We show that solutions of the Bach equation exist which are not conformal Einstein spaces. In connection with fourth order gravitational field equations, cf. e.g. [1, 2] where the breaking of conformal invariance was discussed, the original Bach equation, Bij = 0 , (1) enjoys current interest. Eq. (1) stems from a Lagrangian L = 1 2 √ −gCijklC , and variation gives, cf. Bach [3], 1 √−g δL/δg ij...

In this paper, we obtain the classification theorem for 3-dimensional complete space-like $\lambda$-translators $x:M^{3} \rightarrow \mathbb{R}^{4}_{1}$ with constant norm of second fundamental form and $f_{4} = \sum_{i,j,k,l} h_{ij} h_{jk} h_{kl} h_{li}$ $h_{ij}$ being components in Minkowski space $\mathbb{R}^{4}_{1}$.

Let G = a 1 ,. .. , a n | a i a j a i · · · = a j a i a j. .. , i < j be an Artin group and let m ij = m ji be the length of each of the sides of the defining relation involving a i and a j. We show if all m ij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups a i , a j for which m ij < ∞.

The Analytic Hierarchy Process (AHP) (Saaty, 1990) has been accepted as a leading multiattribute decision model both by practitioners and academics. AHP can solve decision problems in various fields by the prioritization of alternatives. The heart of the most familiar version of the AHP is the Saaty’s eigenvector method (EM) which approximates an positive reciprocal matrix n n× ) ( ij a A = , ,...

We study the existence of fully nontrivial solutions to system ??ui+?iui=?j=1??ij|uj|p|ui|p?2uiin?,i=1,…,?,in a bounded or unbounded domain ? in RN, N?3. The ?i’s are real numbers, and nonlinear term may have subcritical (1NN?2). matrix (?ij) is symmetric admits block decomposition such that diagonal entries ?ii positive, interaction forces w...

We consider the Einstein/Yang-Mills equations in 3 + 1 space time dimensions with SU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymp-totically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and p...

A parallel algorithm for finding the frequent itemsets in a set of transactions is presented. The frequent individual items are identified by their index. We assume that processors number (m) is less than the frequent items number (n). At the first stage, every processor Pi, i ∈ {1, . . . ,m − 1} sequentially computes the frequent itemsets from the interval Ii = [(i − 1) · p + 1, i · p], where ...

The total Hamiltonian in general relativity, which involves the first class and momentum constraints, weakly vanishes. However, when action is expanded around a classical solution as case of single scalar field inflationary model, there appears non-vanishing additional constraints; but this time theory becomes perturbative number fluctuation fields. We show that one can reorganize expansion sol...

Abstract Let a network be represented by simple graph $$\mathcal {G}$$ G with n vertices. A common approach to investigate properties of is use the adjacency matrix $$A=[a_{ij}]_{i,j=1}^n\in \mathbb {R}^{n\times n}$$ A = [ ...

in 2001, s. bulman-fleming et al. initiated the study of three flatness properties (weakly kernel flat, principally weakly kernel flat, translation kernel flat) of right acts $a_{s}$ over a monoid $s$ that can be described by means of when the functor $a_{s} otimes -$ preserves pullbacks. in this paper, we extend these results to$s$-posets and present equivalent descriptions of weakly kernel po...