Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms
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Abstract In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.Keywords:
Duality (order theory)
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The purpose of this article is to investigate the dual nature of agenda-setting processes as they can either occur on a deliberate level or on an automatic one. At present, the factors that lead to one of the processes rather than to the other are almost unknown. From studies on dual processing theories comes evidence that whether information is processed with high or with low cognitive effort strongly depends on the involvement with a certain issue. For that, we assume that the duality of agenda-setting reflects an involvement-determined duality of the underlying learning processes. In line with dual processing theories, we assume a more thoughtful agenda-setting process, if issue involvement is high and a more automatic one, if issue involvement is low. We tested these assumptions with two experimental panel studies. It can be concluded that the duality of agenda-setting processes is a result of different types of information processing.
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This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold structure. But for microbundles this problem was not yet investigated. Continuous homomorphisms of microbundles are studied. Topologies on families of homomorphisms of microbundles are investigated. Relations of their structure with microbundles are scrutinized. Necessary and sufficient conditions are studied under which families of homomorphism of microbundles in their turn can be supplied with a microbundle structure.
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Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}... a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this paper, we investigate $n$-homomorphisms and their relation to homomorphisms. We characterize $n$-homomorphisms in terms of homomorphisms under certain conditions. Some results related to continuity and commutativity are given as well.
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In this paper,we introduce the concepts of star element,star ideal and star congruence of a semiring and star homomorphism of two semirings.We obtain some significant properties of star homomorphism of semirings.
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Duality (order theory)
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Abstract For cyclically ordered groups G, G’, the mapping f: G → G’ is called a homomorphism, if f is a homomorphism with respect to the group operation, and whenever x,y,z in G such that [x,y,z], and f(x), f(y), f(z), are distinct, then [f(x), f(y), f(z)]. In this paper, it will be given some conditions related to group homomorphisms.
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L homomorphisms, i.e. structure preserving mappings between OL systems, are introduced. Every L homomorphism is determined in a unique way by a homomorphism between thefree monoids generated by the alphabets of the related systems and by a nonnegative integer. Thereby the notion of L homomorphism is characterized in a decidable way. L homomorphisms are related to all essential notions of L systems like derivations, adult languages, local catenativity, and ranks of DOL systems. Using the notion of L homomorphism a letter merging procedure for the reduction of OL systems is developed which is similar to the state merging algorithm for the reduction of finite state machines.
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