Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Describing the progression from Chlamydia trachomatis and Neisseria gonorrhoeae to pelvic inflammatory disease: systematic review of mathematical modeling studies

Chlamydia screening is recommended to prevent pelvic inflammatory disease (PID). A systematic review was conducted to determine how the natural history of Chlamydia trachomatis or Neisseria gonorrhoeae infection and progression to PID have been described in mathematical modeling studies.

[Overview of helminth problems in domestic ruminants in Switzerland]

Potent anthelmintics were introduced into the Swiss market several decades ago. Despite this, gastrointestinal nematodes (GIN), lungworms and the large liver fluke (Fasciola hepatica) can successfully inhabit Swiss ruminant farms. This is mainly due to a high reproductive capacity as well as very efficient survival strategies. In addition some species readily develop anthelmintic resistance. GIN-infections in young cattle are under comparatively good control. However, prophylactic measures are compromised where adult stock is also affected due to incomplete development of immune protection. Under these circumstances control measures must include all age groups. This results in fewer helminths in refugia thus may accelerate the development of anthelmintic resistance. This review aims to present a synopsis of the significance of the major helminth infections obtained on pasture by large and small ruminants in Switzerland. Currently available strategies for strategic helminth control are summarized and an outlook is given on new developments which might expand the spectrum of control measures relevant for veterinary practice in the future.

Overview of dermatologic problems following liver transplantation

Liver transplantation recipients, like other solid organ transplantation recipients, have an increased risk of dermatologic problems due to their long-term immunosuppression and benefit from pre-and post-transplantation screenings, and management by a dermatologist and dermatologic care should be integrated into the comprehensive, multidisciplinary care of liver transplantation recipients [1,2]. Cutaneous findings include aesthetic alterations, infections, precancerous lesions, and malignancies. The severity of skin alterations ranges from benign, unpleasant changes to life-threatening conditions [3-5]. In addition to skin cancer diagnosis and management, visits with a dermatologist serve to educate and improve the patient's sun-protection behavior. Among all solid organ transplantations, liver transplantation requires the least amount of immunosuppression, sometimes even permitting its complete cessation [6]. As a result, patients who have undergone liver transplantation tend to have fewer dermatologic complications compared with other solid organ transplantation recipients [7]. However, due to the large volume of the liver, patients undergoing liver transplantation receive more donor lymphocytes than kidney, heart, or lung transplantation recipients. Because of the immunosuppression, the transplanted lymphocytes proliferate and rarely trigger graft-versus-host-disease [8,9]. This topic will provide an overview of dermatologic disorders that may be seen following liver transplantation. A detailed discussion of skin cancer following solid organ transplantation and the general management of patients following liver transplantation are discussed separately. (See "Development of malignancy following solid organ transplantation" and "Management of skin cancer in solid organ transplant recipients" and "Long-term management of adult liver transplant recipients".)

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.