Discontinuous Term Research Articles

Analysis of anti-plane interface cracks in one-dimensional hexagonal quasicrystal coating

The displacement discontinuity method is extended to study the fracture behavior of interface cracks in one-dimensional hexagonal quasicrystal coating subjected to anti-plane loading. The Fredholm integral equation of the first kind is established in terms of displacement discontinuities. The fundamental solution for anti-plane displacement discontinuity is derived by the Fourier transform method. The singularity of stress near the crack front is analyzed, and Chebyshev polynomials of the second kind are numerically adopted to solve the integral equations. The displacement discontinuities across crack faces, the stress intensity factors, and the energy release rate are calculated from the coefficients of Chebyshev polynomials. In combination with numerical simulations, a comprehensive study of influencing factors on the fracture behavior is conducted.

P735 Comparative assessment of probiotics and standard therapies for mild to moderate ulcerative colitis: A systematic review and network meta-analysis

Abstract Background We performed a systematic review and network meta-analysis to compare probiotics to current therapies in the induction and maintenance of remission in ulcerative colitis (UC). Methods We systematically searched Medline, Embase, CENTRAL up to November 2018. We included randomised controlled trials (RCTs) in patients with mild to moderate UC that compared probiotics, sulfasalazine, mesalamine (low dose <2 g/day, standard dose ≥ 2 g/day), olsalazine, balsalazide, budesonide, budesonide MMX and beclomethasone either alone or in combination with topical therapy, to each other or placebo. We excluded trials where <50% of the population had extensive or left-sided colitis. Outcomes were remission (induction studies), relapse (maintenance studies) and discontinuation due to adverse events (tolerability). We conducted random-effects network meta-analysis and ranked treatments based on the surface under the cumulative ranking (SUCRA) probabilities. Results Forty-eight trials (probiotics 6 trials) of induction therapy and 30 trials (probiotics 6 trials) of maintenance therapy were included in the analysis. In studies with probiotics concomitant treatment, mainly mesalamine, were allowed. At induction, probiotics were not superior to placebo (OR 1.43; 95%CI 0.84–2.42) and they were inferior to combined oral and topical mesalamine therapy (OR 0.28; 95%CI 0.12–0.66) and combined mesalamine and beclomethasone therapy (OR 0.27; 95%CI 0.09–0.83). On SUCRA analysis, combination therapies (SUCRA 0.92 and 0.93) were ranked the highest followed by balsalazide (SUCRA 0.71), budesonide ΜΜΧ (SUCRA 0.68), standard dose mesalamine (SUCRA 0.52), beclomethasone (SUCRA 0.50), olsalazine (SUCRA 0.41), probiotics (SUCRA 0.29), low dose mesalamine (SUCRA 0.26) and sulfasalazine (SUCRA 0.23) in terms of inducing remission. Probiotics were well tolerated. At maintenance, probiotics (OR 0.35; 95%CI 0.19–0.62) and their combination with mesalamine (OR 0.38; 95%CI 0.15–0.99) had lower rate of relapse compared with placebo, but there were no differences when compared with other treatments. On SUCRA analysis, probiotics either alone or combined with mesalamine had comparable SUCRA values to standard dose mesalamine (SUCRA 0.59) and sulfasalazine (SUCRA 0.68). The combination of oral and rectal mesalamine was superior to placebo (OR 0.10; 95%CI 0.04–0.26) and all other treatments and it was ranked highest (SUCRA 0.99). Probiotics were ranked the best tolerated option in terms of discontinuation due to adverse events (SUCRA 0.80). Conclusion Probiotics are well tolerated but they are not effective in inducing remission in active UC. They may be effective when added to mesalamine therapy in preventing relapse of quiescent UC, but large, well-designed RCTs are needed.

A robust second order numerical method for a weakly coupled system of singularly perturbed reaction-diffusion problem with discontinuous source term

In this paper, a fitted mesh numerical method on Shishkin mesh is proposed to solve a weakly coupled system of two singularly perturbed reaction-diffusion equations containing equal diffusion parameters with discontinuous source terms. This method uses the standard centred finite difference scheme constructed on piecewise-uniform Shishkin mesh with the average of the source terms on either side of the point of discontinuity and then the problem is solved by an iterative procedure. An error analysis is carried out and the method ensures that the parameter-uniform convergence of almost the second order. Numerical results are provided to confirm the theoretical results and compares well with the existing results.

Kirchhoff-type differential inclusion problems involving the fractional Laplacian and strong damping

<p style='text-indent:20px;'>The aim of this paper is to investigate the existence of weak solutions for a Kirchhoff-type differential inclusion wave problem involving a discontinuous set-valued term, the fractional <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian and linear strong damping term. The existence of weak solutions is obtained by using a regularization method combined with the Galerkin method.</p>

A higher-order hybrid numerical scheme for singularly perturbed convection-diffusion problem with boundary and weak interior layers

In this paper, we study the numerical solutions of singularly perturbed convection-diffusion two-point BVP as well as one-dimensional parabolic convection-diffusion IBVP with discontinuous convection coefficient (positive throughout the domain) and source term. The analytical solutions of these kind of problems exhibit a boundary layer near x = 0 and a weak interior layer near x = ξ. We discretise the spatial domain by the piecewise-uniform Shishkin mesh and the temporal domain by a uniform mesh. To approximate the spatial derivatives, we apply the hybrid finite difference scheme. The implicit-Euler scheme is used for discretising the temporal derivative. For the time independent problem, we derive that the proposed hybrid scheme is e-uniformly convergent of almost second-order and for the time dependent problem, we also prove that the proposed scheme is e-uniformly convergent of almost second-order in space and first-order in time. To validate the theoretical estimates, some numerical results are presented.

A robust second order numerical method for a weakly coupled system of singularly perturbed reaction-diffusion problem with discontinuous source term

In this paper, a fitted mesh numerical method on Shishkin mesh is proposed to solve a weakly coupled system of two singularly perturbed reaction-diffusion equations containing equal diffusion parameters with discontinuous source terms. This method uses the standard centred finite difference scheme constructed on piecewise-uniform Shishkin mesh with the average of the source terms on either side of the point of discontinuity and then the problem is solved by an iterative procedure. An error analysis is carried out and the method ensures that the parameter-uniform convergence of almost the second order. Numerical results are provided to confirm the theoretical results and compares well with the existing results.

A higher-order hybrid numerical scheme for singularly perturbed convection-diffusion problem with boundary and weak interior layers

In this paper, we study the numerical solutions of singularly perturbed convection-diffusion two-point BVP as well as one-dimensional parabolic convection-diffusion IBVP with discontinuous convection coefficient (positive throughout the domain) and source term. The analytical solutions of these kind of problems exhibit a boundary layer near x = 0 and a weak interior layer near x = ξ. We discretise the spatial domain by the piecewise-uniform Shishkin mesh and the temporal domain by a uniform mesh. To approximate the spatial derivatives, we apply the hybrid finite difference scheme. The implicit-Euler scheme is used for discretising the temporal derivative. For the time independent problem, we derive that the proposed hybrid scheme is ε-uniformly convergent of almost second-order and for the time dependent problem, we also prove that the proposed scheme is ε-uniformly convergent of almost second-order in space and first-order in time. To validate the theoretical estimates, some numerical results are presented.

On the Discretization of Robust Exact Filtering Differentiators

The calculation of time derivatives has a state-space representation of the form of a perturbed linear system. This description enables the application of the so-called robust filtering differentiator, i.e. a non-linear state observer with extended state and homogeneous input injection terms. Therefore, given the practical importance of having an accurate discretization of such differentiator, this paper presents the design of two discrete-time implementation schemes. The first discrete-time realization is explicit, while the second one is implicit. The implicit allows reducing the numerical chattering phenomenon caused by the explicit discretization of discontinuous terms. Numerical comparisons between the presented scheme and an existing discrete-time representation show that the performance of the proposed explicit implementation scheme is similar to the most recent results from the literature. Finally, the proposed implicit discrete-time realization presents better accuracy, especially when considering large sampling periods.

Analysis of a Nonlinear Necrotic Tumor Model with Two Free Boundaries

In this paper we study a free boundary problem modeling the growth of necrotic tumor spheroids. The tumor under consideration has a necrotic core consisting of dead cells, and a proliferating shell consisting of living cells. The inner necrotic core boundary and the outer tumor surface are both free boundaries. The nutrient concentration and internal pressure satisfy two nonlinear reaction–diffusion equations, with discontinuous terms across the inner free boundary, respectively. In a general framework of functional approach, we first reduce the free boundary problem into a Cauchy problem of parabolic differential equation in Banach spaces, and then show asymptotic stability of the unique radially symmetric stationary solution.

A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction–convection–diffusion systems with two small parameters and discontinuous source terms

This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction–convection–diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.

Higher Order Sliding Mode Control Using Discontinuous Integral Action

In this article, we propose a novel family of higher order sliding mode (HOSM) controllers with discontinuous integral term for a class of single-input–single-output (SISO) nonlinear systems. They belong to a recently introduced class of controllers, named continuous HOSM since they are able to compensate exactly and in finite-time perturbations/uncertainties using a continuous control signal. They are obtained by introducing a discontinuous integral action at the input of the plant. Here, continuously differentiable Lyapunov functions are used to rigorously prove the stability of the closed-loop system. We also investigate an approximation of this strategy, where a continuous integral term replaces the discontinuous one. The robustness properties of the closed-loop controller with continuous and discontinuous integral term are studied.

Quintic B-Spline Technique for Numerical Treatment of Third Order Singular Perturbed Delay Differential Equation

In this paper, a class of third order singularly perturbed delay differential equation with large delay is considered for numerical treatment. The considered equation has discontinuous convection-diffusion coefficient and source term. A quintic trigonometric B-spline collocation technique is used for numerical simulation of the considered singularly perturbed delay differential equation by dividing the domain into the uniform mesh. Further, uniform convergence of the solution is discussed by using the concept of Hall error estimation and the method is found to be of first-order convergent. The existence of the solution is also established. Computation work is carried out to validate the theoretical results.

Cost-effectiveness and safety of palbociclib and everolimus for treating advanced and recurrent breast cancer.

This retrospective study compares the economic superiority of palbociclib versus everolimus for advanced and recurrent breast cancer. Furthermore, we investigated the safety and treatment continuity of palbociclib and everolimus regimens. Expected costs were calculated based on data from patients with advanced and recurrent breast cancer who were treated with palbociclib and everolimus. The progression-free survival (PFS) from the PALOMA-3 clinical trial and BOLERO-2 clinical trial was used to evaluate the therapeutic efficacy of the regimens. The cost-effectiveness ratio of each chemotherapy agent was calculated by dividing the expected cost by the progression-free survival (PFS). The cost-effectiveness ratio per month was JPY 391,551.3/PFS for palbociclib and JPY 488,690.5/PFS for everolimus (p=0.627). The incremental cost-effectiveness ratio per month of everolimus to palbociclib was JPY 100,133.7/PFS. For patients receiving everolimus, adverse drug reactions included stomatitis (77.3%), rash (59.1%) and leukopenia (59.1%). For patients receiving palbociclib, neutropenia (69.2%), leukopenia (69.2%) and anemia (30.8%) occurred. In terms of discontinuation owing to adverse events (AEs), pneumonitis, thrombocytopenia, edema, fatigue, and neutropenia were experienced in the everolimus group. The cost-effectiveness of everolimus and palbociclib are equivalent, but since the prevalence of AEs is high in patients receiving everolimus, its AE management is important.

Influence of Age on Treatment with Thrombopoietin Receptor Agonists in Patients with Immune Thrombocytopenia; A Retrospective Multicenter Study

Influence of Age on Treatment with Thrombopoietin Receptor Agonists in Patients with Immune Thrombocytopenia; A Retrospective Multicenter Study

Design and Experimental Validation of an Adaptive Sliding Mode Observer-Based Fault-Tolerant Control for Underwater Vehicles

Cost and other practically related reasons can mean that velocity sensors are not available on an underwater vehicle. For such cases, the results in this brief are developed on an observer-based fault-tolerant control for underwater vehicles in the presence of external disturbances and unknown thruster faults. An adaptive sliding mode observer is developed to achieve finite-time convergence where, in comparison to a high-gain-based design for the observer, a nonlinear feedback is constructed based on the position estimation error. Unlike alternatives, a discontinuity term in the developed fault tolerant controller is avoided, and the stability of the controlled dynamics is characterized using the Lyapunov theory. Finally, these new results are supported by both a simulation-based study and experimental verification.

Natural Oscillation Gait in Humanoid Biped Locomotion

Biped locomotion is complex to analyze in general. Most of the models in the literature for biped locomotion utilize hybrid dynamics. This makes the kinematics of the model simple to understand. However, it makes the model difficult to analyze in the presence of discontinuous terms in its differential equations. This article presents a continuous-time mathematical model for biped robots, modeling the discontinuities in impact with a nonlinear function. Natural oscillation is defined as a free response under damping compensation to achieve persistent oscillation. The phenomenon of natural oscillation was previously exploited in the linear dynamics of multi-segmental locomotor, and it is now extended to this continuous-time biped locomotion model with the contact force from the ground modeled as a nonlinear bump function. The idea of natural oscillation is preceded in this article by a complete framework on analysis and entrainment control. The research would ensure that these natural oscillations are responsible for forward locomotion of biped robots under certain conditions. The locomotion profile of the bipeds further validates the model that the velocity achieved through the natural oscillation is comparable to human jogging speeds when practical constraints are enforced.

Extremal bounded complete trajectories for nonautonomous reaction–diffusion equations with discontinuous forcing term

In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term of Heaviside type. Using this principle, we study the structure of the global attractor in both the autonomous and nonautonomous cases. In particular, in the last case we prove that the pullback attractor is confined between two special bounded complete trajectories, which play the role of nonautonomous equilibria.

Synchronization control for memristive high-order competitive neural networks with time-varying delay

This paper concerns the synchronization problem of memristive high-order competitive neural networks with time-varying delay. First, a novel control scheme with a linear term and a discontinuous term is proposed. Then, based on the Lyapunov stability theory, several criteria with algebraic form or matrix form are derived to ensure global exponential synchronization of the networks by adopting some inequality techniques. Finally, two numerical examples are presented to substantiate the effectiveness of the results.

Low Back Pain and Associated Factors among Primary School Teachers in Mekele City, North Ethiopia: A Cross-Sectional Study.

Background Low back pain (LBP) is the most prevalent musculoskeletal disorder among teachers. The pain, which is widely considered to be caused by occupational activities, has a significant impact on teachers' quality of life because it results in frequent sick leaves, functional impairment, and early retirement. It is also demanding in terms of treatment costs, individual suffering, and discontinuation of jobs. Therefore, this study assessed the magnitude of low back pain and associated factors among primary school teachers in Mekele City, north Ethiopia. Methods An institution-based cross-sectional study which included 611 public primary school teachers of Mekele City was conducted from March to April 2015. A multivariable logistic regression analysis was used to identify factors associated with low back pain. The adjusted odds ratio (AOR) with a 95% confidence interval (CI) was used to show the strength of the associations, and variables with a p value of less than 0.05 were considered statistically significant. Results In this study, the prevalence of low back pain was 74.8% (95% CI: 71.4-78.2). According to the multivariate analysis, the pain was associated with teachers' sleeping disturbance (AOR = 6.99; 95% CI: 2.20, 13.63), prolonged standing (AOR = 4.78; 95% CI: 3.75, 9.32), and irregular physical exercise (AOR = 1.46; 95% CI: 1.29, 5.10). Conclusion The study showed that the prevalence of low back pain was high. Sleeping disturbance, prolonged standing during sessions, and irregular physical activity were significantly associated with the problem. Therefore, addressing work-related and individual factors is essential for decreasing the burden.

Fundamental solutions and analysis of the interface crack for two-dimensional decagonal quasicrystal bimaterial via the displacement discontinuity method

The extended displacement discontinuity method is developed to analyze an interface line crack in a two-dimensional decagonal quasicrystal bimaterial. According to the general solutions and Fourier transform, fundamental solutions for phonon and phason displacement discontinuities and phonon and phason stresses are obtained. The delta function in the phonon and phason stresses is replaced by the Gaussian distribution function to eliminate the oscillatory singularity near the crack front. The expressions of phonon and phason stress intensity factors are given in terms of phonon and phason displacement discontinuities. The finite element analysis software COMSOL is used to validate the developed method.