Sharif Digital Repository

The current study investigates the effect of polyacrylonitrile (PAN) addition on morphology and antifouling properties of poly(vinyl chloride) (PVC) asymmetric flat ultrafiltration (UF) membranes. The membranes are prepared via phase inversion method induced by immersion precipitation at different PVC/PAN blending ratio up to 40 wt% PAN. Also, membranes with blending ratio of PVC/ PAN:70/30, which showed the highest water flux and flux recovery ratio, were used for membrane preparation with 4 wt% of Polyethylene glycol (PEG) addition in four different molecular weight, 600 Da, 1,000 Da, 6,000 Da and 20,000 Da, which was used as pore former and hydrophilic polymeric additive. The performance... 

The main goal of this paper is to verify classical properties of morphological operators within the general model of translation invariant (TI) systems. In this model, TI operators are defined on the space of LG-fuzzy sets Φ i.e. Φ = {A: G → Ω ∪ {− ∞}} in which G is an abelian group and Ω is a complete lattice ordered group. A TI operator Y is an operator on Φ which is invariant under translation on G and Ω as groups. We consider the generalization of Minkowski addition (D on Φ and we emphasize that (Φ,⊛) is an involutive residuated topological monoid. We verify all properties of traditional (set-theoretic) morphological operators as well as classical representations (Matheron, 1967) for... 

Let d(σ)d(σ) stand for the defining number of the colouring σσ. In this paper we consider View the MathML sourcedmin=minγd(γ) and View the MathML sourcedmax=maxγd(γ) for the onto χχ-colourings γγ of the circular complete graph Kn,dKn,d. In this regard we obtain a lower bound for dmin(Kn,d)dmin(Kn,d) and we also prove that this parameter is asymptotically equal to χ-1χ-1. Also, we show that when χ⩾4χ⩾4 and s≠0s≠0 then dmax(Kχd-s,d)=χ+2s-3dmax(Kχd-s,d)=χ+2s-3, and, moreover, we prove an inequality relating this parameter to the circular chromatic number for any graph G  

In a previous paper we introduced a generalized model for translation invariant (TI) operators. In this model we considered the space, φ of all maps from an abelian group G to ω U {-∞}, called LG-fuzzy sets, where ω is a complete lattice-ordered group; and we defined TI operators on this space. Also, in that paper, we proved strong reconstruction theorem to show the consistency of this model. This theorem states that for an order-preserving TI operator Y one can explicitly compute Y(A), for any A, from a specific subset of φ called the base of Y. In this paper duality is considered in the same general framework, and in this regard, continuous TI operators are studied. This kind of operators... 

We consider translation invariant (TI) operators on Φ, the set of maps from an abelian group G to Ω ∪ {−∞} , called LG-fuzzy sets, where 0 is a complete lattice ordered group. By defining Minkowski and morphological operations on Φ and considering order preserving operators, we prove a reconstruction theorem. This theorem, which is called the Strong Reconstruction Theorem (SRT), is similar to the Convolution Theorem in the theory of linear and shift invariant systems and states that for an order preserving TI operator Y one can explicitly compute Y ( A ), for any A , from a specific subset of Φ called the base of Y . The introduced framework is a general model for the theory of translation... 

The basic goal of this article is to present an abstract system-theoretic approach to morphological filtering and the theory of translation invariant systems which is mainly based on residuated semigroups. Some new results as well as a number of basic questions are also introduced  

Let G be a simple undirected uniquely vertex k-colorable graph, or a k-UCG for short. M. Truszczyński [Some results on uniquely colorable graphs, in Finite and Infinite Sets, North-Holland, Amsterdam, 1984, pp. 733--748] introduced $e^{^{*}}(G)=|V(G)|(k-1)-{k \choose 2}$ as the minimum number of edges for a k-UCG and S. J. Xu [J. Combin. Theory Ser. B, 50 (1990), pp. 319--320] conjectured that any minimal k-UCG contains a Kk as a subgraph. In this paper, first we introduce a technique called forcing. Then by applying this technique in conjunction with a feedback structure we construct a k-UCG with clique number k-t, for each $t \geq 1$ and each k, when k is large enough. This also... 

In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs