--      product series that have at least a product with analog synthesis and one with digital synthesis

SELECT  ProductSeries.serial_number
FROM ProductSeries
WHERE ProductSeries.series_id= ANY(SELECT ProductModel.part_of FROM ProductModel WHERE ProductModel.type_of_synthesis='Analog')
    AND ProductSeries.series_id= ANY(SELECT ProductModel.part_of FROM ProductModel WHERE ProductModel.type_of_synthesis='Digital')

--  rewrite

SELECT ProductSeries.serial_number
FROM ProductSeries
    inner join ProductModel on ProductModel.type_of_synthesis='Analog' and ProductModel.part_of=ProductSeries.series_id
    inner join ProductModel pm on pm.type_of_synthesis='Digital' and pm.part_of=ProductSeries.series_id
GROUP BY ProductSeries.serial_number
HAVING COUNT(ProductModel.model_id) > 0 and COUNT(pm.model_id) > 0