We obtain several results that distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. These include: (i) If NE 6 = E, then there exists a set L in NP ? P such that search reduces to decision for L, search does not nonadaptively reduces to decision for L, and L is not self-reducible. 1 (ii) If UE 6 = E, then there exists a language L 2 UP ? P...

Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

1.1 The Quantifiable Continuum of Uncertainty. Notice that once uncertainties are acknowledged as unquantified uncertainties, increased knowledge about the uncertainties will determine their position on the continuum.. .. .. 11 1.2 Typology for sources and degree of uncertainty. Adapted from Van Asselt's (2000) proposed typology for uncertainties in integrated assessment.. .. 12 1.3 Some potent...

We present some applications of the deformation theory toric Fano varieties to K-(semi/poly)stability varieties. First, we two examples K-polystable 3-fold with obstructed deformations. In one case, K-moduli spaces and stacks are reducible near closed point associated 3-fold, while in other they non-reduced 3-fold. Second, study K-stability general members families smooth 3-folds by building de...

For a complete, i.e., connuent and terminating term rewriting system (TRS) it is well-known that simpliication (also called interreduction) into an equivalent canonical, i.e., complete and interreduced TRS is easily possible. This can be achieved by rst normalizing all right-hand sides of the TRS and then deleting all rules with a reducible left-hand side. Here we investigate the logical and op...

In the present paper we study representations of Jacobi algebra. More concretely, define, analogously to case semi-simple Lie algebras, Verma modules over algebra ${\cal G}_2$. We their reducibility and give explicit construction reducible exhibiting corresponding singular vectors. Using this information a complete classification modules. than exhibit interrelation embeddings between these Thes...

let $(r,m)$ be a commutative noetherian local ring, $m$ a finitely generated $r$-module of dimension $d$, and let $i$ be an ideal of definition for $m$. in this paper, we extend cite[corollary 10(4)]{p} and also we show that if $m$ is a cohen-macaulay $r$-module and $d=2$, then $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

Let G be a complex reductive algebraic group and let Γ be a finitely generated group. In this paper we study properties of irreducible and completely reducible representations ρ : Γ → G in the context of the geometric invariant theory of the G-action on Hom(Γ, G) by conjugation. In particular, we prove that ρ is poly-stable (i.e. its orbit is closed) if and only if ρ is completely reducible. We...