Search results for "CONST"

On the lattice of J-subnormal subgroups

1992

Lengths of radii under conformal maps of the unit disc

1999

If E f ( R ) E_{f}(R) is the set of endpoints of radii which have length greater than or equal to R > 0 R>0 under a conformal map f f of the unit disc, then cap ⁡ E f ( R ) = O ( R − 1 / 2 ) \operatorname {cap} E_{f}(R)=O(R^{-1/2}) as R → ∞ R\to \infty for the logarithmic capacity of E f ( R ) E_{f}(R) . The exponent − 1 / 2 -1/2 is sharp.

Quantum Algorithm for Dyck Language with Multiple Types of Brackets

2021

We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity \(O(\sqrt{n}(\log n)^{0.5k})\), where n is the length of input and k is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is \(\varOmega (\sqrt{n}c^{k})\) for some constant c.

Local dimensions of sliced measures and stability of packing dimensions of sections of sets

2004

Abstract Let m and n be integers with 0 R n to certain properties of plane sections of μ. This leads us to prove, among other things, that the lower local dimension of (n−m)-plane sections of μ is typically constant provided that the Hausdorff dimension of μ is greater than m. The analogous result holds for the upper local dimension if μ has finite t-energy for some t>m. We also give a sufficient condition for stability of packing dimensions of section of sets.

Type and Cotype in Vector-Valued Nakano Sequence Spaces

2001

AbstractGiven a sequence of Banach spaces {Xn}n and a sequence of real numbers {pn}n in [1,∞), the vector-valued Nakano sequence spaces ℓ({pn},{Xn}) consist of elements {xn}n in ∏nXn for which there is a constant λ>0 such that ∑n(‖xn‖/λ)pn<∞. In this paper we find the conditions on the Banach spaces Xn and on the sequence {pn}n for the spaces ℓ({pn},{Xn}) to have cotype q or type p.

The best constant for the Sobolev trace embedding from into

2004

Abstract In this paper we study the best constant, λ 1 ( Ω ) for the trace map from W 1 , 1 ( Ω ) into L 1 ( ∂ Ω ) . We show that this constant is attained in BV ( Ω ) when λ 1 ( Ω ) 1 . Moreover, we prove that this constant can be obtained as limit when p ↘ 1 of the best constant of W 1 , p ( Ω ) ↪ L p ( ∂ Ω ) . To perform the proofs we will look at Neumann problems involving the 1-Laplacian, Δ 1 ( u ) = div ( Du / | Du | ) .

On embedding Boolean as a subtype of integer

1990

Right-Justified Characterization for Generating Regular Pattern Avoiding Permutations

2017

ECO-method and its corresponding succession rules allow to recursively define and construct combinatorial objects. The induced generating trees can be coded by corresponding pattern avoiding permutations. We refine succession rules by using succession functions in case when avoided patterns are regular or c-regular. Although regular patterns are hard to be recognized in general, we give a characterization for its right-justified property which is a prerequisite in the definition of the regular pattern. Based on this characterization, we show the (c-)regularity for various classes of permutations avoiding sets of patterns with variable lengths. Last, the technique of succession functions per…

The index of stable critical points

2002

Abstract In this paper we show that in dimension greater or equal than 3 the index of a stable critical point can be any integer. More concretely, given any k∈ Z and n⩾3 we construct a C ∞ vector field on R n with a unique critical point which is stable (in positive and negative time) and has index equal to k. This result extends previous ones on the index of stable critical points.

Using Taguchi method for the optimization of processing variables to prepare porous scaffolds by combined melt mixing/particulate leaching

2017

Synthetic biopolymers have made significant inroads into the development of devices for tissue regeneration. In this context, a challenge is the achievement of appropriate properties mimicking the natural extracellular matrix by fabricating scaffolds presenting mechanical properties, specific surface, porosity and pore interconnection adequate for the final application. This study involved a systematic procedure based on Taguchi method for parameters optimization of melt mixing/particulate leaching combined processes aiming to enhance the performance of the scaffolds. In particular, it was evaluated the effect of time and temperature of melt mixing of the poly(lactic acid) matrix with two w…