Order Matrix Research Articles

Rotation Matrix and Angles of Rotation in the Polar Decomposition

This paper aims at computing the rotation matrix and angles of rotations using Newton and Halley’s methods in the generalized polar decomposition. The method extends the techniques of Newton’s and Halley’s methods for iteratively finding the zeros of polynomial equation of single variable to matrix rotation valued problems. It calculates and estimates the eigenvalues using Chevbyshev’s iterative method while computing the rotation matrix. The sample problems were tested on a randomly generated matrix of order from the family of matrix market. Numerical examples are given to demonstrate the validity of this work.

Advances in the design, generation, and application of tissue-engineered myocardial equivalents.

Due to the limited regenerative ability of cardiomyocytes, the disabling irreversible condition of myocardial failure can only be treated with conservative and temporary therapeutic approaches, not able to repair the damage directly, or with organ transplantation. Among the regenerative strategies, intramyocardial cell injection or intravascular cell infusion should attenuate damage to the myocardium and reduce the risk of heart failure. However, these cell delivery-based therapies suffer from significant drawbacks and have a low success rate. Indeed, cardiac tissue engineering efforts are directed to repair, replace, and regenerate native myocardial tissue function. In a regenerative strategy, biomaterials and biomimetic stimuli play a key role in promoting cell adhesion, proliferation, differentiation, and neo-tissue formation. Thus, appropriate biochemical and biophysical cues should be combined with scaffolds emulating extracellular matrix in order to support cell growth and prompt favorable cardiac microenvironment and tissue regeneration. In this review, we provide an overview of recent developments that occurred in the biomimetic design and fabrication of cardiac scaffolds and patches. Furthermore, we sift in vitro and in situ strategies in several preclinical and clinical applications. Finally, we evaluate the possible use of bioengineered cardiac tissue equivalents as in vitro models for disease studies and drug tests.

Ultra‐Strong and Transparent Biomimetic Nanocomposite through Orientation Effects and In Situ Biomineralization

AbstractThe fascinating mechanical property of biomaterials in nature to support living organisms largely relies on their hierarchical and ordered structures. However, for the current biomimetic materials, their organic–inorganic heterostructures typically exhibit poor uniformity, weak interfacial bonding, and various defects, limiting the breakthrough in strength and toughness. Herein, an ultra‐strong and transparent biomimetic nanocomposite is presented by combining orientation effects and in situ biomineralization to precisely engineer each level of the hierarchy. The orientation of nanofiber provides long‐range and order matrix to remarkably eliminate defects, promote multi‐scale interfacial bonding and increase the crystalline degree and size of organic matrix; while the in situ mineralization of amorphous inorganic oligomers firmly welds the organic–inorganic interface together to form a continuous and homogeneous monolithic structure. Due to the unique structural features, the nanocomposite exhibits a tensile strength of up to 1168.1 ± 10.2 MPa and a toughness of 34.1 ± 0.8 MJ m−3. Furthermore, the nanocomposite film is imparted with high transparence and anisotropic optical properties. This work is expected to provide insights into the design of high‐performance biomineralized materials from structural coupling to precisely controlling interfaces and microstructure.

Study of Tribological Properties and Evolution of Morphological Characteristics of Transfer Films in PTFE Composites Synergistically Reinforced with Nano-ZrO2 and PEEK Particles.

The materials tribology community has identified that the transfer film attached to the surface of the counterpart metal during the friction process is not only closely related to the filler modification material but also a key factor affecting the tribological properties of polymer composites; however, there is a lack of feasible methods to quantify the characteristics of the transfer film. In this study, Nano-ZrO2 and polyetheretherketone (PEEK) were filled into a PTFE matrix in order to enhance the wear resistance of polytetrafluoroethylene (PTFE). The tribological properties of the modified PTFE composites were tested using a linear reciprocating friction and wear tester, and the entire friction experiment was designed in seven separate stages. Morphological features were extracted and analyzed from photographs of the transfer film acquired by optical microscopy at each friction stage using an image processing program. The thickness and roughness of the transfer film sections were measured using a non-contact profilometer. Abrasive debris were collected, and their morphological features were observed with an electron microscope. The results showed that the synergistic addition of soft PEEK and hard Nano-ZrO2 particles effectively inhibited interlayer slippage between PTFE molecular chains, dramatically reducing the size and yield of abrasive debris, and facilitated the improvement of the thickness and firmness of the transfer film, which significantly enhanced the wear resistance of the PTFE composites (the lowest volumetric wear rate for Nano-ZrO2/PEEK/PTFE was only 1.76 × 10-4 mm3/Nm). Quantitative analyses of the morphological characteristics of the transfer films revealed that the coverage and roundness of the transfer films gradually increase with the friction stroke, while the aspect ratio and texture entropy subsequently decrease gradually. The coverage, area, mean, third-order moments, and consistency of the transfer film strongly correlated with the volumetric wear rate (correlation coefficient |r| > 0.9).

Factorization of the Partly Non-rational Matrix of Arbitrary Order

Factorization of the Partly Non-rational Matrix of Arbitrary Order

The Effect of Spatially Correlated Errors on Sea Surface Height Retrieval from SWOT Altimetry

The upcoming technology of wide-swath altimetry from space will enable monitoring the ocean surface at 4–5 times better spatial resolution and 2–3 times better accuracy than traditional nadir altimeters. This development will provide a chance to directly observe submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. Taking full advantage of this opportunity requires correct treatment of the correlated SSH errors caused by uncertainties in environmental conditions beneath the satellite and in the geometry and orientation of the on-board interferometer. These observation errors are highly correlated both along and across the surface swath scanned by the satellite, and this presents a significant challenge for accurate processing. In particular, the SWOT precision matrix has off-diagonal elements that are too numerous to allow standard approaches to remain tractable. In this study, we explore the utility of a block-diagonal approximation to the SWOT precision matrix in order to reconstruct SSH variability in the region east of Greenland. An extensive set of 2dVar assimilation experiments demonstrates that the sparse approximation proposed for the precision matrix provides accurate SSH retrievals when the background-to-observation error ratio ν does not exceed 3 and significant wave height is below 2.5 m. We also quantify the range of ν and significant wave heights over which the retrieval accuracy of the exact spatially correlated SWOT error model will outperform the uncorrelated model. In particular, the estimated range is found to be substantially wider (ν<10 with significant wave heights below 8–10 m), indicating the potential benefits of further improving the accuracy of approximations for the SWOT precision matrix.

Banana stem biochar composite with polyaniline for energy storage applications

The production and use of activated carbon from biochar, exclusively for energy storage and environmental applications was attracting attention. In this work, the commonly available banana stem was selected as a precursor to be converted into biochar (BC) at 500℃. The conducting polymer poly aniline (PANI) was then incorporated into the char matrix (BC-PANI) in order to improve the electrical properties. FTIR, UV–visible, XRD, SEM and TEM techniques were used to characterize the polymer composite. The integration PANI onto BC was clearly revealed from SEM and TEM micrographs and also the nanocomposite formation (BC-PANI, 0.37 nm) was confirmed from the XRD analysis. Furthermore, the electrochemical performance was analyzed using cyclicvoltammetry and electrochemical impedance spectroscopy. Both BC and BC-PANI attained maximum specific capacitance of 27.00 and 57.50 Fg−1 respectively. The various resistance that originated at electrode/electrolyte interface was also identified from impedance spectroscopy. These findings highlighted the good capacitive nature of the electrode material (BC-PANI).

Measurements of jet multiplicity and jet transverse momentum in multijet events in proton–proton collisions at {sqrt{s}=13, text {TeV}}

Multijet events at large transverse momentum (p_{textrm{T}}) are measured at sqrt{s}=13,text {TeV} using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3{,text {fb}^{-1}} . The multiplicity of jets with p_{textrm{T}} >50,text {GeV} that are produced in association with a high-p_{textrm{T}} dijet system is measured in various ranges of the p_{textrm{T}} of the jet with the highest transverse momentum and as a function of the azimuthal angle difference varDelta phi _{1,2} between the two highest p_{textrm{T}} jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest p_{textrm{T}} jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

On open neighborhood energy of graphs

The open neighborhood of a vertex u denoted by N(u) in a simple connected graph G is the collection of all vertices other than u and adjacent to u. In this paper, we introduce a square matrix of order n, called the open neighborhood matrix, ONM(G) of a graph G whose (i, j)th entry is |N(vi) ∩ N(vj)|/(di+dj) whenever vi~vj, i≠ j; and zero otherwise, where di and dj, are the degrees of vi and vj respectively. We then establish the relationship between the connectedness of the graph G and the multiplicity of the eigenvalue zero of the matrix ONM(G), if it exists. Furthermore, we found the bounds for the largest open neighbourhood eigenvalue and open neighbourhood energy of graphs.

Fabrication of mixed matrix polyphenylsulfone‐polysulfone blend membranes incorporated with Nickel/Hydrazine@silica core‐shell nanoparticles using VIPS‐NIPS method for efficient dye rejection

AbstractThe dye‐water treatment using nanofiltration membranes is still an important issue. In this work, we have reported the fabrication of silica nanoparticles using a robust approach with well‐controlled aspect ratios. Accordingly, we first fabricated hydrophilic Nickel/Hydrazine@silica core‐shell nanoparticles, in which Ni nanoparticles were coated with a shell of silica. Then, different content of the prepared nanoparticles were incorporated into polyphenylsulfone/ polysulfone membrane matrixes in order to enhance the membranes hydrophilicity. The pristine and mixed matrix membranes (MMMs) were fabricated via the vapor‐induced phase separation coupled with non‐solvent‐induced phase separation (VIPS‐NIPS) approach, where Dioxane was employed as the co‐solvent. The dye rejection performance of the prepared membranes was evaluated for aqueous solutions of a variety of dyes, including direct yellow (DY), crystal violet (CV), methyl green (MG), and methylene blue (MB). Accordingly, it was indicated that the membrane with 0.12 wt.% of nanoparticles could provide an outstanding rejection performance as high as 99.7, 99.3, 98.4 and 97 for DY, MG, CV and MB, respectively, a superb water flux (6.1 L/m2 h bar), a great long‐term durability and an excellent antifouling performance.

A Study on Existence and Controllability of Conformable Impulsive Equations

We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative approach, we introduce the conformable controllability operator and the conformable controllability Gramian matrix in order to obtain the necessary and sufficient conditions for the complete controllability of linear impulsive conformable systems. We present a set of sufficient conditions for the controllability of the conformable semilinear impulsive systems.

Microbiological and physical-chemical characteristics of the Peruvian fermented beverage “Chicha de siete semillas”: Towards the selection of strains with acidifying properties

Traditional fermented beverages have been consumed worldwide for centuries. Such is the case of “Chicha de siete semillas” which is originally from the province of Huanta, in Ayacucho, Peru. In this work we have analyzed the chemical composition and bacterial diversity of products manufactured from six producers, who have used different combinations of cereals, pseudocereals, legumes and aromatic herbs, although maize was present in all of them. The fermented beverages had a low pH, mainly due to the production of lactic acid, whereas ethanol was, in general, present in low concentrations. Most of the products were rich in GABA, the content of biogenic amines being very low, as corresponds to a product with a short maturation time (less than 4 days). A metataxonomic analysis revealed that Streptococcaceae and Leuconostocaceae families were dominant in the majority of the beverages, Streptococcus spp. and Leuconostoc spp. being the representative genera, respectively. The result was corroborated by culture-dependent techniques, since these were the most abundant genera isolated and identified in all samples, with Streptococcus macedonicus and Leuconostoc lactis as representative species. In lower proportions other isolates were identified as Lactobacillus delbrueckii, Lactiplantibacillus plantarum, Furfurilactobacillus rossiae, Weissella confusa and Enterococcus faecium. The genetic profile of 26 S. macedonicus isolates was determined by RAPD-PCR and REP-PCR, showing five different patterns distinguishable with the first technique. One representative strain from each genetic pattern was further characterized and used to ferment a maize-based matrix (with saccharose) in order to know their technological potential. All strains were able to ferment the beverage at 30 °C in a short time (about 6 h) reaching a pH below 4.5 and they remained viable after 24 h; the main organic acid contributing to the pH decrease was lactic acid. Therefore, S. macedonicus is a good candidate for being part of a putative starter culture, since it is a species well adapted to this cereal-based food niche.

A branch-and-price algorithm for the airport gate assignment problem considering the trade-off between robustness and efficiency

In this paper, a novel objective for the airport gate assignment problem which considers the trade-off between robustness and operational efficiency in a unified dimension is developed. A task-based two-phase model is established, where the branch-and-price framework is embedded in the first stage. A set partitioning model is developed, where a series of aircrafts assigned to the same gate of a certain type are defined as a gate plan. The pricing subproblem is also decomposed into three parallel subproblems according to the gate size to account for the heterogeneity of the gates. Each gate plan is allocated to a physical gate in order to minimize the utilization of remote gates in the second stage. The pulse algorithm with two acceleration strategies, that generates a lower bound matrix in reverse order and applies path combination, is used to solve the pricing subproblems. Finally, extensive computational experiments are conducted to demonstrate the high performance of the proposed model, especially for large-scale instances.

Multiple quantum filtered nuclear magnetic resonance of 23Na+ in uniformly stretched and compressed hydrogels.

Stretching or compressing hydrogels creates anisotropic environments that lead to motionally averaged alignment of embedded guest quadrupolar nuclear spins such as 23Na+. These distorted hydrogels can elicit a residual quadrupolar coupling that gives an oscillation in the trajectories of single quantum coherences (SQCs) as a function of the evolution time during a spin-echo experiment. We present solutions to equations of motion derived with a Liouvillian superoperator approach, which encompass the coherent quadrupolar interaction in conjunction with relaxation, to give a full analytical description of the evolution trajectories of rank-1 (T^1±1), rank-2 (T^2±1), and rank-3 (T^3±1) SQCs. We performed simultaneous numerical fitting of the experimental 23Na nuclear magnetic resonance (NMR) spectra and rank-2 (T^2±1) and rank-3 (T^3±1) SQC evolution trajectories measured in double and triple quantum filtered experiments, respectively. We estimated values of the quadrupolar coupling constant CQ, rotational correlation time τC, and 3 × 3 Saupe order matrix. We performed simultaneous fitting of the analytical expressions to the experimental data to estimate values of the quadrupolar coupling frequency ωQ/2π, residual quadrupolar coupling ωQ/2π, and corresponding spherical order parameter S0*, which showed a linear dependence on the extent of uniform hydrogel stretching and compression. The analytical expressions were completely concordant with the numerical approach. The insights gained here can be extended to more complicated (biological) systems such as 23Na+ bound to proteins or located inside and outside living cells in high-field NMR experiments and, by extension, to the anisotropic environments found in vivo with 23Na magnetic resonance imaging.

Accuracy improvement of cooperative localization using UAV and UGV

In a simultaneous localization and mapping (SLAM) system, in general, distribution estimation based on a particle filter is used for localization of Unmanned Ground Vehicle (UGV) with a laser rangefinder, and point estimation based on optimization is used for Unmanned Aerial Vehicle (UAV) with a monocular camera. In order for such robots to perform cooperative localization to improve accuracy, it is necessary to convert the localization results of point estimation and distribution estimation into a format that can be introduced to each other. In this paper, we propose an integration method of estimation results for cooperative localization by UAV and UGV. The UAV point estimation result is converted to a normal distribution by giving a fixed covariance matrix in order to introduce it as the observation likelihood of the UGV. On the other hand, the particle pose with maximum weight obtained from the UGV distribution estimation result is added to the current pose constraint in UAV optimization. As a result, this allows stable localization of both by correcting with the estimation result of the other even in an environment where either one is disadvantageous for localization.

Evaluation of Selected Geosites between Makhul and Khanuqa Anticlines, Northern Salah Al-Din, Iraq

The geopark characteristics in selected sites located between Makhul and Khanuqa anticlines and Tigris River. Eight geosites in the study area are evaluated. The assessment and differentiation of the results in the research depended on two methods, Strengths, weaknesses, opportunities, and threats analysis and Geosite Assessment Model Classification. The results were identical in the two methods as the highest score in the two methods for the third and eighth stations and the research was concluded. The application of the Geosite Assessment Model model to one station was explained, which is the first one, Al-Qusour station, in order to clarify how to apply it to the other stations. After the application of the Geosite Assessment Model model to all stations, the results were located in a Geosite Assessment Model matrix in order to know that each station will fall within a certain range. After completing the evaluation of the stations, all stations in the study area are suitable as geopark areas.

Hadamard Matrices related to Projective Planes

Let $n$ be the order of a quaternary Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-splittable quaternary Hadamard matrix of order $n^2$.

A note on complex conference matrices

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

Homogenization for operators with arbitrary perturbations in coefficients

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. We perturbed it by a first order differential operator arbitrarily depending on a small multi-dimensional parameter and we study the existence of a limiting (homogenized) operator in the sense of the norm resolvent convergence. The first part of our main results states that the norm resolvent convergence is equivalent to the convergence of the coefficients in the perturbing operator in certain space of multipliers. The second part of our results says that the convergence in the mentioned spaces of multipliers is equivalent to the convergence of certain local mean values over small pieces of the considered domains. These results are supported by series of examples. We also provide a series of ways of generating new non-periodically oscillating perturbations for which our results are applicable.

A divide-and-conquer method for constructing a pseudo-Jacobi matrix from mixed given data

For the given signature operator H=Ir⊕−In−r, a pseudo-Jacobi matrix is a self-adjoint matrix relatively to a symmetric bilinear form 〈⋅,⋅〉H, and it is the counterpart of a classical Jacobi matrix to the indefinite scalar product space setting. In this article, we consider an inverse eigenvalue problem for this class of matrices. The main concern is to construct an n×n pseudo-Jacobi matrix from a prescribed n-tuple of distinct real numbers and a Jacobi matrix of order not less than ⌊n2⌋, such that its spectrum is this tuple and the given Jacobi matrix is its trailing principal submatrix. A divide-and-conquer scheme is used to solve this problem, and a necessary and sufficient condition under which the problem is solvable is presented. A numerical algorithm is designed to solve this pseudo-Jacobi matrix inverse eigenvalue problem according to the obtained results. Some illustrative numerical examples are also given to test the reconstructive algorithm.