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In this paper, we are concerned with a class of second-order hemivariational inequalities involving history-dependent operators. For the problem, we first derive a semidiscrete scheme by implicit Euler formula and prove its unique solvability. The existence and uniqueness of a solution to the inequality problem is given by Rothe method. As the core part of the paper, we propose a two-step semidiscrete approximation for the problem, provide its unique solvability and obtain its second-order error estimates. The two-step scheme is more accurate than the standard implicit Euler scheme. Finally, we apply the results to a dynamic frictionless contact problem with long memory. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a dynamic adhesive contact model where the body is composed of a viscoelastic material with long memory. The adhesion process is modeled by a bonding field on part of the contact surface and on which the contact and the friction are modeled by nonmonotone Clarke subdifferential conditions with adhesion. Meanwhile, on another part of the contact surface, the contact is comprised of a normal compliance contact condition while the memory effects of the obstacle are considered, the friction is modeled by a version of Coulomb's law of dry friction and the friction bound is dependent on the normal stress. The variational form of the model generates a system of a doubly-history dependent variational–hemivariational inequality as well as a differential equation. Then, on the basis of the proof of abstract variational–hemivariational inequality, the existence and uniqueness results of the contact problem are established. [ABSTRACT FROM AUTHOR]

In this paper, we study a dynamic contact problem with Clarke subdifferential boundary conditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. The weak form of the model is governed by an evolutionary hemivariational inequality coupled with an integral equation. We study a fully discrete approximation scheme of the problem and bound the errors. Under appropriate solution regularity assumptions, optimal-order error estimates can be derived. Finally, a numerical example is also included to support our theoretical analysis. Particularly, it gives numerical evidence on the theoretically predicted optimal convergence order. [ABSTRACT FROM AUTHOR]

In endoscopic surgery, the surgical navigation system needs to calculate the deformation of soft tissue by biomechanical model which requires elastic properties and boundary conditions. However, patient-specific elastic parameters and boundary conditions of soft tissue are hard to measure accurately from the preoperative images, especially the boundary conditions will change during the operation due to the ligament cutting. In addition, simple boundary conditions such as fixed constraints and free-force constraints are not physically adequate to simulate the elastic effect of ligaments attached to the liver. In this paper, we present a novel method to identify the Young's modulus and equivalent spring constraint boundary conditions of a locally observed soft tissue. Based on the spring constraint boundary condition, a two-step inverse algorithm is developed based on the finite element method (FEM) with integration of energy regularized Gauss-Newton (GN) method and l 1 -regularized method, which takes external forces and displacements of observable nodes as inputs. A series of numerical simulations and physical hydrogel phantom experiments were conducted. The results of simulation and physical experiments show that the Young's modulus and equivalent spring constraint boundary conditions identified by the proposed method agree well with their setup true values. [ABSTRACT FROM AUTHOR]

In this paper, we study a parameter identification problem for elliptic partial differential equations. We reconstruct the coefficient with additional boundary measurements, including both Dirichlet and Neumann boundary conditions. To solve the problem, the coupled complex boundary method (CCBM), originally proposed in Cheng et al. [A novel coupled complex boundary method for solving inverse source problems, Inverse Probl. 30 (2014), p. 055002] is used. With CCBM, a complex boundary problem is introduced in such a way that the boundary conditions are coupled in a complex Robin boundary condition with a parameter τ. Using Tikhonov regularization, the coefficient is sought such that the imaginary part of the solution of the forward Robin boundary value problem vanishes in the problem domain, which brings advantages on robustness in reconstruction. Besides, the reconstruction is feasible even for very small regularization parameter through choosing the values of τ properly. Some theoretical analyses are given. Moreover, noise model is analysed and the finite element method is used for discretization. Numerical examples show the feasibility and stability of the proposed method. [ABSTRACT FROM AUTHOR]

An LC-MS/MS method for analysis of daptomycin in dried blood spot (DBS) was established. The DBS samples were prepared by spotting one droplet of blood onto absorbent paper, and were left to dry at room temperature. The DBS samples were extracted with water followed by deproteinization with acetonitrile. A Hypersil GOLD aQ column was applied to chromatographically separate the analyte, and mobile phase at a flow rate of 0.3 mL/min consisted of methanol and 0.1% formic acid. Detection of analyte was performed on a triple quadrupole mass spectrometer in positive mode, and the mass spectrometer was manipulated in selective reaction monitoring (SRM) mode. The SRM transitions m/z 810.9→811.1 and 810.9→640.8 for quantification and qualification of daptomycin and m/z 837.4→679.4 and 837.4→558.3 for roxithromycin used as internal standard were monitored. The calibration curves covering the range of 1-200 μg/mL exhibited good linearity, and lower limit of quantification (LLOQ) was 1 µg/mL for daptomycin in DBS. The proposed method was fully validated, and hematocrit effect on the quantification of daptomycin in DBS was not obvious. The proposed DBS method was non-invasive and required collection of a micro-volume blood, and was successfully utilized to a pharmacokinetics study in seriously ill patients. [ABSTRACT FROM AUTHOR]

An LC-MS/MS method was developed for simultaneous determination of voriconazole and its main metabolite voriconazoleN-oxide in human plasma. Plasma pretreatment was simple one-step protein precipitation with acetonitrile, and separation was achieved on a Hypersil GOLD aQ column. A triple-quadrupole tandem mass spectrometer with electrospray ionization source was operated by multiple reaction monitoring (MRM) in positive ion mode, and the precursor–product ion pairs used for MRM werem/z350.1→281.0, 365.8→224.1, and 531.3→489.2 for voriconazole, voriconazoleN-oxide, and internal standard, respectively. The total analytical run time was 6 min. The proposed method was linear over the range 0.001–1 µg/mL for voriconazole and voriconazoleN-oxide. The lower limit of quantification was 1 ng/mL for both of them. The specificity, accuracy, precision, recovery, matrix effect, stability as well as dilution integrity of this method were within acceptable limits during validation period. This method was successfully applied to therapeutic drug monitoring of voriconazole and to evaluate its metabolite profile. [ABSTRACT FROM PUBLISHER]

Convergence of a boundary value method (BVM) in Acetoet al. [Boundary value methods for the reconstruction of Sturm–Liouville potentials, Appl. Math. Comput. 219 (2012), pp. 2960–2974] for computing Sturm–Liouville potentials from two spectra is discussed. In Acetoet al.(2012), a continuous approximation of the unknown potential belonging to a suitable function space of finite dimension is obtained by forming an associated set of nonlinear equations and solving these with a quasi-Newton approach. In our paper, convergence of the quasi-Newton approach is established and convergence of the estimate of the unknown potential, provided by the exact solution of the nonlinear equation, to the true potential is proved. To further investigate the properties of the BVM in Acetoet al.(2012), some other spaces of functions are introduced. Numerical examples confirm the theoretically predicted convergence properties and show the accuracy and stability of the BVM. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm for a simplified friction problem which is formulated as an elliptic variational inequality of the second kind. We approximate the simplified friction problem by a discrete system with the finite element method. Based on the use of the linearized technique and by constructing a particular function, we put forward the new algorithm to get the discrete solution. This algorithm is attractive due to its simple proof of convergence and easy implementation. A linear equation is solved in each iteration. Numerical results confirm that our algorithm is efficient and mesh independent. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography (DOT) and bioluminescence tomography (BLT) are different but complementary modalities in optical molecular imaging. The goal of DOT is to reconstruct optical parameters of a medium from surface measurements induced by external sources, whereas that of BLT is to reconstruct running a bioluminescent source distribution in the medium from surface measurements induced by internal bioluminescent sources. A pre-requisite for BLT reconstruction is knowledge on the distribution of optical parameters within the medium, which is the output of DOT. In this paper, we propose a mathematical model integrating BLT and DOT at the fundamental level; that is, performing the two types of reconstructions simultaneously instead of doing them sequentially. The model is introduced through minimizing the difference between predicted quantities and boundary measurements, as well as incorporating regularization terms. In practice, the optical parameters are assumed to be piecewise constants or piecewise smooth functions. Hence, we seek the optical parameters in the space of functions with bounded variation (BV). For the BV-regularized data-fitting functional and its discretized approximations, we demonstrate the existence of minima and show convergence of the minima of the discretized functionals to that of the non-discretized one. We also present numerical results to illustrate the strength of our proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we derive the piecewise linear system (PLS) associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical method for solving the first kind of elliptic variational inequality. We first use the fundamental solution as the basis function to approximate the solution of variational inequality, then we employ Uzawa's algorithm to determine the free boundary and the solution. Numerical examples are given to verify the efficiency of the method. [ABSTRACT FROM PUBLISHER]

In this paper, a linearly semi-implicit compact scheme is developed for the Burgers-Huxley equation. The equation is decomposed into two subproblems, i.e. a Burgers equation and a nonlinear ODE, by the operator splitting technique. The Burgers equation is solved by a linearly self-starting compact scheme which is fourth-order accurate in space and second-order accurate in time. The nonlinear ODE is discretized by a third-order semi-implicit Runge-Kutta method, which possesses good numerical stability with low computational cost. The numerical experiments show that the scheme provides the expected convergence order. Finally, several experiments are conducted to simulate the solutions of the Burgers-Huxley equation to validate our numerical method. [ABSTRACT FROM AUTHOR]