Preparation, Structure, and Thermal Decomposition of Co(II) Complexeswith 2,3- and 2,5-Dichlorobenzoic Acid and Imidazole

 The reaction products of Co(II)-2,3- and -2,5-dichlorobenzoate with imidazole (1, 2; CoL ₂⋯2imdċ2H₂O, L=C₇H₃Cl₂O, imd=imidazole) were characterized by their spectroscopic and thermochemical properties. The compounds crystallize in the monoclonic system with space group = P2₁/c, a=13.848(3), b=12.841(3) ?, c= 7.064(2) ?, β=98.12 °, V=1243.5(4) ?³, Z=2 for 1 and space group =P2₁/n, a=13.293(3), b= 6.964(2), c=13.800(3) ?, β=108.92(3) °, V=1208.6(4) ?³, Z=2 for 2. The complexes lose their crystal water in one step at 333 K and subsequently decompose to CoO with intermediate formation of Co₃O₄.     

Tri(mesityloxy)silanethiol – The First Structurally Characterized Organoxysilanethiol (Contributions to the Chemistry of Silicon–Sulfur Compounds. 77 [1])

Tri(mesityloxy)silanethiol (TMST) was isolated as the only product of the reaction between SiS₂ and 2,4,6‐trimethylphenol. TMST crystallizes in the triclinic system. Good quality of the crystal allowed the unrestricted refinement of the mercapto group; the resulting S–H distance is 1.29(4) Å and the Si–S–H bond angle is 95.4(17)°. Molecules of TMST show no hydrogen bonds in the crystal – the FT‐IR spectrum of the solid sample exhibits a very sharp, well‐resolved band of isolated –SH group at 2562 cm^–1.     

Fluorescent chemosensors for metal ions based on 3-(2-benzoxazol-5-yl)alanine skeleton

The ability of new chelate ligands, benzoxazol-5-yl-alanine derivatives substituted in position 2 by heteroaromatic substituent, to form complexes with selected metal ions in acetonitrile are studied by means of absorption and steady-state and time-resolved fluorescence spectroscopy. Among the ligands studied, only azaaromatic derivatives form stable complexes with transition metal ions in the ground state. Their absorption bands are bathochromically shifted enabling to use those ligands as ratiometric sensors. The fluorescence of each ligand is quenched by metal ions, however, in the presence of Cd(II) and Zn(II) ions a new red shifted emission band is observed.      

Fundamental Problems in the Unification of Physics

We discuss the following problems, plaguing the present search for the “final theory”: (1) How to find a mathematical structure rich enough to be suitably approximated by the mathematical structures of general relativity and quantum mechanics? (2) How to reconcile nonlocal phenomena of quantum mechanics with time honored causality and reality postulates? (3) Does the collapse of the wave function contain some hints concerning the future quantum gravity theory? (4) It seems that the final theory cannot avoid the problem of dynamics, and consequently the problem of time. What kind of time, if this theory is supposed to be background free? (5) Will the dynamics of the “final theory” be probabilistic? Quantum probability exhibits some essential differences as compared with classical probability; are they but variations of some more general probabilistic measure theory? (6) Do we need a radically new interpretation of quantum mechanics, or rather an entirely new theory of which the present quantum mechanics is an approximation? (7) If the final theory is to be background free, it should provide a mechanism of space-time generation. Should we try to explain not only the generation of space-time, but also the generation of its material content? (8) As far as the existence of the initial singularity is concerned, one usually expects either “yes” or “not” answers from the final theory. However, if the mathematical structure of the future theory is supposed to be truly more general that the mathematical structures of the present general relativity and quantum mechanics, is a “third answer“ possible? Could this third answer be related to the probabilistic character of the final theory? We discuss these questions in the framework of a working model unifying gravity and quanta. The analysis reveals unexpected aspects of these rather wildly discussed issues.     

Quasi-Banach spaces of almost universal disposition

We show that for each p∈(0,1]$p\in (0,1]$ there exists a separable p  -Banach space _Gp${\mathbb{G}}_p$ of almost universal disposition, that is, having the following extension property: for each ε>0$\epsilon >0$ and each isometric embedding g:X→Y$g:X\to Y$, where Y is a finite-dimensional p-Banach space and X   is a subspace of _Gp${\mathbb{G}}_p$, there is an ε  -isometry f:Y→_Gp$f:Y\to {\mathbb{G}}_p$ such that x=f(g(x))$x=f(g(x))$ for all x∈X$x\in X$.     

Cohomology of Crystalline Smooth Sheaves

We define and study a candidate for 'arithmetic' cohomology theory with values in crystalline p-adic smooth sheaves. We show that it injects into arithmetic étale cohomology and prove a duality result.     

On relations between non-Archimedean power series spaces

The power series spaces of finite type, A₁(α), and infinite type, A_∞(α), are the most known and important examples of non-Archimedean nuclear Fréchet spaces. We study when Aπ (α) has a subspace (or quotient) isomorphic to A_q(b).     

Test of an optical parametric oscillator (OPO) as a compact and fast tunable stokes source in coherent anti-stokes raman spectroscopy (CARS)

An optical parametric oscillator (OPO), as a novel kind of broadband Stokes source, is employed for coherent anti-Stokes Raman spectroscopy (CARS). Compared to the conventional dye laser configuration OPO-CARS offers practical advantages. The tunable OPO allows a fast and comfortable frequency tuning. The excitation bandwidth of about 35 cm^–1 (FWHM) limits the spectral range of effective and stable single pulse CARS generation but can be used to enhance selected spectral structures.     

Remarks on the Analytic Centers of Convex Sets

In this paper we analyze properties of the analytic centers for perturbed convex problems. In particular we study the continuity of convex regions with respect to such characteristics as boundedness, full dimensionality and the existence of an analytic centre. Furthermore, we state the necessary and sufficient conditions for the existence of the analytic centre for possibly unbounded regions and we show that the analytic centre is identical for any minimal representation of the convex set. We are also concerned with the limiting behaviour of the central path as it approaches the set of optimal solutions of the problem.     

Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups

We give three equivalent conditions for weak convergence of almost orbits of an asymptotically nonexpansive commutative semigroup acting on a nonempty bounded closed convex subset of a uniformly convex Banach space whose dual has the Kadec property.