The New Turkish Trademark Law

Since 1980, the Turkish economy has gradually gained a liberal character through the elimination of government intervention in the economy and the removal of exchange restrictions and customs barriers. These changes in economic policy are related to Turkey\u27s desire to foster closer economic links with the European Union (“EU” or “Community”). Relations between Turkey and the European Union take place within the framework of an Association Agreement (“Ankara Agreement”). The Ankara Agreement was signed on September 12, 1963, and became effective on January 1, 1973. The Ankara Agreement provides the possibility of Turkey\u27s eventual membership in the European Union. Undoubtedly, relations with the European Union have had an important impact on recent reforms in the fields of intellectual and industrial property rights in Turkey. Following Turkey\u27s application for full Community membership, the necessity for reform in the field of trademark law, as in other fields of intellectual and industrial property rights, has become an important issue for the country. This Article summarizes the current Turkish trademark laws, and discusses their harmony with EU trademark law

Equivariant Moore spaces and the Dade group

Let $G$ be a finite $p$-group and $k$ be a field of characteristic $p$. A topological space $X$ is called an $n$-Moore space if its reduced homology is nonzero only in dimension $n$. We call a $G$-CW-complex $X$ an $\underline{n}$-Moore $G$-space over $k$ if for every subgroup $H$ of $G$, the fixed point set $X^H$ is an $\underline{n}(H)$-Moore space with coefficients in $k$, where $\underline{n}(H)$ is a function of $H$. We show that if $X$ is a finite $\underline{n}$-Moore $G$-space, then the reduced homology module of $X$ is an endo-permutation $kG$-module generated by relative syzygies. A $kG$-module $M$ is an endo-permutation module if ${\rm End}_k (M) =M \otimes _{k} M^*$ is a permutation $kG$-module. We consider the Grothendieck group of finite Moore $G$-spaces $\mathcal{M}(G)$, with addition given by the join operation, and relate this group to the Dade group generated by relative syzygies.Comment: 22 page

From Plurality Rule to Proportional Representation

I consider the decision of a parliament that might change the electoral system for the forthcoming elections from plurality rule to proportional representation. Parties are o¢ ce-motivated. They care about winning and about the share of seats obtained. I consider two di¤erent scenarios of how parties in the government share the spoils of o¢ ce: Equally or proportionally to their share of seats. If the government is formed by a single party and parties expect that each party will obtain the same share of votes in the next election the electoral rule will never be changed. That is, for a change to occur the government should be formed by a coalition. I ?nd that a change is more likely to occur when the number of parties is larger and also when the spoils of o¢ ce are shared equally among the members in the governing coalition. I extend these results to analyze the decision of a change from a less proportional rule to a more proportional one.Electoral systems, Plurality, Proportional Representation, Coalitions.

Linear colorings of simplicial complexes and collapsing

A vertex coloring of a simplicial complex $\Delta$ is called a linear coloring if it satisfies the property that for every pair of facets $(F_1, F_2)$ of $\Delta$, there exists no pair of vertices $(v_1, v_2)$ with the same color such that $v_1\in F_1\backslash F_2$ and $v_2\in F_2\backslash F_1$. We show that every simplicial complex $\Delta$ which is linearly colored with $k$ colors includes a subcomplex $\Delta'$ with $k$ vertices such that $\Delta'$ is a strong deformation retract of $\Delta$. We also prove that this deformation is a nonevasive reduction, in particular, a collapsing.Comment: 18 page

Centrist's Curse? An Electoral Competition Model with Credibility Constraints

I analyze a model of electoral competition in which a candidate?s reputation and his need of cred- ibility restricts his policy choice to a certain subset of the policy space, its ideology set. Candidates are o¢ ce-motivated. They care about winning and also about the share of votes they get. I consider both two and three party systems. I describe the equilibrium outcomes assuming that plurality rule applies, and obtain for two party competition, in some cases, equilibrium outcomes di¤erent than what the median voter theorem suggests because of the restrictions on the ideology sets implied by the credibility constraints. I show that centrist parties are disadvantaged compared to leftist and rightist ones, since, in equilibrium, leftist and rightist parties choose policy points that are as close as possible to each other and obtain votes from the centrist parties?ideology set. A centrist candidate needs a higher concentration of voters in his credibility set compared to his opponents in order to have a chance to win. I also analyze a run-off system for three parties and show that centrist parties have more opportunities to win under this rule than under plurality rule.Electoral competition, plurality, run-off, credibility, spatial models.

Bockstein Closed 2-Group Extensions and Cohomology of Quadratic Maps

A central extension of the form $E: 0 \to V \to G \to W \to 0$, where $V$ and $W$ are elementary abelian 2-groups, is called Bockstein closed if the components q_i \in H^*(W, \FF_2) of the extension class of $E$ generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of $G$ when $E$ is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of $G$ has a simple form and it is easy to calculate. The main result of the paper is the calculation of the Bocksteins of the generators of the mod-2 cohomology ring using an Eilenberg-Moore spectral sequence. We also find an interpretation of the second page of the Bockstein spectral sequence in terms of a new cohomology theory that we define for Bockstein closed quadratic maps $Q : W \to V$ associated to the extensions $E$ of the above form.Comment: 31 pages. To appear in Journal of Algebr