lossless

Suppose the relation R( K, L, M, N, P) , and the functional dependencies that hold on R are: - L -> P - MP -> K - KM -> P - LM -> N Suppose we decompose it into 3 relations as follows: - R1(K, L, M) - R2(L, M, N) - R3(K, M, P) How can we tell whether this decomposition is lossless? I used this example R1 ∩ R2 = {L, M}, R2 ∩ R3 = {M}, R1 ∩ R3 = {K,M} we use functional dependencies, and this is not lossless in my opinion, but a little bit confused. It helps if we demystify the concept of lossless decomposition a bit: it really just means that joining R1, R2 and R3 should yield the original R. Do

Is there a Java library for rotating JPEG files in increments of 90 degrees, without incurring image degradation? I found this: http://mediachest.sourceforge.net/mediautil/ API: http://mediachest.sourceforge.net/mediautil/javadocs/mediautil/image/jpeg/LLJTran.html Building on Henry's answer, here's an example of how to use MediaUtil to perform lossless JPEG rotation based on the EXIF data: try { // Read image EXIF data LLJTran llj = new LLJTran(imageFile); llj.read(LLJTran.READ_INFO, true); AbstractImageInfo<?> imageInfo = llj.getImageInfo(); if (!(imageInfo instanceof Exif)) throw new