If [Formula: see text] is a directed graph and field, the Leavitt path algebra of over naturally graded by group integers We formulate properties which are equivalent with being crossed product, skew ring, or ring respect to this natural grading. state main result so that also characterized in terms pre-ordered Grothendieck text]-group text]. has finitely many vertices, we characterize when str...

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a nonsurjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through t...

The teaching of mathematics is used by several methods; one them the cooperative learning jigsaw method to improve student's higher ordered thinking skills. study intended investigate that how effective on higher-order skills in subject at elementary level. major objectives were; understand result students' analysis skills, examine effect assessment abilities, explore outcome creation hypothesi...

When implementing the DSmT, a difficulty may arise from the possible huge dimension of hyper-power sets, which are indeed free structures. However, it is possible to reduce the dimension of these structures by involving logical constraints. In this chapter, the logical constraints will be related to a predefined order over the logical propositions. The use of such orders and their resulting log...

BACKGROUND Recent reports have suggested a rotational strength weakness in rotations to the concave side in patients with idiopathic scoliosis. There have been no studies presenting normative values of female adolescent trunk rotational strength to which a comparison of female adolescents with idiopathic scoliosis could be made. The purpose of this study was to determine trunk rotational streng...

William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for lattice-ordered groups: Theorem: A finitely generated lattice-ordered group has soluble word problem if and only if it can be `-embedded in an `-simple lattice-or...

Algorithms for the all-pairs min-cut problem in bounded tree-width and sparse networks are presented. The approach used is to preprocess the input network so that, afterwards, the value of a min-cut between any two vertices can be eeciently computed. A tradeoo between the preprocessing time and the time taken to compute min-cuts subsequently is shown. In particular, after O(n log n) preprocessi...

the phenylthiourea-substituted triethoxysilane as a silane agent was synthesized and grafted on highly ordered nanoporous silica (lus-1) with a textured morphology and hexagonal array. this material (tu-lus-1) contained 0.8 mmol/g of soft base phenylthiourea group and surface area 760 m2g-1 and was able to adsorb 0.75 mmolhg/g of tu-lus-1 in endothermic reaction.

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

Using both instantaneous snapshots and simulation generated scattering data, the steady-state ̄ ow behaviour of a concentrated aggregated colloidal suspension is analysed in terms of its structure factor S(k). We ® nd that in the shear thinning regime, unlike model hard sphere results, S(k) exhibits pre-peaks at small k, which we interpret as indicative of intermediate range order in the shear i...