LOS ANGELES, CALIFORNIA.- The new exhibition at the Los Angeles County Museum of Art, ''Central European Avant-Gardes: Exchange and Transformation, 1910-1930,'' looks at cross-fertilization of influences among painters, sculptors and designers in Germany, Hungary, Poland, Romania, the former Yugoslavia and what is now the Czech Republic during the evolution of modernism. As modernism was taking hold, the cities that fostered it were growing into cosmopolitan centers, and the show looks at exhibitions and performances that inspired cultural exchange.