Parabolic equations with the second order Cauchy conditions on the boundary

The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs that allows some regularity is suggested and described explicitly in frequency domain. This class is everywhere dense in the space of square integrable functions.Comment: 7 page

On the number of solutions of a transcendental equation arising in the theory of gravitational lensing

The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can actually occur.Comment: 26 pages, 12 figure

Do You Hear Us? Amplifying Alternative Pathways for High School Pushouts Through Youth Participatory Action Research

The school-to-prison pipeline (STPP) metaphor encapsulates and describes a set of legislative policies and educational practices that systematically funnel African American, Indigenous, and Latinx students from the classroom into the juvenile and criminal justice system at disparate rates. An emerging solution to address high school pushout and the STPP has been to develop Alternative Education Campuses (AECs). However, there is a current gap in the research that amplifies the counter narratives of students currently enrolled at an AEC, through their own words, using Youth Participatory Action Research (YPAR). Studies conducted with students who have been labeled “high-risk” are especially lacking. Using a YPAR methodology, the goal of this study was to add to a growing body of literature on the STPP and AECs by contributing findings, analysis, and recommendations co-designed and constructed with voices from within the STPP. By using YPAR methods, the youth co-researchers (YCRs) collectively designed the research and maintained agency throughout each stage of the process. In total, two focus groups, eight interviews, and a photovoice project were completed. In this study, the YCRs and I demonstrated that African American, Indigenous, and Latinx students who have been labeled as “high risk” hold an innate ability to conduct educational research, critically analyze findings, and offer informed recommendations for bridging the opportunity gap and creating a more equitable education system through improving the programming at AECs. I also offer recommendations for decolonizing AECs and explore implications and future research

Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of convolution integrals over future time by integrals over past time. We found that all band-limited processes are predictable in this sense, as well as high-frequency processes with zero energy at low frequencies. It follows that a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.Comment: 10 page

Interface growth in two dimensions: A Loewner-equation approach

The problem of Laplacian growth in two dimensions is considered within the Loewner-equation framework. Initially the problem of fingered growth recently discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77, 041602 (2008)] is revisited and a new exact solution for a three-finger configuration is reported. Then a general class of growth models for an interface growing in the upper-half plane is introduced and the corresponding Loewner equation for the problem is derived. Several examples are given including interfaces with one or more tips as well as multiple growing interfaces. A generalization of our interface growth model in terms of ``Loewner domains,'' where the growth rule is specified by a time evolving measure, is briefly discussed.Comment: To appear in Physical Review

Regularity of a inverse problem for generic parabolic equations

The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary value inputs.Comment: 9 page

Interaction between hydrodynamics and seagrass canopy structure: Spatially explicit effects on ammonium uptake rates

The hypotheses that (1) different seagrass morphologies may facilitate different nutrient uptake rates under similar hydrodynamic forcing and (2) this effect on nutrient uptake rates is spatially explicit, with the highest uptake rates at edges of patches, where currents and turbulence are highest, were examined under unidirectional flow conditions.We thank Jos van Soelen, Bas Koutstaal, and Louie Haazen for invaluable technical assistance. In addition, we are grateful to Britta Gribsholt, Bart Veuger, Miguel Bernal, Juan Jose Vergara, and Alfredo Izquirdo for helpful discussion. In addition, we thank Josef D. Ackerman and the anonymous reviewers for comments that greatly improved the manuscript. This work and the first author were supported by an EU Marie Curie host fellowship for transfer of knowledge, MTKD-CT-2004-509254, and the Spanish national project EVAMARIA, CTM2005-00395/MAR. F.G.B. holds an EU Marie Curie individual fellowship, MEIF-CT-2005-515071. This is publication 4251 of the Netherlands Institute of Ecology (NIOO-KNAW)

Aerosol lidar observations of atmospheric mixing in Los Angeles: Climatology and implications for greenhouse gas observations

Atmospheric observations of greenhouse gases provide essential information on sources and sinks of these key atmospheric constituents. To quantify fluxes from atmospheric observations, representation of transport—especially vertical mixing—is a necessity and often a source of error. We report on remotely sensed profiles of vertical aerosol distribution taken over a 2 year period in Pasadena, California. Using an automated analysis system, we estimate daytime mixing layer depth, achieving high confidence in the afternoon maximum on 51% of days with profiles from a Sigma Space Mini Micropulse LiDAR (MiniMPL) and on 36% of days with a Vaisala CL51 ceilometer. We note that considering ceilometer data on a logarithmic scale, a standard method, introduces, an offset in mixing height retrievals. The mean afternoon maximum mixing height is 770 m Above Ground Level in summer and 670 m in winter, with significant day‐to‐day variance (within season σ = 220m≈30%). Taking advantage of the MiniMPL’s portability, we demonstrate the feasibility of measuring the detailed horizontal structure of the mixing layer by automobile. We compare our observations to planetary boundary layer (PBL) heights from sonde launches, North American regional reanalysis (NARR), and a custom Weather Research and Forecasting (WRF) model developed for greenhouse gas (GHG) monitoring in Los Angeles. NARR and WRF PBL heights at Pasadena are both systematically higher than measured, NARR by 2.5 times; these biases will cause proportional errors in GHG flux estimates using modeled transport. We discuss how sustained lidar observations can be used to reduce flux inversion error by selecting suitable analysis periods, calibrating models, or characterizing bias for correction in post processing.Key PointsAerosol lidar maps LA mixing depth in space (pilot mobile study) and time (2 years data)Automatic mixing depth retrieval system finds daily variability far exceeds seasonal differencePBL heights in models used for GHG monitoring show biases that will carry over to flux estimatesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134180/1/jgrd53200_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134180/2/jgrd53200.pd