Dependence of the pinning of fluxoids on grain boundaries on the direction of magnetic field

The angular dependence of surface pinning on the direction of the Lorentz force is calculated for special types of superconducting grains. Especially, sinusoidal and ellipsoidal grain shapes are considered. The filling of plane with close-packed sinusoidal shapes is evaluated and compared with those of ellipsoidal (or spherical) shapes. From the features of the calculated angular dependences of the pinning some conclusions are suggested for the experimental and structural study of superconducting Nb₃Sn tapes prepared by various methods.The detailed comparison of the results presented above and the explanation of the possibility of creating such grain shapes is the subject of the following work [2].     

On generalized Dedekind sums

In this paper we give a simple proof for the reciprocity formula for the generalized Dedekind sums and derive an explicit expression for these sums.     

Mössbauer spectroscopic study of the reductive decomposition of iron(III) complexes

Iron injections containing high spin iron(III) complexes may undergo a reductive decomposition during preparation or storage. This process was investigated by the Mössbauer spectroscopy of ice samples prepared by quick-freezing of the injection. The comparison of three model compounds and the correlation between the osmotic pressure of the solutions and their iron(II) concentration formed in the decomposition process and determined by Mössbauer measurements revealed the reason and mechanism of the decomposition.     

A fundamental identity in the theory of queues

Summary The main result of this paper is a fundamental identity for single-server queueing processes. By using the fundamental identity it is possible to find the mathematical laws describing the behavior of a queue in continuous time if we know the mathematical laws describing the behavior of the same queue in discrete time. The case of single-server queues with recurrent input and general service times is discussed in detail. This research was supported by the National Science Foundation under Contract No. GP-7847.     

Universal method for synthesis of artificial gel antibodies by the imprinting approach combined with a unique electrophoresis technique for detection of minute structural differences of proteins, viruses, and cells (bacteria): II. Gel antibodies against virus (Semliki Forest Virus)

Artificial and highly selective antibodies (in the form of gel granules) against proteins can easily be synthesized by a simple, cost-effective imprinting technique [Liao, J.-L. et al., Chromatographia 1996, 42, 259-262]. Using the same method for synthesis of gel antibodies against viruses in combination with analysis by free zone electrophoresis in a rotating narrow bore tube we have shown that artificial gel antibodies against Semliki Forest Virus (wild type) can sense the difference between this virus and a mutant, although they differ in their chemical composition only by three amino acids in one of the three proteins on the surface of the virus particle. The reason for this extremely high resolution is explained by the fact that we use three types of selectivity: (i) shape selectivity (created by the close fit between the antigen and its imprint in the gel), (ii) bond selectivity in the contact area between the antigen and its imprint in the gel antibody, and (iii) charge selectivity, originating from slightly different structures or/and conformations of the antigens.     

A Variational Approach to the Fredholm Alternative for the p-Laplacian near the First Eigenvalue

We are concerned with the existence of a weak solution to the degenerate quasi-linear Dirichlet boundary value problem

On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy

We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided and some particular cases are discussed.     

A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach

Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity‐based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one‐period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous‐time intensity‐based approaches. This paper first proposes a discrete‐time dynamic extension to the BET in order to incorporate the time‐dependent and time‐varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the ‘true’ default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of ‘true’ default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided.     

Precisely Controlled Delivery of Abaloparatide through Injectable Hydrogel to Promote Bone Regeneration

Side‐effects from allograft, limited bone stock, and site morbidity from autograft are the major challenges to traditional bone defect treatments. With the advance of tissue engineering, hydrogel injection therapy is introduced as an alternative treatment. Therapeutic drugs and growth factors can be carried by hydrogels and delivered to patients. Abaloparatide, as an analog of human recombinant parathyroid hormone protein (PTHrp) and an alternative to teriparatide, has been considered as a drug for treating postmenopausal osteoporosis since 2017. Since only limited cases of receiving abaloparatide with polymeric scaffolds have been reported, the effects of abaloparatide on pre‐osteoblast MC3T3‐E1 are investigated in this study. It is found that in vitro abaloparatide treatment can promote pre‐osteoblast MC3T3‐E1 cells’ viability, differentiation, and mineralization significantly. For the drug delivery system, 3D porous structure of the methacrylated gelatin (GelMA) hydrogel is found effective for prolonging the release of abaloparatide (more than 10 days). Therefore, injectable photo‐crosslinked GelMA hydrogel is used in this study to prolong the release of abaloparatide and to promote healing of defected bones in rats. Overall, data collected in this study show no contradiction and imply that Abaloparatide‐loaded GelMA hydrogel is effective in stimulating bone regeneration.