In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

Let q be a power of a prime p. Matrices over Fq in which every subset of basis size of the columns are independent, are of interest in coding theory, matroid theory, and projective geometry. For any positive integer m ≤ p and bijection σ : N≤q−1 ∪ {0} → Fq, we show that the m× (q + 1) matrix Hq,m, with {Uq}i,j = 

The development of a reliable power filter is essential for meeting the need high-quality power. Current and voltage harmonics are major contributor to poor quality must be eliminated. Shunt active filters (SAPFs) can installed reduce negative effects harmonics. Fuzzy logic proportional integral (PI) controllers excel at regulating DC link in shunt (SAPFs). This research assessed how well Parti...

Polyethersulfone (PES)-based anion exchange blend membranes were prepared from quaternized-PES (Q-PES) and N-Methyl-2-pyrrolidone (NMP) casting solutions with water as coagulant via non-solvent induced phase inversion. The compatibility of the blend system was investigated through thermodynamic studies while membrane formation was determined using the cloud point techni...

Let ZF denote the Zermelo-Fraenkel set theory and ZFI the theory obtained from it by the addition of an axiom which asserts the existence of at least one inaccessible number. If ZF is consistent then ZFI contains number-theoretic theorems which are not theorems of ZF, e.g. the arithmetical sentence which asserts the consistency of ZF—Con(ZF). Mostowski [4] introduced a sentence of the theory of...

Let p > q and let G be the group U(p, q) or Spin0(p, q). Let P = LN be the maximal parabolic subgroup of G with Levi subgroup L ∼=M × U where (M,U) = { (GLq(C),U(p− q)) if G = U(p, q) (GLq (R),Spin(p− q)) if G = Spin0(p, q). Let χ be a 1 dimensional character of M and τ an irreducible representation of U with highest weight μ. Let πχ,μ be the representation of P which is trivial on N and πχ,μ|L...