The classification theory for shifts of finite type (topological Markov chains) in the strictest sense, that is to say, up to topological conjugacy, was initiated by Williams ([17]). Additions to this theory are represented by [1], [4], [6], [7], [11], [12] and [14]. Williams's work can be viewed either as topological or as a combined topological and measure-theoretic theory, where invariant me...

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

Protein kinase C-zeta (PKC-zeta) is a serine/threonine kinase downstream from phosphatidylinositol 3-kinase in insulin signaling pathways. However, specific substrates for PKC-zeta that participate in the biological actions of insulin have not been reported. In the present study, we identified insulin receptor substrate-1 (IRS-1) as a novel substrate for PKC-zeta. Under in vitro conditions, wil...

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

Holomorphic maps between complex manifolds have many properties which distinguish them among general smooth maps. Consider, for example, the case of a map between Riemann surfaces. A holomorphic map is represented locally, in suitable co-ordinates, by one of the models z 7→ z for k ≥ 0. These models are very different from the models of generic smooth maps between surfaces, which are, in additi...

We give a new and bijective proof for the formula of the growth function of the positive braid monoid with respect to Artin generators.

Let f = (f1, . . . , fl) : U → Kl, with K = R or C, be a K-analytic mapping defined on an open set U ⊆ Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f , Φ) in terms of a log-principalization of the ideal If = (f1, . . . , fl). When f is a non-degenerate mapping, we give an explicit...

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2 + iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riem...

In 2009, Cooper presented an infinite family of pairs of graphs which were conjectured to have the same Ihara zeta function. We give a proof of this result by using generating functions to establish a one-to-one correspondence between cycles of the same length without backtracking or tails in the graphs Cooper proposed. Our method is flexible enough that we are able to generalize Cooper’s graph...

Syntrophins are scaffold proteins that regulate the subcellular localization of diacylglycerol kinase zeta (DGK-zeta), an enzyme that phosphorylates the lipid second-messenger diacylglycerol to yield phosphatidic acid. DGK-zeta and syntrophins are abundantly expressed in neurons of the developing and adult brain, but their function is unclear. Here, we show that they are present in cell bodies,...