Abstract:
In this paper we verify a conjecture by Kozlov (Discrete Comput Geom 18 (1997) 421--431), which describes the convex hull of the set of face vectors of $r$-colorable complexes on $n$ vertices. As part of the proof we derive a generalization of Tur\'{a}n's graph theorem.

Abstract:
The clique vector $\mathfrak{c}(G)$ of a graph $G$ is the sequence $(c_1, c_2, \ldots,c_d)$ in $\mathbb{N}^d$, where $c_i$ is the number of cliques in $G$ with $i$ vertices and $d$ is the largest cardinality of a clique in $G$. In this note, we use tools from commutative algebra to characterize all possible clique vectors of $k$-connected chordal graphs.

Abstract:
Herzog and Takayama constructed explicit resolutions for the class of so called ideals with a regular linear quotient. This class contains all matroidal and stable ideals. The resolutions of matroidal and stable ideals are known to be cellular. In this note we show that the Herzog--Takayama resolution is also cellular.

Abstract:
Let $\k$ be a field and let $A$ be a standard $\mathbb{N}$-graded $\k$-algebra. Using numerical information of some invariants in the primary decomposition of $0$ in $A$, namely the so called dimension filtration, we associate a bivariate polynomial $\BW(A;t,w)$, that we call the Bj\"{o}rner--Wachs polynomial, to $A$. It is shown that the Bj\"{o}rner--Wachs polynomial is an algebraic counterpart of the combinatorially defined $h$-triangle of finite simplicial complexes introduced by Bj\"{o}rner \& Wachs. We provide a characterisation of sequentially Cohen--Macaulay algebras in terms of the effect of the reverse lexicographic generic initial ideal on the Bj\"{o}rner--Wachs polynomial. More precisely, we show that a graded algebra is sequentially Cohen--Macaulay if and only if it has a stable Bj\"{o}rner--Wachs polynomial under passing to the reverse lexicographic generic initial ideal. We conclude by discussing connections with the Hilbert series of local cohomology modules.

Abstract:
In this note we show that every discrete polymatroid is $M$-shellable. This gives, in a partial case, a positive answer to a conjecture of Chari and improves a recent result of Schweig where he proved that the $h$-vector of a lattice path matroid satisfies a conjecture of Stanley.

Abstract:
The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis and Bjorner. In this note, we provide a unifying approach which allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley--Reisner rings.

Abstract:
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dimensions and codimensions in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree at most d and shifted pure (d-1)-dimensional simplicial complexes.

Abstract:
The propagation of surface plasmon waves in metallic single-walled carbon nanotubes is analyzed within the frame-work of the classical electrodynamics. The conduction electrons of the system are modelled by an in?nitesimally thin layer of free-electron gas which is described by means of the semiclassical kinetic theory of the electron dynamics. The effects of the energy band structure is taken into account and a more accurate dispersion relation for surface plasmon oscillations in the zig-zag and armchair nanotubes of metallic character is obtained.

Abstract:
Using of the Internet technology and the field of Fuzzy expert systems has proposed new branches of sharing and distributing knowledge. However, there has been a general lack of investigation in the area of web-based Fuzzy expert systems (FES). In this paper the issues associated with the design, development, and use of web-based FES from a standpoint of the benefits and challenges of developing and using them. The original theory and concepts in conventional FES were reviewed and a knowledge engineering framework for developing them was revisited. Student in an educational place need an educational advisor for solve problems. Some of educational circulars order changing because advisor must update information away. The student's request is linguistic and crisp Expert System cannot solve problems completely. In my approach we build Web-Based Fuzzy Expert System for Student Education Advisor (FES-SEA) and stays in university portal. This system implemented with ASP.NET, SQL-SERVER 2008.

Abstract:
The present study reports data from a cross-sectional investigation of the psychiatric and psychosocial functioning of 55 children diagnosed with acute lymphocytic leukemia and their families at three points in time: diagnosis (newly diagnosed), 1 year postdiagnosis, and 1 year after the completion of chemotherapy (offtherapy). Results reveal minimal psychopathology in these children and their parents based on self-and informantreports and structured diagnostic interviews. These families appear to be functioning adequately and report more family cohesiveness and marital satisfaction after chemotherapy was completed. Coping strategies commonly used by children and their parents include problem solving, a positive outlook, and good communication. Implications for psychiatric consultation are presented.