The polynomial and linear time hierarchies in V0

We show that the bounded arithmetic theory V⁰ does not prove that the polynomial time hierarchy collapses to the linear time hierarchy (without parameters). The result follows from a lower bound for bounded depth circuits computing prefix parity, where the circuits are allowed some auxiliary input; we derive this from a theorem of Ajtai (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiplicity theorems for scalar periodic problems at resonance with <Emphasis Type="Italic">p</Emphasis>-Laplacian-like operator

In this paper, we study the existence of multiple solutions for nonlinear scalar periodic problems at resonance with p-Laplacian-like operator. Using the Ekeland variational principle a two-solution theorem is obtained and using also a local linking theorem a three-solution theorem is proved.      

Entropy Numbers of Embeddings of Weighted Besov Spaces

We investigate the asymptotic behavior of the entropy numbers of the compact embedding $$ B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}). $$ Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is given by $w_\alpha (x) = (1+| x |^2)^{\alpha/2}$, and $B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of parameters: $s_2 < s_1$, $0 < p_1,p_2 \le \infty$, and $$ \alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} > d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big). $$ In almost all cases we give a sharp two-sided estimate.     

Extremal Solutions and Strong Relaxation for Second Order Multivalued Boundary Value Problems

In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants No. 2 P03A 003 25 and No. 4 T07A 027 26.     

Particle dark matter — A theorist’s perspective

Dark matter (DM) is presumably made of some new, exotic particles that appear in extensions of the standard model. After giving a brief overview of some popular candidates, I discuss in more detail the most appealing case of the supersymmetric neutralino.     

The nearest adjoining order method for pairwise comparisons in the form of difference of ranks

The problem of ranking of elements from some finite set on the basis of nearest adjoining order method for pairwise comparisons is investigated in this paper. It is assumed that in the set under consideration there exists a weak preference relation, which is to be identified (estimated) on the basis of pairwise comparisons in the form of difference of ranks. Moreover, the results of comparisons may be disturbed with random errors; the assumptions made about error distributions are not restrictive. The paper comprises: the problem formulation (definitions, assumptions, and optimisation problem, which provides the NAO solution) and the theoretical background – the form of distributions of random variables which make it possible to determine the properties of NAO solution, in particular, evaluation of the probability, that the NAO solution is equivalent to the errorless one. The approach presented in the paper can be extended to the case of more than one comparison for each pair of elements, i.e., completely formalised multi-experts ranking procedure. This revised version was published online in June 2006 with corrections to the Cover Date.     

The effect of anode surface area on nanoporous oxide formation during anodizing of low purity aluminum (AA1050 alloy)

Porous anodic alumina layers were obtained by a simple two-step anodization of low purity aluminum (99.5 % Al, AA1050 alloy) in a 0.3 M oxalic acid electrolyte at 45 V and 20 °C. The effect of anode surface area on structural features of nanoporous oxide and process of oxide formation was investigated. An ordered structure composed of nanostripes or nanopores was formed on the Al surface during electrochemical polishing in a mixture of perchloric acid and ethanol. This nanopattern is then replicated during the anodic oxide formation. It was found that the pore diameter, interpore distance, and porosity increase slightly with increasing surface area of the aluminum sample exposed to the anodizing electrolyte. On the other hand, a slight decrease in pore density and cell wall thickness was observed with increasing surface area of the sample. The detailed inspection of current density vs. time curves was also performed. The obtained results revealed that the higher surface area of the anode, the local current density minimum, was reached faster during first step of anodization and the increase in current density corresponding to the pore rearrangement process was observed earlier. Finally, a dense array of Pd nanowires (～90 nm in diameter) was synthesized by simple electrodeposition of metal inside the channels of through-hole nanoporous anodic alumina templates with relatively large surface areas (4 cm²).     

On the influence of the chiral side linking bridge type upon the synclinic vs. anticlinic balance in the case of 2′,3′-difluoroterphenyl derivatives

A homologous series of new ferro- and antiferroelectric liquid crystals, containing 2′,3′-difluorosubstituted terphenyl core as a mesogenic core, has been recently synthesised. Synthetic routes and mesomorphic properties were described. Liquid crystal phases were preliminarily determined by thermomicroscopic and microcalorimetric measurements and verified by dielectric measurements and miscibility methods. Temperatures and enthalpies of phase transitions are given.     

An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems

This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones and Vassilevski 2001. Then, the algebraic construction from Jones, Vassilevski and Woodward 2003 of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. A numerical illustration is also provided.This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory: contract/grant number: W-7405-Eng-48. The contribution of the second author was also partially supported by Polish Scientific Grant 2/P03A/005/24.