On the equality of quasi-arithmetic and Lagrangian means

The paper deals with the equality problem of quasi-arithmetic and Lagrangian means which is to determine all pairs of continuous strictly monotone functions φ,ψ:I→R such that, for all x,y∈I,

     

Strengthening of strong and approximate convexity?

Let X be a real linear space and $D\subseteq X$ be a nonempty convex subset. Given an error function E:[0,1]×(D?D)?????{+??} and an element $t\in\left]0,1\right[$ , a function f:D??? is called (E,t)-convex if $$f(tx+(1-t)y)\le tf(x)+(1-t)f(y)+E(t,x-y)$$ for all x,y??D. The main result of this paper states that, for all a,b??(???{0})+{0,t,1?t} such that {a,b,a+b}??????, every (E,t)-convex function is also $\big(F,\frac{a}{a+b}\big)$ -convex, where $$F(s,u):=\frac{{(a+b)}^2s(1-s)}{t(1-t)}E\left(t,\frac{u}{a+b}\right),\qquad (u\in (D-D), \, s\in\left]0,1\right[).$$ As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened.     

Plan-view preparation of TEM specimens from thin films using adhesive tape

A simple plan-view sample preparation technique for transmission electron microscopy (TEM) specimens is proposed for thin films by tearing-off the film with adhesive tape. The demand for very thin samples is highest for nanostructured materials where the structure of 2-5 nm sized features (grains) needs to be resolved; therefore, overlapping of nanometer-sized features should be avoided. The method provides thin areas at the fracture edges of plan-view specimens with thickness in the range of the grain size in the film allowing for artifact free high-resolution TEM imaging. Nanostructured materials typically fracture between the grains providing areas with the thickness of the grain size. Besides the swiftness of the method, the samples are free of surface amorphization artifacts, which can occur in ion beam milling up to 1 nm depth even at low energy ion bombardment. The thin film tear-off technique is demonstrated on a CuMn alloy thin film with grain size of 2 nm.     

On the equality of two-variable general functional means

Aequationes mathematicae - Given two functions $$f,g:I\rightarrow \mathbb {R}$$ and a probability measure $$\mu $$ on the Borel subsets of [0, 1], the two-variable mean $$M_{f,g;\mu...     

Behaviour of Bu(CH2—CHCH2)SnCl2 in water and water-cosolvent media: An approach to understanding the chemical degradation of organotins in aquatic environments

The behaviour of allylbutyltin dichloride in water, water–ethanol and water–hexane media, under either homogeneous or heterogeneous conditions, has been studied. 1,3-Diallyl-1,3-dibutyl-1,3-dichlorodistannoxane, butyltin di(hydroxy)chloride and butyltin trichloride arise from the solvolytic, acid–base and degradation processes. The degradation process involving the cleavage of the tin–carbon allyl bond has been interpreted to occur via an intramolecular reaction at the expense of the cation [Bu(CH₂=CHCH₂)Sn(OH)(H₂O)_n]⁺. The mechanistic pathway is ascribable to an internal interaction of the electrophilic cation with a bonded water molecule. This mechanistic proposal may be of some help with understanding of the chemical degradation of diorganotin derivatives in aquatic environments.     

Preparation dependent superconductivity in TlCaBa2Cu3O7.5±d above 100 K

Different heat treatment procedures were applied during sample preparation, which resulted in different superconducting properties in samples of the same nominal composition, TlCaBa₂Cu₃O_7.5±d . This manifests itself in different critical temperatures: 104 K, 107 K and 93 K. The highestT _c belongs to the best-crystallized samples in which the tetragonal Tl₂Ca₁Ba₂Cu₂O_8±d phase is responsible for the superconductivity. The effect of heat treatments is reflected in the structural and magnetic properties as well.     

Proposal to improve the behaviour of self-energy contributions to the S-matrix

A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is verified in a few examples using perturbation theory. The proposed formula is written in terms of the total Hamiltonian operator and a free Hamiltonian operator and is therefore applicable in any case when these Hamiltonian operators are known.     

The VIP Experimental Limit on the Pauli Exclusion Principle Violation by Electrons

In this paper we describe an experimental test of the validity of the Pauli Exclusion Principle (for electrons) which is based on a straightforward idea put forward a few years ago by Ramberg and Snow (Phys. Lett. B 238:438, 1990). We perform a very accurate search of X-rays from the Pauli-forbidden atomic transitions of electrons in the already filled 1S shells of copper atoms. Although the experiment has a very simple structure, it poses deep conceptual and interpretational problems. Here we describe the experimental method and recent experimental results, which we interpret in the framework of quon theory. We also present future plans to upgrade the experimental apparatus using Silicon Drift Detectors.     

On approximately monotone and approximately Hölder functions

Periodica Mathematica Hungarica - A real valued function f defined on a real open interval I is called $$\Phi $$ -monotone if, for all $$x,y\in I$$ with $$x\le y$$ it satisfies $$\begin{aligned}...