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1.
A toroidal polyhex H(p, q, t) is a cubic bipartite graph embedded on the torus such that each face is a hexagon, which can be described by a string (p, q, t) of three integers (p≥ 1, q≥ 1, 0≤ t≤ p−1). A set of mutually disjoint hexagons of H(p, q, t) is called a resonant pattern if H(p, q, t) has a prefect matching M such that all haxgons in are M-alternating. A toroidal polyhex H(p, q, t) is k-resonant if any i (1 ≤ i ≤ k) mutually disjoint hexagons form a resonant pattern. In [16], Shiu, Lam and Zhang characterized 1, 2 and 3-resonant toroidal
polyhexes H(p, q, t) for min(p, q)≥ 2. In this paper, we characterize k-resonant toroidal polyhexes H(p, 1, t). Furthermore, we show that a toroidal polyhex H(p, q, t) is k-resonant (k≥ 3) if and only if it is 3-resonant.
相似文献
2.
This paper considers the k -resonance of a toroidal polyhex (or toroidal graphitoid) with a string (p, q, t) of three integers (p ≥ 2, q ≥ 2, 0 ≤ t ≤ p − 1). A toroidal polyhex G is said to be k-resonant if, for 1≤ i ≤ k, any i disjoint hexagons are mutually resonant, that is, G has a Kekulé structure (perfect matching) M such that these hexagons are M-alternating (in and off M). Characterizations for 1, 2 and 3-resonant toroidal polyhexes are given respectively in this paper.
*This work is supported by FRG, Hong Kong Baptist University; NSFC and TRAPOYT. 相似文献
3.
The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number
of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given
Mei Lu: Partially supported by NNSFC (No. 60172005)
Lian-zhu Zhang: Partially supported by NNSFC (No. 10271105)
Feng Tian: Partially supported by NNSFC (No. 10431020) 相似文献
4.
The Randić index of an organic molecule whose molecular graph G is defined as the sum of (d(u)d(v))−1/2 over all pairs of adjacent vertices of G, where d(u) is the degree of the vertex u in G. In Delorme et al., Discrete Math. 257 (2002) 29, Delorme et al gave a best-possible lower bound on the Randić index of a
triangle-free graph G with given minimum degree δ(G). In the paper, we first point out a mistake in the proof of their result (Theorem 2 of Delorme et al., Discrete Math. 257
(2002) 29), and then we will show that the result holds when δ(G)≥ 2. 相似文献
5.
Tomislav Došlić 《Journal of mathematical chemistry》2007,41(3):217-229
A global forcing set in a simple connected graph G with a perfect matching is any subset S of E(G) such that the restriction of the characteristic function of perfect matchings of G on S is an injection. The number of edges in a global forcing set of the smallest cardinality is called the global forcing number
of G. In this paper we prove several results concerning global forcing sets and numbers of benzenoid graphs. In particular, we
prove that all catacondensed benzenoids and catafused coronoids with n hexagons have the global forcing number equal to n, and that for pericondensed benzenoids the global forcing number is always strictly smaller than the number of hexagons. 相似文献
6.
Iwona Zięborak-Tomaszkiewicz P. Gierycz 《Journal of Thermal Analysis and Calorimetry》2008,93(3):693-699
The change of thermal functions (ΔH
0(T), ΔS
0(T), ΔG
0(T)) and formation functions (ΔH
f0(T), ΔG
f0(T), K
f(T)) with temperature for gallium nitride and indium nitride have been formulated based on the reliable experimental data obtained
by the use the same equipment in one laboratory. 相似文献
7.
Quasielastic light scattering measurements are reported for experiments performed on mixtures of gelatin and glutaraldehyde
(GA) in the aqueous phase, where the gelatin concentration was fixed at 5 (w/v) and the GA concentration was varied from 1×10−5 to 1×10−3 (w/v). The dynamic structure factor, S(q,t), was deduced from the measured intensity autocorrelation function, g
2(τ), with appropriate allowance for heterodyning detection in the gel phase. The S(q,t) data could be fitted to S(q,t)=Aexp(−D
f
q
2
t)+Bexp(−t/τc)β, both in the sol (50 and 60 ∘C) and gel states (25 and 40 ∘C). The fast-mode diffusion coefficient, D
f showed almost negligible dependence on the concentration of the crosslinker GA; however, the resultant mesh size, ξ, of the
crosslinked network exhibited strong temperature dependence, ξ∼(0.5−χ)1/5exp(−A/RT) implying shrinkage of the network as the gel phase was approached. The slow-mode relaxation was characterized by the stretched
exponential factor exp(−t/τc)β. β was found to be independent of GA concentration but strongly dependent on the temperature as β=β0+β1
T+β2
T
2. The slow-mode relaxation time, τc, exhibited a maximum GA concentration dependence in the gel phase and at a given temperature we found τc(c)=τ0+τ1
c+τ2
c
2. Our results agree with the predictions of the Zimm model in the gel case but differ significantly for the sol state.
Received: 25 May 1999 /Accepted in revised form: 27 July 1999 相似文献
8.
The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertex u and v in G. A graph G is called quasi-tree, if there exists such that G − u is a tree. In the paper, we give sharp lower and upper bounds on the Randić index of quasi-tree graphs.
Mei Lu: Partially supported by NSFC (No. 10571105). 相似文献
9.
Lebedev B. V. Bykova T. A. Lobach A. S. 《Journal of Thermal Analysis and Calorimetry》2000,62(1):257-265
The temperature dependence of the molar heat capacity (C0
p) of hydrofullerene C60H36 between 5 and 340 K was determined by adiabatic vacuum calorimetry with an error of about 0.2%. The experimental data were
used for the calculation of the thermodynamic functions of the compound in the range 0 to340 K. It was found that at T=298.15 K and p=101.325 kPa C0
p (298.15)=690.0 J K−1 mol−1,Ho(298.15)−Ho(0)= 84.94 kJ mol−1,So(298.15)=506.8 J K−1 mol−1, Go(298.15)−Ho(0)= −66.17 kJ mol−1. The standard entropy of formation of hydrofullerene C60H36 and the entropy of reaction of its formation by hydrogenation of fullerene C60 with hydrogen were estimated and at T=298.15 K they were ΔfSo= −2188.4 J K−1 mol−1 and ΔrSo= −2270.5 J K−1mol−1, respectively.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
N. N. Smirnova T. A. Bykova V. N. Larina T. G. Kulagina A. D. Pomogailo G. I. Dzhardimalieva 《Polymer Science Series A》2010,52(4):349-355
The temperature dependences of the heat capacities of hydrated acrylamide and poly(acrylamide) complexes of cobalt nitrate
are studied via high-precision adiabatic calorimetry at 6 to 300–380 K. The energy of combustion is estimated via isothermic
calorimetry. This evidence makes it possible to calculate thermodynamic functions C
p
ℴ(T), H
ℴ(T) − H
ℴ(0), S
ℴ(T), G
ℴ(T) − H
ℴ(0) at 0 to 300–380 K; the standard enthalpy of combustion, ΔcH
ℴ; and the thermodynamic parameters of formation, Δ
f
H
ℴ, Δ
f
S
ℴ, and Δ
f
G
ℴ, of monomer and polymer complexes composed of simple compounds at 298.15 K. The results are used for the estimation of enthalpy
Δpol
H
ℴ, entropy Δpol
S
ℴ, and Gibbs function Δpol
G
ℴ of bulk polymerization for hydrated acrylamide complexes of cobalt nitrate at 0–300 K. 相似文献
11.
E. Vessally 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2011,85(2):245-247
Energy differences, ΔX
s−t (X = E, H, and G) (ΔX
s−t = X(singlet) − X(triplet)) between singlet (s) and triplet (t) states of C12H8M were calculated at B3LYP/6-311+G*. The DFT calculations indicated that the ΔG
s−t between singlet (s) and triplet (t) states of C12H8M were increased from M = C to M = Pb. The ΔG
s−t of C12H8M was compared with its analogue C4H4M through replacement of heavy atoms from M = C to M = Pb. Configurations of the electrons in orbitals (σ2 or π2) for the singlet state of C12H8M were discussed. 相似文献
12.
The spread s(G) of a graph G is defined as s(G) = max
i,j
|λ
i
− λ
j
|, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U
*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U
*(n,k), and the graph with the largest spread in U(n,k).
相似文献
13.
The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. Let T be a tree with n vertices and k pendant vertices. In this paper, we give a sharp upper bound on Randić index of T. 相似文献
14.
A. F. Santos L. Polese M. S. Crespi C. A. Ribeiro 《Journal of Thermal Analysis and Calorimetry》2009,96(1):287-291
The non-isothermal data given by TG curves for poly(3-hydroxybutyrate) (PHB) were studied in order to obtain a consistent
kinetic model that better represents the PHB thermal decomposition. Thus, data obtained from the dynamic TG curves were suitably
managed in order to obtain the Arrhenius kinetic parameter E according to the isoconversional F-W-O method. Once the E parameters is found, a suitable logA and kinetic model (f(α)) could be calculated. Hence, the kinetic triplet (E±SD, logA±SD and f(α)) obtained for the thermal decomposition of PHB under non-isothermal conditions was E=152±4 kJ mol−1, logA=14.1±0.2 s−1 for the kinetic model, and the autocatalytic model function was: f(α)=αm(1−α)n=α0.42(1−α)0.56. 相似文献
15.
N. N. Smirnova T. A. Bykova N. A. Polotnyanko N. D. Shikina I. L. Khodakovskii 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2010,84(11):1851-1855
The temperature dependence of the heat capacity C
p
o = f(T) of palladium oxide PdO(cr.) was studied for the first time in an adiabatic vacuum calorimeter in the range of 6.48–328.86
K. Standard thermodynamic functions C
p
o(T), H
o(T) — H
o(0), S
o(T), and G
o(T) — H
o(0) in the range of T → 0 to 330 K (key quantities in different thermodynamic calculations with the participation of palladium compounds) were
calculated on the basis of the experimental data. Based on an analysis of studies on determining the thermodynamic properties
of PdO(cr.), the following values of absolute entropy, standard enthalpy, and Gibbs function of the formation of palladium
oxide are recommended: S
o(298.15) = 39.58 ± 0.15 J/(K mol), Δf
H
o(298.15) = −112.69 ± 0.32 kJ/mol, Δf
G
o(298.15) = −82.68 ± 0.35 kJ/mol. The stability of Pd(OH)2 (amorph.) with respect to PdO(cr.) was estimated. 相似文献
16.
Deprotonation constants of phthalic (H2A) and biphthalic (HA−) acids and of mono-protonated (BH+) and di-protonated (BH22+) piperazine acids have been determined at 25 °C by measuring the Emf of galvanic cells comprising H+-sensitive glass GE(H+) and Ag,AgCl electrodes in non-aqueous isodielectric mixtures of protic ethylene glycol (EG) and dipolar aprotic N,N-dimethylformamide
(DMF). Solvent effects on deprotonation of the acids: ∂(ΔG
disso)=2.303RT[p(s
K
a)−p(R
K
a)], have been dissected into transfer Gibbs energies, ΔG
to
, of the species involved by evaluating ΔG
to of the uncharged phthalic acid and base piperazine (B) from the measured solubilities of the acid and base, respectively,
and using ΔG
to of H+ based on the TATB reference electrolyte assumptions, as evaluated earlier. The contributions of the different species involved
in the protolytic equilibria i.e., H+,H2A,HA−,BH22+ and BH+ and their respective conjugate bases HA−,A2−,BH+ and B have been discussed in terms of their solvation behavior as guided by the ‘acid-base’, dispersion, structural and electronic
characteristics of the acid-base species and of the co-solvent molecules and binary mixtures, ignoring the Born-type electrostatic
interactions on the ionic species as the solvent system is quasi isodielectric. 相似文献
17.
T. G. Kulagina Ya. S. Samosudova I. A. Letyanina E. V. Sevast’yanov N. N. Smirnova L. A. Smirnova A. E. Mochalova 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2012,86(5):747-751
The temperature dependence of the heat capacity C
p
o= f(T) 2 of 2-ethylhexyl acrylate was studied in an adiabatic vacuum calorimeter over the temperature range 6–350 K. Measurement
errors were mainly of 0.2%. Glass formation and vitreous state parameters were determined. An isothermic shell calorimeter
with a static bomb was used to measure the energy of combustion of 2-ethylhexyl acrylate. The experimental data were used
to calculate the standard thermodynamic functions C
p
o(T), H
o(T)-H
o(0), S
o(T)-S
o(0), and G
o(T)-H
o(0) of the compound in the vitreous and liquid states over the temperature range from T → 0 to 350 K, the standard enthalpies of combustion Δc
H
o, and the thermodynamic characteristics of formation Δf
H
o, Δf
S
o, and Δf
G
o at 298.15 K and p = 0.1 MPa. 相似文献
18.
A complete characterization for <Emphasis Type="Italic">k</Emphasis>-resonant Klein-bottle polyhexes
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
19.
Lebedev B. V. Kulagina T. G. Smirnova N. N. Shifrina Z. B. Averina M. S. Rusanov A. L. 《Journal of Thermal Analysis and Calorimetry》2003,74(3):735-748
In an adiabatic vacuum calorimeter, the temperature dependence of the heat capacity C
p of phenylated polyphenylene and initial comonomer 1,4-bis(2,4,5-triphenylcyclopentadienone-3-yl)benzene was studied between
6 and 340 K with an uncertainty of about 0.2%. In a calorimeter with a static bomb and an isothermal shield their energies
of combustion DUcomb were measured. From the experimental data, the thermodynamic functions C
p
0 (T), H
0(T)-H
0(0), S
0(T)-S0(0), G
0(T)-H
0(0) were calculated from 0 to 340 K, and standard enthalpies of combustion ΔH
comb
0 and thermodynamic parameters of formation-enthalpies ΔH
f
0, entropies ΔH
f
0, Gibbs functions ΔG
f
0 - of the substances studied were estimated at T=298.15 K at standard pressure. The results were used to calculate the thermodynamic characteristics (ΔH
f
0 ,ΔS
f
0, ΔG
f
0) of phenylated polyphenylene synthesis in the range from 0 to 340 K.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Yu. G. Papulov O. V. Artyukhova 《Russian Journal of Physical Chemistry A, Focus on Chemistry》2010,84(8):1455-1457
The methodology of calculations of the physicochemical properties of substituted benzenes C6H6 − p
X
p
, C6H6 − p − q
X
p
Y
q
, ... (X and Y are univalent substituents) and C6H5A, where A = OH (phenol), NH2 (aniline), etc. by the phenomenological methods of chemical structure theory is discussed. 相似文献