal, crocin, and picrocrocin quantification was proposed and validated. The crocins content in Ukrainian saffron was from 17.80% to 33.25%. Based on qualitative and quantitative assessment results, the saffron sample from Zaporizhzhia (Ukraine) had the highest compounds content and was chosen to obtain the working standards of picrocrocin and crocins (trans-4GG, trans-2G, trans-3Gg) by preparative chromatography. The compounds were isolated from lyophilized extract of saffron using a Symmetry Prep C₁₈ column (300 × 19 mm × 7 µm), and identified by spectroscopic techniques (HPLC-DAD, UPLC-ESI-MS/MS). The purity of crocins and picrocrocin was more than 97%. A novel method proposed to obtain working standards is simple and reproducible for the routine analysis of saffron quality control.     

On the Power of R/S-Type Tests under Contiguous and Semi-Long Memory Alternatives

The paper deals with the power and robustness of the R/S type tests under contiguous alternatives. We briefly review some long memory models in levels and volatility, and describe the R/S-type tests used to test for the presence of long memory. The empirical power of the tests is investigated when replacing the fractional difference operator (1–L) ^d by the operator (1–rL) ^d , with r<1 close to 1, in the FARIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero.     

Functional Non-Central and Central Limit Theorems for Bivariate Appell Polynomials

We consider quadratic forms in bivariate Appell polynomials involving strongly dependent time series. Both the spectral density of these time series and the Fourier transform of the kernel of the quadratic forms are regularly varying at the origin and hence may diverge, for example, like a power function. We obtain functional limit theorems for these quadratic forms by extending the recent results on the convergence of their finite-dimensional distributions. Some of these are functional central limit theorems where the limiting process is Brownian motion. Others are functional non-central limit theorems where the limiting processes are typically not Gaussian or, if they are Gaussian, then they are not Brownian motion.     

Effect of the Amount of Polysorbate 80 and Oregano Essential Oil on the Emulsion Stability and Characterization Properties of Sodium Alginate Microcapsules

Essential oils have a high volatility that leads to evaporation and loss of their pharmacological effect when exposed to the environment. The objectives of the present work were to prepare microcapsules with oregano essential oil by extrusion using sodium alginate as a shell material and non-ionic surfactant polysorbate 80 as an emulsifier to stabilize the emulsion. The present study was aimed to evaluate the physical parameters of microcapsules and to compare the influence of the amount of emulsifier and the essential oil-to-emulsifier ratio on the capsules’ physical parameters and encapsulation efficiency; to our knowledge, the existing research had not yet revealed whether unstable emulsion affects the encapsulation efficiency of oregano essential oil. This study showed that increasing the emulsifier amount in the formulation significantly influenced encapsulation efficiency and particle size. Moreover, increasing the emulsion stability positively influenced the encapsulation efficiency. The emulsion creaming index depended on the emulsifier amount in the formulation: the highest creaming index (%) was obtained with the highest amount of polysorbate 80. However, the essential oil-to-polysorbate 80 ratio and essential oil amount did not affect the hardness of the microcapsules (p > 0.05). In conclusion, the obtained results could be promising information for production of microcapsules. Despite the fact that microencapsulation of essential oils is a promising and extremely attractive application area for the pharmaceutical industry, further basic research needs to be carried out.     

Prediction of Chromatography Conditions for Purification in Organic Synthesis Using Deep Learning

In this research, a process for developing normal-phase liquid chromatography solvent systems has been proposed. In contrast to the development of conditions via thin-layer chromatography (TLC), this process is based on the architecture of two hierarchically connected neural network-based components. Using a large database of reaction procedures allows those two components to perform an essential role in the machine-learning-based prediction of chromatographic purification conditions, i.e., solvents and the ratio between solvents. In our paper, we build two datasets and test various molecular vectorization approaches, such as extended-connectivity fingerprints, learned embedding, and auto-encoders along with different types of deep neural networks to demonstrate a novel method for modeling chromatographic solvent systems employing two neural networks in sequence. Afterward, we present our findings and provide insights on the most effective methods for solving prediction tasks. Our approach results in a system of two neural networks with long short-term memory (LSTM)-based auto-encoders, where the first predicts solvent labels (by reaching the classification accuracy of 0.950 ± 0.001) and in the case of two solvents, the second one predicts the ratio between two solvents (R² metric equal to 0.982 ± 0.001). Our approach can be used as a guidance instrument in laboratories to accelerate scouting for suitable chromatography conditions.     

Measurement of viscosity of highly viscous non-Newtonian fluids by means of ultrasonic guided waves

In order to perform monitoring of the polymerisation process, it is necessary to measure viscosity. However, in the case of non-Newtonian highly viscous fluids, viscosity starts to be dependent on the vibration or rotation frequency of the sensing element. Also, the sensing element must possess a sufficient mechanical strength. Some of these problems may be solved applying ultrasonic measurement methods, however until now most of the known investigations were devoted to measurements of relatively low viscosities (up to a few Pa s) of Newtonian liquids.