纳米固体超酸SO42-/TiO2的研究

The new nanosolid superacid catalyst SO₄^2-/TiO₂ is compounded with nanometer chemical technology. This catalyst SO₄^2-/TiO₂ has good catalytic effects on esterificational reactions of ethylic acid and ethyl alcohol. It has many other advantages such as strong water-proof quality, being able to be used repeatedly, being easy to be re-claimed, non-corroding, non-polluting. So it is a green industrial catalyst which is helpful to the environment and possesses wide prospect of applications. The crystallo-process, specific surface area and sulphur content of the SO₄^2-/TiO₂ system have been studied with the method of XRD, XPS and the chemical analysis, the result of which indicates that catalytic activity and acid strength of SO₄^2-/TiO₂ is affected by the H₂SO₄ saturant concentration, baking temperature, precipitating condition, specific surface area and sulphur content. The best preparation conditions of SO₄^2-/TiO₂ are: ageing temperature at 0℃, 0.5mol·L^-1 of H₂SO₄ concentration, baking temperature at 500℃and 3 hours of baking time.     

Network robustness and irreversibility of information diffusion in Complex networks

Complex networks are characterized based on a newly proposed parameter, “degree of diffusion α”. It defines the ratio of information adopters to non-adopters within a diffusion process over consecutive penetration depths. Furthermore, the perfectness of a social network is evaluated by exploring different variations of α such as the reverse diffusion (α_reverse) and the random-kill-diffusion (RKD) processes. The analysis of α_reverse and RKD processes shows information diffusion irreversibility in small-world and scale-free but not in random networks. It also shows that random networks are more stable toward attacks, resulting a complete information diffusion process over the entire network. Finally, a real Complex network example, represented as a “virtual friendship network” was analyzed and found to share properties of both random and small-world networks. Therefore, it is characterized to be somewhere between random and small-world network models or in other words, it is a randomized small-world network model.     

Graphic sequences with a realization containing a generalized friendship graph

Gould, Jacobson and Lehel [R.J. Gould, M.S. Jacobson, J. Lehel, Potentially G-graphical degree sequences, in: Y. Alavi, et al. (Eds.), Combinatorics, Graph Theory and Algorithms, vol. I, New Issues Press, Kalamazoo, MI, 1999, pp. 451-460] considered a variation of the classical Turán-type extremal problems as follows: for any simple graph H, determine the smallest even integer σ(H,n) such that every n-term graphic sequence π=(d₁,d₂,…,d_n) with term sum σ(π)=d₁+d₂+?+d_n≥σ(H,n) has a realization G containing H as a subgraph. Let F_t,r,k denote the generalized friendship graph on kt−kr+r vertices, that is, the graph of k copies of K_t meeting in a common r set, where K_t is the complete graph on t vertices and 0≤r≤t. In this paper, we determine σ(F_t,r,k,n) for k≥2, t≥3, 1≤r≤t−2 and n sufficiently large.     

现象学视域下友爱的多重地位及其演变—兼论亚里士多德友爱哲学的现象学效应

相对于注重在纵向神人关系中厘定人类生活方式及其命运的中世纪哲学,以及具有明显意识主体主义形而上学特征的近现代西方哲学,亚里士多德特别重视主要涉及横向人类关系的友爱问题,并摆置于显著地位。海德格尔、伽达默尔、德里达三位现象学家在反对意识主体性形而上学以及相应的伦理政治生活之形式主义、规则主义乃至虚无主义的过程中,某种程度上通过对亚里士多德友爱哲学及其一般实践哲学的化用、重构、批判或革新,逐渐将友爱重新引入哲学视野,甚至推向哲学思考的中心地带。在相对意义上,三位现象学家友爱之思的具体领域和重心以及相应的友爱定位有所不同,但是,在他们各自的哲思整体中,友爱问题都并不单纯局限于某一领域,而是与存在、生存、语言、真理、时间、伦理和政治等议题错综交织。友爱问题的广泛牵涉性和深厚渗透性,也映现了现象学的一个突出特征与趋势,亦即,在更源初、更深厚的层次上重新思考理论与实践、存在与伦理、主体与客体、自我与他者之间源始关联和沟通的可能性与必要性,并由此走向一种更富前景之现象学的实践哲学。     

Symmetric graph designs on friendship graphs

We settle completely the existence of symmetric graph designs on friendship graphs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8:201–206, 2000     

Uniquely Cycle‐Saturated Graphs

Given a graph F, a graph G is uniquely F‐saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F. In this article, we study uniquely ‐saturated graphs. We prove the following: (1) a graph is uniquely C₅‐saturated if and only if it is a friendship graph. (2) There are no uniquely C₆‐saturated graphs or uniquely C₇‐saturated graphs. (3) For , there are only finitely many uniquely ‐saturated graphs (we conjecture that in fact there are none). Additionally, our results show that there are finitely many k‐friendship graphs (as defined by Kotzig) for .     

On the Existence of Friendship Hypergraphs

A 3‐uniform friendship hypergraph is a 3‐uniform hypergraph in which, for all triples of vertices x, y, z there exists a unique vertex w, such that , and are edges in the hypergraph. Sós showed that such 3‐uniform friendship hypergraphs on n vertices exist with a so‐called universal friend if and only if a Steiner triple system, exists. Hartke and Vandenbussche used integer programming to search for 3‐uniform friendship hypergraphs without a universal friend and found one on 8, three nonisomorphic on 16 and one on 32 vertices. So far, these five hypergraphs are the only known 3‐uniform friendship hypergraphs. In this paper we construct an infinite family of 3‐uniform friendship hypergraphs on 2^k vertices and edges. We also construct 3‐uniform friendship hypergraphs on 20 and 28 vertices using a computer. Furthermore, we define r‐uniform friendship hypergraphs and state that the existence of those with a universal friend is dependent on the existence of a Steiner system, . As a result hereof, we know infinitely many 4‐uniform friendship hypergraphs with a universal friend. Finally we show how to construct a 4‐uniform friendship hypergraph on 9 vertices and with no universal friend.     

A Doubling Construction for 3‐Uniform Friendship Hypergraphs with the Universal Pairs Property

In this note, we present a simple doubling construction for 3‐uniform friendship hypergraphs which generalizes the cubeconstructed hypergraphs from another study (L. Jørgensen and A. Sillasen, J Combin Designs (2014)). As a by‐product, we build point‐transitive 3‐uniform friendship hypergraphs of sizes and for all .     

Friendship Networks Through Time: An Actor-Oriented Dynamic Statistical Network Model

We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.