Search results for "Mathematica"
showing 10 items of 7971 documents
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.
EXISTENCE OF THREE SOLUTIONS FOR A MIXED BOUNDARY VALUE PROBLEM WITH THE STURM-LIOUVILLE EQUATION
2012
Abstract. The aim of this paper is to establish the existence of threesolutions for a Sturm-Liouville mixed boundary value problem. The ap-proach is based on multiple critical points theorems. 1. IntroductionThe aim of this paper is to establish, under a suitable set of assumptions, theexistence of at least three solutions for the following Sturm-Liouville problemwith mixed boundary conditions(RS λ )ˆ−(pu ′ ) ′ +qu = λf(t,u) in I =]a,b[u(a) = u ′ (b) = 0,where λ is a positive parameter and p, q, f are regular functions. To be precise,if f : [a,b] × R→ Ris a L 2 -Carath´eodory function and p,q ∈ L ∞ ([a,b]) suchthatp 0 := essinf t∈[a,b] p(t) > 0, q 0 := essinf t∈[a,b] q(t) ≥ 0,then we prove …
Regular subclasses in the Sobolev space
2009
Abstract We study some slight modifications of the class α - A C n ( Ω , R m ) introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. and Appl. 303 (2005) 119–134]. In particular we prove that the classes α - A C λ n ( Ω , R m ) , 0 λ 1 , introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R n , Rend. Circ. Matem. Palermo 55 (2006) 296–304] are independent by λ and contain properly the class α - A C n ( Ω , R m ) . Moreover we prove that α - A C n ( Ω , R m ) = ( α - A C λ n ( Ω , R m ) ) ∩ ( α - A C n , λ ( Ω , R m ) ) , where α - A C n , λ ( Ω , R m ) is the symmetric class of α - A C λ n ( Ω , R m ) , 0 λ 1 .
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 | ) .
Escape transition of a polymer chain from a nanotube: How to avoid spurious results by use of the force-biased pruned-enriched Rosenbluth algorithm
2008
A polymer chain containing $N$ monomers confined in a finite cylindrical tube of diameter $D$ grafted at a distance $L$ from the open end of the tube may undergo a rather abrupt transition, where part of the chain escapes from the tube to form a "crown-like" coil outside of the tube. When this problem is studied by Monte Carlo simulation of self-avoiding walks on the simple cubic lattice applying a cylindrical confinement and using the standard pruned-enriched Rosenbluth method (PERM), one obtains spurious results, however: with increasing chain length the transition gets weaker and weaker, due to insufficient sampling of the "escaped" states, as a detailed analysis shows. In order to solve…
Table of periodic properties of human immunodeficiency virus inhibitors
2010
Classification algorithms are proposed based on information entropy. The feasibility of mixing a given human immunodeficiency virus (HIV) inhibitor with dissimilar ones is studied. The 31 inhibitors are classified by their structural chemical properties. Many classification algorithms are based on information entropy. An excessive number of results appear compatible with the data and suffer combinatorial explosion. However, after the equipartition conjecture one has a selection criterion. According to this conjecture, the best configuration is that in which entropy production is most uniformly distributed. The structural elements of an inhibitor can be ranked according to their inhibitory a…
Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles
2014
Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodic…
Norms of harmonic projection operators on compact Lie groups
1988
In order to simplify the notation, we will assume throughout that G is connected, simply connected and semisimple. Sharp estimates for vp(z 0 when G = SU(2) have been obtained by Sogge [6], who proved that Vp(Zt) ~ d~ tl/v), where y(t) is the function which is affine on [1/2, 3/4] and on [3/4, 1] and is such that 7(1/2)=0, 7(3/4)=1/4, 7(1)=1. Two results in the literature give crucial estimates from below for vp(n) in the general case. The first estimate concernes the LP'-norm of the character X, : if ,~, is the highest weight of n and 0 is half the sum of the positive roots, then II x=llp,--> + 011-dimG/p" (1.2)
Compactness of a conformal boundary of the Euclidean unit ball
2011
We study conformal metrics d‰ on the Euclidean unit ball B n : We assume that either the density ‰ associated with the metric d‰ satisfies a logarithmic volume growth condition for small balls or that ‰ satisfies a Harnack inequality and a suitable sub-Euclidean volume growth condition. We prove that the ‰-boundary @‰ B n is homeomorphic to S ni1 if and only if @‰ B n is compact. In the planar case, the compactness of @‰ B 2 is further equivalent to local connectivity of the ‰-boundary together with the boundedness of (B 2 ;d‰):