Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.

Corrigendum for "Weierstrass Points with first Non-Gap four on a Double Covering of a Hyperelliptic Curve"

In the proof of Lemma 3.1 in [1] we need to show that we may take the two points p and q with p ≠ q such that p+q+(b-2)g21(C′)∼2(q1+… +qb-1) where q1,…,qb-1 are points of C′, but in the paper [1] we did not show that p ≠ q. Moreover, we hadn't been able to prove this using the method of our paper [1]. So we must add some more assumption to Lemma 3.1 and rewrite the statements of our paper after Lemma 3.1. The following is the correct version of Lemma 3.1 in [1] with its proof.

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26.

Spectral width and pulse duration tuning in Yb+ modelocked fiber laser with birefringent Lyot filter

A method of pulse duration and spectral width control in all-fiber Ytterbium modelocked laser with SWCNT is presented. It is shown that PM-fiber can also serve as a spectrally selective filter. © 2012 OSA.

Optically tuning of chromatic dispersion compensators

We present a new tuning method for chromatic dispersion compensators, which can be optically tunable. The dispersion compensators were made in Er/Yb co-doped fiber and were pumped with 980nm laser diodes. The tunable dispersion for a chirped grating and also a uniform-period grating was successfully demonstrated in the experiment.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

An automatic tuning strategy for local fuzzy logic ramp metering algorithm using Particle Swarm Optimization (PSO)

Freeway systems are becoming more congested each day. One contribution to freeway traffic congestion comprises platoons of on-ramp traffic merging into freeway mainlines. As a relatively low-cost countermeasure to the problem, ramp meters are being deployed in both directions of an 11-mile section of I-95 in Miami-Dade County, Florida. The local Fuzzy Logic (FL) ramp metering algorithm implemented in Seattle, Washington, has been selected for deployment. The FL ramp metering algorithm is powered by the Fuzzy Logic Controller (FLC). The FLC depends on a series of parameters that can significantly alter the behavior of the controller, thus affecting the performance of ramp meters. However, the most suitable values for these parameters are often difficult to determine, as they vary with current traffic conditions. Thus, for optimum performance, the parameter values must be fine-tuned. This research presents a new method of fine tuning the FLC parameters using Particle Swarm Optimization (PSO). PSO attempts to optimize several important parameters of the FLC. The objective function of the optimization model incorporates the METANET macroscopic traffic flow model to minimize delay time, subject to the constraints of reasonable ranges of ramp metering rates and FLC parameters. To further improve the performance, a short-term traffic forecasting module using a discrete Kalman filter was incorporated to predict the downstream freeway mainline occupancy. This helps to detect the presence of downstream bottlenecks. The CORSIM microscopic simulation model was selected as the platform to evaluate the performance of the proposed PSO tuning strategy. The ramp-metering algorithm incorporating the tuning strategy was implemented using CORSIM's run-time extension (RTE) and was tested on the aforementioned I-95 corridor. The performance of the FLC with PSO tuning was compared with the performance of the existing FLC without PSO tuning. The results show that the FLC with PSO tuning outperforms the existing FL metering, fixed-time metering, and existing conditions without metering in terms of total travel time savings, average speed, and system-wide throughput.

Coral Thermal Tolerance: Tuning Gene Expression to Resist Thermal Stress

The acclimatization capacity of corals is a critical consideration in the persistence of coral reefs under stresses imposed by global climate change. The stress history of corals plays a role in subsequent response to heat stress, but the transcriptomic changes associated with these plastic changes have not been previously explored. In order to identify host transcriptomic changes associated with acquired thermal tolerance in the scleractinian coralAcropora millepora, corals preconditioned to a sub-lethal temperature of 3°C below bleaching threshold temperature were compared to both non-preconditioned corals and untreated controls using a cDNA microarray platform. After eight days of hyperthermal challenge, conditions under which non-preconditioned corals bleached and preconditioned corals (thermal-tolerant) maintained Symbiodinium density, a clear differentiation in the transcriptional profiles was revealed among the condition examined. Among these changes, nine differentially expressed genes separated preconditioned corals from non-preconditioned corals, with 42 genes differentially expressed between control and preconditioned treatments, and 70 genes between non-preconditioned corals and controls. Differentially expressed genes included components of an apoptotic signaling cascade, which suggest the inhibition of apoptosis in preconditioned corals. Additionally, lectins and genes involved in response to oxidative stress were also detected. One dominant pattern was the apparent tuning of gene expression observed between preconditioned and non-preconditioned treatments; that is, differences in expression magnitude were more apparent than differences in the identity of genes differentially expressed. Our work revealed a transcriptomic signature underlying the tolerance associated with coral thermal history, and suggests that understanding the molecular mechanisms behind physiological acclimatization would be critical for the modeling of reefs in impending climate change scenarios.

Self-tuning algorithm for dsp-based motion control in cnc applications

This thesis describes the development of an adaptive control algorithm for Computerized Numerical Control (CNC) machines implemented in a multi-axis motion control board based on the TMS320C31 DSP chip. The adaptive process involves two stages: Plant Modeling and Inverse Control Application. The first stage builds a non-recursive model of the CNC system (plant) using the Least-Mean-Square (LMS) algorithm. The second stage consists of the definition of a recursive structure (the controller) that implements an inverse model of the plant by using the coefficients of the model in an algorithm called Forward-Time Calculation (FTC). In this way, when the inverse controller is implemented in series with the plant, it will pre-compensate for the modification that the original plant introduces in the input signal. The performance of this solution was verified at three different levels: Software simulation, implementation in a set of isolated motor-encoder pairs and implementation in a real CNC machine. The use of the adaptive inverse controller effectively improved the step response of the system in all three levels. In the simulation, an ideal response was obtained. In the motor-encoder test, the rise time was reduced by as much as 80%, without overshoot, in some cases. Even with the larger mass of the actual CNC machine, decrease of the rise time and elimination of the overshoot were obtained in most cases. These results lead to the conclusion that the adaptive inverse controller is a viable approach to position control in CNC machinery.

(Supporting Information) 14Cage plateau tuning of local Atlantic sediment cores

Modeling studies predict that changes in radiocarbon (14C) reservoir ages of surface waters during the last deglacial episode will reflect changes in both atmospheric 14C concentration and ocean circulation including the Atlantic Meridional Overturning Circulation. Tests of these models require the availability of accurate 14C reservoir ages in well-dated late Quaternary time series. We here test two models using plateau-tuned 14C time series in multiple well-placed sediment core age-depth sequences throughout the lower latitudes of the Atlantic Ocean. 14C age plateau tuning in glacial and deglacial sequences provides accurate calendar year ages that differ by as much as 500-2500 years from those based on assumed global reservoir ages around 400 years. This study demonstrates increases in local Atlantic surface reservoir ages of up to 1000 years during the Last Glacial Maximum, ages that reflect stronger trades off Benguela and summer winds off southern Brazil. By contrast, surface water reservoir ages remained close to zero in the Cariaco Basin in the southern Caribbean due to lagoon-style isolation and persistently strong atmospheric CO2 exchange. Later, during the early deglacial (16 ka) reservoir ages decreased to a minimum of 170-420 14C years throughout the South Atlantic, likely in response to the rapid rise in atmospheric pCO2 and Antarctic temperatures occurring then. Changes in magnitude and geographic distribution of 14C reservoir ages of peak glacial and deglacial surface waters deviate from the results of Franke et al. (2008) but are generally consistent with those of the more advanced ocean circulation model of Butzin et al. (2012).

Luoghi geometrici e curve celebri

Scopo di questo elaborato è affrontare lo studio di luoghi geometrici piani partendo dagli esempi più semplici che gli studenti incontrano nel loro percorso scolastico, per poi passare a studiare alcune curve celebri che sono definite come luoghi geometrici. Le curve nell'elaborato vengono disegnate con l'ausilio di Geogebra, con il quale sono state preparate delle animazioni da mostrare agli studenti. Di alcuni luoghi si forniscono dapprima le equazioni parametriche e successivamente, attraverso il teorema di eliminazione e il software Singular, viene ricavata l'equazione cartesiana.

Cyclostratigraphy and eccentricity tuning of the early Oligocene through early Miocene record from Walvis Ridge

Few astronomically calibrated high-resolution (<=5 kyr) climate records exist that span the Oligocene-Miocene time interval. Notably, available proxy records show responses varying in amplitude at frequencies related to astronomical forcing, and the main pacemakers of global change on astronomical time-scales remain debated. Here we present newly generated X-ray fluorescence core scanning and benthic foraminiferal stable oxygen and carbon isotope records from Ocean Drilling Program Site 1264 (Walvis Ridge, southeastern Atlantic Ocean). Complemented by data from nearby Site 1265, the Site 1264 benthic stable isotope records span a continuous ~13-Myr interval of the Oligo-Miocene (30.1-17.1 Ma) at high resolution (~3.0 kyr). Spectral analyses in the stratigraphic depth domain indicate that the largest amplitude variability of all proxy records is associated with periods of ~3.4 m and ~0.9 m, which correspond to 405- and ~110-kyr eccentricity, using a magnetobiostratigraphic age model. Maxima in CaCO3 content, d18O and d13C are interpreted to coincide with ~110 kyr eccentricity minima. The strong expression of these cycles in combination with the weakness of the precession- and obliquity-related signals allow construction of an astronomical age model that is solely based on tuning the CaCO3 content to the nominal (La2011_ecc3L) eccentricity solution. Very long-period eccentricity maxima (~2.4-Myr) are marked by recurrent episodes of high-amplitude ~110-kyr d18O cycles at Walvis Ridge, indicating greater sensitivity of the climate/cryosphere system to short eccentricity modulation of climatic precession. In contrast, the responses of the global (high-latitude) climate system, cryosphere, and carbon cycle to the 405-kyr cycle, as expressed in benthic d18O and especially d13C signals, are more pronounced during ~2.4-Myr minima. The relationship between the recurrent episodes of high-amplitude ~110-kyr d18O cycles and the ~1.2-Myr amplitude modulation of obliquity is not consistent through the Oligo-Miocene. Identification of these recurrent episodes at Walvis Ridge, and their pacing by the ~2.4-Myr eccentricity cycle, revises the current understanding of the main climate events of the Oligo-Miocene.