We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d − 1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that A ∩B = H and A ∪B = G and such that the complementary graphs A,B are both d-balls. The graph theoretic definitions are due to Evako: the unit sphere of a vertex x of a graph G = (V,E) is the graph generated by ...

1,3-butadiene, bd is produced from c4-cut by extractive distillation. the separation of 1,3-butadiene from c4-cut is not possible through the conventional distillation processes, because several mixtures have consisted of close boiling points constituents and make azeotrope. the basf extraction distillation process in bd unit of jam and amirkabir petrochemical company improves the relative vola...

Flow separation at water intake is the main cause of head loss and flow discharge reduction. As a result, study of shape and size of separation is very essential when designing an optimum water intake. Water intake is normally built with a 90 degree angle to the main channel flow direction. However, the flow structure in this type of water intake consists of large separation size along with ...

We present two complementary topic models to address the analysis of mixture data lying on manifolds. First, we propose a quantization method with an additional midlayer latent variable, which selects only data points that best preserve the manifold structure of the input data. In order to address the case of modeling all the in-between parts of that manifold using this reduced representation o...

A shift-invariant non-negative tensor factorisation algorithm for musical source separation is proposed which generalises previous work by allowing each source to have its own parameters rather a fixed set of parameters for all sources. This allows independent control of the number of allowable notes, number of harmonics and shifts in time for each source. This increased flexibility allows the ...

1,3-Butadiene, BD is produced from C4-cut by extractive distillation. The separation of 1,3-Butadiene from C4-cut is not possible through the conventional distillation processes, because several mixtures have consisted of close boiling points constituents and make azeotrope. The BASF extraction distillation process in BD unit of Jam and Amirkabir Petrochemical Company improves the relative vola...