Der quadratfreie Kern der Eulerschen φ-Funktion

It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers.     

The Mitsunobu Reaction: Origin,Mechanism, Improvements,and Applications

The Mitsunobu reaction is a widely used and versatile method for the dehydrative oxidation–reduction condensation of an acid/pronucleophile usually with a primary or secondary alcohol that requires the combination of a reducing phosphine reagent together with an oxidizing azo reagent. The utility of this reaction stems from the fact that it is generally highly stereoselective and occurs with inversion of the stereochemical configuration of the alcohol starting material. Furthermore, as carboxylic acids, phenols, imides, sulfonamides, and other compounds can be used as the acid/pronucleophile, this reaction is useful for the preparation of a wide variety of functional groups. This Focus Review of the Mitsunobu reaction summarizes its origins, the current understanding of its mechanism, and recent improvements and applications.     

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐Molybdate(II) Anions: Synthesis,Spectroscopy, and Density Functional Theory Calculations

Carbonyldinitrosyltris(fluorosulfato)tungstate(II) and ‐molybdate‐(II) anions, [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo), which are novel weakly coordinating anions that contain a metal carbonyl/nitrosyl moiety, have been generated in fluorosulfonic acid and completely characterized by multinuclear NMR, IR, and Raman spectroscopy as well as ESI mass spectrometry. ESI MS measurements performed for the first time on a superacidic solution system unambiguously reveal the formation of the monoanionic, mononuclear W and Mo complexes formulated as [M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo). Multinuclear NMR spectroscopic studies at natural abundance and ¹³C and ¹⁵N enrichment clearly indicate the presence of one CO ligand, two equivalent NO ligands, and two types of nonequivalent SO₃F^? groups in a 2:1 ratio. The IR and Raman spectra reveal that the two equivalent NO ligands have a cis conformation, thus indicating a fac structure. Density functional calculations at the B3LYP level of theory predict that these anions have a singlet ground state (¹A′) with a C_s symmetry along with C–O and N–O vibrational frequencies that are in agreement with the experimental observations. Mulliken population analysis shows that the monovalent negative charge is dispersed on the bulky sphere, the surface of which is covered by all the negatively charged O and F atoms with charge densities much lower than SO₃F^?, suggesting that [fac‐M(CO)(NO)₂(SO₃F)₃]^? (M=W, Mo) are weakly nucleophilic and poorly coordinating anions.     

"ENERGY"-DEPENDENT QUENCHING OF CHLOROPHYLL FLUORESCENCE and THERMAL ENERGY DISSIPATION IN INTACT LEAVES DURING INDUCTION OF PHOTOSYNTHESIS

Abstract— Intact leaves, previously adapted to darkness for a prolonged period of time, were suddenly illuminated with a strong, photosynthetically saturating, white light (ca 1500 μmol m⁻² s^_1), resulting in the rapid establishment of a large energy-dependent chlorophyll fluorescence quenching (q_E) as shown by in vivo fluorescence measurements with a pulse amplitude modulation technique. Two different photothermal methods, photoacoustic spectroscopy and photothermal deflection spectroscopy, were used to monitor thermal deactivation of excited pigments during the dark-light transitions. The in vivo photothermal signals measured with both techniques were shown to remain constant during induction of photosynthesis under high light conditions, suggesting that, in contrast to current hypotheses, energy-dependent quenching q_E is not associated with significant changes in thermal dissipation of absorbed light energy in the chloroplasts. When photosynthesis was induced with a low-intensity modulated light, a noticeable decrease in the heat emission yield was observed resulting from the progressive activation of the competing photochemical processes.     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

---

Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

---

Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables     

Über 1-Alkyl-bzw. 1-Aryl-dihydro-6-methyl-2(1H)-pyrimidinthione

The title compounds7 are formed in a general reaction by heating β-isothiocyanoketones3 with primary amines in inert solvents, or by thermal elimination of water from tetrahydro-6-hydroxy-6-methyl-2(1H)-pyrimidinethiones5, also in inert solvents. The 1-alkyl compounds can also be prepared under similar conditions from α,β-unsaturated ketones by reaction with alkylammonium rhodanides. The NMR-spectra show that the 1-substituted dihydro-6-methyl-2(1H)-pyrimidinethiones are in tautomeric equilibrium with the tetrahydro-6-methylene-2(1H)-pyrimidinethiones13. The reactivity of 1-alkyl and 1-aryldihydro-6-methyl-2(1H)-pyrimidinethiones is similar to that of dihydro-4,4,6-trimethyl-2(1H)-pyrimidinethione7 j, although their ring stability is certainly less.     

Beiträge zur Chemie des Sulfamids, 1. Mitt.: Zur Konstitution des Disilber-sulfamids

According to spectroscopic (IR, broadline proton NMR) and chemical (alkylation) investigations of disilver sulphamide the following molecular structure is assumed: $$\begin{gathered} O \hfill \\ || \hfill \\ H_2 N\_\_S\_\_NAg| \hfill \\ OAg \hfill \\ \end{gathered}$$ From the IR and NMR data deduction concerning the nature of the chemical bonds in this compound is possible. The instability of the still unknown mono-and trisilver sulphamide is discussed with regard to the structure of disilver sulphamide.     

Un nouveau type d'alcaloïdes isoquinoleiques,les bisaporphines

The structures of Beccapoline and Beccapolinium, two new isoquinoline alkaloids from $\text{Polyathia beccarii}$, Annonaceae, have been elucidated by spectroscopic analysis. They are the first examples of natural bisaporphines.     

Chemical ionization desorption mass spectrometry of some quaternary ammonium salts

The ammonia chemical ionization desorption spectra of N,N-dimethyl quaternary ammonium iodides in addition to high protonated molecular ion [M + H]⁺ intensity, show signals for an ion radical composed of N-methyl abstracted salt cation and ammonia [C + NH₃? CH₃]^+˙. These ions corresponding to the cation +2 show increased importance in the chemical ionization mode, using the same reagent gas. The technique of chemical ionization desorption appears suitable for the analysis of salts, and thus for the determination of the molecular weight of both anion and cation.     

Utilization of cyclotron produced fast neutrons in the activation analysis for oxygen

The possible application of cyclotron-produced fast neutrons to activation analysis for oxygen based on the¹⁶O(n, p)¹⁶N reaction has been investigated. Neutrons were produced by bombarding a thick beryllium target with 22 to 45 MeV deuterons. It was found that the sensitivity increases rapidly with the energy of the deuterons. Using 45 MeV deuterons and a 10 μA beam current a sensitivity of about 20 counts per 1 μg oxigen could be achieved, enabling the determination of less than 1 μg oxigen. In a direct comparison it was experimentally established that the sensitivity for cyclotron-produced neutrons assuming a deuteron beam of about 10 μA, is up to two orders of magnitude higher than that achievable for 14 MeV neutrons with a flux of about 10¹⁰ n/s. The interference of fluorine is at about the same level for both the cyclotron-produced and 14 MeV neutrons. Using cyclotron-produced fast neutrons in the investigated energy range, sodium and magnesium can also interfere, but only to a very much lower extent.