On maximal chains of systems of word equations

We consider systems of word equations and their solution sets. We discuss some fascinating properties of those, namely the size of a maximal independent set of word equations, and proper chains of solution sets of those. We recall the basic results, extend some known results and formulate several fundamental problems of the topic.     

The Role of Nebulizer Gas Flow in Electrosonic Spray Ionization (ESSI)

In this work, we investigated the role of the nebulizer gas flow in electrosonic spray ionization (ESSI), by systematically studying the relation between the flow and the ion signals of proteins, such as cytochrome c and holomyoglobin using ESSI-mass spectrometry (MS). When a neutral solution was delivered with a small sample flow rate (≤5 μL/min), no obvious transition from electrospray ionization (ESI) to ESSI was found as the gas velocity varies from subsonic to supersonic speed. Droplets mostly experienced acceleration instead of breakup by the high-speed nebulizer gas. On the contrary, using particular experimental conditions, such as an acidic solution or high sample flow rate (≥200 μL/min), more folded protein ions appear to be kept in droplets of diminishing size due to breakup by the high-speed nebulizer gas in ESSI compared with ESI. Theoretical analyses and numerical simulations were also performed to explain the observed phenomena. These systematic studies clarify the ionization mechanism of ESSI and provide valuable insight for optimizing ESSI and other popular pneumatically assisted electrospray ionization methods for future applications.     

A generalized mean value inequality for subharmonic functions

If u ≥ 0 is subharmonic on a domain Ω in ⁿ and 0 < p < 1, then it is well-known that there is a constant C(n,p) ≥ 1 such u(x)^p ≤ C)n,p) MV )u^p,B(x,r)) for each ball B(x,r)) Ω. We show more generally that a similar result holds for functions ψ : ₊ → ₊ may be any surjective, concave function whose inverse ψ⁻¹ satisfies the Δ₂-condition.     

Convex functions and subharmonic functions

It is a classical result that a composition of a convex, increasing function and of a subharmonic function is subharmonic. We give related results for a composition of a convex function of several variables and of several subharmonic functions, thus imporving some recent results in this area.     

DECSERVIS: a tool for radioactive decay series visualisation

We have developed an interactive visualisation tool, decay series visualisation (DECSERVIS), for exploring the three natural radioactive decay chains. Through DECSERVIS, one can investigate the full decay scheme of any natural decay chain radionuclide to obtain the number of nuclides, their masses, activities, and activity ratios, accounting for all the daughters, starting from initial conditions freely chosen by the user. The tool has been developed particularly for user friendly and flexible operation. Chain decay in closed systems can be explored as a function of time with various graphical presentations such as solid curve and column diagrams or animation. We present several exploration examples related to geological dating. DECSERVIS will be freely available on request.     

Decidability of the binary infinite Post Correspondence Problem

We shall show that it is decidable for binary instances of the Post Correspondence Problem whether the instance has an infinite solution. In this context, a binary instance (h,g) consists of two morphisms h and g with a common two element domain alphabet. An infinite solution ω is an infinite word ω=a₁a₂… such that h(ω)=g(ω). This problem is known to be undecidable for the unrestricted instances of the Post Correspondence Problem.     

A note on morphic characterization of languages

It is noted, by using ideas of Culik, Fich and Salomaa [3], that for each language L and each regular language R the language L ∩ R is obtained from L# by applying the operation ‘a morphism followed by an inverse morphism' twice. As a consequence new purely morphic characterizations, based on the Dyck language D₂ and the twin-shuffle language L₂, are derived for the families of context-free and recursively enumerable languages, respectively. Also a morphic representation result for rational transductions follows.     

Boundary subspaces for the finite element method with Lagrange multipliers

Summary The paper is concerned with the problem of constructing compatible interior and boundary subspaces for finite element methods with Lagrange multipliers to approximately solve Dirichlet problems for secondorder elliptic equations. A new stability condition relating the interior and boundary subspaces is first derived, which is easier to check in practice than the condition known so far. Using the new condition, compatible boundary subspaces are constructed for quasiuniform triangular and rectangular interior meshes in two dimensions. The stability and optimal-order convergence of the finite element methods based on the constructed subspaces are proved.This work was supported by the Finnish National Research Council for Technical Sciences and by the Finnish-American ASLA-Fulbright Foundation     

The self-consistent symmetrized OPW method with an application to crystalline selenium

A review of the nonrelativistic self-consistent symmertrized orthogonalized-plane-wave (SCSOPW ) method used for determining electronic energy bands in periodic solids is given. Working equations based on the full use of group theory at all stages are presented for elemental crystals. As an example the method is applied to the trigonal selenium crystal.     

Computing partial information out of intractable: Powers of algebraic numbers as an example

We consider an algorithmic problem of computing the first, i.e., the most significant digits of n² (in base 3) and of the nth Fibonacci number. While the decidability is trivial, efficient algorithms for those problems are not immediate. We show, based on Baker's inapproximability results of transcendental numbers that both of the above problems can be solved in polynomial time with respect to the length of n. We point out that our approach works also for much more general expressions of algebraic numbers.