We use an algebraic description of surfaces with boundary to study covering maps. The focus is on the relationship between automor-phisms in the base and lifted maps. We show how to introduce and/or prohibit additional automorphisms in the lift. Using this control we give proofs of MacBeath's Theorem, Gr unbaum's Conjecture, and settle a conjecture of Nedela and Skoviera.

It is shown that if the neuronal gains are small compared with the synaptic connection weights, then a bidirectional associative memory network with axonal signal transmission delays converges to the equilibria associated with exogenous inputs to the network. Both discrete and continuously distributed delays are considered; the asymptotic stability is global in the state space of neuronal activ...

We have synthesized a set of double-labeled fluorescent probes and evaluated the performance of these fluorescent probes in sequencing by ligation (SBL). The results indicated that the ligation efficiency and specificity of double-labeled fluorescent probes was as higher as that of singe-labeled fluorescent probes. Moreover, double-labeled f luorescent p robes y ielded a r emarkable i ncrease i...

In this paper, phosphorene nanoribbons (PNRs) are theoretically studied using a multiscale simulation flow from the ab initio level to the tight binding (TB) level. The scaling effects of both armchair PNRs (aPNRs) and zigzag PNRs (zPNRs) from material properties to device properties are explored. The much larger effective mass of holes compared to that of electrons in zPNR is responsible for i...

In this note we consider several maps that occur naturally between modular Shimura varieties, Hilbert-Blumenthal varieties and the moduli spaces of polarized abelian varieties when forgetting certain endomorphism structures. We prove that, up to birational equivalences, these forgetful maps coincide with the natural projection by suitable abelian groups of Atkin-Lehner involutions.

In this paper, intuitionistic fuzzy matrices are considered. Szpilrajn's theorem on orderings is generalized to intuitionistic fuzzy orderings by Zedam et al. We give another generalization in intuitionistic fuzzy matrix form and theorem is represented in terms of intuitionistic fuzzy matrix operations.

We discuss the loading capacity of the neuronic equation for temporal associative memory. We show explicitly how to synthesize a perfect temporal associative memory using a network of such neurons, where all non-linear aspects can be linearized in tensorial space. Keyword: temporal associative memory, neuronic equation, neural network, inverse problem, music perception

The theoretical, practical and technical development of neural associative memories during the last 40 years is described. The importance of sparse coding of associative memory patterns is pointed out. The use of associative memory networks for large scale brain modeling is also mentioned.

Creation procedure of associative patterns ensemble in terms of formal logic with using neural network (NN) model is formulated. It is shown that the associative patterns set is created by means of unique procedure of NN work which having individual parameters of entrance stimulus transformation. It is ascertained that the quantity of the selected associative patterns possesses is a constant.