We establish the long time existence of complete non-compact weakly convex and smooth hypersurfaces $$\Sigma _t$$ evolving by $$Q_k$$ -flow. show that maximum T depends on dimension $$d_W$$ vector space $$W{:}{=}\{w \in \mathbb {R}^{n+1}: \sup _{X\in \Sigma _0} |\langle X,w\rangle | = +\infty \}$$ which contains each direction in our initial data _0$$ is infinite. If $$d_W=\text {dim}(W) \ge n-...

We give a complete and consistent solution to string corrected (deformed), D=10, N=1 Supergravity as the non-minimal low energy limit of string theory. We solve the Bianchi identities with suitable constraints to second order in the string slope parameter. In so doing we pave the way for continuing the study of the many applications of these results. We also modify, reaffirm and correct a previ...

The purpose of this paper is to address a number of issues raised by Avramov and Miller in a recent paper [1]. Let (R,m, k) be a Noetherian local ring of characteristic p > 0 with residue field k, and let φ : R → R be the the Frobenius homomorphism defined by φ(a) = a. For r ≥ 1, we denote by φrR the R-module structure on R via φ. That is, for a ∈ R and b ∈ φ r R, a · b = a r b. When R is a reg...

We show that it is consistent with ZFC that L(Y,B, ν) has no linear lifting for many non-complete probability spaces (Y,B, ν), in particular for Y = [0, 1], B = Borel subsets of Y , ν = usual Radon measure on B. AMS Subject Classification 1980 (1985 revision): Primary: 28A51 Secondary: 03E35 1) Research supported by UPEI Senate Grant no 602101, by the Research Institute for Mathematical Science...

In this note based on paper [3] we deal with domains D (i.e. connected open subsets) of a Finsler manifold (M, F ). At first we carry out a comparison between different notions of convexity for their boundaries. Then a careful application of variational methods to the geodesic problem yields that the convexity of ∂D is equivalent to the existence of a minimal geodesic for each pair of points of...

In this paper it has been studied the sequence of membership functions and of join spaces (see [7]), determined by a class of 1–hypergroups which are not complete (see [2]).

In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G is G-cr. This essentially reduces the problem of determining G-complete reducibility to the con...

We define a problem “exact non-identity check”: Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a sense of the strict equivalence condition, this problem is different from a QMA-complete problem, non-identity check defined in [1]. As corollaries, it is der...

For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus extending to non-algebraic lattices a result of L. Libkin. We illustrate this by various examples and counterexamples.

A finite set S of words over the alphabet Σ is called noncomplete if Fact(S∗) 6= Σ∗. A word w ∈ Σ∗ \ Fact(S∗) is said to be uncompletable. We present a series of non-complete sets Sk whose minimal uncompletable words have length 5k − 17k+13, where k ≥ 4 is the maximal length of words in Sk. This is an infinite series of counterexamples to Restivo’s conjecture, which states that any non-complete...