A Finite Element Galerkin Method for a Unidimensional Single-Phase Nonlinear Stefan Problem with Dirichlet Boundary Conditions

Based on straightening the free boundary, an H¹-Galerkin methodis proposed and analysed for a single-phase nonlinear Stefanproblem with Dirichlet boundary conditions. Optimal H¹ estimatesfor continuous-time Galerkin approximations are derived.     

Evaluation of a novel nanocrystalline hydroxyapatite powder and a solid hydroxyapatite/Chitosan-Gelatin bioceramic for scaffold preparation used as a bone substitute material

Artificially fabricated hydroxyapatite (HAP) shows excellent biocompatibility with various kinds of cells and tissues which makes it an ideal candidate for a bone substitute material. In this study, hydroxyapatite nanoparticles have been prepared by using the wet chemical precipitation method using calcium nitrate tetra-hydrate [Ca(NO₃)₂.4H₂O] and di-ammonium hydrogen phosphate [(NH₄)₂ HPO₄] as precursors. The composite scaffolds have been prepared by a freeze-drying method with hydroxyapatite, chitosan, and gelatin which form a 3D network of interconnected pores. Glutaraldehyde solution has been used in the scaffolds to crosslink the amino groups (|NH₂) of gelatin with the aldehyde groups (|CHO) of chitosan. The X-ray diffraction (XRD) performed on different scaffolds indicates that the incorporation of a certain amount of hydroxyapatite has no influence on the chitosan/gelatin network and at the same time, the organic matrix does not affect the crystallinity of hydroxyapatite. Transmission electron microscope (TEM) images show the needle-like crystal structure of hydroxyapatite nanoparticle. Scanning Electron Microscope (SEM) analysis shows an interconnected porous network in the scaffold where HAP nanoparticles are found to be dispersed in the biopolymer matrix. Fourier transforms infrared spectroscopy (FTIR) confirms the presence of hydroxyl group (OH^-) , phosphate group (PO^3-₄) , carbonate group (CO^2-₃) , imine group (C=N), etc. TGA reveals the thermal stability of the scaffolds. The cytotoxicity of the scaffolds is examined qualitatively by VERO (animal cell) cell and quantitatively by MTTassay. The MTT-assay suggests keeping the weight percentage of glutaraldehyde solution lower than 0.2%. The result found from this study demonstrated that a proper bone replacing scaffold can be made up by controlling the amount of hydroxyapatite, gelatin, and chitosan which will be biocompatible, biodegradable, and biofriendly for any living organism.     

A Priori Error Estimates for a Single-Phase Quasilinear Stefan Problem in one Space Dimension

Fixing the free boundary with the help of a Landau-type transformation,a finite element Galerkin method is applied to a single-phasequasilinear Stefan problem in one space dimension. Optimal errorestimates both for semidiscrete and fully discrete Galerkinapproximations are derived.     

On Berezin Number Inequalities for Operator Matrices

In this article, we refine certain earlier existing bounds for Berezin number of operator matrices. We also prove some new Berezin number inequalities for general n × n operator matrices.Further, we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices. Finally, some interesting examples are discussed.     

Energy in the Kantowski–Sachs space-time using teleparallel geometry

The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity and in the Hamiltonian structure of the teleparallel equivalent of general relativity. The teleparallel versions of field equations are also derived in such a space-time.     

Fixed Points of Mappings Satisfying a Weakly Contractive Type Condition

In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points.     

Properties of MgFe2O4 Nanoparticles Synthesized by Ultrasonic Aerosol Pyrolysis for Biomedical Applications

Physics of the Solid State - We present the data of studies on the structure, phase states, and magnetic properties of magnetic nanoparticles (MNPs) of magnesium ferrite spinel (MgFe2O4),...     

Distance signless Laplacian eigenvalues of graphs

Suppose that the vertex set of a graph G is V(G)=\{v\mathrm{1},v\mathrm{2},\mathrm{...},vn\}. The transmission Tr(vi) (or D_i) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let Tr(G) be the n\times n diagonal matrix with its (i, i)-entry equal to {{\displaystyle Tr}}_G(vi). The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as L(G)=Tr(G)+D(G), where D(G) is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs.     

Insight into 3D micro‐CT data: exploring segmentation algorithms through performance metrics

Three‐dimensional (3D) micro‐tomography (µ‐CT) has proven to be an important imaging modality in industry and scientific domains. Understanding the properties of material structure and behavior has produced many scientific advances. An important component of the 3D µ‐CT pipeline is image partitioning (or image segmentation), a step that is used to separate various phases or components in an image. Image partitioning schemes require specific rules for different scientific fields, but a common strategy consists of devising metrics to quantify performance and accuracy. The present article proposes a set of protocols to systematically analyze and compare the results of unsupervised classification methods used for segmentation of synchrotron‐based data. The proposed dataflow for Materials Segmentation and Metrics (MSM) provides 3D micro‐tomography image segmentation algorithms, such as statistical region merging (SRM), k‐means algorithm and parallel Markov random field (PMRF), while offering different metrics to evaluate segmentation quality, confidence and conformity with standards. Both experimental and synthetic data are assessed, illustrating quantitative results through the MSM dashboard, which can return sample information such as media porosity and permeability. The main contributions of this work are: (i) to deliver tools to improve material design and quality control; (ii) to provide datasets for benchmarking and reproducibility; (iii) to yield good practices in the absence of standards or ground‐truth for ceramic composite analysis.     

Surface extenders and an optimal pore size promote high dynamic binding capacities of antibodies on cation exchange resins

Increased recombinant protein expression yields and a large installed base of manufacturing facilities designed for smaller bulk sizes has led to the need for high capacity chromatographic resins. This work explores the impact of three pore sizes (with dextran distribution coefficients of 0.4, 0.53, and 0.64), dextran surface extender concentration (11–20 mg/mL), and ligand density (77–138 μmol H+/mL resin) of cation exchange resins on the dynamic binding capacity of a therapeutic antibody. An intermediate optimal pore size was identified from three pore sizes examined. Increasing ligand density was shown to increase the critical ionic strength, while increasing dextran content increased dynamic binding capacity mainly at the optimal pore size and lower conductivities. Dynamic binding capacity as high as 200 mg/mL was obtained at the optimum pore size and dextran content.