Spectral multiplicity of some stochastic processes

In this paper we consider the connection between the canonical and the weak-canonical representations for the given second-order stochastic process in a separable Hilbert space and we extend a well-known theorem of H. Cramer concerning sufficient conditions for a process to be of multiplicity one.

     

d‐Secoestrone derivatives. VI. 17β‐Benzyl‐17α‐hydroxy‐3‐methoxyestra‐1,3,5(10)‐trien‐16‐one

The title mol­ecule, C₂₆H₃₀O₃, shows a novel chemical rearrangement of the substituents at position 17, i.e. an α‐­orientation of the hydroxy group and a β‐orientation of the bulky benzyl moiety. The packing arrangement consists of coils formed by O2?O3 hydrogen bonds along the c axis. The compound shows complete loss of oestrogenic activity, and neither does it exhibit an antagonistic effect.     

Newly generated cells are increased in hippocampus of adult mice lacking a serine protease inhibitor

Background  

Neurogenesis in the hippocampal dentate gyrus and the subventricular zone occurs throughout the life of mammals and newly generated neurons can integrate functionally into established neuronal circuits. Neurogenesis levels in the dentate gyrus are modulated by changes in the environment (enrichment, exercise), hippocampal-dependent tasks, NMDA receptor (NMDAR) activity, sonic hedgehog (SHH) and/or other factors.     

Stochastic modeling of the growth process

In this paper we estimate the upper boundary of the number of trees in the selection stand determined for harvesting in a future. At the same time we showed that the present resource of the number of trees in selection stand is sustained. This is achieved by stochastic modeling of the number of trees and the number of felled trees and by solving the partial differential equation. The same problem is solved in the papers, Mitrović (Stochastic modeling of the number of trees and the number of felled trees in selection stands, YUJOR, vol 14(1), pp 57–64, 2004; Stochastic modeling of the number of felled trees in selection stands, Computational and Applied Mathematics, vol 24(2), pp 285–292, 2005). In this paper the modified mathematical model is represented.      

Convex additively slowly varying functions

We study the problem of subtraction of slowly varying functions. It is well-known that the difference of two slowly varying functions need not be slowly varying and we look for some additional conditions which guarantee the slow variation of the difference. To this end we consider all possible decompositions L=F+G of a given increasing convex additively slowly varying function L into a sum of two increasing convex functions F and G. We characterize the class of functions L for which in every such decomposition the summands are necessarily additively slowly varying. The class OΠ₂⁺ we obtain is related to the well-known class OΠ_g where, instead of first order differences as in OΠ_g, we have second order differences.     

Ozonation of 3β-acetoxy-5α-chloro-cholestane in solution. X-ray study of 3β-acetoxy-5α-chloro-14-cholestene-ozonide.

A selected saturated steroid derivative has been subjected to ozonation in solution. As the main reaction product 14,15-ozonide has been isolated in crystalline form whose structure has been unambiguously confirmed by the X-ray difraction method.     

d‐Secoestrone derivatives. V

The two title 16,17‐secoestrone derivatives, 3‐methoxy‐17‐oxo‐17‐phenyl‐16,17‐secoestra‐1,3,5(10)‐triene‐16‐nitrile, C₂₅H₂₇NO₂, (I) (17‐oxo substituent), and 17‐hydroxy‐3‐methoxy‐17‐phenyl‐16,17‐secoestra‐1,3,5(10)‐triene‐16‐nitrile, C₂₅H₂₉NO₂, (II) (17‐hydroxy substituent), have quite different conformations in the solid state. These conformational differences can be minimized by molecular mechanics calculations. Thus, the remarkable difference in the biological activity of the two compounds, e.g. the strong oestrogenic characteristics of (I) and the moderate antioestrogenic action of (II), must be caused by the difference in substitution at C17. In (II), the mol­ecules are linked by O—H?N hydrogen bonds, forming spirals along the b direction.     

Stereospecific ligands and their complexes. IV: Synthesis,characterization and cytotoxicity of novel platinum(IV) complexes with ethylenediamine-N,N′-di-S,S-2-propanoate and halogenido ligands: Crystal structure of s-cis-[Pt(S,S-eddp)Cl2]·4H2O and uns-cis-[Pt(S,S-eddp)Br2]

The syntheses of two novel platinum(IV) complexes of formula [PtX₂(S,S-eddp)]·nH₂O (S,S-eddp = ethylenediamine-N,N′-di-S,S-2-propanoate ion, X = chlorido (1) or bromido (2), n = 4, 0) are reported. The complexes have been obtained by direct reaction of corresponding potassium hexahalogenidoplatinate(IV) with neutralized ethylenediamine-N,N′-di-S,S-2-propanoic acid (H₂-S,S-eddp). The complexes were characterized by elemental analysis, infrared, ¹H and ¹³C NMR spectroscopy. The spectroscopically predicted geometrical configurations of the obtained complexes were confirmed by X-ray analyses of the crystal structures of the s-cis-[Pt(S,S-eddp)Cl₂]·4H₂O and uns-cis-[Pt(S,S-eddp)Br₂]. These complexes displayed significantly lower in vitro cytotoxicity in comparison to cisplatin.     

Synthesis and unusual beckmann fragmentation reaction of syn-3-Methoxy-6α,17β-Dihydroxyestra-1,3,5(10)-trien-7-one oxime

Sodium borohydride reduction of anti-3-methoxy-17β-hydroxyestra-1,3,5(10)-trien-6,7-dione 7-oxime (4a) afforded syn-3-methoxy-6α,17β-dihydroxyestra-1,3,5(10)-trien-7-one oxime (5), which in thionyl chloride at −18 °C undenvent Beckmann fragmentation reaction to the unexpected 3-methoxy-6-oxo-17β-hydroxy-6.7-secoestra-1.3.5(10)-trien-7-nitrile (6). A mechanism of this fragmentation process was proposed.