Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.

Superior copper-mixed type. Barnharts big blue book, containing specimens ... type, borders, ornaments, rule, etc. manufactured by Barnhart brothers & Spindler ...

Mode of access: Internet.

Quality of life changes following peripheral blood stem cell transplantation and participation in a mixed-type, moderate-intensity, exercise program

The purpose of this investigation was to evaluate the impact of undertaking peripheral blood stem cell transplantation (PBST) on quality of life (QoL), and to determine the effect of participating in a mixed-type, moderate-intensity exercise program on QoL. It was also an objective to determine the relationship between peak aerobic capacity and QoL in PBST patients. QoL was assessed via the CARES questionnaire and peak aerobic capacity by a maximal graded treadmill test, pretransplant (PI), post transplant (PII) and following a 12-week intervention period (PIII). At PII, 12 patients were divided equally into a control or exercise intervention group. Undergoing a PBST was associated with a statistically but not clinically significant decline in QoL (P < 0.05). Following the intervention, exercising patients demonstrated an improved QoL when compared with pretransplant ratings (P < 0.01) and nonexercising transplant patients (P < 0.05). Moreover, peak aerobic capacity and QoL were correlated (P < 0.05). The findings demonstrated that exercise participation following oncology treatment is associated with a reduction in the number and severity of endorsed problems, which in turn leads to improvements in global, physical and psychosocial QoL. Furthermore, a relationship between fitness and QoL exists, with those experiencing higher levels of fitness also demonstrating higher QoL.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

A framework for mixed-type multi-outcome prediction with applications in healthcare

Health analysis often involves prediction of multiple outcomes of mixed-type. Existing work is restrictive to either a limited number or specific outcome types. We propose a framework for mixed-type multi-outcome prediction. Our proposed framework proposes a cumulative loss function composed of a specific loss function for each outcome type - as an example, least square (continuous outcome), hinge (binary outcome), poisson (count outcome) and exponential (non-negative outcome). Tomodel these outcomes jointly, we impose a commonality across the prediction parameters through a common matrix-Normal prior. The framework is formulated as iterative optimization problems and solved using an efficient Block coordinate descent method (BCD). We empirically demonstrate both scalability and convergence. We apply the proposed model to a synthetic dataset and then on two real-world cohorts: a Cancer cohort and an Acute Myocardial Infarction cohort collected over a two year period. We predict multiple emergency related outcomes - as example, future emergency presentations (binary), emergency admissions (count), emergency length-of-stay-days (non-negative) and emergency time-to-next-admission-day (non-negative). Weshow that the predictive performance of the proposed model is better than several state-of-the-art baselines.

Exercise and secondary lymphedema : safety, potential benefits, and research issues

Participating in regular physical activity is encouraged following breast cancer (BC) treatment, except for those who have subsequently developed lymphoedema. We designed a randomised controlled trial to investigate the effect of participating in a supervised, mixed-type, moderate-intensity exercise program among women with lymphoedema following breast cancer. Women <76 years who had completed BC treatment at least six months prior and subsequently developed unilateral, upper-limb lymphoedema were randomly allocated to an intervention (n=16) or control (n=16) group. The intervention group (IG) participated in 20 supervised group exercise sessions over 12 weeks, while the control group (CG) was instructed to continue habitual activities. Lymphoedema status was assessed by bioimpedance spectroscopy (impedance ratio between limbs) and perometry (volume difference between limbs). Mean baseline measures were similar for the IG (1.13+0.15 and 337+307ml, respectively) and CG (1.13+0.15 and 377+416ml, respectively) and no changes were observed over time. However, 2 women in the IG no longer had evidence of lymphoedema by study end. Average attendance was over 70% of supervised sessions, and there were no withdrawals. The results indicate that, at worst, exercise does not exacerbate secondary lymphoedema. Women with secondary lymphoedema should be encouraged to be physically active, optimising their physical and psychosocial recovery.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

Turbulence and Mixing in the Environment: Multi-Device Study in a Sub-tropical Estuary

In an estuary, mixing and dispersion result from a combination of large-scale advection and smallscale turbulence, which are complex to estimate. The predictions of scalar transport and mixing are often inferred and rarely accurate, due to inadequate understanding of the contributions of these difference scales to estuarine recirculation. A multi-device field study was conducted in a small sub-tropical estuary under neap tide conditions with near-zero fresh water discharge for about 48 hours. During the study, acoustic Doppler velocimeters (ADV) were sampled at high frequency (50 Hz), while an acoustic Doppler current profiler (ADCP) and global positioning system (GPS) tracked drifters were used to obtain some lower frequency spatial distribution of the flow parameters within the estuary. The velocity measurements were complemented with some continuous measurement of water depth, conductivity, temperature and some other physiochemical parameters. Thorough quality control was carried out by implementation of relevant error removal filters on the individual data set to intercept spurious data. A triple decomposition (TD) technique was introduced to access the contributions of tides, resonance and ‘true’ turbulence in the flow field. The time series of mean flow measurements for both the ADCP and drifter were consistent with those of the mean ADV data when sampled within a similar spatial domain. The tidal scale fluctuation of velocity and water level were used to examine the response of the estuary to tidal inertial current. The channel exhibited a mixed type wave with a typical phase-lag between 0.035π– 0.116π. A striking feature of the ADV velocity data was the slow fluctuations, which exhibited large amplitudes of up to 50% of the tidal amplitude, particularly in slack waters. Such slow fluctuations were simultaneously observed in a number of physiochemical properties of the channel. The ensuing turbulence field showed some degree of anisotropy. For all ADV units, the horizontal turbulence ratio ranged between 0.4 and 0.9, and decreased towards the bed, while the vertical turbulence ratio was on average unity at z = 0.32 m and approximately 0.5 for the upper ADV (z = 0.55 m). The result of the statistical analysis suggested that the ebb phase turbulence field was dominated by eddies that evolved from ejection type process, while that of the flood phase contained mixed eddies with significant amount related to sweep type process. Over 65% of the skewness values fell within the range expected of a finite Gaussian distribution and the bulk of the excess kurtosis values (over 70%) fell within the range of -0.5 and +2. The TD technique described herein allowed the characterisation of a broader temporal scale of fluctuations of the high frequency data sampled within the durations of a few tidal cycles. The study provides characterisation of the ranges of fluctuation required for an accurate modelling of shallow water dispersion and mixing in a sub-tropical estuary.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Regulation of the activity of mung bean (Phaseolus aureus) glutamine synthetase by amino acids and nucleotides

The activity of glutamine synthetase isolated from the germinated seedlings of Phaseolus aureus was regulated by feedback inhibition by alanine, glycine, histidine, AMP, and ADP. When glutamate was the varied substrate, alanine, histidine, and glycine were partial noncompetitive, competitive, and mixed-type inhibitors, respectively. The type of inhibition by these amino acids was confirmed by fractional inhibition analysis. The adenine nucleotides, AMP and ADP, completely inhibited the enzyme activity and were competitive with respect to ATP. Multiple inhibition analyses revealed the presence of separate and nonexclusive binding sites for the amino acids and mutually exclusive sites for adenine nucleotides. Cumulative inhibition was observed with these end products.

Modeling of seepage flow through layered solis

A two-dimensional finite difference model, which solves mixed type of Richards' equation, whose non-linearity is dealt with modified Picard's iteration and strongly implicit procedure to solve the resulting equations, is presented. Modeling of seepage flow through heterogeneous soils, which is common in the field is addressed in the present study. The present model can be applied to both unsaturated and saturated soils and can handle very dry initial condition and steep wetting fronts. The model is validated by comparing experimental results reported in the literature. Newness of this two dimensional model is its application on layered soils with transient seepage face development, which has not been reported in the literature. Application of the two dimensional model for studying unconfined drainage due to sudden drop of water table at seepage face in layered soils is demonstrated. In the present work different sizes of rectangular flow domain with different types of layering are chosen. Sensitivity of seepage height due to problem dimension of layered system is studied. The effect of aspect ratio on seepage face development in case of the flow through layered soil media is demonstrated. The model is also applied to random heterogeneous soils in which the randomness of the model parameters is generated using the turning band technique. The results are discussed in terms of phreatic surface and seepage height development and also flux across the seepage face. Such accurate modeling of seepage face development and quantification of flux moving across the seepage face becomes important while modeling transport problems in variably saturated media.