We construct an infinitely narrow N-soliton solution in an associated sense to a system of conservation laws in the frame of Colombeau’s generalized functions with arbitrary initial data which are infinitely narrow solitons. With additional assumptions on the first derivatives of initial data, the solution is modified so that it also becomes the solution to the system of conservation laws in th...

In this paper, hyperclone lattice is studied via three kinds of embeddings. One is from the clone lattice on A to the hyperclone lattice on A, the second is from the hyperclone lattice on A to the clone lattice on P (A) \ {∅} and the third one is from the hyperclone lattice on A′ to the hyperclone lattice on A, for A′ ⊂ A and the finite set A. The second map has usually been used for the descri...

The symmetric inverse monoid In is the set of all partial permutations of an n-element set. The largest possible size of a 2-generated subsemigroup of In is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)/|In| → 1 as n →∞. Furthermore, we may deduce, the already known fact, that In embeds as a local submonoid of an...

In the present paper we have studied an N(k)-quasi Einstein manifold satisfying R(ξ, X).P̃ , where P̃ is the pseudo-projective curvature tensor. Among others, it is shown that if quasi-Einstein manifold with constant associated scalars is Ricci symmetric then the generator of the manifold is a Killing vector field. AMS Mathematics Subject Classification (2000): 53C25

Let W (3, k) denote the largest integer w such that there is a red/blue coloring of {1, 2, . . . , w} which has no red 3-term arithmetic progression and no block of k consecutive blue integers. We show that for some absolute constant c, W (3, k) ≥ k log k for all k. AMS Mathematics Subject Classification: 05D10

Let X be a smooth, closed, connected spin 4-manifold with b1(X) = 0 and non-positive signature σ(X). In this paper we use SeibergWitten theory to prove that if X admits a spin Z6 action of even type, then b+2 (X) ≥ |σ(X)|/8 + 2 under some non-degeneracy conditions. AMS Mathematics Subject Classification (2000): 57R57, 57M60, 57R15

In this article we consider a Brownian motion with drift, denoted by S = (St)t≥0, of the form dSt = μtdt+ dBt for t ≥ 0, with a specific non-trivial drift predictable with respect to F , the natural filtration of the Brownian motion B = (Bt)t≥0. We construct a process H = (Ht)t≥0, also predictable with respect to F , such that ((H · S)t)t≥0 is a Brownian motion in its own filtration. Furthermor...

We present a geometric approach to the classification of monogenic invariant subspaces, alternative to the classical algebraic one, which allows us to obtain several matricial canonical forms for each class. Some applications are derived: canonical coordinates of a vector with regard to an endomorphism, and a canonical form for uniparametric linear control systems, not necessarily controllable,...

The valuation monoids and pseudo-valuation monoids have been established through valuation domains and pseudo-valuation domains respectively. In this study we continue these lines to describe the almost valuation monoids, almost pseudo-valuation monoids and pseudoalmost valuation monoids. Further we also characterized the newly described monoids as the spirit of valuation monoids pseudo-valuati...

In this brief note, I will describe a variety of problems from Ramsey theory on which I would like to see progress made. To encourage this progress, I am offering modest rewards for most of these problems. This material is based on a 20-minute talk I gave at the meeting in Carrollton. AMS Mathematics Subject Classification: 05D10