An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

Optimisation of microstructured waveguides in z-cut LiNbO3 crystals

We present a practical approach to the numerical optimisation of the guiding properties of buried microstructured waveguides, which can be fabricated in a z-cut lithium niobate (LiNbO3) crystal by the method of direct femtosecond laser inscription. We demonstrate the possibility to extend the spectral range of low-loss operation of the waveguide into the mid-infrared region beyond 3um.

Microstructured waveguides in z-cut LiNbO3 by high-repetition rate direct femtosecond laser inscription

We report on the operational parameters that are required to fabricate buried, microstructured waveguides in a z-cut lithium niobate crystal by the method of direct femtosecond laser inscription using a highrepetition-rate, chirped-pulse oscillator system. Refractive index contrasts as high as −0.0127 have been achieved for individual modification tracks. The results pave the way for developing microstructured WGs with low-loss operation across a wide spectral range, extending into the mid-infrared region up to the end of the transparency range of the host material.

Optimisation of micro-structured waveguides in lithium niobate (z-cut)

We present an optimization procedure to improve the propagation properties of the depressed cladding, buried micro-structured waveguides formed in a z-cut lithium niobate (LN) crystal by high repetition rate femtosecond (fs) laser writing. It is shown that the propagation wavelength for which the confinement losses of ordinary (O) and extraordinary ordinary (E) polarizations are below 1 dB/cm can be optimized beyond 3 micro meter for hexagonal WG structures with seven rings of tracks.

On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions

We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.

Cut mowing and grazing effects with grey cattle on plant species composition in case of Pannon wet grasslands

Examined area can be found at Balaton Uplands National Park (Hungary). 5 sample areas were examined in Badacsonytördemic: 1: 32 hectare under-grazed pasture, 2: 38 hectare overgrazed pasture, 3: 34 hectare hayfield, 4: trampled area, 5: beaten track. Livestock population was 118 in the monitored pastures. Sampling was executed along five 52m long circular transects, within 5cm × 5cm interlocking quadrates. Based on the data we can state that the curve of the drinking area was the highest of speciesarea examinations however weed appeared because of degradation which provided more species. According to species-area examinations overgrazed areas were richer in species then other examined areas. Based on diversity data drinking area considered degraded, while meadow and overgrazed areas was considered as proper state. Diversity of meadow was larger, but dominance of economically useful species was smaller. The amount of less valuable species – Carex hirta – increased.

Time series of air chemistry measurements at Georg-von-Neumayer station, Dronning Maud Land, Antarctica in the years 1982 to 1991

The first Air Chemistry Observatory at the German Antarctic station Georg von Neumayer (GvN) was operated for 10 years from 1982 to 1991. The focus of the established observational programme was on characterizing the physical properties and chemical composition of the aerosol, as well as on monitoring the changing trace gas composition of the background atmosphere, especially concerning greenhouse gases. The observatory was designed by the Institut für Umweltphysik, University of Heidelberg (UHEIIUP). The experiments were installed inside the bivouac lodge, mounted on a sledge and put upon a snow hill to prevent snow accumulation during blizzards. All experiments were under daily control and daily performance protocols were documented. A ventilated stainless steel inlet stack (total height about 3-4 m above the snow surface) with a 50% aerodynamic cut-off diameter around 7-10 µm at wind velocities between 4-10 m/s supplied all experiments with ambient air. Contamination free sampling was realized by several means: (i) The Air Chemistry Observatory was situated in a clean air area about 1500 m south of GvN. Due to the fact that northern wind directions are very rare, contamination from the base can be excluded for most of the time. (ii) The power supply (20 kW) is provided by a cable from the main station, thus no fuel-driven generator is operated in the very vicinity. (iii) Contamination-free sampling is controlled by the permanently recorded wind velocity, wind direction and by condensation particle concentration. Contamination was indicated if one of the following criteria were given: Wind direction within a 330°-30° sector, wind velocity <2.2 m/s or >17.5 m/s, or condensation particle concentrations >2500/cm**3 during summer, >800/cm**3 during spring/autumn and >400/cm**3 during winter. If one or a definable combination of these criteria were given, high volume aerosol sampling and part of the trace gas sampling were interrupted. Starting at 1982 through 1991-01-14 surface ozone was measured with an electrochemical concentration cell (ECC). Surface ozone mixing ratio are given in ppbv = parts per 10**9 by volume. The averaging time corresponds to the given time intervals in the data sheet. The accuracy of the values are better than ±1 ppbv and the detection limit is around 1.0 ppbv. Aerosols were sampled on two Whatman 541 cellulose filters in series and analyzed by ion chromatography at the UHEI-IUP. Generally, the sampling period was seven days but could be up to two weeks on occasion. The air flow was around 100 m**3/h and typically 10000-20000 m**3 of ambient air was forced through the filters for one sample. Concentration values are given in nanogram (ng) per 1 m**3 air at standard pressure and temperature (1013 mbar, 273.16 K). Uncertainties of the values were approximately ±10% to ±15% for the main components MSA, chloride, nitrate, sulfate and sodium, and between ±20% and ±30% for the minor species bromide, ammonium, potassium, magnesium and calcium.

Women holding a "Cut back the Pentagon" sign at an ERA demonstration

Inscription: Verso: New York.

Planned Parenthood members attend pro-abortion demonstration in Cherry Hill, N.J.

General note: Title and date provided by Bettye Lane.

Pro-abortion march in front of hotel where anti-abortion conference is being held in Cherry Hill, N.J.

General note: Title and date provided by Bettye Lane.

In support of Anita Hill in NYC

General note: Title and date provided by Bettye Lane.

1959 Joyce Hill

1959-1960 Miss Lincoln

1963 Velois Hill

1963-1964 Miss Lincoln Homecoming Queen