Properties Of Matrix Research Articles

High-frequency optimally windowed chirp rheometry for rapidly evolving viscoelastic materials: Application to a crosslinking thermoset

Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated.

Water-Insoluble, Thermostable, Crosslinked Gelatin Matrix for Soft Tissue Implant Development

In this present study, the material science background of crosslinked gelatin (GEL) was investigated. The aim was to assess the optimal reaction parameters for the production of a water-insoluble crosslinked gelatin matrix suitable for heat sterilization. Matrices were subjected to enzymatic degradation assessments, and their ability to withstand heat sterilization was evaluated. The impact of different crosslinkers on matrix properties was analyzed. It was found that matrices crosslinked with butanediol diglycidyl ether (BDDE) and poly(ethylene glycol) diglycidyl ether (PEGDE) were resistant to enzymatic degradation and heat sterilization. Additionally, at 1 v/v % crosslinker concentration, the crosslinked weight was lower than the starting weight, suggesting simultaneous degradation and crosslinking. The crosslinked weight and swelling ratio were optimal in the case of the matrices that were crosslinked with 3% and 5% v/v BDDE and PEGDE. FTIR analysis confirmed crosslinking, and the reduction of free primary amino groups indicated effective crosslinking even at a 1% v/v crosslinker concentration. Moreover, stress–strain and compression characteristics of the 5% v/v BDDE crosslinked matrix were comparable to native gelatin. Based on material science measurements, the crosslinked matrices may be promising candidates for scaffold development, including properties such as resistance to enzymatic degradation and heat sterilization.

Submission to Journal of Polymers and the Environment Evaluation of Thermal Properties and Crystallinity in PHB-Based Systems – A DoE Approach

AbstractComplex formulations based on poly(hydroxybutyrate) (PHB) and poly(hydroxybutyrate-co-valerate) (PHBV) were studied to statistically assess the effect of formulation (i.e., hydroxyvalerate (HV) content, plasticiser chemistry and content, filler type and content) on their thermal properties and degree of crystallinity (Xc). In binary systems, thermal properties were mainly influenced by filler type rather than its content, while for plasticised systems the changes were dependent on both increasing plasticiser content and PHB-plasticiser compatibility. Variations in HV content affected the ability of the polymer chain to fold, leading to significant changes in both thermal properties and Xc. In ternary systems, presence of multiple additives and consequent changes in intermolecular interactions lead to multifaceted behaviours that were not easily predicted by results from binary systems alone. For example, melting temperature did not show dependence on filler presence in PHBV systems despite introducing variations in pure PHB systems. In general, thermal properties and Xc are affected by all parameters studied, with changes in system free volume (i.e. changes in HV content and plasticisation) playing the most significant role. These results expand the understanding of factors controlling crystallisation in complex polymer systems and can be used to control matrix properties in new generations of packaging materials.

The Relationship Between Structural Features and Local Mechanical Properties of a Fine-Grained Matrix in Refractory Ceramic Materials. SiO2 Ceramics Case Study

The Relationship Between Structural Features and Local Mechanical Properties of a Fine-Grained Matrix in Refractory Ceramic Materials. SiO2 Ceramics Case Study

Co-culture of RhoA-overexpressed Microtia Chondrocytes and Adipose-Derived Stem Cells in the Construction of Tissue-engineered Ear-shaped Cartilage.

Microtia is a congenital auricle dysplasia with a high incidence and tissue engineering technology provides a promising strategy to reconstruct auricles. We previously described that the engineered cartilage constructed from microtia chondrocytes exhibited inferior levels of biochemical and biomechanical properties, which was proposed to be resulted from the decreased migration ability of microtia chondrocytes. In the current study, we found that Rho GTPase members were deficient in microtia chondrocytes. By overexpressing RhoA, Rac1 and CDC42, respectively, we further demonstrated that RhoA took great responsibility for the decreased migration ability of microtia chondrocytes. Moreover, we constructed PGA/PLA scaffold-based cartilages to verify the chondrogenic ability of RhoA overexpressed microtia chondrocytes, and the results showed that overexpressing RhoA was of limited help to improve the quality of microtia chondrocyte engineered cartilage. However, co-culture of ADSCs significantly improved the biochemical and biomechanical property of engineered cartilage. Especially, co-culture of RhoA overexpressed microtia chondrocytes and ADSCs produced an excellent effect on the wet weight, cartilage-specific extracellular matrix and biomechanical property of engineered cartilage. Furthermore, we presented that co-culture of RhoA overexpressed microtia chondrocytes and ADSCs combined with human ear-shaped PGA/PLA scaffold and titanium alloy stent fabricated by CAD/CAM and 3D printing technology effectively constructed and maintained auricle structure in vivo. Collectively, our results provide evidence for the essential role of RhoA in microtia chondrocytes and a developed strategy for the construction of patient-specific tissue-engineered auricular cartilage.

Rheological, functional properties, and stability of peach puree added with normal and high amylose retrograded starches

ABSTRACT Texture-modified foods have become a growing trend in the market and retrograded starch can enhance the rheological properties of foods. This study assessed the effect of adding 10% (w/w) of normal (RNS) or high amylose (RHS) retrograded starches on the physicochemical and rheological properties of commercial peach puree stored at 4°C. The resistant starch content (RS), syneresis, and rheological behavior were evaluated during 14-day storage. Control puree exhibited high syneresis (60%), low consistency (6 Pa·sn), and decreasing viscosity during storage. These characteristics improved after adding retrograded starches. Samples with RNS exhibited higher viscosity, lower syneresis, lower RS (2%), and poor stability; meanwhile, the systems with RHS exhibited greater stability maintaining their viscosity, syneresis, and RS (10%) relatively constant during storage. Therefore, RHS can be recommended to enhance and maintain the physicochemical, nutraceutical, and rheological properties of a food matrix like peach puree during storage.

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

   The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

Asymptotic performance of reconfigurable intelligent surface assisted MIMO communication for large systems using random matrix theory

AbstractReconfigurable intelligent surface (RIS) can provide unprecedented spectral efficiency gains and excellent ability to manipulate electromagnetic waves. This article considered a RIS‐assisted multiuser multiple‐input multiple‐output (MIMO) downlink system, where the beamforming at the base station and RIS are jointly designed to maximize the sum‐rate. For the large dimension scenario and high‐rank beamforming matrix, the accurate deterministic approximations from random matrix theory are then utilized to simplify the RIS‐assisted MIMO systems. The asymptotical signal‐to‐interference‐plus‐noise ratio values obtained through random matrix theory is infinitely close to the theoretical limits calculated by accurately iteration. And the performance of the proposed algorithm computed via the sharing second‐order channel statistics matches that of the RIS algorithm with sharing full channel state information asymptotically. The deterministic approximations are instrumental to get improvement into the structure of the optimal beamforming and to reduce the implementation complexity in large‐scale MIMO system. Numerical simulations results are provided to evaluate and verify the accuracy of the asymptotic results obtained from the proposed algorithm in the finite system regime. With the complex operation process of large dimension matrix reducing to the deterministic approximations, a lower computational complexity can be obtained compared with other methods.

Toeplitz covariance estimation with applications to MUSIC

We consider the maximum likelihood estimation of a covariance matrix that is known to be Toeplitz. The corresponding optimization problem is nonconvex, and to compute a local minimizer we propose an efficient implementation of Newton’s method. The cost per iteration of a straightforward implementation is of order O(n4), where n+1 is the dimension of the covariance matrix. By exploiting fast Fourier transforms to assemble the gradient and Hessian we reduce the iteration cost to order O(n3). Through extensive simulations we demonstrate that for direction-of-arrival estimation, the performance of MUSIC is significantly enhanced by using it together with the maximum likelihood Toeplitz covariance estimate. The simulations also demonstrate that our open-source implementation is orders of magnitude faster than two existing Toeplitz covariance estimators.

SimuCell3D: three-dimensional simulation of tissue mechanics with cell polarization.

The three-dimensional (3D) organization of cells determines tissue function and integrity, and changes markedly in development and disease. Cell-based simulations have long been used to define the underlying mechanical principles. However, high computational costs have so far limited simulations to either simplified cell geometries or small tissue patches. Here, we present SimuCell3D, an efficient open-source program to simulate large tissues in three dimensions with subcellular resolution, growth, proliferation, extracellular matrix, fluid cavities, nuclei and non-uniform mechanical properties, as found in polarized epithelia. Spheroids, vesicles, sheets, tubes and other tissue geometries can readily be imported from microscopy images and simulated to infer biomechanical parameters. Doing so, we show that 3D cell shapes in layered and pseudostratified epithelia are largely governed by a competition between surface tension and intercellular adhesion. SimuCell3D enables the large-scale in silico study of 3D tissue organization in development and disease at a great level of detail.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Cucurbit[8]uril Mediated Supramolecular and Photocrosslinked Interpenetrating Network Hydrogel Matrices for 3D-Bioprinting.

Printing of biologically functional constructs is significant for applications in tissue engineering and regenerative medicine. Designing bioinks remains remarkably challenging due to the multifaceted requirements in terms of the physical, chemical, and biochemical properties of the three-dimensional matrix, such as cytocompatibility, printability, and shape fidelity. In order to promote matrix and materials stiffness, while not sacrificing stress relaxation mechanisms which support cell spreading, migration, and differentiation, this work reports an interpenetrating network (IPN) bioink design. The approach makes use of a chemically defined network, combining physical and chemical crosslinking units with a tunable composition and network density, as well as spatiotemporal control over post-assembly material stiffening. To this end, star-shaped poly(ethylene glycol)s functionalized with Phe-Gly-Gly tripeptide or photoactive stilbazolium are synthesized, and used to prepare three-dimensional networks with cucurbit[8]uril (CB[8]) through supramolecular host-guest complexation. The hydrogel obtained shows fast relaxation and thus supports the proliferation and differentiation of cells. Upon irradiation, the mechanical properties of the hydrogel can be rapidly adapted via selective photochemical dimerization of stilbazolium within CB[8], leading to IPNs with increased form stability while retaining the dynamic nature of the hydrogels. This modular approach opens new design opportunities for extrudable and cell-friendly dynamic biomaterials for applications in 3D-bioprinting.

Repurpose of used frying sunflower oil as an ecofriendly plasticizer for polylactic acid

The development of competitive and sustainable additives for use in semicrystalline polymers is currently an area of growing interest in scientific and engineering areas. However, the feasibility of using waste oils as raw materials to produce effective plasticizers for these polymers has not yet been thoroughly investigated. In this work, the plasticization of polylactic acid (PLA), which is essential to improve its ductility, was studied using different contents of low molecular weight plasticizers: one synthesized from sunflower (Helianthus annuus) oil used in frying (USOP) and the bio-based commercial tributyrin (TB), selected as a control plasticizer. The experimental results revealed changes in the properties of pure PLA matrix that were explained considering the shape and chemical structure of the different plasticizers. Both compounds drastically decreased the glass transition temperature of PLA as well as the elastic modulus and tensile strength, although increase the elongation at break. The greatest plasticizing effect was obtained by adding 15 percent by weight of TB to the biodegradable matrix. However, the synthesized bio-based plasticizer exhibits a desirable low volatility, thus its thermal degradation occurs at higher temperatures in comparison with that of TB. Furthermore, the water vapor permeability of the PLA is not affected when USOP is used as plasticizer, which is a very interesting result for applications in which the material is in contact with food or humid environments.

Effects of aging on the biomechanical properties of the lung extracellular matrix: dependence on tissular stretch

Introduction: Aging induces functional and structural changes in the lung, characterized by a decline in elasticity and diminished pulmonary remodeling and regenerative capacity. Emerging evidence suggests that most biomechanical alterations in the lung result from changes in the composition of the lung extracellular matrix (ECM), potentially modulating the behavior of pulmonary cells and increasing the susceptibility to chronic lung diseases. Therefore, it is crucial to investigate the mechanical properties of the aged lung. This study aims to assess the mechanical alterations in the lung ECM due to aging at both residual (RV) and functional (FV) lung volumes and to evaluate their effects on the survival and proliferation of mesenchymal stromal cells (MSCs).Methods: The lungs from young (4-6-month-old) and aged (20-24-month-old) mice were inflated with optimal cutting temperature compound to reach FV or non-inflated (RV). ECM proteins laminin, collagen I and fibronectin were quantified by immunofluorescence and the mechanical properties of the decellularized lung sections were assessed using atomic force microscopy. To investigate whether changes in ECM composition by aging and/or mechanical properties at RV and FV volumes affects MSCs, their viability and proliferation were evaluated after 72 h.Results: Laminin presence was significantly reduced in aged mice compared to young mice, while fibronectin and collagen I were significantly increased in aged mice. In RV conditions, the acellular lungs from aged mice were significantly softer than from young mice. By contrast, in FV conditions, the aged lung ECM becomes stiffer than that of in young mice, revealing that strain hardening significantly depends on aging. Results after MSCs recellularization showed similar viability and proliferation rate in all conditions.Discussion: This data strongly suggests that biomechanical measurements, especially in aging models, should be carried out in physiomimetic conditions rather than following the conventional non-inflated lung (RV) approach. The use of decellularized lung scaffolds from aged and/or other lung disease murine/human models at physiomimetic conditions will help to better understand the potential role of mechanotransduction on the susceptibility and progression of chronic lung diseases, lung regeneration and cancer.

Mesoscale mechanics investigation of multi-component solid propellant systems

Abstract To enhance the mechanical properties of the Nitrate Ester Plasticized Polyether solid propellant matrix, the uniaxial tension of multi-component systems is simulated and the factors influencing the mechanical properties of the propellant matrix are investigated. First, mesoscale models of five types of systems include poly alpha olefin (PAO(3)), polyethylene glycol (PEG200, PEG400, PEG600), and 1,4-butanediol (BDO) are established, followed by uniaxial tensile simulations. The results show PEG600, PEG400, PEG200, BDO, and PAO(3) in order of enhancing the mechanical performance of the matrix. Second, the diffusion behavior of nitroglycerin (NG) and butanetriol trinitrate (BTTN) in various systems is investigated. The results show that NG exhibits higher diffusion capacity than BTTN, and the diffusion coefficient increases with an increment in the molecular weight of PEG. Additionally, the influence of different plasticizer ratios (2.8–3.0), curing parameters (1.58–1.62), and chain extension parameters (0.08–0.10) on the mechanical properties of the PEG600 system are investigated. The results demonstrate that as the plasticizer ratio increases, there is a gradual decrease in the modulus of the matrix. Additionally, an increase in the curing parameter leads to a substantial enhancement in the tensile strength of the matrix, while increasing the chain extension parameter significantly expands the maximum tensile length of the matrix. Finally, employing the Slip-Spring model, the effects of the physical and chemical cross-linked network of the propellant are simulated. The result shows that increasing the content of a chemical cross-linked network significantly improves the tensile strength of the matrix.

Combining raloxifene and mechanical loading improves bone composition and mechanical properties in a murine model of chronic kidney disease (CKD)

IntroductionPatients with chronic kidney disease (CKD) are at an alarming risk of fracture compared to age and sex-matched non-CKD individuals. Clinical and preclinical data highlight two key factors in CKD-induced skeletal fragility: cortical porosity and reduced matrix-level properties including bone hydration. Thus, strategies are needed to address these concerns to improve mechanical properties and ultimately lower fracture risk in CKD. We sought to evaluate the singular and combined effects of mechanical and pharmacological interventions on modulating porosity, bone hydration, and mechanical properties in CKD. MethodsSixteen-week-old male C57BL/6J mice underwent a 10-week CKD induction period via a 0.2 % adenine-laced casein-based diet (n = 48) or remained as non-CKD littermate controls (Con, n = 48). Following disease induction (26 weeks of age), n = 7 CKD and n = 7 Con were sacrificed (baseline cohort) to confirm a steady-state CKD state was achieved prior to the initiation of treatment. At 27 weeks of age, all remaining mice underwent right tibial loading to a maximum tensile strain of 2050 μƐ 3× a week for five weeks with the contralateral limb as a non-loaded control. Half of the mice (equal number CKD and Con) received subcutaneous injections of 0.5 mg/kg raloxifene (RAL) 5× a week, and the other half remained untreated (UN). Mice were sacrificed at 31 weeks of age. Serum biochemistries were performed, and bi-lateral tibiae were assessed for microarchitecture, whole bone and tissue level mechanical properties, and composition including bone hydration. ResultsRegardless of intervention, BUN and PTH were higher in CKD animals throughout the study. In CKD, the combined effects of loading and RAL were quantified as lower cortical porosity and improved mechanical, material, and compositional properties, including higher matrix-bound water. Loading was generally responsible for positive impacts in cortical geometry and structural mechanical properties, while RAL treatment improved some trabecular outcomes and material-level mechanical properties and was responsible for improvements in several compositional parameters. While control animals responded positively to loading, their bones were less impacted by the RAL treatment, showing no deformation, toughness, or bound water improvements which were all evident in CKD. Serum PTH levels were negatively correlated with matrix-bound water. DiscussionAn effective treatment program to improve fracture risk in CKD ideally focuses on the cortical bone and considers both cortical porosity and matrix properties. Loading-induced bone formation and mechanical improvements were observed across groups, and in the CKD cohort, this included lower cortical porosity. This study highlights that RAL treatment superimposed on active bone formation may be ideal for reducing skeletal complications in CKD by forming new bone with enhanced matrix properties.

Guaranteed-performance consensus for multi-agent systems with Lipschitz nonlinearity

This paper mainly addresses the guaranteed-performance consensus problem of multi-agent systems (MASs), under the energy constraints and Lipschitz nonlinear dynamics. First, to reach consensus under energy constraints, the consensus protocol and the quadratic performance function are proposed. Afterward, by using the properties of nonsingular transformation matrix and Lipschitz’s nonlinear representation, the consensus function conditions are expressed. Moreover, considering the guaranteed-performance cost, this paper designs the quadratic performance function derived from the Riccati inequality and Lyapunov–Krasovskii theorem. Eventually, numerical simulations are implemented to validate the theoretical results.

From Generation to Reuse: A Circular Economy Strategy Applied to Wind Turbine Production

The environmental impact of wind turbine rotor blades, both during manufacturing and at the end of their life cycle, can be significant. The aim of this study was to define and test a methodology for recycling the waste resulting from their production. Particles of waste from the mechanical machining of rotor blades, which were made up of a glass fibre/epoxy matrix mixture, were used to produce toe caps for use by the footwear industry. The addition of 1 wt.% of particles improved the mechanical properties of the epoxy matrix, with a 5.50% improvement in tension and an 8% improvement in stiffness. Characterisation of the laminates, manufactured by hand lay-up technique, revealed that in the three-point bending tests, the additive laminates showed improvements of 18.60% in tension, 7.50% in stiffness, and 10% in deformation compared to the control laminate. The compression test showed that the additive glass fibre toe cap had greater resistance to compression than the control glass fibre toe cap, with a reduction in deformation of 23.10%. The toe caps are suitable for use in protective footwear according to European standard EN ISO 20346:2022. They guaranteed protection against low-velocity impacts at an energy level of at least 100 J and against compression when tested at a compression load of at least 10 kN.

Ultrasonication-induced re-dispersion of freeze-dried cellulose nanoparticles for improving strength and durability of PAN polymer matrix

Cellulose nanocrystals (CNCs) have acquired considerable attention owing to their noteworthy properties, including high crystallinity, biodegradability, high specific surface area, and excellent mechanical characteristics that alter the inherent features of the polymer matrix upon reinforcement. Typically, CNCs undergo freeze-drying or spray-drying to facilitate handling and dispersion in a hydrophobic polymer medium. Unfortunately, these drying procedures compromise the intrinsic nano-scale properties of CNCs. Therefore, achieving a uniform re-dispersion of dried CNCs is imperative to attain the desired characteristics in the polymer composite. This study specifically focuses on achieving a homogeneous re-dispersion of freeze-dried CNCs within a waste polyacrylonitrile (PAN) matrix through a simple ultrasonication treatment. The enhanced mechanical properties of the PAN polymer matrix validate the impact of ultrasound energy on re-dispersing CNCs. A noticeable improvement in the tensile properties of the composite polymer film is observed when CNC particles are well-dispersed in the PAN matrix. This observation is substantiated through SEM imaging, XRD, and FTIR data of both neat PAN and PAN–CNC composite films. The results affirm that particle dispersion plays a crucial role in augmenting the tensile properties of PAN composite films.

Video fragment processing by Ky Fan norm

In this study, we focused on the formalization of video frame descriptions in the context of solving video segmentation problem. Since native video data can have various sizes, dividing each frame into blocks allows present image frame as a square matrix for a formal description. The frame block is a matrix of arbitrary dimensions. The ability to skip the step of matrix transformation to a square dimension or vectorization using some descriptor allows to reduce computational costs, freeing up computational resources required for this transformation. In our study, we used Ky Fan norm value as image frame block descriptor. The Ky Fan norm is built on top of matrix singular values. A singular decomposition does not impose restrictions on either the dimension orthe character of the elements of the original matrix. We conducted a comparative analysis of the effectiveness of the obtained descriptor for different video data sizesand with different aspect ratios, showing that the change in the descriptor for each block is independent of the video sizeand aspect ratios. Changes in the descriptorsfor each block from frame to frame are identical for video data of varying sizes. This means that as a result of such fragment transform, a square matrix of a fixed size iscreated, regardless of the output video size.This makes it possible to unify further processing of the video, which can be useful for the task of information search in large video databases under the conditions of providing a query "ad exemplum". In thiscase, we can analyze the existing database in offline mode and match each video with a fixed square matrix of descriptors, which will significantly reduce the time and amount of resources when matching with the query. Also, this approach can be effectively used to analyze video data for the motion detection and scene change tracking.