Abstract:
We prove that the action of the semigroup generated by a $C^r$ generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.

Abstract:
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting "large" robustly transitive sets. We show that the $C^\infty$ closure of such open sets contains a variety of systems, including so-called a priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of the proof is a combination of studying minimal dynamics of symplectic iterated function systems and a new tool in Hamiltonian dynamics which we call symplectic blender.

Abstract:
We prove that any compact manifold without boundary admits a pair of diffeomorphisms that generates $C^1$ robustly minimal dynamics. We apply the results to the construction of blenders and robustly transitive skew product diffeomorphisms.

Abstract:
We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\'eordory's prime ends rotation number, similar to Poincar\'e's theory for circle homeomorphisms. In particular, we prove the converse of a classic result of Cartwright and Littlewood. This has a number of consequences for generic area preserving surface diffeomorphisms. For instance, we extend previous results of J. Mather on the boundary of invariant open sets for $C^r$-generic area preserving diffeomorphisms. Most results are proved in a general context, for homeomorphisms of arbitrary surfaces with a weak nonwandering-type hypothesis. This allows us to prove a conjecture of R. Walker about co-basin boundaries, and it also has applications in holomorphic dynamics.

Abstract:
The objective is to delineate postmodern learning and mentoring interrelation, elite-thinker-generating skills development, optimum mentor-staff-mentee interactions, mentors’ soci-economic security, and advanced mentorship evaluation strategies. Education is a foremost cause to find merits in life. Advancements in science and technology result from improved education. For creative science education to achieve optimums, it must be improved globally. Science and technology mentors must be continually educated and updated with artistic and creative mentorship skills. Effective education will optimize social interactions. Efforts should be made to optimize mentor-staff-mentee interactions in academia to effectively facilitate education and improve science quality. Effective mentorship requires making policies for effective management of mentors’ time and socio-economic life. Theoretical and applied aspects in different majors need to be educated in integrated manners to generate multiple perspectives. Focusing on a single science without appreciating the multiple nature of science will no longer advance scientific accomplishments in the postmodern era. Mentees should be directed to gain expertise in multiple sciences in ways an artist gains excellence in multiple. Harmony makes higher quality arts, science and life. A devastating failure would be producing follower graduates who despite having high scores in written tests are unable to mentor, design, direct, conduct, and conclude experiments that aim to sustain and advance science. Postmodern mentees are to be provided with opportunities to simultaneously act as mentor and mentee to appreciate their unique responsibilities. Improved education will improve social economics and human life quality worldwide.

Abstract:
In this study, Abderaz Formation at six stratigraphical sections, in east and center of the Kopeh-Dagh sedimentary basin, has been investigated, based on biserial planktonic foraminifera. Totally, 831 samples, with 3 meter distance, were gathered from a sequence with 2800 meter thickness. Also 4 genera and 17 species of biserial planktonic foraminifera have been identified and two biozones and two subzones recognized. Based on obtained data, the age of Early Turonian-Earliest Campanian for the Padeha, Abderaz village and Shorab sections, Midle Turonian-Earliest Campanian for type section, Early Turonian-Late Santonian for Qarehso section and Early Turonian-Earliest Santonian for Hajgelichkhan section were determined. The least amount of plank-tonic foraminifera was identified at Hajgelichkhan, while the maximum amount recognized at Qarehso section.

Abstract:
Most financial managers believe that there are different factors hindering decision-making about the capital structure of a company. This hindrance is so that, in some financial management literatures capital structure is called the mystery of capital. Financial managers widely believe that financial leverage enjoys a noticeable status in managerial decision making as well as management of the framework of balance sheet. The primary purpose of this research is to present applications of equity modules and to study effective factors on such models on Tehran stock exchange. The study covers data over a period of five years from 2001 to 2005. The study analyzes and tests relevant data to firm’s debt ratio and corporate size as effective factors on cost-of-equity. The preliminary findings indicate that contrary to the commonly held belief in financial management theorems, debts ratio has the least effect on cost-of-equity. Nevertheless, the study suggests that the variant of company’s size has a meaningful relationship with cost-of-equity. To calculate cost-of-equity, CAPM, Gordon and return ratio methods are used. Findings show that CAPM has more validity compared with other varieties. On the other hand, the results indicate that there is a 95-percent probability proving that liquidity has a significant negative effect on financial leverage.

Abstract:
In this article, the electrochemical synthesis and the characterization of Cu nanoparticles dispersed poly (o-aminophenol) (POAP) nanotube electrode is reported. The morphology of the electrode was characterized by scanning electron microscopy (SEM). Catalytic activity and stability for the oxidation of methanol were studied by using cyclic voltammetry and electrochemical impedance spectroscopy (EIS) were performed. The results show that poly (o-aminophenol) nanotubes electrodes significantly enhance the catalytic activity of copper nanoparticles for oxidation of methanol. The results obtained affirm that the dispersion of the copper particles is connected with catalytic response to a higher activity. The nanotubular morphology of poly (o- aminophenol) helps in the effective dispersion of Cu particles facilitating the easier access of methanol to the catalytic sites. The poly (o-aminophenol) nanotubes modified with copper nanoparticles cause a great increase in electroactivity and the electro-catalytic oxidation of methanol.

Abstract:
A dynamic coloring of a graph $G$ is a proper coloring such that for every vertex $v\in V(G)$ of degree at least 2, the neighbors of $v$ receive at least 2 colors. It was conjectured [B. Montgomery. {\em Dynamic coloring of graphs}. PhD thesis, West Virginia University, 2001.] that if $G$ is a $k$-regular graph, then $\chi_2(G)-\chi(G)\leq 2$. In this paper, we prove that if $G$ is a $k$-regular graph with $\chi(G)\geq 4$, then $\chi_2(G)\leq \chi(G)+\alpha(G^2)$. It confirms the conjecture for all regular graph $G$ with diameter at most 2 and $\chi(G)\geq 4$. In fact, it shows that $\chi_2(G)-\chi(G)\leq 1$ provided that $G$ has diameter at most 2 and $\chi(G)\geq 4$. Moreover, we show that for any $k$-regular graph $G$, $\chi_2(G)-\chi(G)\leq 6\ln k+2$. Also, we show that for any $n$ there exists a regular graph $G$ whose chromatic number is $n$ and $\chi_2(G)-\chi(G)\geq 1$. This result gives a negative answer to a conjecture of [A. Ahadi, S. Akbari, A. Dehghan, and M. Ghanbari. \newblock On the difference between chromatic number and dynamic chromatic number of graphs. \newblock {\em Discrete Math.}, In press].

Abstract:
A dynamic coloring of a graph $G$ is a proper coloring such that for every vertex $v\in V(G)$ of degree at least 2, the neighbors of $v$ receive at least 2 colors. In this paper we present some upper bounds for the dynamic chromatic number of graphs. In this regard, we shall show that there is a constant $c$ such that for every $k$-regular graph $G$, $\chi_d(G)\leq \chi(G)+ c\ln k +1$. Also, we introduce an upper bound for the dynamic list chromatic number of regular graphs.