Methods for Determining the Re-order Point of an (<Emphasis Type="Italic">s</Emphasis>, <Emphasis Type="Italic">S</Emphasis>) Ordering Policy when a Service Level is Specified

This paper deals with a periodic review inventory system. Methods are discussed for determining the re-order point s of an (s, S) order policy, when a certain service level is required. The results differ from those presented for a (Q, s) model which is usually considered in literature and implemented in practice. Methods are discussed for determining the re-order point of an (s, S) policy when demand is normal or gamma distributed. A numerical investigation demonstrates the applicability of the described methods. In particular, it is shown that these methods are superior to a formula that is implemented in many inventory control systems.     

On the zeros of polynomials over arbitrary finite dimensional algebras

In [3] it was shown that a polynomial of degree n with coefficients in an associative division algebra, which is d-dimensional over its center, has either infinitely many or at most n^d zeros. In this paper we raise the same question for arbitrary m-ary F-algebras A which are d-dimensional over the algebraically closed field F. Our main result states that in the affine space of m-ary algebras of dimension d there is a non-empty Zariski-open set whose elements A have the following property: in the space of polynomial of precise degree n with coefficients in A there is a non-empty Zariski-open set whose elements have precisely n^d zeros. It is shown that all simple algebras, all semi-simple associative algebras, all semisimple Jordan algebras (char F2), all semi-simple Lie algebras (char F=0), and the generic algebra possess this property.     

Symmetrische Permutationsmengen

A permutation set (M, I) consisting of a setM and a set of permutations ofM, is calledsymmetric, if for any two permutations, the existence of anx M with (x) (x) and ^–1 (x) = ^–1 (x) implies ^–1 = ^–1 , andsharply 3-transitive, if for any two triples (x ₁,x ₂,x ₃), (y ₁,y ₂,y ₃) M ³ with|{x ₁,x ₂,x ₃ }| = |{y ₁,y ₂,y ₃ }| = 3 there is exactly one permutation with(x ₁) =y ₁,(x ₂) =y ₂,(x ₃) =y ₃. The following theorem will be proved.THEOREM.Let (M, ) be a sharply 3-transitive symmetric permutation set with |M|3, such that contains the identity. Then is a group and there is a commutative field K such that and the projective linear group PGL(2, K) are isomorphic.     

Platinum complexes of oxopurines: cis‐bis(theophyllinato‐N7)bis(triphenylphosphine)platinum(II) and cis‐chloro(theobrominato‐N1)bis(triphenylphosphine)platinum(II) ethanol hemisolvate

The syntheses and structures of two mixed‐ligand complexes of platinum(II) with deprotonated oxopurine bases and tri­phenyl­phosphine are reported, namely the theophyllinate complex cis‐bis(1,2,3,6‐tetra­hydro‐1,3‐di­methyl­purine‐2,6‐dionato‐κN⁷)­bis(tri­phenyl­phosphine‐κP)­platinum(II), [Pt(C₇H₇N₄O₂)₂(C₁₈H₁₅P)₂], (I), and the theobrominate complex cis‐chloro(1,2,3,6‐tetrahydro‐3,7‐dimethylpurine‐2,6‐dionato‐κN¹)­bis(tri­phenyl­phosphine‐κP)­platinum(II) ethanol hemisolvate, [PtCl(C₇H₇N₄O₂)(C₁₈H₁₅P)₂]·0.5C₂H₅OH, (II). In (I), the coordination geometry of Pt is square planar, formed by the two coordinating N atoms of the theophyl­linate anions in a cis arrangement and two P atoms from the tri­phenyl­phosphine groups. In (II), there are two crystallographically independent mol­ecules. They both exhibit a square‐planar coordination geometry around Pt involving one Cl atom, the coordinating N atom of the theobrominate anion and two P atoms from the tri­phenyl­phosphine groups. The two tri­phenyl­phosphine groups are arranged in a cis configuration in both structures. The heterocyclic rings are rotated with respect to the coordination plane of the metal by 82.99 (8) and 88.09 (8)° in complex (I), and by 85.91 (16) and 88.14 (18)° in complex (II). Both structures are stabilized by intramolecular stacking interactions involving the purine rings and the phenyl rings of adjacent tri­phenyl­phosphine moieties.     

Kinetische und mechanistische untersuchungen von übergangsmetallkomplex-reaktionen : IX. Substitution von CO durch PPh3 in aminocarbinkomplexen: Präparative und kinetische untersuchungen

Pentacarbonyl(diethylaminocarbyne)chromium tetrafluoroborate, [(CO)₅₋ CrCNEt₂]BF₄ (I), reacts with PPh₃ with substitution of CO and formation of trans-tetracarbonyl(diethylaminocarbyne)triphenylphosphanechromium tetra-fluoroborate, trans-[PPh₃(CO)₄CrCNEt₂]BF₄ (III). Substitution of CO by PPh₃ in neutral trans-tetracarbonyl(halo)(diethylaminocarbyne)chromium complexes, trans-X(CO)₄CrCNEt₂ (IVa: X = Br, IVb: X = I), leads in a reversible reaction to the corresponding tricarbonyl complexes, mer-X(PPh₃)(CO)₃₋ CrNEt₂ (V), PPh₃ occupying the cis-position to the carbyne ligand. With PPh₃ in large excess both reactions follow a first-order rate law. This as well as the activation parameters (ΔH≠ = 104–113 kJ mol⁻¹, ΔS≠ = 64–71 J mol⁻¹ K⁻¹) indicate a dissociative mechanism.     

Effect of Glass Substrates on the Formation of Gold-Silver Colloids in Nanocomposite Thin Films

A sol-gel route to synthesize nanocomposite thin films containing phase separated metal colloids of gold (Au) and silver (Ag) was developed. Ag—Au colloids were prepared in silica films using dip coating technique. The annealing of the samples in air results in the formation of phase separated Ag and Au colloids in SiO₂ thin films, showing the surface plasmon peaks at 410 nm and 528 nm. For the synthesis of phase separated Ag and Au colloids on float glass substrates, formation of the silver colloids was found strongly dependent on the surface of the float glass. On the tin rich surface formation of both gold and silver colloids took place, whereas, on the tin poor surface the formation of only gold colloids was observed. The surface dependence of the formation of silver colloids was attributed to the presence of tin as Sn²⁺ state on the glass surface, which oxidizes into Sn⁴⁺ during heat treatment, reducing Ag⁺ into silver colloids.     

Gasförmige Acetate

Gaseous Acetates Thermoanalytical and mass-spectrometrical observations are undertaken with some acetates and oxiacetates. The volatilization of copper(I) acetate takes place like that of the silver acetate as M₂Ac₂⁺ (besides the deposition of Ag). On the volatilization of the anhydrous compounds Cu₂Ac₄, Cr₂Ac₄, Rh₂Ac₄, and Mo₂Ac₄ in the vacuum of a mass spectrometer is observed that Cu₂Ac₄ vaporizes dissociative as Cu₂Ac₂⁺ (+ 2 “Ac”), while the other compounds vaporize as M₂Ac₄⁺ and simultaneously is formed an oxidic (e.g. Cr₂O₄) or metallic residue. PdAc₂ vaporizes in the mass spectrometer as a trimeric molecule Pd₃Ac₆. M₄OAc₆, which is formed from the dihydrates, vaporizes in a mass spectrometer with M ? Co, Mn as M₄OAc₆⁺. Other complexes of the same type appear as Be₄OAc₅⁺, Mg₄OAc₅⁺, and Zn₄OAc₅⁺.     

Xylose-DNA Containing the Four Natural Bases

Oligonucleotides containing (2′-deoxy-β-D -xylofuranosyl)guanine have been prepared. For this purpose 2-aminoadenosine ( 5 ) was synthesized and converted to 2′-deoxy-β-D -xyloguanosine ( 1 ). The related 2′-deoxy-β-D -xyloisoguanosine ( 3 ) and 2′-deoxy-β-D -xyloxanthosine ( 4 ) were also synthesized. Compound 1 was converted to the phosphonate and phosphoramidite building blocks 10 and 11 , respectively. The oligodeoxynucleotide (5′-3′)d(xG-xT-xA-xG-xA-xA-xT-xT-xC-xT-xA-xC-T) ( 18 ) formed a duplex with the same T_m as the parent (5′-3′)-(G-T-A-G-A-A-T-T-C-T-A-C) ( 19 ), but with an inverted CD spectrum.     

Phosphaniminato-Komplexe des Antimons. Die Kristallstrukturen von [Sb2Cl5(NPMe3)2][SbCl6] · CH3CN und [SbCl(NPPh3)]2[SbCl6]2 · 6 CH3CN

Phosphorane Iminato Complexes of Antimony. The Crystal Structures of [Sb₂Cl₅(NPMe₃)₂][SbCl₆] · CH₃CN and [SbCl(NPPh₃)]₂[SbCl₆]₂ · 6 CH₃CN The title compounds are formed by reaction of antimony pentachloride in acetonitrile solution with the phosphorane iminato complexes SbCl₂(NPMe₃) and SbCl₂(NPPh₃), respectively, which themselves are synthesized by reaction of antimony trichloride with Me₃SiNPR₃ (R = Me, Ph). The complexionic compounds are characterized by ¹²¹Sb Mössbauer spectroscopy and by crystal structure determinations. [Sb₂Cl₅(NPMe₃)₂][SbCl₆] · CH₃CN: Space group P4₁, Z = 4, 3 698 observed unique reflections, R = 0.022. Lattice dimensions at ?60°C: a = b = 1 056.0(1), c = 2 709.6(2) pm. The structure consists of SbCl₆^? ions and cations [Sb₂Cl₅(NPMe₃)₂(CH₃CN)]⁺, in which one Sb^III atom and one Sb^V atom are bridged by the N atoms of the phosphorane iminato ligands. [SbCl(NPPh₃)]₂[SbCl₆]₂ · 6 CH₃CN: Space group P1 , Z = 2, 5 958 observed unique reflections, R = 0.033. Lattice dimensions at ?60°C: a = 989.4(11), b = 1 273(1), c = 1 396(1) pm, α = 78.33(7), β = 77.27(8)°, γ = 86.62(8)°. The structure consists of SbCl₆^? ions and centrosymmetric cations [SbCl(NPPh₃)(CH₃CN)₂]₂²⁺, in which the antimony atoms are bridged by the N atoms of the phosphorane iminato ligands.