Stability criteria for certain delay integral equations of Volterra type

AbstractIn this paper we study the asymptotic stability of the solution of the following delay integral equation of Volterra type: α ∫ox (a0 + a1 (x − s))y(s)ds + (1 − alpha; ∫ox(a0 + a1 (x − s))y(s − τ) ds, y(x) = ψ(x), −τ ⩽ x < 0, where τ > 0 is constant and 0 ⩽ α ⩽ 1. Stability criteria are provided for certain α's and the parameters a0, a1 and τ. The aim of this study is to understand the effect of the delay on the asymptotic stability of the solution of Volterra integral equations. As such the parameters α and 1 − α appear with the same kernel in both integrals of the equation. We also provide four algorithmic stability tests and include several examples and stability regions for certain values of the parameters α, a0, a1 and τ

Generic Oscillations for Delay Differential Equations

AbstractIn this article we study oscillation and nonoscillation of the solutions of linear delay differential equations. We define generic oscillation and generic nonoscillation as a topological assessment of the extent of oscillatory or nonoscillatory solutions of a delay differential equation. We provide sufficient conditions for both phenomena based on the roots of the characteristic equation and concrete conditions for some special cases

Advising to Support Meaning Making and Purpose: Helping Honors Students Focus on Priorities and Evaluate Opportunities Through Intention Setting

Section headings: What is an intention? The value of setting an intention Setting an intention with honors students Ron’s intention Katherine’s intention Final thoughts The experiences provided are just two examples of how, with the guidance of an advisor, honors students might formulate and incorporate an intention into their lives. This simple yet profound technique is a useful addition to the advisor’s toolbox; it presents the opportunity to help students examine their values, who they are, who they want to be, and how they want to live their lives. This critical reflection can result in a clear focus and systematic means for prioritizing actions in the future. Setting an intention is a deeply personal process and a valuable activity for college students. The unique and evolving role of the honors advisor provides the ideal situation to engage in this meaningful guided exercise with students. The intention-setting process can be boiled down to a few quick, but thought-provoking steps: 1. Reflect on prior experiences and consider personal aspirations and priorities. 2. Create a quiet space to draw the focus to the present and allow the mind to wander unassumingly and without criticism. 3. Brainstorm ideas, phrases, and words to help set an intention; be creative with the process. 4. Set an intention and find a useful way to commit it to memory. 5. Focus regularly on the intention for support and guidance. 6. Evaluate the significance of the intention on a recurring basis. When intention setting is incorporated into a larger discussion with students about their ambitions and definition of success, advisors create rich and useful pathways for understanding students’ educational, personal, and professional goals. Advising encounters and the powerful one-on-one exchange that they entail are an ideal environment to support meaning-making and living life with purpose

A Unique Complication Associated with Concurrent Chemoradiation for the Treatment of Locally Advanced Head and Neck Cancer

Background Concurrent chemoradiation is becoming an increasingly popular treatment for patients with locally advanced head and neck cancer. The full extent of treatment related complications has not been completely documented in the literature. Methods We present the case of a patient treated with definitive intensity modulated radiation therapy and concurrent carboplatin and fluorouracil for a locally advanced oral cavity and base of tongue cancer. Results The patient suffered acute grade 4 dermatitis and mucositis during treatment. One month after completion of treatment, the patient was found to have permanent adherence of the tongue to the buccal mucosa as a result of severe scar tissue formation. Conclusions As more patients undergo chemoradiation for the treatment of locally advanced head and neck cancer, the full extent of treatment related complications are being identified. To our knowledge, this is the first report of chemoradiation for head and neck cancer resulting in adherence of the tongue to the buccal mucosa

A Parsec-Scale Catalog of Molecular Clouds in the Solar Neighborhood Based on 3D Dust Mapping: Implications for the Mass-Size Relation

We dendrogram the Leike et al. 2020 3D dust map, leveraging its $\sim 1$ pc spatial resolution to produce a uniform catalog of molecular clouds in the solar neighborhood. Using accurate distances, we measure the properties of 65 clouds in true 3D space, eliminating much of the uncertainty in mass, size, and density. Clouds in the catalog contain a total of $1.1 \times 10^5 \; \rm M_{\odot}$, span distances of $116-440$ pc, and include a dozen well-studied clouds in the literature. In addition to deriving cloud properties in 3D volume density space, we create 2D dust extinction maps from the 3D data by projecting the 3D clouds onto a 2D "Sky" view. We measure the properties of the 2D clouds separately from those of the 3D clouds. Using the 2D and 3D derived results, we compare the scaling relation between the masses and sizes of clouds following Larson 1981. We find that our 2D projected mass-size relation, $M \propto r^{2.1}$, agrees with Larson's Third Relation, but our 3D derived properties lead to a scaling relation of about one order larger: $M \propto r^{2.9}$. Validating predictions from numerical simulations and analytic theory, our results indicate that the mass-size relation is sensitive to whether column or volume density is used to define clouds, since mass scales with area in 2D space ($M \propto r^{2}$) and with volume in 3D space ($M \propto r^{3}$). Our results imply a roughly constant column and volume density for molecular clouds, as would be expected for clouds where the lower density, larger volume-filling gas dominates the cloud mass budget.Comment: Submitted to Ap

Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices

We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model, and the properties of the solutions are analyzed. An expression for the current is obtained. Finally, Zener-tunneling in a two-band tight-binding model is considered. The present work gives the background and an extension of the theoretical framework underlying our recent Letter [J. Rotvig {\it et al.}, Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache

An investigation of intensity-modulated radiation therapy versus conventional two-dimensional and 3D-conformal radiation therapy for early stage larynx cancer

<p>Abstract</p> <p>Introduction</p> <p>Intensity modulated radiation therapy (IMRT) has been incorporated at several institutions for early stage laryngeal cancer (T1/T2N0M0), but its utility is controversial.</p> <p>Methods</p> <p>In three representative patients, multiple plans were generated: 1) Conventional 2D planning, with the posterior border placed at either the anterior aspect ("tight" plan) or the mid-vertebral body ("loose" plan), 2) 3D planning, utilizing both 1.0 and 0.5 cm margins for the planning target volume (PTV), and 3) IMRT planning, utilizing the same margins as the 3D plans. A dosimetric comparison was performed for the target volume, spinal cord, arytenoids, and carotid arteries. The prescription dose was 6300 cGy (225 cGy fractions), and the 3D and IMRT plans were normalized to this dose.</p> <p>Results</p> <p>For PTV margins of 1.0 cm and 0.5 cm, the D95 of the 2D tight/loose plans were 3781/5437 cGy and 5372/5869 cGy, respectively (IMRT/3D plans both 6300 cGy). With a PTV margin of 1.0 cm, the mean carotid artery dose was 2483/5671/5777/4049 cGy in the 2D tight, 2D loose, 3D, and IMRT plans, respectively. When the PTV was reduced to 0.5 cm, the the mean carotid artery dose was 2483/5671/6466/2577 cGy to the above four plans, respectively. The arytenoid doses were similar between the four plans, and spinal cord doses were well below tolerance.</p> <p>Conclusions</p> <p>IMRT provides a more ideal dose distribution compared to 2D treatment and 3D planning in regards to mean carotid dose. We therefore recommend IMRT in select cases when the treating physician is confident with the GTV.</p

Evidence-based Review on the Use of Proton Therapy in Lymphoma From the Particle Therapy Cooperative Group (PTCOG) Lymphoma Subcommittee.

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Proton Therapy for Breast Cancer:A Consensus Statement From the Particle Therapy Cooperative Group Breast Cancer Subcommittee

Radiation therapy plays an important role in the multidisciplinary management of breast cancer. Recent years have seen improvements in breast cancer survival and a greater appreciation of potential long-term morbidity associated with the dose and volume of irradiated organs. Proton therapy reduces the dose to nontarget structures while optimizing target coverage. However, there remain additional financial costs associated with proton therapy, despite reductions over time, and studies have yet to demonstrate that protons improve upon the treatment outcomes achieved with photon radiation therapy. There remains considerable heterogeneity in proton patient selection and techniques, and the rapid technological advances in the field have the potential to affect evidence evaluation, given the long latency period for breast cancer radiation therapy recurrence and late effects. In this consensus statement, we assess the data available to the radiation oncology community of proton therapy for breast cancer, provide expert consensus recommendations on indications and technique, and highlight ongoing trials' cost-effectiveness analyses and key areas for future research. (c) 2021 Elsevier Inc. All rights reserved