Couplings and Strong Approximations to Time-Dependent Empirical Processes Based on I.I.D. Fractional Brownian Motions

We define a time-dependent empirical process based on n i.i.d. fractional Brownian motions and establish Gaussian couplings and strong approximations to it by Gaussian processes. They lead to functional laws of the iterated logarithm for this process.     

Reversibly self-assembled pH-responsive PEG-p(CL-g-TMC) polymersomes

Polymersomes have gained much interest within the biomedical field as drug delivery systems due to their ability to transport and protect cargo from the harsh environment inside the body. For an improved drug efficacy, control over cargo release is however also an important factor to take into account. An often employed method is to incorporate pH sensitive groups in the vesicle membrane, which induce disassembly and content release when the particles have reached a target site in the body with the appropriate pH, such as the acidic microenvironment of tumor tissue or the endosome. In this paper, biodegradable poly(ethylene glycol)-poly(caprolactone-gradient-trimethylene carbonate)-based polymeric vesicles have been developed with disassembly features at mild acidic conditions. Modifying the polymer backbone with imidazole moieties results in vesicle disassembly upon protonation due to the lowered pH. Furthermore, upon increasing the pH efficient re-assembly into vesicles is observed due to the switchable amphiphilic nature of the polymer. When this re-assembly process is conducted in presence of cargo, enhanced encapsulation is achieved. Furthermore, the potency of the polymeric system for future biomedical applications such as adjuvant delivery is demonstrated.     

An Approximate Analytical Solution for Counter-Current Spontaneous Imbibition

An approximate analytical solution is provided for one-dimensional, counter- current, spontaneous imbibition of a wetting phase (water) into a semi-infinite porous medium. The solution is based on the assumption that a similarity solution exists for the displacement process. This assumption, in turn, rests on the assumption that the set of relative permeability and capillary pressures curves are unique functions of saturation and do not depend on the nature of the displacement. It further rests on the assumption that the saturation at the imbibition face does not vary with time. It is demonstrated that the solution is in agreement with results obtained from experiments and also numerical analyses of these experiments. The experiments utilize cylindrical samples with the radial surface and one end-face sealed, and with counter-current imbibition occurring at the open end-face. The stage of the experiment that is modeled by the present solution is the period before the imbibition front contacts the sealed end-face. An important finding of the present analysis is that the pressure upstream of the advancing invasion front is a constant. A second, improved solution is also presented; this solution is an iterative, series solution of an integral-differential equation. It converges to a stable solution in very few terms.     

Equivalent linearization for systems subjected to non-stationary random excitation

The method of eauivalent linearization is applied to the general problem of the response of non-linear discrete systems to non-stationary random excitation. Conditions for minimum equation difference are determined which do not depend explicitly on lime but only on the instantaneous statistics of the response process. Using the equivalent linear parameters, a deterministic non-linear ordinary differential equation for the covariance matrix is derived. An example is given of a damped Duffing oscillator subjected to modulated white noise.     

Stochastic vehicle mobility forecasts using the nato reference mobility model

The NATO Reference Mobility Model (NRMM) is a comprehensive means of predicting the speeds of military vehicles in on-road, off road, and gap-crossing contexts. The model has been in service for many years and helps user communities concerned with vehicle design, wargaming, and strategic planning. Recent developments in computer hardware and software are creating an opportunity for NRMM to serve a tactical role on the battlefield. Adaptation of NRMM to this role requires that its users come to grips with the collection of digital data to describe vehicle, terrain, and scenario data in a real-time environment. This paper discusses the performance of NRMM when selected inputs and algorithms contain random components. A developmental pathway is outlined that leads from current deterministic mobility forecasts to stochastic forecasts capable of suggesting the risks taken when speed predictions must be made in the presence of data and algorithm errors. Concepts that express measures of confidence for wide-area mobility forecasts when errors are known with small-area detail are described. Several numerical examples are given.     

Layer Communities in Multiplex Networks

Journal of Statistical Physics - Multiplex networks are a type of multilayer network in which entities are connected to each other via multiple types of connections. We propose a method, based on...     

Asking mathematical questions mathematically

It is proposed that the style and format of the questions used by lecturers and tutors profoundly influence students' conceptions of what mathematics is about and how it is conducted. By looking at reasons for asking questions, and becoming aware of different types of questions which mathematicians typically ask themselves, we can enrich students' experience of mathematics. Drawing on recent work by Watson and Mason stimulated by the ideas of Zygfryd Dyrszlag, the paper proposes that mathematical themes, powers, heuristics and activities generate a mathematical discourse which is not always represented in the questions students are asked, and that the real purpose of questions is to provoke students into construal, into constructing their own stories which constitute meaning and understanding, and which equip them for the future. The use of questions of whatever type depends on both scaffolding and fading their use with and in front of students, so that students internalize the questions into their own learning and doing of mathematics. The framework directed—prompted—spontaneous is proposed as an alternative to scaffolding—fading for informing interactions with students.     

A novel method for the detection of plasma jet boundaries by exploring DNA damage

The coupled-channel optical method (CCOM) is implemented in this work to study the scattering of electron on rubidium atom at 20 eV. In order to provide a realistic calculation, the continuum effect of the scattering system is accounted by incorporate an ab initio optical potential into the CCOM calculation. The differential cross sections (DCS), as well as the reduced Stokes parameters of 5p excitation are reported and compared to the available experimental and theoretical data.     

An efficient synthesis of highly functionalized chiral lactams

A new method was developed to synthesize highly functionalized lactams via a one pot reductive amination/lactam formation reaction. This methodology is amenable for parallel synthesis and was used to prepare a large number of lactam analogs in a library format with good ee (de) retention.