Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations

We consider nonnegative solutions of a parabolic equation in a cylinder D \timesI, where $D$ is a noncompact domain of a Riemannian manifold and $I =(0,T)$ with $0 < T \le \infty$ or $I=(-\infty,0)$. Under the assumption [SSP] (i.e., the constant function 1 is a semismall perturbation of the associated elliptic operator on $D$), we establish an integral representation theorem of nonnegative solutions: In the case $I =(0,T)$, any nonnegative solution is represented uniquely by an integral on $(D \times \{0 \}) \cup (\partial_M D \times [0,T))$, where $\partial_M D$ is the Martin boundary of $D$ for the elliptic operator; and in the case $I=(-\infty,0)$, any nonnegative solution is represented uniquely by the sum of an integral on $\partial_M D \times (-\infty,0)$ and a constant multiple of a particular solution. We also show that [SSP] implies the condition [SIU] (i.e., the associated heat kernel is semi-intrinsically ultracontractive).Comment: 35 page

On dynamical bit sequences

Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random variables, each taking the values 1 or 0 with respective probabilities p and 1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in two very different settings: (i) Where \ell is a constant; and (ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is described by the Kolmogorov capacitance of F for case (i) and Howroyd's 1/2-dimensional box-dimension profiles for case (ii). We also present sample-path consequences, and a connection to capacities that answers a question of Benjamini et. al. (2003)Comment: 25 pages. This a substantial revision of an earlier paper. The material has been reorganized, and Theorem 1.3 is ne

MXE: A package for simulating long-term diffusive mass transport phenomena in nanoscale systems

We present a package to simulate long-term diffusive mass transport in systems with atomic scale resolution. The implemented framework is based on a non-equilibrium statistical thermo-chemo-mechanical formulation of atomic systems where effective transport rates are computed using a kinematic diffusion law. Our implementation is built as an add-on to the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code, it is compatible with other LAMMPS’ functionalities, and shows a good parallel scalability and efficiency. In applications involving diffusive mass transport, this framework is able to simulate problems of technological interest for exceedingly large time scales using an atomistic description, which are not reachable with the state-of-the-art molecular dynamics techniques. Several examples, involving complex diffusive behavior in materials, are investigated with the framework. We found good qualitative and quantitative comparison with known theories and models, with Monte Carlo methods, as well as with experimental results. Thus, our implementation can be used as a tool to understand diffusive behavior in materials where experimental characterization is difficult to perform

The Effects of Exercise Interventions for Patients with Venous Lower Limb Ulcers: A Systematic Review

The Effects of Exercise Interventions for Patients with Venous Lower Limb Ulcers: A Systematic Review Student Researchers: Christian San Pedro, SPT Jordan Hoffman, SPT Sabrina Mendez, SPT Mentored by: Kristen Karnish, PT, MPH, DEd, GCS, CEEAA Background: Approximately 30 million Americans are affected by vascular disease with greater numbers world wide. Chronic wound care is costly, as seen by the 1.5 billion dollars Medicare spent treating wounds in 2014. Vascular disease can predispose individuals to lower limb ulcers, chronic wounds, necrosis, and amputation. In patients with chronic wounds, exercise has been hypothesized to decrease healing times by triggering cortisol release and increasing blood flow to the tissue. The purpose of this study was to evaluate the effects of exercise on wound healing, functional status and quality of life for patients with lower limb venous wounds. Methods: An article search was conducted between August 2020 and September 2020 and again in February 2021. Databases, PEDRO, Medline, and PubMed, were searched using the terms “Venous Ulcer” or “Venous Leg Ulcer” and “physical therapy” or “physiotherapy” or “rehabilitation” or “exercise” and “lower leg”. Articles were also obtained from forward search of included articles. Inclusion criteria included: peer reviewed articles, publication between 2015-2020, randomized controlled trials, and PEDro score ≥ 4/10. Nine articles were included based on the inclusion criteria. Articles addressed the effects of exercise on wound healing, functional outcomes, and quality of life. Results: Wound healing measures included healing rates, wound size, and PUSH scores. Wound healing rates and PUSH scores of the exercise groups showed significant improvement when compared to control groups, however ulcer size measurements between exercise and control groups were not significantly different. Functional outcome measures included: ankle ROM, strength, and gait outcome measures. Ankle ROM measurements between control and exercise groups were not significantly different overall with some outliers, while strength measurements between control and exercise groups were not significantly different. Gait measures between control and exercise groups were not significantly different at final assessment. Quality of life measures included pain scales and quality of life questionnaires. Quality of life questionnaires showed no significant differences and no trends between exercise and control groups, however pain scores showed significant improvement within intervention groups and significant difference when comparing exercise and control groups. Conclusions: Exercise is an effective adjunct intervention when treating patients with venous leg ulcers. Physical activity can aid in speeding up the healing process and can lead to better functional and quality of life outcomes. Even modest movement and activity was beneficial to aid in the rehabilitation and healing of those with venous leg ulcers, however further research is required to determine the most effective interventions to be provided by physical therapists.https://digitalcommons.misericordia.edu/research_posters2021/1009/thumbnail.jp

Correlacion entre el tiempo operativo de exodoncia de terceros molares inferiores y las clasificaciones de pell-gregory y winter, expresadas a través del índice de pederson

79 p.Se examinaron clínica y radiográficamente 120 terceros molares inferiores los cuales se clasificaron preoperatoriamente según Pell – Gregory, Winter y el índice de Pederson, los que fueron extraídos durante los meses de julio a octubre de 2008 en los pabellones de cirugía bucal de las Clínicas Odontológicas de la Universidad de Talca y en el Servicio de Cirugía Maxilofacial del Hospital Regional de Talca. El objetivo del estudio fue determinar la existencia de correlación entre el tiempo operatorio de exodoncia de estas piezas dentarias y las clasificaciones preoperatorias previamente nombradas, lo cual fue ampliamente demostrado, asociándose las clasificaciones de III, C, mesioangular y horizontal a un incremento en la duración de las exodoncias. El tiempo promedio fue de 15,68 minutos. La realización de osteotomía y odontosección aumentó significativamente el tiempo del acto quirúrgico. Se evidenció una diferencia significativa de tiempo quirúrgico entre la Universidad y el Hospital debido a las diferencias de dificultad vistas. Tanto la edad como el género no se asociaron a un aumento en el tiempo operatorio