We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields over Q( √ −m) for all m. For each imaginary quadratic field Q( √ −m), we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note t...

1. Simplices, ∆-Complexes, and Homology: 1/8/15 1 2. Properties of Singular Homology: 1/13/15 4 3. Homotopy Invariance of Singular Homology: 1/15/15 7 4. Applications of Homotopy Invariance and Excision: 1/20/15 10 5. Equivalence of Singular and Simplicial Homology: 1/22/15 14 6. Degrees of Maps on Sn: 1/27/15 17 7. The Mayer-Vietoris Sequence and Applications: 1/29/15 20 8. CW Complexes: 2/3/1...

We consider a fuzzy linear system with crisp coefficient matrix and with an arbitrary fuzzy number in parametric form on the right-hand side. It is known that the well-known existence and uniqueness theorem of a strong fuzzy solution is equivalent to the following: The coefficient matrix is the product of a permutation matrix and a diagonal matrix. This means that this theorem can be applicable...

The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in...

After introducing many different types of prefilter convergence, we introduce an universal method to define various notions of compactness using cluster point and convergence of a prefilter and to prove the Tychonoff theorem using characterizations of ultra(maximal) prefilters. : prefilter convergence, universal method, Tychonoff theorem, ultra prefilter, good extension

A variant of a theorem of Ekin, Foldes, Hammer and Hellerstein concerning equational characterizations of Boolean function classes is proved using methods of universal algebra. The proof is not constructive but establishes a direct connection with the Birkhoff-Tarski HSP Theorem and the theory of equational classes of universal algebras.

We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q( √ −m) for all m. For each imaginary quadratic field Q( √ −m), we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that t...

Good simpliication strategies are essential for implementing any kind of eeective real quantiier elimination. Given a quantiier-free rst-order formula over the theory of ordered elds, the aim is to nd an equivalent rst-order formula that is simpler. The notion of a formula being simpler will be speciied. An overview is given over various methods, which we have implemented in reduce. Our methods...

This is the final one in the series of papers where we introduce and study the C∗-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C∗-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C∗-algebras associated with topological graphs. 0. Introduc...