Critical regularity of nonlinearities in semilinear classical damped wave equations

In this paper we consider the Cauchy problem for the semilinear damped wave equation $u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$ where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$ is a modulus of continuity. Our goal is to obtain sharp conditions on $\mu$ to obtain a threshold between global (in time) existence of small data solutions (stability of the zerosolution) and blow-up behavior even of small data solutions.Comment: 14 page

Diagnosis of endometrial cancer complicated by morbid obesity—a case report

A 47 year old morbidly obesity nulligravid female presented to a local hospital with chest pain and shortness of breath, CT of the chest confirmed pulmonary embolism, and endometrial biopsy performed showed grade 1 endometrioid adenocarcinoma with squamous differentiation. CT scan performed demonstrated pelvic, retroperitoneal, inguinal and right axillary lymphadenopathy, and hepatomegaly with grossly unremarkable uterus and ovaries. Due to the burden of disease, axillary and inguinal lymph node biopsy was attempted, however due to depth of nodes, the tissue was not reached and biopsy efforts were abandoned. It required a great deal of discussion with the radiology department to decide which lesion would be least morbid to biopsy. After failed attempts at several methods, the gastroenterologist consulted felt the retroperitoneal lymphadenopathy adjacent to the duodenum was a possibility. The sample was sparse, but confirmed a metastatic adenocarcinoma and ruled out an inflammatory or granulomatous process. Ultimately, this unfortunate woman’s obesity caused her to have a worse outcome, not only due to medical comorbidities, but also with regards to delayed diagnosis and treatment and progression of disease. As the obesity epidemic worsens, this is likely to occur more commonly. It is important to realize the limitations of our consults as all aspects and fields of medicine are limited by morbid obesity

Development of a Fluxless Flip Chip Bonding Process for Optical Military Electronics

As military electronics tend to become lighter, smaller, thinner, and lower cost, the use of flip chip technology is becoming more common place to meet system requirements, yet survive environments. This paper explores the development of an optical flip chip application and details the selection/qualification of the substrate. The selected assembly consists of a procured 1x12 Vertical Cavity Surface Emitting Laser (VCSEL) die, having 80um diameter eutectic AuSn solder bumps at 250um pitch and flip chip bonded to a .006” thick 99.6% alumina substrate with .006” diameter thru holes and metallized with 500Å WTi, under minimum 2.0-3.0μm (80-120μ”) thin film deposited Au. An 8 run, 3 factor, 2 level Full Factorial Design of Experiments (DOE) was completed on procured detector arrays and procured ceramic substrates using the Suss Microtec FC150. The optimum settings for the peak temperature, peak time and final die z-height were selected using the ANOVA results and interaction plots. Additional studies were completed to qualify in-house produced substrates. An epoxy glob-top encapsulant was selected to dissipate stress on the flip chip solder joints and to enhance thermal shock performance

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

Complement activation induces dysregulation of angiogenic factors and causes fetal rejection and growth restriction

Immune mechanisms have been implicated in placental dysfunction in patients with recurrent miscarriages and intrauterine growth restriction (IUGR), but the mediators are undefined. Here we show that complement activation, particularly C5a, is a required intermediary event in the pathogenesis of placental and fetal injury in an antibody-independent mouse model of spontaneous miscarriage and IUGR, and that complement activation causes dysregulation of the angiogenic factors required for normal placental development. Pregnancies complicated by miscarriage or growth restriction were characterized by inflammatory infiltrates in placentas, functional deficiency of free vascular endothelial growth factor (VEGF), elevated levels of soluble VEGF receptor 1 (sVEGFR-1, also known as sFlt-1; a potent anti-angiogenic molecule), and defective placental development. Inhibition of complement activation in vivo blocked the increase in sVEGFR-1 and rescued pregnancies. In vitro stimulation of monocytes with products of the complement cascade directly triggered release of sVEGFR-1, which sequesters VEGF. These studies provide the first evidence linking the complement system to angiogenic factor imbalance associated with placental dysfunction, and identify a new effector of immune-triggered pregnancy complications