Approximations of inventory models

Summary A general procedure is presented for constructing approximations of discrete review single product dynamic inventory models. Bounds are derived for the approximations and compared with the ones ofHinderer [1978],Whitt [1978] for the approximation of a general dynamic program. Good order-policies are constructed. Finally, conditions are given under which the sequence of bounds associated with a sequence of approximating models converges to zero.

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Zusammenfassung Es wird ein allgemeines Verfahren zur Approximation periodisch inspizierter dynamischer Ein-Produkt-Lagerhaltungsmodelle betrachtet. Dazu werden Fehlerschranken gegeben. Diese werden verglichen mit denen vonHinderer [1978],Whitt [1978] für ein allgemeines dynamisches Entscheidungsmodell. Außerdem werden gute Bestellpolitiken konstruiert und hinreichende Bedingungen gegeben, unter denen die Fehlerschranken einer Folge von approximierenden Modellen gegen Null konvergiert.

     

Synthetic Strategies To Obtain V-P-O Open Frameworks Containing Organic Species as Structural Directing Agents. Crystal Structure of the V(IV)-Fe(III) Bimetallic Phosphate [H(3)N(CH(2))(2)NH(3)](2)[H(3)N(CH(2))(2)NH(2)][Fe(III)(H(2)O)(2)(V(IV)O)(8)(OH)(4)(HPO(4))(4)(PO(4))(4)].4H(2)O

A general synthetic approach to rationalize the solution preparative chemistry of oxovanadium phosphates containing organic species as structural directing agents is presented. Careful attention is payed to the hydrolysis and condensation processes involving the ionic species in solution, and a simple restatement of the partial charge model (PCM) has been used in order to organize the experimental results. The structure of a new V(IV)-Fe(III) bimetallic oxovanadium phosphate, [H(3)N(CH(2))(2)NH(3)](2)[H(3)N(CH(2))(2)NH(2)] [Fe(III)(H(2)O)(2)(V(IV)O)(8)(OH)(4)(HPO(4))(4)(PO(4))(4)].4H(2)O, has been determined by X-ray single crystal diffraction methods. This compound crystallizes in the monoclinic system, space group P2(1)/n and the cell dimensions are as follows: a = 14.383(3) ?, b = 10.150(2) ?, c = 18.355(4) ?, and beta = 90.39(3) degrees (Z = 2). The existence of a complex intercrossing channel system, including a very large channel of 18.4 ? of diameter (in which both water molecules and ethylenediamine species are located), is the more interesting feature of this structure. Thermal decomposition, including the dehydration/rehydration process, has been studied by thermal analysis and variable temperature X-ray powder diffraction techniques. A complementary SEM study of the different intermediate decomposition products is presented.     

The role of β-cyclodextrin and hydroxypropyl β-cyclodextrin in the secondary chemical equilibria associated to the separation of β-carbolines by HPLC

The use of cyclodextrins (CDs) in HPLC as mobile phase additives provides a flexible alternative for the separation of chemically related compounds because these separations can be performed on conventional columns and are economically advantageous over the use of chiral stationary phases. The present paper describes the influence of the presence of β-cyclodextrin (β-CD) and 2-hydroxypropyl-β-cyclodextrin (HPβ-CD) on the separation of the β-carboline alkaloids norharmane, harmane and harmine. The nature of the stationary phase (reverse phases C₁ and C₁₈) affects the chromatographic separations and also the stability of the inclusion complexes that are developed. The changes in the proportion of the organic solvents at constant concentration of CDs (3 mM for β-CD and 15 mM for HPβ-CD) modify the retention factors (k′) for all alkaloids studied. The nature of the organic solvent in the mobile phase also changes the chromatographic parameters. The logarithm of the capacity factor (k′) is linearly increased with the proportion of water in the hydro-organic mobile phase (ethanolic or methanolic) but the slopes obtained vary depending on the CD added to the mobile phase. The role of competitive equilibria, i.e., chromatographic distribution and inclusion complexes formation is discussed. This paper was presented at XIIIth International Cyclodextrin Symposium. Torino, Italy, May, 14–17, 2006     

Facile Synthesis and Palladium‐Catalyzed Cross‐Coupling Reactions of 2,3‐Bis(pinacolatoboryl)‐1,3‐butadiene

Treatment of 1,1‐bis(pinacolatoboryl)ethene with an excess of 1‐bromo‐1‐lithioethene gave 2,3‐bis(pinacolatoboryl)‐1,3‐butadiene in high yield. Palladium‐catalyzed cross‐coupling of the resulting diborylbutadiene with aryl iodides took place smoothly in the presence of a catalytic amount of Pd(OAc)₂/PPh₃ and aqueous KOH to give 2,3‐diaryl‐1,3‐butadienes in good yields. The coupling reaction with commercially available 4‐acetoxyphenylmethyl chloride under the same conditions followed by hydrolysis of the acetyl groups gave anolignan B in a one‐pot manner. A variety of [3]‐ to [6]dendralenes were synthesized by palladium‐catalyzed coupling of the diene or 1,1‐bis(pinacolato)borylethene with alkenyl or dienyl halides, respectively, in good yields.     

(Me2NH2)[(Ph3Sn)3(MoO4)2], ein Triorganozinnmolybdat mit Schichtstruktur

(Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂], a Triorganotin Molybdate with Layer Structure The reaction of [(Ph₃Sn)₂MoO₄] with (Me₂NH₂)Cl in an acetonitrile/water mixture leads to the formation of (Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂] ( 1 ). ( 1 ) crystallizes in the space group Pca2₁ with a = 1967.0(4), b = 1353.1(2) and c = 2176.6(5) pm. In the crystal structure of 1 Ph₃SnO₂ bipyramides and MoO₄ tetrahedra are linked by corner sharing to give a layer structure. Additionally the layers are connected by O···H···N hydrogen bridges between MoO₄ groups and [Me₂NH₂]⁺ ions to give a 3D network structure.     

On triazoles XIX: The reaction of 5-amino-1,2,4-triazoles with functionalized acetoacetic esters

Summary Different functionalized alkyl 3-oxo-butyrates (2) were reacted with 5-amino-3-Q-1H-1,2,4-triazoles (1) to yield3 and4 type 1,2,4-triazolo[1,5-a]pyrimidinones. In case of2 (R ¹=methyl,R ²=1-ethoxycarbonylethyl,R ³=ethyl) beside the corresponding derivative4 the unexpected 5,6-dihydro-6,8-dimethyl-7-ethoxycarbonyl-3-methylthio-1,2,4-triazolo[4,3-a]-1,3-diazepin-5(9H)-one (7) was isolated, representing a novel ring system.

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Über Triazole, 19. Mitt.: Die Reaktion von 5-Amino-1,2,4-triazolen mit funktionalisierten Acetoessigestern

Zusammenfassung Verschiedene funktionalisierte 3-Oxo-buttersäurealkylester (2) wurden mit 5-Amino-3-Q-1H-1,2,4-triazolen (1) umgesetzt, wobei 1,2,4-Triazolo[1,5-a]pyrimidinone der Typen3 und4 erhalten wurden. Im Fall von2 (R ¹=Methyl,R ²=1-Ethoxycarbonylethyl,R ³=Ethyl) wurde neben dem erwarteten Derivat4 das unerwartete 5,6-Dihydro-6,8-dimethyl-7-ethoxycarbonyl-3-me-thylthio-1,2,4-triazolo[4,3-a]-1,3-diazepin-5(9H)-on (7) isoliert, welches ein neues Ringsystem darstellt.

     

Regioselectivity in methylation and phenylation of the zwitterionic pyrido[2,1-f]-as-triazinium-1- and 3-olates and thiolates

Substituted derivatives of the title ring system have been synthesized and the regioselectivity in methylation and phenylation of the zwitterionic pyrido[2,1-f]-as-triazinium 1- and 3-olates 4a-g and 10 and thiolates 7a,b and 12 has been studied by nmr techniques. Depending on the soft or hard nature of the used reagent (methyl iodide, trimethyloxonium hexafluorophosphate or diphenyliodonium tetrafluoroborate), the reaction yielded NMe 5 and/or OMe 6,11a and NPh 14 or OPh 11b products in the case of olates; while thiolates gave NMe 8 and/or SMe 9,13a and SPh 13b, 15 compounds. Mechanistic suggestions are given to rationalize the observed phenomena.     

Conformational analysis of trans-2,3-diaryloxy-1,4-dioxanes. A tool for discriminating between steric and electronic effects in the position of

The conformation of several $\text{trans}$-2,3-diaryloxy-1,4-dioxanes has been studied using ¹H NMR techniques. $\text{Trans}$-2,3-bis(4-nitrophenoxy)-1,4-dioxane and $\text{trans}$-2,3-bis(4-methoxyphenoxy)-1,4-dioxane have been found to be predominantly ( ≈98%) in diaxial conformation in CDCl₃). On the other hand, $\text{trans}$-2,3-bis(2,6-dimethylphenoxy)-1,4-dioxane exists in the same conditions as a 66:33 mixture of diaxial and diequatorial conformers. An explanation based on the fulfilment of the exo-anomeric effect is provided.     

Alkynyldiphenylphosphine d8 (Pt, Rh, Ir) complexes: contrasting behavior toward cis-[Pt(C6F5)2(THF)2

The synthesis and characterization of a series of mononuclear d(8) complexes with at least two P-coordinated alkynylphosphine ligands and their reactivity toward cis-[Pt(C(6)F(5))(2)(THF)(2)] are reported. The cationic [Pt(C(6)F(5))(PPh(2)C triple-bond CPh)(3)](CF(3)SO(3)), 1, [M(COD)(PPh(2)C triple-bond CPh)(2)](ClO(4)) (M = Rh, 2, and Ir, 3), and neutral [Pt(o-C(6)H(4)E(2))(PPh(2)C triple-bond CPh)(2)] (E = O, 6, and S, 7) complexes have been prepared, and the crystal structures of 1, 2, and 7.CH(3)COCH(3) have been determined by X-ray crystallography. The course of the reactions of the mononuclear complexes 1-3, 6, and 7 with cis-[Pt(C(6)F(5))(2)(THF)(2)] is strongly influenced by the metal and the ligands. Thus, treatment of 1 with 1 equiv of cis-[Pt(C(6)F(5))(2)(THF)(2)] gives the double inserted cationic product [Pt(C(6)F(5))(S)mu-(C(Ph)=C(PPh(2))C(PPh(2))=C(Ph)(C(6)F(5)))Pt(C(6)F(5))(PPh(2)C triple-bond CPh)](CF(3)SO(3)) (S = THF, H(2)O), 8 (S = H(2)O, X-ray), which evolves in solution to the mononuclear complex [(C(6)F(5))(PPh(2)C triple-bond CPh)Pt(C(10)H(4)-1-C(6)F(5)-4-Ph-2,3-kappaPP'(PPh(2))(2))](CF(3) SO(3)), 9 (X-ray), containing a 1-pentafluorophenyl-2,3-bis(diphenylphosphine)-4-phenylnaphthalene ligand, formed by annulation of a phenyl group and loss of the Pt(C(6)F(5)) unit. However, analogous reactions using 2 or 3 as precursors afford mixtures of complexes, from which we have characterized by X-ray crystallography the alkynylphosphine oxide compound [(C(6)F(5))(2)Pt(mu-kappaO:eta(2)-PPh(2)(O)C triple-bond CPh)](2), 10, in the reaction with the iridium complex (3). Complexes 6 and 7, which contain additional potential bridging donor atoms (O, S), react with cis-[Pt(C(6)F(5))(2)(THF)(2)] in the appropriate molar ratio (1:1 or 1:2) to give homo- bi- or trinuclear [Pt(PPh(2)C triple-bond CPh)(mu-kappaE-o-C(6)H(4)E(2))(mu-kappaP:eta(2)-PPh(2)C triple-bond CPh)Pt(C(6)F(5))(2)] (E = O, 11, and S, 12) and [(Pt(mu(3)-kappa(2)EE'-o-C(6)H(4)E(2))(mu-kappaP:eta(2)-PPh(2)C triple-bond CPh)(2))(Pt(C(6)F(5))(2))(2)] (E = O, 13, and S, 14) complexes. The molecular structure of 14 has been confirmed by X-ray diffraction, and the cyclic voltammetric behavior of precursor complexes 6 and 7 and polymetallic derivatives 11-14 has been examined.     

Efficient synthesis and spectral determination of 11‐[(o‐ m‐ and p‐substituted)‐phenyl]‐8‐chloro‐3,3‐dimethyl‐2,3,4,5,10,11‐hexahydro‐1H‐dibenzo[b,e][1,4]diazepin‐1‐ones

A new synthesis to obtain eleven novel derivatives of 11‐[(o‐ m‐ and p‐substituted)‐phenyl]‐8‐chloro‐3,3‐dimethyl‐2,3,4,5,10,11‐hexahydro‐1H‐dibenzo[b,e][1,4]diazepin‐1‐ones with possible pharmacological activity in the central nervous system in two efficient steps has been developed. The final products were obtained by condensation and cyclization between 3‐[4‐chloro‐1,2‐phenylenediamine]‐5,5‐dimethyl‐2‐cyclohexenone with (o‐ m‐ and p‐substituted)benzaldehyde. The structure of all products was corroborated by ir, ¹H‐nmr, ¹³C‐nmr and high resolution in ms.