Báo cáo toán học: "Construction of Codes Identifying Sets of Vertices" docx

... the assumption of the case it follows that we can find a (2m − 5)-set partition P of the terms of D which has at least (m − 2) sets of cardinality 1, and consequently at most m − 3sets with cardinality ... most a − 2termsofD are all elements of H a , and, furthermore, that there exists a (2m − 2)-set partition P 1 of the terms of D which are elements of H a such that the sum...

Ngày tải lên: 07/08/2014, 13:21

... recovering sets R L and strongly cancellative sets C L on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, ... the other hand, the study of recovering sets is prompted by the previous work of Simonyi [9] on recovering pairs. A recovering pair (A, B) is an ordered pair of subsets A, B...

Ngày tải lên: 08/08/2014, 14:23

... separates all the sets of at most  vertices of G.The dedicated terminology [12] for such codes is (1, ≤ ) -identifying codes. ThesetsI(X)are said to be the identifying sets of the corresponding ... sets of at most  vertices of G,andifalltheI(X, C)’s are nonempty then we say that C covers the sets of at most  vertices of G.WesaythatC is a code identifying set...

Ngày tải lên: 07/08/2014, 08:22

... called the r -identifying set,oridentifying set,ofv and will be denoted by I(v). Two vertices which have different identifying sets are said to be r-separated,orseparated. The concept of identifying ... the same type of argument as in the proof of Proposition 2, that each vertex of the infinite graph belongs to e elements E i,j ∈E. Now, the proof is nearly the same as the previou...

Ngày tải lên: 07/08/2014, 06:22

... using the bracketing result [11, Thm. 1.15] instead of the result of Haussler.) An advantage of (1) is that the dependence of the inverse of the discrepancy on d is optimal. This was verified ... the cardinality of a minimal δ-bracketing cover of C d . Then n ∗ ∞ (ε, d) ≤  2 ε 2  ln N [ ] (C d , ε/2) + ln 2   , (2) see [8, Proof of Thm. 3.2]. Thus improved bounds of the b...

Ngày tải lên: 07/08/2014, 21:20

... (P2). Proof. Without loss of generality, let c = (0, 0). Recall Case 2 of the proof of Lemma 8. That is, p(c)  8 and, without loss of generality, equality implies I 2 (c) = {c}. Further- more, one of ...  Finally, we can finish the proof of Lemma 9 by way of the discharging method. (For a more ext ensive application of the discharging method on vertex identifying codes, se...

Ngày tải lên: 08/08/2014, 12:22

... damage. These findings highlight the importance of assay selection and of dissection of different cellular responses in in-vitro characterisation of nanostructures. Keywords: magnetic nanoparticle; ... applications of MNPs emerging, little is known of the adverse biological side effects due to their nanoscale size. Recently, the importance of such biological characterisati...

Ngày tải lên: 20/06/2014, 20:20

... the height of GaSb/In 0.53 Ga 0.47 As QDs. (a) The AFM image of GaSb/In 0.53 Ga 0.47 As QDs, (b) histogram of the height of GaSb/In 0.53 Ga 0.47 As QDs, and (c) the STEM image of GaSb/In 0.53 Ga 0.47 As ... dependence of the PL peak energies over the third root of the excitation density [20]. The inset of Figure 3b shows the linear dependence of the PL peak energies and...

Ngày tải lên: 20/06/2014, 20:20

... primitive cell, where all of the atoms are occupying the C 3V sites. According to the group theory, single crystalline ZnO has eight sets of optical phonon modes at Γ point of the Brillouin zone, ... well [31]. The XPS data of Zn2p and Mn2p further provide evidences for the incorporation of Mn 2+ ions into ZnO. To obtain a better understanding of the formation of Mn-do...

Ngày tải lên: 20/06/2014, 20:20

... mathematical 21 comparison of the rate of convergence. The first one was introduced by Berinde [27]. He used this idea to compare the rate of convergence of Picard and Mann iterations for a class of Zamfirescu ... method by using the con- cept of K-mapping for finding a common fixed point of a finite family of nonexpansive mappings and a solution of an equilibrium problem. Applic...

Ngày tải lên: 20/06/2014, 20:20