mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H;K-entry is the number of fixed points of the set G=K under the action of H is called the table of marks of G where H;K run through all elements in C(G). In this paper, we compute the table of marks and the markaracter table of groups of order pqr where p, q, r are prime numbers.

We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...

Fuzzy techniques may be used to represent uncertainty in both data and knowledge, and fuzzy inference systems (FISs) may be used to reason with such uncertain data and knowledge. In this paper, definitions are first provided for conventional type-1 fuzzy sets, more complex type-2 fuzzy sets and the recently introduced non-stationary fuzzy sets. Two medical applications in which such fuzzy sets ...

A Bh set (or Sidon set of order h) in an Abelian group G is any subset {b0, b1, . . . , bn} ⊂ G with the property that all the sums bi1 + · · ·+ bih are different up to the order of the summands. Let φ(h, n) denote the order of the smallest Abelian group containing a Bh set of cardinality n+1. It is shown that, as h → ∞ and n is kept fixed, φ(h, n) ∼ 1 n! δl(△) h n , where δl(△ ) is the lattice...

The type-1 OWA operator is a new aggregation operator that is used to directly aggregate fuzzy sets via an OWA mechanism. In this paper, an α-level type-1 OWA operator capable of aggregating the α-cuts of fuzzy sets is proposed. Based on the fuzzy set Representation Theorem, we indicate that a general type-1 OWA operator can be represented by its α-level type-1 OWA operators. This result is ver...

Let G be a countably infinite group and (X,μ) a standard non-atomic probability space. We denote by A(G,X, μ) the space of measure preserving actions of G on (X,μ) with the weak topology. If a,b ∈ A(G,X, μ), we say that a is weakly contained in b, in symbols a b, if a is in the closure of the set of isomorphic copies of b (i.e., it is in the closure of the orbit of b under the action of the aut...

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Motion-compensated prediction based on multiple previous or future frames can enhance the compression efficiency of video coding. Multi-frame prediction can be applied as an extension to P-Pictures, but also to B-Pictures in the form of multi-hypothesis prediction. We review recent advances, several of which have been embraced by the ITU-T Rec. H.263 and the emerging JVT/H.26L standard, jointly...

the general objective of this study was to develop a highly efficient, economical andintegrated technology for the removal of nitrogen compounds through denitrification via nitrite. toachieve this, a modified uasb reactor was designed, set-up and operated using chilean zeolite asmicrobial support. the results were compared to a conventional uasb reactor used as control. thevolume of each reacto...