Special Matrix Research Articles

ФОРМИРОВАНИЕ РАСЧЕТНЫХ СХЕМ ОБОБЩЕННЫХ КИНЕМАТИЧЕСКИХ УСТРОЙСТВ, ПРИЦЕЛЬНО РЕГУЛИРУЮЩИХ СПЕКТР ЧАСТОТ СОБСТВЕННЫХ КОЛЕБАНИЙ УПРУГИХ СИСТЕМ С КОНЕЧНЫМ ЧИСЛОМ СТЕПЕНЕЙ СВОБОДЫ МАСС, У КОТОРЫХ НАПРАВЛЕНИЯ ДВИЖЕНИЯ ПАРАЛЛЕЛЬНЫ, НО НЕ ЛЕЖАТ В ОДНОЙ ПЛОСКОСТИ

To date, for some elastic systems with a finite number of degrees of mass freedom, in which the directions of mass movement are parallel and lie in the same plane, methods have been developed for creating additional generalized targeted constraints and generalized targeted kinematic devices. Each generalized targeted constraint increases, and each generalized targeted kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and natural modes. Earlier, for elastic systems with a finite number of degrees of mass freedom, in which the directions of mass motion are parallel, but do not lie in the same plane (for example, plates), an approach for the computing of a matrix of additional stiffness and a method for the development of computational schemes of additional generalized targeted constraints were developed. Also earlier, for such systems, an approach was proposed for the computing of a special matrix with allowance for additional inertial forces that determine a generalized targeted kinematic device. At the same time, the method of development of computational schemes of kinematic devices was not proposed. The first part of the paper was devoted to approach, that made it possible to develop computational schemes of generalized targeted kinematic devices for such systems as well. A variant of the computational scheme of constraint for the rod system with one degree of activity was considered. Some special properties of such targeted kinematic devices were revealed. The distinctive second part of the paper is devoted to corresponding samples of analysis.

ФОРМИРОВАНИЕ РАСЧЕТНЫХ СХЕМ ОБОБЩЕННЫХ КИНЕМАТИЧЕСКИХ УСТРОЙСТВ, ПРИЦЕЛЬНО РЕГУЛИРУЮЩИХ СПЕКТР ЧАСТОТ СОБСТВЕННЫХ КОЛЕБАНИЙ УПРУГИХ СИСТЕМ С КОНЕЧНЫМ ЧИСЛОМ СТЕПЕНЕЙ СВОБОДЫ МАСС, У КОТОРЫХ НАПРАВЛЕНИЯ ДВИЖЕНИЯ ПАРАЛЛЕЛЬНЫ, НО НЕ ЛЕЖАТ В ОДНОЙ ПЛОСКОСТИ

To date, for some elastic systems with a finite number of degrees of mass freedom, in which the directions of mass movement are parallel and lie in the same plane, methods have been developed for creating additional generalized targeted constraints and generalized targeted kinematic devices. Each generalized targeted constraint increases, and each generalized targeted kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and natural modes. Earlier, for elastic systems with a finite number of degrees of mass freedom, in which the directions of mass motion are parallel, but do not lie in the same plane (for example, plates), an approach for the computing of a matrix of additional stiffness and a method for the development of computational schemes of additional generalized targeted constraints were developed. Also earlier, for such systems, an approach was proposed for the computing of a special matrix with allowance for additional inertial forces that determine a generalized targeted kinematic device. At the same time, the method of development of computational schemes of kinematic devices was not proposed. The first part of the paper was devoted to approach, that made it possible to develop computational schemes of generalized targeted kinematic devices for such systems as well. A variant of the computational scheme of constraint for the rod system with one degree of activity was considered. Some special properties of such targeted kinematic devices were revealed. The distinctive second part of the paper is devoted to corresponding samples of analysis.

New Banach Sequence Spaces Defined by Jordan Totient Function

In this study, a special lower triangular matrix derived by combining Riesz matrix and Jordan totient matrix is used to construct new Banach spaces. $\alpha-$,$\beta-$,$\gamma-$duals of the resulting spaces are obtained and some matrix operators are characterized.

Left-Invariant PID Control Almost Globally Stabilizes Rigid-Body Attitudes with Right-Invariant Biases

This paper studies the robust stabilization of rigid-body attitudes represented by a special orthogonal matrix. A geometric proportional–integral–derivative (PID) controller is proposed with all the input commands defined in the dual space so*(3) of a Lie algebra for left-invariant systems evolving on a Lie group SO(3). Almost global asymptotic stability (AGAS) of the close system is proved by constructing a gradient-descent Lyapunov function after explicitly performing two stages of variable change. The attitudes are stabilized to the stable equilibrium despite the influence of inertially fixed biases. The convergent behaviors and the robustness to biases are verified by numerical simulations.

Metal-grade laminated nanofiber films with outstanding EMI shielding performances and high-temperature resistance

With the growing demands in electronics, communications, and energy, conductive composites face a daunting challenge as criteria for conductivity and mechanical properties rise. Extensive search on nanocomposites and amorphous metals has been motivated by the quest for a conductive material that can enhance strength and deformability. However, finding conductive materials that can overcome the drawbacks of their conventional counterparts and exhibit great strength, toughness and quick charge transmission while accomplishing large-scale production remains a significant challenge. This paper describes an approach to high-temperature flexible conductive materials by utilizing composites composed of aramid nanofiber (ANF) and silver nanoparticles (Ag NPs). The ANF is derived from macro-aramid fibers and retains its excellent mechanical properties and heat resistance. Within the composite, Ag NPs effectively enter the special nanofiber matrix to build a tightly connected conductive pathway on the ANF, thus facilitating efficient charge transport. The resulting Ag-ANF composite films exhibit an impressive electrical conductivity of 36,989.68 S m−1 and a tensile strength of 30.3 MPa. Additionally, they provide outstanding EMI shielding with a value of 107.9 dB. This significant achievement opens up the possibility of metallizing the surface of insulated polymer fibers, thereby enabling effective EMI shielding applications even in challenging and extreme conditions.

Xylan clustering on the pollen surface is required for exine patterning.

Xylan is a crosslinking polymer that plays an important role in the assembly of heterogeneous cell wall structures in plants. The pollen wall, a specialized cell wall matrix, exhibits diverse sculpted patterns that serve to protect male gametophytes and facilitate pollination during plant reproduction. However, whether xylan is precisely anchored into clusters and its influence on pollen wall patterning remain unclear. Here, we report xylan clustering on the mature pollen surface in different plant species that is indispensable for the formation of sculpted exine patterns in dicot and monocot plants. Chemical composition analyses revealed that xylan is generally present at low abundance in the mature pollen of flowering plants and shows plentiful variations in terms of substitutions and modifications. Consistent with the expression profiles of their encoding genes, genetic characterization revealed IRREGULAR XYLEM10-LIKE (IRX10L) and its homologous proteins in the GT47 family of glycosyltransferases as key players in the formation of these xylan micro-/nano-compartments on the pollen surface in Arabidopsis (Arabidopsis thaliana) and rice (Oryza sativa). A deficiency in xylan biosynthesis abolished exine patterning on pollen and compromised male fertility. Therefore, our study outlines a mechanism of exine patterning and provides a tool for manipulating male fertility in crop breeding.

DEVELOPMENT OF COMPUTATIONAL SCHEMES OF GENERALIZED KINEMATIC DEVICES THAT PRECISELY REGULATE THE NATURAL FREQUENCY SPECTRUM OF ELASTIC SYSTEMS WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM, IN WHICH THE DIRECTIONS OF MOTION ARE PARALLEL, BUT DO NOT LIE IN THE SAME PLANE

To date, for some elastic systems with a finite number of degrees of mass freedom, in which the directions of mass movement are parallel and lie in the same plane, methods have been developed for creating additional generalized targeted constraints and generalized targeted kinematic devices. Each generalized targeted constraint increases, and each generalized targeted kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and natural modes. Earlier, for elastic systems with a finite number of degrees of mass freedom, in which the directions of mass motion are parallel, but do not lie in the same plane (for example, plates), an approach for the computing of a matrix of additional stiffness and a method for the development of computational schemes of additional generalized targeted constraints were developed. Also earlier, for such systems, an approach was proposed for the computing of a special matrix with allowance for additional inertial forces that determine a generalized targeted kinematic device. At the same time, the method of development of computational schemes of kinematic devices was not proposed. The distinctive paper is devoted to approach, that makes it possible to develop computational schemes of generalized targeted kinematic devices for such systems as well. A variant of the computational scheme of constraint for the rod system with one degree of activity, is considered. Some special properties of such targeted kinematic devices are revealed.

Inverse Spectral Problems for a Special Acyclic Matrix

In this paper, we consider the reconstruction of matrices whose graph is a star with root at the central vertex from given partial eigen data. Three inverse spectral problems are discussed. The necessary and sufficient conditions for the solvability of the problems are studied. Furthermore, the corresponding numerical algorithms are presented. Some numerical examples are also provided to demonstrate the applicability of the results obtained here.

RETRACTED: A Global Structural Hypergraph Convolutional Model for Bundle Recommendation

Bundle recommendations provide personalized suggestions to users by combining related items into bundles, aiming to enhance users’ shopping experiences and boost merchants’ sales revenue. Existing solutions based on graph neural networks (GNN) face several significant challenges: (1) it is demanding to explicitly model multiple complex associations using standard graph neural networks, (2) numerous additional nodes and edges are introduced to approximate higher-order associations, and (3) the user–bundle historical interaction data are highly sparse. In this work, we propose a global structural hypergraph convolutional model for bundle recommendation (SHCBR) to address the above problems. Specifically, we jointly incorporate multiple complex interactions between users, items, and bundles into a relational hypergraph without introducing additional nodes and edges. The hypergraph structure inherently incorporates higher-order associations, thereby alleviating the training burden on neural networks and the dilemma of scarce data effectively. In addition, we design a special matrix propagation rule that captures non-pairwise complex relationships between entities. Using item nodes as links, structural hypergraph convolutional networks learn representations of users and bundles on a relational hypergraph. Experiments conducted on two real-world datasets demonstrate that the SHCBR outperforms the state-of-the-art baselines by 11.07–25.66% on Recall and 16.81–33.53% on NDCG. Experimental results further indicate that the approach based on hypergraphs can offer new insights for addressing bundle recommendation challenges. The codes and datasets have been publicly released on GitHub.

Robust Leaderless Time-Varying Formation Control for Nonlinear Unmanned Aerial Vehicle Swarm System With Communication Delays.

This article investigates the tracking-oriented robust leaderless time-varying formation (TVF) control problem for unmanned aerial vehicle swarm systems (UAVSSs) with Lipschitz nonlinear dynamics under directed topology, where external disturbances are random and bounded, and communication delays (CDs) are bounded. In this article, a state-feedback control approach is adopted to make sure that a UAVSS forms a desired TVF and follows a specified trajectory when CDs and external disturbances occur. First, a novel PD-like formation control protocol with several unknown parameters and CDs is designed. The protocol contains the information of the local neighborhood status and its differential quantities. Second, the tracking-oriented robust leaderless TVF control problem with Lipschitz dynamics, external disturbances, and CDs is transformed into a problem about asymptotic stability of a lower dimensional closed-loop control system through a special matrix decomposition. Third, a theorem is proposed to determine the unknown parameters of the control protocol and the upper bound of CDs. In the theorem, sufficient conditions for a UAVSS to attain the anticipated TVF and trajectory tracking are obtained. A Lyapunov-Krasovskii (LK) functional is constructed to verify that the error among the practical flight state of UAVs, the anticipant TVF configuration, and tracking trajectory can asymptotically converge to 0. Finally, with the presentation of a simulation case, the effectiveness of the theoretical results is illustrated.

Statistical Modeling of Implicit Functional Relations

This study considers the statistical estimation of relations presented by implicit functions. Such structures define mutual interconnections of variables rather than outcome variable dependence by predictor variables considered in regular regression analysis. For a simple case of two variables, pairwise regression modeling produces two different lines of each variable dependence using another variable, but building an implicit relation yields one invertible model composed of two simple regressions. Modeling an implicit linear relation for multiple variables can be expressed as a generalized eigenproblem of the covariance matrix of the variables in the metric of the covariance matrix of their errors. For unknown errors, this work describes their estimation by the residual errors of each variable in its regression by the other predictors. Then, the generalized eigenproblem can be reduced to the diagonalization of a special matrix built from the variables’ covariance matrix and its inversion. Numerical examples demonstrate the eigenvector solution’s good properties for building a unique equation of the relations between all variables. The proposed approach can be useful in practical regression modeling with all variables containing unobserved errors, which is a common situation for the applied problems.

Some Relations on the rRs(P,Q,z) Matrix Function

In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationship with other generalized special matrix functions in the context of the Konhauser and Laguerre matrix polynomials.

Euler-type integrals for the generalized hypergeometric matrix function

Abstract The special matrix functions have received significant attention in many fields, such as theoretical physics, number theory, probability theory, and the theory of group representations. In 2017, Dwivedi and Sahai introduced the generalized hypergeometric matrix function using matrix parameters and proved the convergence on | z | = 1 {|z|=1} . Recently, hypergeometric matrix functions and their potential applications have played a major role in mathematical physics and engineering. Motivated by aforesaid works and in order to enrich this flourishing field, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and determine various transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have been provided for several particular cases.

Diagnosis of insolvency signs and pre-crisis condition in commercial organizations: Developing organizational and methodological approaches

Subject. This article discusses the problems of financial stability of the Russian economy. Objectives. The article aims to develop a methodology for multivariate analysis of the financial condition of the organization. Methods. For the study, we used the method of expert assessment. Results. The article presents the results of the analysis of the proportion of unprofitable organizations by type of economic activity. It identifies the main causes of bankruptcy and builds a special matrix that helps determine the feasibility of implementing anti-crisis measures within the organization. Conclusions. The use of the results of the study will contribute to the optimization of the financial and economic activities of business structures.

Hierarchical coupling control of cable-driven multi-loop crane for underactuated positioning

For the low-cost anti-swing retrofit of existing offshore heavy cranes, a (2-UPPU/UPU)UP multi-loop configuration with six cable-driven prismatic pairs and a UP underactuated pendulum is introduced. Each UPPU branch contains a fast-moving prismatic pair and a slow-moving one. A configuration tracking method utilizing three slow cable motions in 2-UPPU/UPU is proposed by motion compensation technology. A multi-loop underactuated end positioning scheme is given to achieve the cargo's horizontal positioning in inertia frame, i.e., two fast cable motions in 2-UPPU are used to drive four states comprising their tracking trajectories and two cargo swings, which frees the wave compensation and swing suppression task from crane joints and retains the original crane system. A hierarchical coupling controller with a special coupling relation matrix is designed, where the matrix-based sub-controller fusion technique provides a standardized design approach with distinct physical meaning for the application of hierarchical methodology in underactuated multi-loop systems. The stability analysis by Lyapunov method reveals multiple coupling relation matrices matching stability conditions, giving birth to five attractive coupling control modes. Simulations and experiments are conducted to compare and verify performance.

Density-oriented deep eutectic solvent-based system for the selective separation of polysaccharides from Astragalus membranaceus var. Mongholicus under ultrasound-assisted conditions

The water extraction and ethanol precipitation method is an extraction method based on the solubility characteristics of polysaccharides that offers wide applicability in the extraction and separation of plant polysaccharides. However, this method leads to large amounts of proteins, nucleic acids, pigments, and other impurities in the polysaccharides products, which makes downstream purification complicated and time-consuming. In this study, a green, high-density natural deep eutectic solvents was used for the high-purity extraction and separation of polysaccharides from Astragalus membranaceus (Fisch) Bge. var. Mongholicus (Bge.) Hsiao roots under ultrasound-assisted conditions. In this study, 16 different natural deep eutectic solvents were designed to screen the best solvent for extracting Astragalus polysaccharides (APSs). Based on the yield and recovery of APSs, a natural deep eutectic solvents composed of choline chloride and oxalic acid with a molar ratio of 1:2 was selected. The related factors affecting polysaccharides extraction and solvent precipitation were investigated. To improve the operating methodology, single-factor trials, a Plackett-Burman design, and a Box-Behnken design were used. The optimal extraction process conditions were obtained as follows: water content of 55%, liquid–solid ratio of 24 mL/g, ultrasonic irradiation time of 54 min, ultrasonic irradiation temperature of 50 °C, ultrasonic irradiation power of 480 W, ethanol precipitation time of 24 h, and ethanol concentration of 75%. Under optimal extraction conditions, the recovery of APSs was 61.4 ± 0.6 mg/g. Considering the special matrix characteristics of A. membranaceus var. Mongholicus roots, physical-technology-based ultrasonic waves promote penetration, and the mass transfer function also solves the bottleneck of high-viscosity deep eutectic solvents in the extraction stage. In comparison with the conventional method, the proposed method based on deep eutectic solvents isolation can significantly increase APSs recovery, which is beneficial to simplifying the process of polysaccharides purification by using solvent properties to separate extracts and reduce impurities in APSs.

Safety verification for Regime-Switching Jump Diffusions via barrier certificates

It is well known that for a stochastic hybrid system, if its failure probability does not exceed a given safety threshold, the safety of the system can be guaranteed. Thus, in this paper, we concern with the upper bound of failure probability for failure analysis of a class of nonautonomous stochastic hybrid systems, denoted as Regime-Switching Jump Diffusions (RSJDs). We start with the definition of RSJDs, which contain not only continuous flows described by stochastic differential equations, but also instantaneous behavior described by Markovian switching and instantaneous behavior described by Lévy jump. Then we decompose the failure probability of RSJDs in [t0,+∞) into two segments: one is defined over [T,+∞), and the other is defined over [t0,T]. For failure probability over [T,+∞), by utilizing multiple vectorial barrier certificates, an asymptotically decreasing bound of failure probability with respect to T is established, where a general nonnegative matrix is used instead of a special nonnegative matrix defined by the exponent of essentially nonnegative matrix for a broader applicability. For failure probability over [t0,T], a generalized c-martingale condition is adopted to obtain a T-dependent failure probability bound, in which two non-negative scalar functions are utilized to relax the conservativeness of infinitesimal generators. Finally, for rational RSJDs, we transform the decomposed failure analysis problems into two semi-definite programming (SDP) problems, and then solve them via sum of squares programming. The applicabilities and effectiveness of our computable decomposition methodology are illustrated through three examples.

Incremental specialized and specialized-generalized matrix factorization models based on adaptive learning rate optimizers

Recommender systems suggest items that are likely to be preferred by a particular user based on historical behavior, actions, and feedback. In real-world applications, data on users and items are continuously generated at a fast pace, such as in e-commerce, social media, digital marketing, and content consumption applications. Since interactions occur over time, these scenarios can be formulated as a data stream where users’ interests are potentially dynamic, i.e., they change over time. Given that changes are expected to occur, one of the current research challenges in streaming recommender systems is that models must adapt their parameters when changes occur to maintain performance. As such changes do not occur for all users and items in the stream at the same time, we consider adapting learning schemes to account for user or item identifiers and model individual parameters. Therefore, we used specialized parameters to adjust the step size for each dataset user or item. More specifically, this study proposes four specialized and specialized-generalized variants of four well-known adaptive learning rate optimizers and shows how they are combined with incremental matrix factorization methods. We tested our proposed optimization strategies on different datasets and showed that one of the proposed specialized variants, that is, InAMSGradUser, improves the RECALL and NDCG rates by up to 11.1 and 7.5 percentage points, respectively, compared to the traditional stochastic gradient descent (SGD) optimizer.

Identification of Basement Membrane Genes and Related Molecular Subtypes in Nonalcoholic Fatty Liver Disease.

Basement membranes (BMs) are widely distributed and highly specialized extracellular matrix (ECM). The goal of this study was to explore novel genes associated with nonalcoholic fatty liver disease (NAFLD) from the perspective of BMs. Sequencing results of 304 liver biopsy samples about NAFLD were systematically obtained from the Gene Expression Omnibus (GEO) database. Biological changes during NAFLD progression and hub BM-associated genes were investigated by differential gene analysis and weighted gene co-expression network analysis (WGCNA), respectively. The nonalcoholic steatohepatitis (NASH) subgroups were identified based on hub BM-associated genes expression, as well as the differences in Kyoto Encyclopedia of Genes and Genomes (KEGG) signaling pathways and immune microenvironment between different subgroups were compared. Extracellular matrix (ECM) seems to play an important role in the development of NAFLD. Three representative BM-associated genes (ADAMTS2, COL5A1, and LAMC3) were finally identified. Subgroup analysis results suggested that there were significant changes in KEGG signaling pathways related to metabolism, extracellular matrix, cell proliferation, differentiation, and death. There were also changes in macrophage polarization, neutrophils, and dendritic cells abundance, and so on. In conclusion, the present study identified novel potential BM-associated biomarkers and further explored the heterogeneity of NASH that might provide new insights into the diagnosis, assessment, management, and personalized treatment of NAFLD.

Component-specific reduction in perineuronal nets in senescence-accelerated mouse strains.

With increased life expectancy, age-related diseases are a significant health concern in Western societies. Animal models (e.g., rodents) have been used to understand age-related changes in brain function-particularly through the senescence-accelerated mouse (SAM) strain. Previous reports have shown that the senescence-accelerated mouse propensity (SAMP)8 and SAMP10 strains have learning disabilities. In this study, we analyzed the prefrontal cortex, which is involved in cognitive function. We aimed to clarify the changes in parvalbumin-positive interneurons (PV-positive neurons), which are related to cognitive function, and perineuronal nets (PNNs), which are special extracellular matrix molecules formed around them. We performed histological analysis of PV-positive neurons and PNNs in the prefrontal cortex to elucidate the mechanism of behavioral abnormalities in SAMP8 and SAMP10 strains. Expression of Cat-315-positive PNN was not confirmed in the prefrontal cortex of SAMP10 mice. However, the density of AB1031-positive PNN, tenascin-R-positive PNN, and brevican-positive PNN decreased in the prefrontal cortex of SAMP8 and SAMP10 mice compared to that of the senescence-accelerated mouse resistance (SAMR1) mice. In addition, the density of PV-positive neurons was lower in SAMP8 mice than in SAMR1 mice. These mice, which exhibited behavioral and neuropathological phenotypes with age, showed different PV-positive neurons and PNNs in the prefrontal cortex compared with the SAMR1 mice. We believe that the results of this study will be useful for elucidating the mechanisms of age-related decline in cognitive and learning functions using SAM.