We construct a Spanier-Whitehead type duality functor relating finite $\mathcal{C}$-spectra to $\mathcal{C}^{\mathrm{op}}$-spectra and prove that every $\mathcal{C}$-homology theory is given by taking the homotopy groups of balanced smash product with fixed $\mathcal{C}^{\mathrm{op}}$-spectrum. use this Chern characters for certain rational theories.

The paper deals with the context of the inner DaniellStone and Riesz representation theorems, which arose within the new development in measure and integration in the book 1997 and subsequent work of the author. The theorems extend the traditional ones, in case of the Riesz theorem to arbitrary Hausdorff topological spaces. The extension enforces that the assertions attain different forms. The ...

With every Lie semi-group, Π, possessing certain regularity properties, there is associated a Lie algebra, A; and with every strongly continuous representation of Π in a Banach space there is associated a representation A(a) of A. Certain theorems regarding this representation are established. The above theorems are valid for a representation of a Lie group also. In this case, it is shown that ...

We consider natural variants of Lehmer's unresolved conjecture that Ramanujan's tau-function never vanishes. Namely, for n>1 we prove thatτ(n)∉{±1,±3,±5,±7,±691}. This result is an example general theorems (see Theorems 1.2 and 1.3 [2]) newforms with trivial mod 2 residual Galois representation. well-known congruences τ(n) allow the simplified proof in these special cases. make use theory Lucas...

Proved here are two integral representation theorems related to complex variables. They illustrate one way in which Choquet's Theorem and its relatives can be used. Other examples, analyzed in a similar way, can be found in [i0], [4], [2]. Both of the theorems proved here were originally proved by other methods, but here I have proved them by analyzing the extremal structure of an appropriate c...

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. fluctuations its length, supremum, time it is attained and value at T) Lévy process on [0,T] as T→∞. The scale length other statistics, well their asymptotic dependence, vary significantly with tail behaviour measure. key tool in proofs recent representation all processes using stick-breaking represe...

General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built, connection with the standard theory is considered and several concrete examples are constructed. For clarity the shortened versions of classical Gluskin-Hosszú and Post theorems are given for them.

This article presents a concept interpretation of patterns for bidirectional associative memory (BAM) and a representation of hierarchical structures of concepts (concept lattices) by BAMs. The constructive representation theorem provides a storing rule for a training set that allows a concept interpretation. Examples demonstrating the theorems are presented.

T*-categories are introduced as a ternary generalization of C*-categories. Their linking C*-categories constructed and the Gelfand-Naimark representation theorems Zettl for C*-ternary rings W*-ternary rings, generalized to T*-categories. Biduals considered.

Morse theory describes the relationship between a function's critical points and the homotopy type of the function's domain. The theorems of Morse theory were developed speci cally for functions on a manifold. This work adapts these theorems for use with parameterized families of implicit surfaces in computer graphics. The result is a theoretical basis for the determination of the global topolo...