let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is de ned. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

The relative homotopy theory of modules, including the (module) homotopy exact sequence, was developed by Peter Hilton (1965). Our thrust is to produce an alternative proof of the existence of the injective homotopy exact sequence with no reference to elements of sets, so that one can define the necessary homotopy concepts in arbitrary abelian categories with enough injectives and projectives, ...

1. Exact couples and spectral sequences 2 1.1. Spectral sequences 2 1.2. Exact couples 2 1.3. The spectral sequence associated to an exact couple 3 1.4. Example: the spectral sequence of a filtered space 3 References 4 2. Pages of the spectral sequence 4 2.1. Iterated subquotients 4 2.2. Formula for the rth page 5 2.3. Filtered spaces 6 3. Convergence 6 3.1. Simplest case: first quadrant spectr...

We show that for each aspherical compact complex surface X whose fundamental group π fits into a short exact sequence 1 → K → π → π1(S) → 1 where S is a compact hyperbolic Riemann surface and the group K is finitelypresentable, there is a complex structure on S and a nonsingular holomorphic fibration f : X → S which induces the above short exact sequence. In particular, the fundamental groups o...

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the com-plexity of the above model and uncertainty involved in real-world scheduling probl...

1. Local coefficient systems 2 1.1. The fundamental groupoid 2 1.2. Coefficient systems 3 1.3. Path connected based spaces 4 1.4. Singular chains with local coefficients 4 1.5. Homology with local coefficients 5 1.6. Universal covers 7 2. Exact couples and spectral sequences 9 2.1. Spectral sequences 9 2.2. Exact couples 9 2.3. The spectral sequence associated to an exact couple 10 2.4. Example...

In this study, a new numerical method is introduced to obtain the exact shape of output pulse in the chalcogenide fiber Bragg grating (FBG). A Gaussian pulse shape with 173 ps width is used as an input pulse for lunching to a 6.6 mm nonlinear FBG. Because of bistable and hysteresis nature of nonlinear FBG the time sequence of each portion of pulse is affected the shape of output pulse. So we di...

Computing the edit distance between two genomes is a basic problem in the study of genome evolution. The double-cut-and-join (DCJ) model has formed the basis for most algorithmic research on rearrangements over the last few years. The edit distance under the DCJ model can be computed in linear time for genomes without duplicate genes, while the problem becomes NP-hard in the presence of duplica...