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In this paper we prove the containment I(nm) ⊂ M(n-1)mIm, for a radical ideal I of s general points in Pn, where s ≥ 2n. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least 2n points in Pn. [ABSTRACT FROM AUTHOR]

This paper discusses the twisted conjugacy classes in loop groups. We restrict to classical groups and give some explicit classifications. [ABSTRACT FROM AUTHOR]

In this paper, we compare the virtual fundamental classes of the stacks of (g, β, μ)-stable ramified maps ,Ug, μ(X, β) and of (g, β, μ)-log stable ramified maps Ulog g,μ(X, β). For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula. [ABSTRACT FROM AUTHOR]

This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all $n > 3$, there are $n$-point sets which are not zero dimensional, so this paper answers the question for the last remaining case. [ABSTRACT FROM AUTHOR]

We give a detailed and clear exposition of the basic result describing the structure of a finite subset A of a nonabelian group G with a small doubling |A²| < 1.5|A|. [ABSTRACT FROM AUTHOR]

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module $ B$. Conversely, we show that if such a $ B$, then there exists a closure operation that satisfies the given axioms. [ABSTRACT FROM AUTHOR]

In this short paper we prove that, for $3 le N le 9$, the problem $ -Delta u = e^u$ on the entire Euclidean space $mathbb {R}^N$ does not admit any solution stable outside a compact set of $mathbb {R}^N$. This result is obtained without making any assumption about the boundedness of solutions. Furthermore, as a consequence of our analysis, we also prove the non-existence of finite Morse Index solutions for the considered problem. We then use our results to give some applications to bounded domain problems. [ABSTRACT FROM AUTHOR]

In this paper we describe an algorithm for producing infinitely many examples of set-theoretic complete intersection monomial curves in $mathbb {P}^{n+1}$, starting with a single set-theoretic complete intersection monomial curve in $mathbb {P}^{n}$. Moreover we investigate the numerical criteria to decide when these monomial curves can or cannot be obtained via semigroup gluing. [ABSTRACT FROM AUTHOR]

In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of $T_0$ spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order. [ABSTRACT FROM AUTHOR]

In this paper, we investigate dense subsets of the boundary of a Coxeter system. We show that for a Coxeter system $(W,S)$, if $W^{\{s_0\}}$ is quasi-dense in $W$ and the order $o(s_0t_0)=\infty$ for some $s_0,t_0\in S$, then there exists a point $\alpha$ in the boundary $\partial\Sigma(W,S)$ of the Coxeter system $(W,S)$ such that the orbit $W\alpha$ is dense in $\partial\Sigma(W,S)$. Here $W^{\{s_0\}}=\{w\in W|\ell(ws)<\ell(w) \text{for each} s\in S\setminus\{s_0} \}\setminus \{1\}$. We also show that if the set $\bigcup\{W^{\{s\}}| s\in S \text{such that} o(st)=\infty \text{for some} t\in S\}$ is quasi-dense in $W$, then $\{w^\infty| w\in W \text{such that} o(w)=\infty\}$ is dense in $\partial\Sigma(W,S)$. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. On the one hand, we show that the kernel $\overline{C(A)}$ of the Bousfield periodization functor $P_A$ is cellularly generated by a space $B$, i.e., we construct a space $B$ such that the smallest closed class $C(B)$ containing $B$ is exactly $\overline{C(A)}$. On the other hand, we show that the partial order $(Spaces,\gg)$ is a complete lattice, where $B\gg A$ if $B\in C(A)$. Finally, as a corollary we obtain Bousfield's theorem, which states that $(Spaces,>)$ is a complete lattice, where $B>A$ if $B\in\overline{C(A)}$. [ABSTRACT FROM AUTHOR]

In this paper, we prove that if a perfect GO-space $X$ has a $ \sigma$-discrete dense set, then $X$ has a perfect linearly ordered extension. This answers a problem raised by H. R. Bennett, D. J. Lutzer and S. Purisch. And the result is also a partial answer to an old problem posed by H. R. Bennett and D. J. Lutzer. [ABSTRACT FROM AUTHOR]

If E ⊆ Rn is closed and the structure (R,+, ·, E) is d-minimal (that is, in every structure elementarily equivalent to (R,+, ·, E), every unary definable set is a disjoint union of open intervals and finitely many discrete sets), then for each p ∈ N, there exist Cp functions f : Rn → R definable in (R,+, ·, E) such that E is the zero set of f. [ABSTRACT FROM AUTHOR]

We will show that (1 − q)(1 − q2) . . . (1 − qm) is a polynomial in q with coefficients from {−1, 0, 1} iff m = 1, 2, 3, or 5 and explore some interesting consequences of this result. We find explicit formulas for the q-series coefficients of (1−q2)(1−q3)(1−q4)(1−q5) . . . and (1−q3)(1−q4)(1−q5)(1− q6) . . . . In doing so, we extend certain observations made by Sudler in 1964. We also discuss the classification of the products (1 − q)(1 − q2) . . . (1 − qm) and some related series with respect to their absolute largest coefficients. [ABSTRACT FROM AUTHOR]

In this work we prove that the set of the difference of primes is a Δr*-set. The work is based on the recent dramatic new developments in the study of bounded gaps between primes, reached by Zhang, Maynard and Tao. [ABSTRACT FROM AUTHOR]

A Turing degree a satisfies the join property if, for every nonzero b < a, there exists c < a with b ∨ c = a. It was observed by Downey, Greenberg, Lewis and Montalban that all degrees which are non-GL2 satisfy the join property. This, however, leaves open many questions. Do all a.n.r. degrees satisfy the join property? What about the PA degrees or the Martin- Löf random degrees? A degree b satisfies the cupping property if, for every a > b, there exists c < a with b ? c = a. Is satisfying the cupping property equivalent to all degrees above satisfying join? We answer all of these questions by showing that above every low degree there is a low degree which does not satisfy join. We show, in fact, that all low fixed point free degrees a fail to satisfy join and, moreover, that the non-zero degree below a without any joining partner can be chosen to be a c.e. degree. [ABSTRACT FROM AUTHOR]