Posttranslational modification of a protein by ubiquitin usually results in rapid degradation of the ubiquitinated protein by the proteasome. The transfer of ubiquitin to substrate is a multistep process. Cdc4p is a component of a ubiquitin ligase that tethers the ubiquitin-conjugating enzyme Cdc34p to its substrates. Among the domains of Cdc4p that are crucial for function are the F-box, which...

We present the fuzzy description logic ALCFH where primitive concepts are modified by means of hedges taken from hedge algebras. ALCFH is strictly more expressive than Fuzzy-ALC defined in [9]. We show that given a linearly ordered set of hedges primitive concepts can be modified to any desired degree by prefixing them with appropriate chains of hedges. Furthermore, we define a decision procedu...

In this paper we wish to prove that under certain conditions the Fourier coefficients of the Eisenstein series for an arithmetic group acting on a tube domain are all rational numbers. Let G be a connected, simply-connected, semisimple, and almost Q-simple linear algebraic group defined over the rational number field Q. Let R be the real number field. Then GR is connected, and we assume that if...

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

We describe a second-order calculus of objects. The calculus supports object subsumption, method override, and the type Self. It is constructed as an extension of System F with subtyping, recursion, and first-order object types.

We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a germ of a holomorphic function in two variables with an isolated critical point, what is the minimal degree of a polynomial, equivalent to the given function...

In open field arenas, Drosophila adults exhibit a preference for arena boundaries over internal walls and open regions. Herein, we investigate the nature of this preference using phenomenological modeling of locomotion to determine whether local arena features and constraints on movement alone are sufficient to drive positional preferences within open field arenas of different shapes and with d...

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |XXX|/|X| bounded is close to a finite subgroup, or else to a subset of a proper algebraic subgroup of G. We also find a connection with Lie groups, and use it to obtain some consequences s...

Throughout this paper, k denotes a field of characteristic 0. We write E8 for the split simple algebraic group with Killing-Cartan type E8. The Galois cohomology set H (k, E8) classifies simple algebraic groups of type E8 over k. One of the goals of the theory of algebraic groups over arbitrary fields is to understand the groups of type E8, equivalently, understand the set H(k, E8). The main to...

In this paper we will generalize  some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .