Some representations of midconvex set-valued functions

Summary In this note we establish conditions under which every midconvex set-valued function can be represented as sum of an additive function and a convex set-valued function. These results improve some theorems obtained in [8], [10] and [3]. Some results on local Jensen selections of midconvex set-valued functions are also given.     

Strong convexity and separation theorems

Characterizations of pairs of functions that can be separated by a strongly convex, approximately concave or c-quadratic-affine function are presented. As consequences, stability results of the Hyers-Ulam type are obtained.     

A note on three-parameter families and generalized convex functions

The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, Generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363–371] is extended to the two-dimensional case. Using three-parameter families, we define generalized convex (midconvex, M-convex) functions and show some continuity properties of them.     

A variational formulation of relativistic hydrodynamics

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.     

A new method for the synthesis of mixed orthoesters from O-allyl acetals

Two new methods for the synthesis of orthoesters and compounds containing an orthoester moiety (dihydroisoxazoles) are presented. Mixed orthoesters of general formulas RC(OR¹)(OR²)₂ and RC(OR¹)(OR²)(OR³) were prepared via addition of ROH (R = Bu or m-methylphenyl) to O-allyl acetals (acrolein acetals: diethyl or cyclic, i.e., 2-vinyl-1,3-dioxanes or dioxolanes). The catalytic systems for these reactions were generated from [RuCl₂(PPh₃)₃] and Na₂CO₃; {[RuCl₂(COD)]_x} or {[OsCl₂(1,5-COD)]_x}, PPh₃, and Na₂CO₃. Compounds containing an orthoester moiety (dihydroisoxazoles) were prepared via tandem isomerization of O-allyl acetals (to O-vinyl acetals) catalyzed by ruthenium complexes followed by cycloaddition to in situ-generated 2,6-dichlorophenylnitrile oxide.     

Intracavity polarization control in mode-locked Er-doped fibre lasers using liquid crystals

In this paper we present a novel configuration of an NPR mode-locked Er-doped laser. This new optical setup uses voltage controlled LC cells to replace standard retarders (quarter-and half-waveplates) inside the laser cavity. Using this novel, mechanical-adjustment-free setup a mode-locking was obtained with sub-500 fs pulse duration and an average power exceeding 40 mW. Presented results show that using simple LC cells, an optical layout of an NPR mode-locked laser can be greatly simplified.     

On the behavior of the cathodically polarized Pd/D system: Search for emanating radiation

Evidence for the emission of low intensity X-rays during cathodic polarization of the Pd/D system(s) is presented. The Pd/D system was prepared by charging with electrochemically generated deuterium either palladium foil or palladium electrodeposited from D₂O electrolytes. Experimental and analytical procedures are described in detail.     

Chirped laser dispersion spectroscopy with harmonic detection of molecular spectra

Chirped laser dispersion spectroscopy (CLaDS) has been introduced recently as a technique that performs molecular detection based on measurement of optical dispersion. In this paper, a new detection scheme based on chirp modulation (CM) and subsequent phase-sensitive detection is described. CM-CLaDS inherits the full advantages of conventional CLaDS and additionally overcomes some of its limitations. A prototype CM-CLaDS instrument has been developed and characterized in laboratory conditions. The system is based on a distributed feedback quantum cascade laser which operates around 4.52???m and can probe the most intense nitrous oxide (N₂O) ro-vibrational transitions. Preliminary performance tests are presented and provide a path/bandwidth normalized minimum N₂O detection limit below 100?ppbv?m/Hz^1/2.     

Big bounce from spin and torsion

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density e μ gT⁴{\epsilon \propto gT^4} was on the order of n²/m_Pl²{n^2/m_{\rm Pl}^2} (in natural units), where n μ gT³{n \propto gT^3} is the fermion number density and g is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles (g ≈ 100), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about 10³² times smaller than its present value, giving ≈ 50 μm. If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.