Iterated oscillation criteria for delay dynamic equations of first order

We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results

Behavior of solutions of a third-order dynamic equation on time scales

In this paper, we will establish some sufficient conditions which guarantee that every solution of the third-order nonlinear dynamic equatio

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

The progress of early phase bone healing using porous granules produced from calcium phosphate cement

<p>Abstract</p> <p>Objective</p> <p>Bone grafting is a vital component in many surgical procedures to facilitate the repair of bone defects or fusions. Autologous bone has been the gold standard to date in spite of associated donor-site morbidity and the limited amount of available donor bone. The aim of this study was to investigate the progress of bone regeneration and material degradation of calcium phosphate granules (CPG) produced from a calcium phosphate self-setting cement powder compared to the use of autologous bone grafting in the treatment of "critical size defects" on load-bearing long bones of minipigs.</p> <p>Methods</p> <p>A critical size defect in the tibial metaphysis of 16 mini-pigs was filled either with autologous cancellous graft or with micro- and macroporous carbonated, apatic calcium phosphate granules (CPG) produced from a calcium phosphate self-setting cement powder. After 6 weeks, the specimens were assessed by X-ray and histological evaluation. The amount of new bone formation was analysed histomorphometrically.</p> <p>Results</p> <p>The semi-quantitative analysis of the radiological results showed a complete osseous bridging of the defect in three cases for the autograft group. In the same group five animals showed a beginning, but still incomplete bridging of the defect, whereas in the CPG group just two animals developed this. All other animals of the CPG group showed only a still discontinuous new bone formation. Altogether, radiologically a better osseous bridging was observed in the autograft group compared to the CPG group.</p> <p>Histomorphometrical analysis after six weeks of healing revealed that the area of new bone was significantly greater in the autograft group concerning the central area of the defect zone (p < 0.001) as well as the cortical defect zone (p < 0.002). All defects showed new bone formation, but only in the autograft group defects regenerated entirely</p> <p>Conclusions</p> <p>Within the limits of the present study it could be demonstrated that autologous cancellous grafts lead to a significantly better bone regeneration compared to the application of calcium phosphate granules (CPG) produced from a calcium phosphate self-setting cement powder after 6 weeks. In the early phase of bone-healing, the sole application of CPG appears to be inferior to the autologous cancellous grafts in an <it>in vivo </it>critical size defect on load-bearing long bones of mini-pigs.</p

Tumour-derived PGD2 and NKp30-B7H6 engagement drives an immunosuppressive ILC2-MDSC axis.

Group 2 innate lymphoid cells (ILC2s) are involved in human diseases, such as allergy, atopic dermatitis and nasal polyposis, but their function in human cancer remains unclear. Here we show that, in acute promyelocytic leukaemia (APL), ILC2s are increased and hyper-activated through the interaction of CRTH2 and NKp30 with elevated tumour-derived PGD2 and B7H6, respectively. ILC2s, in turn, activate monocytic myeloid-derived suppressor cells (M-MDSCs) via IL-13 secretion. Upon treating APL with all-trans retinoic acid and achieving complete remission, the levels of PGD2, NKp30, ILC2s, IL-13 and M-MDSCs are restored. Similarly, disruption of this tumour immunosuppressive axis by specifically blocking PGD2, IL-13 and NKp30 partially restores ILC2 and M-MDSC levels and results in increased survival. Thus, using APL as a model, we uncover a tolerogenic pathway that may represent a relevant immunosuppressive, therapeutic targetable, mechanism operating in various human tumour types, as supported by our observations in prostate cancer.Group 2 innate lymphoid cells (ILC2s) modulate inflammatory and allergic responses, but their function in cancer immunity is still unclear. Here the authors show that, in acute promyelocytic leukaemia, tumour-activated ILC2s secrete IL-13 to induce myeloid-derived suppressor cells and support tumour growth

Sturm-Liouville operators with measure-valued coefficients

We give a comprehensive treatment of Sturm-Liouville operators with measure-valued coefficients including, a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical Sturm-Liouville operators, Lax operators arising in the treatment of the Camassa-Holm equation, Jacobi operators, and Sturm-Liouville operators on time scales as special cases.Comment: 58 page