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Title: On the spectrum problem for some digraphs of order 4 and size 6
Consider the multigraph obtained by adding a double edge to $K_4-e$. Now, let $D$ be a directed graph obtained by orientating the edges of that multigraph. We establish necessary and sufficient conditions on $n$ for the existence of a $(K^{*}_{n},D)$-design for four such orientations.  more » « less
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Journal of Combinatorial Mathematics and Combinatorial Computing (ISSN: 0835-3026)
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Medium: X
Sponsoring Org:
National Science Foundation
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    The wind stress curl (WSC) fields used for the MCL and ZCL calculations extend from 80W to 45W and 30N to 45N at the 1.25 by 1.25-degree resolution.  The MCL is defined as the maximum WSC values greater than zero within the domain per 1.25 degree longitude. As such, it is a function of longitude and is not a constant WSC value unlike the zero contour. High wind stress curl values that occurred near the coast were not included within this calculation. After MCL at the 1.25 resolution was obtained the line was smoothed with a gaussian smoothing and interpolated on to a 0.1 longitudinal resolution. The smoothed MCL lines at 0.1 degree resolution are provided in separate files for monthly and annual averages (2 files). Similarly, 2 other files (monthly and annual) are provided for the ZCL.    

    Like the MCL, the ZCL is a line derived from 1.25 degree longitude throughout the domain under the condition that it's the line of zero WSC. The ZCL is constant at 0 and does not vary spatially like the MCL. If there are more than one location of zero curl for a given longitude the first location south of the MCL is selected. Similar to the MCL, the ZCL was smoothed with a gaussian smoothing and interpolated on to a 0.1 longitudinal resolution.   

    The above files span the years from 1980 through 2019. So, the monthly files have 480 months starting January 1980, and the annual files have 40 years of data. The files are organized with each row being a new time step and each column being a different longitude. Therefore, the monthly MCL and ZCL files are each 480 x 351 for the 0.1 resolution data. Similarly, the annual files are 40 x 351 for the 0.1 degree resolution data.  

    Note that the monthly MCLs and ZCLs are obtained from the monthly wind-stress curl fields. The annual MCLs and ZCLs are obtained from the annual wind-stress curl fields.

    Since the monthly curl fields preserves more atmospheric mesoscales than the annual curl fields, the 12-month average of the monthly MCLs and ZCLs will not match with the annual MCLs and ZCLs derived from the annual curl field.  The annual MCLs and ZCLs provided here are obtained from the annual curl fields and representative metrics of the wind forcing on an annual time-scale. 

    Furthermore, the monthly Gulf Stream axis path (25 cm isoheight from Altimeter, reprocessed by Andres (2016) technique) from 1993 through 2019 have been made available here. A total of 324 monthly paths of the Gulf Stream are tabulated. In addition, the annual GS paths for these 27 years (1993-2019) of altimetry era have been put together for ease of use. The monthly Gulf Stream paths have been resampled and reprocessed for uniqueness at every 0.1 degree longitude from 75W to 50W and smoothed with a 100 km (10 point) running average via matlab. The uniqueness has been achieved by using Consolidator algorithm (D’Errico, 2023). 

    Each monthly or annual GS path has 251 points between 75W to 50W at 0.1 degree resolution.  

    Please contact for any queries. {"references": ["Andres, M., 2016. On the recent destabilization of the Gulf Stream path downstream of Cape Hatteras. Geophysical Research Letters, 43(18), 9836-9842.", "D'Errico, J., 2023. Consolidator ( 8354-consolidator), MATLAB Central File Exchange. Retrieved June 17, 2023.", "Gifford, Ian. H., 2023. The Synchronicity of the Gulf Stream Free Jet and the Wind Induced Cyclonic Vorticity Pool. MS Thesis, University of Massachusetts Dartmouth. 75pp.", "Gifford, Ian, H., Avijit Gangopadhyay, Magdalena Andres, Glen Gawarkiewicz, Hilde Oliver, Adrienne Silver, 2023. Wind Stress, Wind Stress Curl, and Upwelling Velocities in the Northwest Atlantic (80-45W, 30-45N) during 1980-2019,", "Kobayashi, S., Ota, Y., Harada, Y., Ebita, A., Moriya, M., Onoda, H., Onogi, K., Kamahori, H., Kobayashi, C., Endo, H. and Miyaoka, K., 2015. The JRA-55 reanalysis: General specifications and basic characteristics.\u202fJournal of the Meteorological Society of Japan. Ser. II,\u202f93(1), pp.5-48. Kobayashi, S., Ota, Y., Harada, Y., Ebita, A., Moriya, M., Onoda, H., Onogi, K., Kamahori, H., Kobayashi, C., Endo, H. and Miyaoka, K., 2015. The JRA-55 reanalysis: General specifications and basic characteristics.\u202fJournal of the Meteorological Society of Japan. Ser. II,\u202f93(1), pp.5-48."]} 
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