On distance local connectivity and the hamiltonian index

In this paper we introduce the concept of distance local connectivity of a graph. We give several sufficient conditions in terms of the independence number and of the vertex degrees, and we show a relation between the distance local connectivity and the hamiltonian index of a graph.     

“舆论审判”还是“媒体审判”？——理念辨析与解决之道

目前，学界将“舆论审判”与“媒体审判”分别加以讨论并无必要，从舆论学和法理学的视角看，二者没有根本性的差别。“媒体审判”背后实际上是两种理念的冲突：表达自由与司法独立。在中国现实语境中，这两种价值都有保护的必要，因此应当采取有效手段对表达自由和司法独立之间的紧张关系进行平衡，从而建构司法和传媒间的和谐关系。     

Relating broadcast independence and independence

An independent broadcast on a connected graph $G$ is a function $f:V\left(G\right)\to {\mathbb{N}}_0$ such that, for every vertex $x$ of $G$, the value $f\left(x\right)$ is at most the eccentricity of $x$ in $G$, and $f\left(x\right)>0$ implies that $f\left(y\right)=0$ for every vertex $y$ of $G$ within distance at most $f\left(x\right)$ from $x$. The broadcast independence number ${\alpha }_b\left(G\right)$ of $G$ is the largest weight $\sum _{x\in V\left(G\right)}f\left(x\right)$ of an independent broadcast $f$ on $G$. Clearly, ${\alpha }_b\left(G\right)$ is at least the independence number $\alpha \left(G\right)$ for every connected graph $G$. Our main result implies ${\alpha }_b\left(G\right)\le 4\alpha \left(G\right)$. We prove a tight inequality and characterize all extremal graphs.     

On the maximum number of minimum dominating sets in forests

Fricke, Hedetniemi, Hedetniemi, and Hutson asked whether every tree with domination number $\gamma$ has at most $2^{\gamma }$ minimum dominating sets. Bień gave a counterexample, which allows us to construct forests with domination number $\gamma$ and $2.0598^{\gamma }$ minimum dominating sets. We show that every forest with domination number $\gamma$ has at most $2.4606^{\gamma }$ minimum dominating sets, and that every tree with independence number $\alpha$ has at most $2^{\alpha -1}+1$ maximum independent sets.     

辅导员专业化发展的伦理困境及其应对——基于辅导员主体性视角

辅导员主体性价值的实现是推进专业化的关键。当前专业化异化折煞了辅导员专业活动的自觉性，技术工具理性的把持遮蔽了辅导员专业发展的主体意识，专业化运动中辅导员的失语阻滞着其专业能力的提升。加强制度建设规避专业化异化，强化辅导员的主体意识、发掘辅导员专业化的应有价值，拓展话语空域、提升专业能力是有效解决辅导员专业化的必然选择。     

On posets and independence spaces

By constructing a correspondence relationship between independence spaces and posets, under isomorphism, this paper characterizes loopless independence spaces and applies this characterization to reformulate certain results on independence spaces in poset frameworks. These state that the idea provided in this paper is a new approach for the study of independence spaces. We outline our future work finally.     

Independence polynomials of circulants with an application to music

The independence polynomial of a graph G is the generating function I(G,x)=∑_k≥0i_kx^k, where i_k is the number of independent sets of cardinality k in G. We show that the problem of evaluating the independence polynomial of a graph at any fixed non-zero number is intractable, even when restricted to circulants. We provide a formula for the independence polynomial of a certain family of circulants, and its complement. As an application, we derive a formula for the number of chords in an n-tet musical system (one where the ratio of frequencies in a semitone is 2^1/n) without ‘close’ pitch classes.     

Combinatorial independence in measurable dynamics

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their counterparts in topological dynamics. Local characterizations of the Pinsker von Neumann algebra and its sequence entropy analogue are given in terms of combinatorial independence, ?₁ geometry, and Voiculescu's completely positive approximation entropy. Among the novel features of our local study is the treatment of general discrete acting groups, with the structural assumption of amenability in the case of entropy.     

Persistency and matroid intersection

In this paper, we show that for any independence system, the problem of finding a persistency partition of the ground set and that of finding a maximum weight independent set are polynomially equivalent. This research has been partially funded by the Greek Ministry of Education under the program Pythagoras.