In this paper, we introduce and investigate new concepts of L-weakly M-weakly demicompact operators. Let E be a Banach lattice. An operator T : ? is called demicompact, if for every norm bounded sequence (xn) in BE such that {xn Txn, n N} an compact subset E, have {xn, E. Additionally, disjoint ?xn ?Txn? 0, ?xn? 0. (resp. M-weakly) operators generalize known classes which are We also elaborate ...

and Applied Analysis 3 Lemma 2.5. Let {xn}n −1 be a positive solution of 1.1 and limn→∞Pn S. Then S lim supn→∞xn. Proof. Since Pn is a subsequence of xn, it follows that S ≤ lim sup n→∞ xn. 2.6 On the other hand, by xn 1 ≤ Pn for all n ≥ 1, we obtain lim sup n→∞ xn ≤ lim sup n→∞ Pn S. 2.7 The proof is complete. Remark 2.6. Let {xn}n −1 be a positive solution of 1.1 . By Lemma 2.2, we see that i...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

The substituted activator ions Eu(2+) in the β-Ca3(PO4)2-type structure, Ca9NaMg(PO4)7 compound, have been studied as emission centers, as well as structural probes. The crystal structure and crystallographic sites of Eu(2+) in Ca9NaMg(PO4)7 have been identified by Rietveld refinements, electron paramagnetic resonance (EPR) spectroscopy analysis and combined photoluminescence spectral analysis,...

One of the fundamental tasks Symbolic Computation is factorization polynomials into irreducible factors. The aim paper to produce new families polynomials, generalizing previous results in area. example our general result that for a near-separated polynomial, i.e., form F(x,y)=f1(x)f2(y)−f2(x)f1(y), then F(x,y)+r always any constant r different from zero. We also provide biggest known family HI...

Fluoride can be removed from wastewater by addition of calcite. However, fluoride is often found in complex mixtures where other contaminants can affect the removal process. Batch experiments were used to determine the impact of phosphate (PO4 3 ) on the removal of fluoride from solution by calcite. In the experiments, up to 2,000 mg/L F and 500 mg/L PO4 3 were used with 150 mm and 1.18 mm calc...