, LNCS 10388 1 13 2017 [2] J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, On the periods of parallel dynamical systems, Complexity 2017 (2017), Article ID 7209762, 6 pages. 10.1155/2017/7209762 . Aledo J.A. Diaz L.G. Martinez S. Valverde J.C. On the periods of parallel dynamical systems Complexity 2017 2017 Article ID 7209762 6 10.1155/2017/7209762 [3] J.A. Aledo, L.G. Diaz, S. Martinez, J.C. Valverde, On periods and equilibria of sequential dynamical systems, Inf. Sci. 409–410 (2017) 27–34. 10.1016/j.ins.2017.05.002 . Aledo J.A. Diaz L.G. Martinez S

# Search Results

### Juan A. Aledo, Luis G. Diaz, Silvia Martinez and Jose C. Valverde

### S.O. Pyskunov, Yu.V. Maksimyk and V.V. Valer

strains: ( Δ σ i j ) m = C i j k l ( { Δ ε k l } m − { ( Δ ε k l ) T } m ) . $$\begin{array}{} \displaystyle [{\left( {\Delta {\sigma _{ij}}} \right)_m} = {C_{ijkl}}\left( {{{\left\{ {\Delta {\mkern 1mu} {\varepsilon _{kl}}} \right\}}_m} - {{\left\{ {{{\left( {\Delta {\mkern 1mu} {\varepsilon _{kl}}} \right)}^T}} \right\}}_m}} \right). \end{array}$$ (10) Creep problem solution considering damage accumulation is being executed by means of step-by-step algorithm on the parameter of time. When starting each iteration n of a step m , stress values σ ij are

### Arturo Álvarez-Arenas, Juan Belmonte-Beitia and Gabriel F. Calvo

biological literature, there is a vast range of values for the diffusion and proliferation coefficients. To carry out the estimations, we resort to the following value for the proliferation ρ = 0.2 day −1 , which is in the range [0.01–0.5] day −1 , taken from [ 28 , 54 ] and D = 0.05 mm 2 /day (which is in the range [0.0004–0.1] mm 2 /day) [ 39 ]. Finally, we take α = 1/10 day −1 , L = 85 mm, x 0 = 10 mm, c = c min = 2 ( 1 − β ) , $\begin{array}{} c=c_{\text{min}}=2\sqrt{(1-\beta)}, \end{array} $ M = 0.3, b = 0.005, a = ( c − c 2 − 4 ( 1 − β − V

## Biological Letters

### The Journal of Adam Mickiewicz University, Faculty of Biology; Poznan Society for the Advancement of the Arts and Sciences

### Bo Zhao and Hualong Wu

structures (See Farahani et al. [ 1 ], Jamil et al. [ 2 ], Gao et al. [ 3 – 7 ] and Gao and Wang [ 8 – 10 ] for more details). The notation and terminology that were used but undefined in this paper can be found in [ 11 ]. Now, we present some important indices which will be computed in the next section. The Shultz polynomial is denoted as S c ( G , x ) = Σ { u , v } ⊆ V ( G ) ( d ( u ) + d ( v ) ) x d ( u , v ) . $$\begin{array}{} \displaystyle Sc(G,x) = \mathop \Sigma \limits_{\{ u,v\} \subseteq V(G)} (d(u) + d(v)){x^{d(u,v)}}. \end{array}$$ The additively

## Vestnik Zoologii

### The Journal of National Academy of Sciences of Ukraine, Schmalhauzen Institute of Zoology

### Muhammad Kamran Jamil, Mohammad Reza Farahani, Muhammad Imran and Mehar Ali Malik

: ∏ 1 ( G ) = ∏ ν ∈ V ( G ) d ( ν ) 2 ∏ 2 ( G ) = ∏ u ν ∈ E ( G ) d ( u ) ⋅ d ( ν ) $$\begin{array}{} \displaystyle \begin{array}{*{20}{c}} {{\prod _1}(G) = {\prod _{\nu \in V(G)}}d{{(\nu )}^2}} \hfill \\ {{\prod _2}(G) = {\prod _{u\nu \in E(G)}}d(u) \cdot d(\nu )} \hfill \\ \end{array} \end{array}$$ More history and results on Zagreb and multiplicative Zagreb indices can be found in [ 4 ]– [ 10 ]. Recently, Ghorbani and Hosseinzadeh [ 11 ] defined the eccentric versions of Zagreb indices. These are named as third and fourth Zagreb indices and defined

### O. Boyacioglu, A. Sulakvelidze, M. Sharma and I. Goktepe

ListShield™ bacteriophage cocktail and stored under MAP with ambient atmosphere (AA) or modified atmosphere (MA); a) storage at 4°C; b) storage at 10°C. The experiments were performed three times in duplicates. NP: no phage (control); P: phage treatment. Application of the ListShield™ phage cocktail to fresh-cut spinach leaves stored at 10°C for 1 d significantly (P < 0.05) lowered the populations of Lm- Nal R by 1.50 log CFU/cm 2 when compared to control-treated inoculated leaf pieces stored under AA ( Figure 3b ). When packaged under MA, the phage mixture

### Mohammad Reza Farahani, Muhammad Kamran Jamil and Muhammad Imran

-dimensional graph of the Titania nanotube, TiO 2 [ m , n ], is shown in Figure 1 , where m and n denotes the number of octagons in a column and the number of octagons in a row of the Titania nanotube. This graph has 2(3n+2)(m+1) vertices and 10 mn + 6 m + 8 n + 4 edges. Fig. 1 2-dimensional model to Titania nanotube TiO 2 [m,n] . By using the orthogonal cuts and cut method of the Titania nanotubes, we can determine all edge cuts of the Titania nanotubes. The edge cut C(e) is an orthogonal cut, such that the set of all edges f ∈ E

### J. Llibre

partial results about the center–focus problem for degenerate centers, see for instance [ 10 ]. The following result about the C ∞ first integrals of all centers is due to Mazzi and Sabatini [ 18 ]. Theorem 2 Any analytic differential system having a center has a local C ∞ first integral defined in its neighborhood. About the analytic integrals of all centers there is the next result prove in [ 15 ]. Theorem 3 Any analytic differential system having a center at the point p has a local analytic first integral defined in a punctured neighborhood of p