We consider complexes (X , d) of nuclear Fréchet spaces and continuous boundary maps dn with closed ranges and prove that, up to topological isomorphism, (Hn(X , d)) ∗ ∼= H(X ∗, d∗), where (Hn(X , d)) ∗ is the strong dual space of the homology group of (X , d) and H(X ∗, d∗) is the cohomology group of the strong dual complex (X ∗, d∗). We use this result to establish the existence of topologica...

The Higgs faotopization of a strong map between matroids on a fixed set is that factorization into elementary naps in which each matroid is the Higgs lift of its successor. This factorization is characterized by properties of the modular filters which induce the elementary maps of the factorizations in two different ways. It is also sho~m to be minimal in a natural order on factorizations arisi...

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of Kn(Z[G])⊗Z Q...

A cellular embedding of a connected graph (also known as a map) on an orientable surface has trinity symmetry if it is isomorphic to both its dual and its Petrie dual. A map is regular if for any two incident vertex-edge pairs there is an automorphism of the map sending the first pair onto the second. Given a map M with all vertices of the same degree d, for any e relatively prime to d the powe...

‎‎a natural generalization of two dimensional cyclic code ($t{tdc}$) is two dimensional skew cyclic code‎. ‎it is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $r_n:=f[x,y;rho,theta]/_l$‎. ‎in this paper we characterize the left ideals of the ring $r_n$ with two methods and find the generator matrix for two dimensional s...

A gradient in the density of hyperpolarization-activated cyclic-nucleotide gated (HCN) channels is necessary for the emergence of several functional maps within hippocampal pyramidal neurons. Here, we systematically analyzed the impact of dendritic atrophy on nine such functional maps, related to input resistance and local/transfer impedance properties, using conductance-based models of hippoca...

objective: cell vital function has correlation with mechanical loadings that cell experiences. here, effects of in-vitro combined cyclic-static stretch on proliferation of human mesenchymal stem cell (hmsc) were evaluated. materials and methods: hmscs were cultured on gelatin coated elastic membranes, and exposed to stretch loading. four different regimes of cyclic, static, combined cyclic-sta...

An exposition of the 1918 paper of Lattès, together with its historical antecedents, and its modern formulations and applications. 1. The Lattès paper. 2. Finite Quotients of Affine Maps 3. A Cyclic Group Action on C/Λ . 4. Flat Orbifold Metrics 5. Classification 6. Lattès Maps before Lattès 7. More Recent Developments 8. Examples References §1. The Lattès paper. In 1918, some months before his...

Abstract There is a need of secure and robust encryption algorithm that can be implemented on each diverse software hardware platforms. In this paper, we investigate semifield substitution boxes using permutation symmetric group set size 8 $$S_8$$ S 8 establish an effec...

This study is an attempt to gain insight into the malleability of representational maps in the primary somatosensory cortex in relation to the expression of proteins involved in inhibitory and excitatory neurotransmitter systems that contribute to maintain these maps in a dynamic state. Malleability of somatosensory maps is characterized by changes in the sizes of neuron receptive fields (RFs) ...