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1.
The forcing number, denoted by f(G), of a graph G with a perfect matching is the minimum number of independent edges that completely determine the perfect matching of G. In this paper, we consider the forcing number of a toroidal polyhex H(p,q,t) with a torsion t, a cubic graph embedded on torus with every face being a hexagon. We obtain that f(H(p,q,t)) ≥ min{p,q}, and equality holds for pq or p > q and t∈{ 0,pq,pq + 1,..., p−1}. In general, we show that f(H(p,q,t)) is equal to the side length of a maximum triangle on H(p,q,t). Based on this result, we design a linear algorithm to compute the forcing number of H(p,q,t).  相似文献   

2.
The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let U(k) be the set of all unicyclic graphs with a perfect matching. Let C g(G) be the unique cycle of G with length g(G), and M(G) be a perfect matching of G. Let U 0(k) be the subset of U(k) such that g(G)≡ 0 (mod 4), there are just g/2 independence edges of M(G) in C g(G) and there are some edges of E(G)\ M(G) in G\ C g(G) for any GU 0(k). In this paper, we discuss the graphs with minimal and second minimal energies in U *(k) = U(k)\ U 0(k), the graph with minimal energy in U 0(k), and propose a conjecture on the graph with minimal energy in U(k).   相似文献   

3.
Embedding on alphabet overlap digraphs   总被引:1,自引:0,他引:1  
Alphabet overlap digraphs can be viewed as a generalization of directed de Bruijn graphs. Given three integers α ≥ 1, k ≥ 2 and 1 ≤ i < k, the alphabet overlap digraph O(α, k ; i) is a digraph: the set of all words of length k over a certain alphabet with cardinality α is vertex set, and there is an arc from a vertex u to a vertex v if and only if the word of last ki letters of u coincides with the word of first ki letters of v. In this paper, we consider whether O(α, k ; i) can be embedded in O(α, k ; j) for given integers 1 ≤ i < j < k. In order to resolve this problem, we give an O(1)-time algorithm to decide whether there exists a permutation on {1, . . . ,k} from O(α, k ; i) to O(α, k ; j). If such a permutation exists, for any vertex of O(α, k ; i), we apply the permutation to change its label’s position and map it to a vertex of O(α, k ; j). Furthermore, we obtain an embedding from O(α, k ; i) to O(α, k ; j). Hence, we solve partly the problem. As a consequence, we show that every directed de Bruijn graph can be embedded in all alphabet overlap digraphs with the same parameters α and k.  相似文献   

4.
Developmental efforts to improve the yield of the chemical synthesis of (3R,3′R)-zeaxanthin resulted in the isolation, partly by chromatography from reaction mixtures, and full spectroscopic characterization by 1H-NMR, UV/VIS, and CD spectrosocpy of eleven (Z/E)-isomers of zeaxanthin: (7Z)-, (9Z), (13Z)-, (15Z)-, (7Z,7′Z)-, (9Z,9′Z)- (7Z,9Z,7Z)-, (7Z,11Z,7′Z)-, (9Z,13Z,9′Z)-, (7Z,9Z,7′Z,9′Z)-, and (7Z,9Z,11Z,7′Z,9′Z)-zeaxanthin. Five of these isomers were obtained by specific synthesis, namely the (7Z)-, (7Z,7′Z)-, (9Z,9′Z)-, (7Z,9Z,7′Z)-, and (7Z,9Z,7′Z-9Z)-isomers.  相似文献   

5.
A hexagonal tessellation K(p, q, t) on Klein bottle, a non-orientable surface with cross-cap number 2, is a finite-sized elemental benzenoid which can be produced from a p × q-parallelogram of hexagonal lattice with usual identifications of sides and with torsion t. Unlike torus, Klein bottle polyhex K(p, q, t) is not transitive except for some degenerated cases. We shall show, however, that K(p, q, t) does not depend on t. Accordingly, criteria for K(p, q, t) to be k-resonant for every positive integer k will be given. Moreover, we shall show that K(3, q, t) of 3-resonance are fully-benzenoid.   相似文献   

6.
The synthesis and catalytic properties of a new type of enantioselective phase-transfer catalysts, incorporating both the quinuclidinemethanol fragment of Cinchona alkaloids and a 1,1′-binaphthalene moiety, are described. Catalyst (+)-(aS,3R,4S,8R,9S)- 4 with the quinuclidine fragment attached to C(7′) in the major groove of the 1,1′-binaphthalene residue was predicted by computer modeling to be an efficient enantioselective catalyst for the unsymmetric alkylation of 6,7-dichloro-5-methoxy-2-phenylindanone ( 1 ; Scheme 1, Fig. 1). Its synthesis involved the selective oxidative cross-coupling of two differently substituted naphthalen-2-ols to afford the asymmetrically substituted 1,1′-binaphthalene derivative (±)- 17 in high yield (Scheme 3). Chromatographic optical resolution via formation of diastereoisomeric camphorsulfonyl esters and functional-group manipulation gave access to the 7-bromo-1,1′-binaphthalene derivative (−)-(aS)- 11 (Scheme 4). Nucleophilic addition of lithiated (−)-(aS)- 11 to the quinuclidine Weinreb amide (+)-(3R,4S,8R)- 8 afforded the two ketones (aS,3R,4S,8R)- 27 and (aS,3R,4S,8S)- 28 as an inseparable mixture of diastereoisomers (Scheme 6). Stereoselective reduction of this mixture with DIBAL-H (diisobutylaluminum hydride; preferred formation of the C(8)−C(9) erythro-pair of diastereoisomers with 18% de) or with NaBH4 (preferred formation of the threo-pair of diastereoisomers with 50% de) afforded the four separable diastereoisomers (+)-(aS,3R,4S,8S,9S)- 29 , (+)-(aS,3R,4S,8R,9R)- 30 , (−)-(aS,3R,4S,8S,9R)- 31 , and (+)-(aS,3R,4S,8R,9S)- 32 (Scheme 6). A detailed conformational analysis, combining 1H-NMR spectroscopy and molecular-mechanics computations, revealed that the four diastereoisomers displayed distinctly different conformational preferences (Figs. 2 and 3). These novel Cinchona-alkaloid analogs were quaternized to give (+)-(aS,3R,4S,8R,9S)- 4 , (+)-(aS,3R,4S,8S,9S)- 5 , (+)-(aS,3R,4S,8R,9R)- 6 , and (−)-(aS,3R,4S,8S,9R)- 7 (Scheme 7) which were tested as phase-transfer agents in the asymmetric allylation of phenylindanone 1 . Without any optimization work, (+)-(aS,3R,4S,8R,9S)- 4 was found to catalyze the allylation of 1 yielding the predicted enantiomer (+)-(S)- 3b in 32% ee. The three diastereoisomeric catalysts (+)- 5 , (+)- 6 , and (−)- 7 gave access to lower enantioselectivities (6 to 22% ee's), which could be rationalized by computer modeling (Fig. 4).  相似文献   

7.
The stability conditions of phase equilibrium for various concentration variables are educed according to thermodynamic principle. When a system with k components arrives at stable equilibrium, if the mole number ni or the mole fraction yi(=ni/nk) or molality mi[= ni/(nkMk)] of component i(i = 1,2,...,k − 1) are elected as concentration variables, thermodynamic theory is able to confirm that the sign of every order determinant composed of the second-order partial differential of chemical potential with respect to these concentration variables is positive; if the mole fraction xi(= ni/n) or mass fraction wi(= niMi/W are elected as the concentration variables, thermodynamic theory is only able to confirm that the sign of (k−1) order determinant is positive; if molarity ci(= ni/V are elected as the concentration variables, thermodynamic theory is not able to confirm the sign of every order determinant.  相似文献   

8.
The marine sponge Spongia zimocca SCHMIDT , 1862, collected in front of the torrent II Rogiolo, south of Livorno, contains the sesquiterpene rogiolol acetate (= (+)-(2R,3S,6R,8R,9R)-2,8-dibromo-9-chloro-1,1,9-trimethyl-5-methylidenespiro[5.5]undec-3-yl acetate; (+)- 3a ), which represents the first chamigrane isolated from a sponge. Although compounds of this class are common in red seaweeds of the genus Laurencia, and our sponge actually contains 9-bromochamigrene and a variety of other metabolites of nearby growing Laurencia sp., (+)- 3a is unique to our sponge.  相似文献   

9.
The syntheses and characterization of four new linear pentadentate ligands and their CoIII complexes are described: N,N′-[(pyridine-2,6-diy)bis(methylene)]bis[sarcosine] (sarmp), N,N′-[(pyridine-2,6-diyl)bis(methylene)]bis[(R)- or (S)-proline] ((R,R)- or (S,S)-promp), N,N′-[(pyridine-2,6-diyl)bis(methylene)]bis[N-(methyl)-(R)- or (S)-alanine] ((R,R)- or (S,S)-malmp); 2,2′-[pyridine-2,6-diyl]bis[(S)- or rac-N-(acetic acid)pyrrolidine] ((S,S)- or rac-bapap). The complexes were characterized and, with but one exception, complex formation is stereospecific: Δ-exo-(R,R) (or Λ-exo-(S,S)) for promp and Λ-(R,R) (or Δ-(S,S)) for bapap. The exception is [Co((R,R)- or (S,S)-malmp)H2O]ClO4 for which two forms are obtained, to which Λ-endo-(R,R) (or Δ-endo-(S,S)) and, tentatively, Δ-unsymmetric-(R,R)- (or Λ-unsymmetric-(S,S)-) configurations are assigned. X-Ray crystal structures are presented for the complexes [Co(sarmp)H2O]ClO4, [Co((S,S)-promp)H2O]ClO4, [Co(rac-bapap)H2O]ClO4 and endo-[Co(rac-malmp)H2O]ClO4. Ligand acid dissociation and CoII and FeII complex-formation constants are reported.  相似文献   

10.
The ten new acylated presenegenin (=(2β,3β,4α)‐2,3,27‐trihydroxyolean‐12‐ene‐23,28‐dioic acid) glycosides 1 – 10 have been isolated by successive MPLC from the roots of Polygala myrtifolia L. as five inseparable mixtures of the trans‐ and cis‐4‐methoxycinnamoyl derivatives, i.e., myrtifoliosides A1/A2 ( 1 / 2 ), B1/B2 ( 3 / 4 ), C1/C2 ( 5 / 6 ), D1/D2 ( 7 / 8 ), and E1/E2 ( 9 / 10 ). Their structures were elucidated mainly by extensive spectroscopic experiments, including 2D NMR techniques, as 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{Oβ‐D ‐galactopyranosyl‐(1→3)‐Oβ‐D ‐xylopyranosyl‐(1→4)‐O‐[D ‐apio‐β‐D ‐furanosyl‐(1→3)]‐Oα‐L ‐rhamnopyranosyl‐(1→2)‐O‐[α‐L ‐arabinopyranosyl‐(1→3)]‐4‐O‐(trans‐4methoxycinnamoyl)‐β‐D ‐fucopyranosyl} ester ( 1 ) and its cis‐isomer 2 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{Oβ‐D ‐galactopyranosyl‐(1→3)‐Oβ‐D ‐xylopyranosyl‐(1→4)‐O‐[D ‐apio‐β‐D ‐furanosyl‐(1→3)]‐α‐L ‐rhamnopyranosyl‐(1→2)‐4‐O‐(trans‐4methoxycinnamoyl)‐β‐D ‐fucopyranosyl} ester ( 3 ) and its cis‐isomer 4 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{Oβ‐D ‐galactopyranosyl‐(1→3)‐Oβ‐D ‐xylopyranosyl‐(1→4)‐Oα‐L ‐rhamnopyranosyl‐(1→2)‐4‐O‐(trans‐4methoxycinnamoyl)‐β‐D ‐fucopyranosyl} ester ( 5 ) and its cis‐isomer 6 , 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{O‐D ‐apio‐β‐D ‐furanosyl‐(1→3)‐O‐[β‐D ‐xylopyranosyl‐(1→4)]‐Oα‐L ‐rhamnopyranosyl‐(1→2)4‐O‐(trans‐4methoxycinnamoyl)‐β‐D ‐fucopyranosyl} ester ( 7 ) and its cis‐isomer 8 , and 3‐O‐(β‐D ‐glucopyranosyl)presenegenin 28‐{Oα‐L ‐arabinopyranosyl‐(1→3)‐O‐[β‐D ‐xylopyranosyl‐(1→4)]‐Oα‐L ‐rhamnopyranosyl‐(1→2)‐4‐O‐(trans‐4 methoxycinnamoyl)‐β‐D ‐fucopyranosyl} ester ( 9 ) and its cis‐isomer 10 .  相似文献   

11.
The hydrolysis reactions of N-(O,O'diisopropyl)phosphoryl-L-α-alanine (DIPP-L-α-Ala), N-(O,O'diisopropyl)- phosphoryl-D-α-alanine (DIPP-D-α-Ala), N-(O,O'-diisopropyl)phosphoryl-β-alanine (DIPP-β-Ala) and N-(O,O'-diisopropyl)phosphoryl-γ-amino butyric acid (DIPP-γ-Aba), were studied by HPLC and their hydrolysis reaction kinetic equations were obtained. Under acid conditions, the reaction rate of DIPP-L-α-Ala was close to that of DIPP-D-α-Ala and the same rule was true between DIPP-β-Ala and DIPP-γ-Aba. Meantime, the reaction rate of DIPP-L/D-α-Ala was as 10 times as that of DIPP-β-Ala or DIPP-γ-Aba. Under basic conditions, the hydrolysis reactions of DIPP-β-Ala and DIPP-γ-Aba almost did not take place and the reaction rate of DIPP-L/D-α-Ala was about 1/10 of that under acid conditions. Moreover, theoretical calculation further illuminated the differences of the hydrolysis rate from the view of energy. The results would provide some helpful clues to why nature chose a-amino acids but not other kinds of analogs as protein backbones.  相似文献   

12.
Disproportionation-combination ratios have been obtained for small alkyl radicals produced in the mercury-photosensitized hydrogenation of ethylene, propylene, butene-1, butene-2, and isobutene. For conditions favoring thermalized radicals, kd/kc (ethyl, ethyl) = 0.14, kd/kc (isopropyl, isopropyl) = 0.69, kd/kc (isopropyl, n-propyl) = 0.41, kd/kc (2-butyl, 2-butyl) = 0.77, kd/kc (2-butyl, n-butyl) = 0.45, and kd/kc (t-butyl, t-butyl) = 3.1. The results are consistent with kd/kc (n-propyl, n-propyl) = 0.15 and kd/kc (n-butyl, n-butyl) = 0.14. The general agreement between these disproportionation-combination ratios and those obtained where photolytic radical sources have been used indicates that under appropriate conditions, H atom addition to olefins is a suitable source for the study of thermalized alkyl radicals and may be especially useful for larger alkyl radicals for which clean photolytic precursors are not available.  相似文献   

13.
Obesity is a complex health issue and it can cause many health and social problems. Previous studies reported that lipase is a main target for obesity treatment. We synthesized Rexo‐2‐norbornyl‐Nn‐butylcarbamate and Sexo‐2‐norbornyl‐Nn‐butylcarbamate as potential pseudomonas lipase inhibitors to probe the enantioselectivity of the enzyme and demonstrated that Rexo‐2‐norbornyl‐Nn‐butylcarbamate had better enzyme enantioselectivity, ki and the docking model with Pseudomonas species lipase in our previous studies. In this article, we reported the property of the Pseudomonas species lipase inhibitors, R‐and Sendo‐2‐norbornyl‐Nn‐butylcarbamate and compared the docking models of these two compounds with R‐ and Sexo‐2‐norbornyl‐Nn‐butylcarbamates by AutoDock. We found that Sendo‐2‐norbornyl‐Nn‐butylcarbamate has the best enantioselectivity, ki and docking model and this study could provide useful information about enzyme enantioselectivity for the development of Pseudomonas species lipase inhibitors for obesity treatment.  相似文献   

14.
Suppose G is a chemical graph with vertex set V(G). Define D(G) = {{u, v} ⊆ V (G) | d G (u, v) = 3}, where d G (u, v) denotes the length of the shortest path between u and v. The Wiener polarity index of G, W p (G), is defined as the size of D(G). In this article, an ordering of chemical unicyclic graphs of order n with respect to the Wiener polarity index is given.  相似文献   

15.
Poly(ethylene glycol)-block-poly(γ-benzyl L-glutamate)-graft-poly(ethylene glycol) (PEG-b-PBLG-g-PEG) copolymer was synthesized by the ester exchange reaction of poly(γ-benzyl L-glutamate)-block-poly(ethylene glycol) (PBLG-block-PEG) copolymer with PEG chain, and PBLG-block-PEG copolymer was prepared by a standard N-carboxyl-γ-benzyl-L-glutamate anhydride (NCA) method. Nuclear magnetic resonance (NMR) spectroscopy was used to confirm the components of PBLG-block-PEG and PEG-b-PBLG-g-PEG. The self-association behaviors of PBLG-block-PEG and PEG-b-PBLG-g-PEG in ethanol were investigated by transmission electron microscopy (TEM), dynamic laser scattering (DLS), and viscometry. The experimental results revealed that the different molecular structures could exert marked effects on the self-assembly behaviors of PBLG-block-PEG and PEG-b-PBLG-g-PEG in ethanol. PBLG-block-PEG and PEG-b-PBLG-g-PEG could self-assemble to form polymeric micelles with a core-shell structure in the shapes of plump spherical and regular rice-like, respectively. Effects of the introduction of PBLG homopolymer on the average particle diameter of the micelles of PBLG-block-PEG and PEG-b-PBLG-g-PEG and influence of testing temperature on the critical micelle concentration of different copolymers were studied.  相似文献   

16.
Karpoxanthin (=(all-E,3S,5R,6R,3′R)-5,6-dihydro-β,β-carotene-3,5,6,3′-tetrol; 7 ), 6-epikarpoxanthin (=(all-E,3S,5R,6S,3′R)-5,6-dihydro-β,β-carotene-3,5,6,3′-tetrol; 4 ), 5-epikarpoxanthin (=(all-E,3S,5S,6R,3′-R)-5,6-dihydro-β,β-carotene-3,5,6,3′-tetrol; 11 ), cucurbitaxanthin A (=(all-E,3S,5R,6R,3′R)-3,6-epoxy-5,6-dihydro-β,β-carotene-5,3′-diol; 10 ), epicucurbitaxanthin A (=(all-E-3S,5S,6R,3′R)-3,6-epoxy-5,6-dihydro-β,β-carotene-5,3′-diol; 14 ), and the corresponding mutatoxanthin epimers 8 , 9 , 12 , and 13 were prepared in crystalline state by the acid-catalyzed hydrolysis of (3S,5R,6S,3′R)- and (3S,5S,6R,3′R)-antheraxanthin ( 5 and 6 , resp.) and characterized by their UV/VIS, CD, 1H- and 13C-NMR, and mass spectra.  相似文献   

17.
Acylation of 2H-thiopyran-3,5(4H,6H)-dione and 2-methyl-2H-thiopyran-3,5(4H,6H)-dione with acetyl chloride or propionyl chloride afforded the corresponding 4-acyl-2H-thiopyran-3,5(4H,6H)-diones. Oxidation of 4-acetyl-2H-thiopyran-3,5(4H,6H)-dione with m-chloroperoxybenzoic acid gave 4-acetyl-2H-thiopyran-3,5(4H,6H)-dione 1-oxide. 4-Acyl-2H-thiopyran-3,5(4H,6H)-diones and 4-acetyl-2H-thiopyran-3,5(4H,6H)-dione 1-oxide reacted with pyrrolidine, allylamine, and p-anisidine, resulting in formation of the corresponding 4-aminomethylene derivatives.  相似文献   

18.
A formalism is developed for the construction of relativistic symmetry-adapted molecular basis functions under consideration of time reversal invariance. The theory is applicable to the finite double point groups Cn, Cnh, Sn, Cnv, Dn, Dnd, Dnh, T, Th, Td, O, and Oh. It is based on the LCAO method. A projection operator technique is employed to construct molecular symmetry orbitals from atomic orbitals. The search for linearly independent basis function is simplified by means of group theoretical considerations.  相似文献   

19.
Summary The extraction behaviour of Co and Ni chlorides withAliquat 336-TBP andAliquat 336-TOPO (Aliquat 336: tri-n-octylmethylammonium chloride,TBP: tri-n-butylphosphate,TOPO: tri-n-octylphosphine oxide) was investigated. The synergistic action ofTOPO in the extraction of Co and Ni withAliquat 336 manifested itself in an increase of the distribution ratio of Co with increasing ofTOPO concentration at constantAliquat 336 concentration without deterioration of the separation factor Co/Ni which still was above 200. Mixed complexes of the general formulaMeCl2+mAmBn (Me: Co or Ni,A:Aliquat 336, A:TBP orTOPO) withm ranging from 2 to 5 andn from 1 to 3 were present in the organic phase of both systems. The coexistence of several synergistic Co/Ni species in the equilibrium organic phase is reported for the first time.
Zur Abtrennung von Co und Ni aus chloridhaltigen Medien mitAliquat 336-TBP undAliquat 336-TOPO
Zusammenfassung Das Extraktionsverhalten von Kobalt- und Nickelchloriden mitAliquat 336-TBP undAliquat 336-TOPO (Aliquat 336: Tri-n-octylmethylammoniumchlorid,TBP: Tri-n-butylphosphat,TOPO: Tri-n-octylphosphinoxid) wurde untersucht. Die synergistische Wirkung vonTOPO bei der Extraktion von Co und Ni mitAliquat 336 manifestiert sich in einer Erhöhung des Verteilungsverhältnisses von Co mit steigenderTOPO-Konzentration, ohne daß dadurch der Co/Ni-Trennfaktor verschlechtert wird (> 200). Für beide Systeme konnten in der organischen Phase gemischte Komplexe der allgemeinen FormelMeCl2+m A mBn nachgewiesen werden (Me: Co oder Ni,A:Aliquat 336,B:TBP orderTOPO,m : 2–5,n: 1–3). Zum ersten Mal wird über die Koexistenz verschiedener synergistischer Co/Ni-Spezies in der organischen Phase im Gleichgewicht berichtet.
  相似文献   

20.
The Friedel-Crafts mono and double acylations of trans-μ-[(1RS,2RS,3SR,5RS,6SR,7SR)-C,2,3,C-η:C,6,7,C-η-(2,3,6,7-tetramethylidenebicyclo[3.2.1]octane)]bis(tricarbonyliron) ( 4 ) are highly stereoselective and yield trans-μ-{(1RS,2RS,3SR,5RS,6SR,7RS)-C,2,3,C-η :C,6,7,C-η-[(Z)-1-(3,6,7-trimethylidenebicyclo[3.2.1]-oct-2-ylidene)-2-propanone]}bis(tricarbonyliron) ( 5 ) and trans-μ-{(1RS,2RS,3SR,5RS,6SR,7SR)-C,2,3,C-η :C,6,7,C-η-[(Z,Z)-1,1′-(3,7-dimethylidenebicyclo [3.2.1] octane-2,6-diylidene)di(2-propanone)]}bis(tricarbonyliron) ( 6 ) whose structure has been established by single-crystal X-ray diffraction.  相似文献   

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