On the Adjacent Eccentric Distance Sum Index of Graphs

For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as ξsv(G)=∑v∈V(G)ε(v)D(v)deg(v), where D(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as independence number, covering number, vertex connectivity, chromatic number, diameter and some other graph topological indices.     

The effect of encapsulated fine grain sediment and test morphology on the resistance of planktonic foraminifera to dissolution

The tests of planktonic foraminifera recovered from deep-sea sediment are commonly observed to encapsulate fine grain carbonate sediment within their chambers. In sediment below the lysocline, the interstitial water within the chambers may not be as corrosive as the seawater in contact with the outer surface of the test due to slow continuous dissolution of the encapsulated carbonate. As a consequence, the pore walls of the foram dissolve more slowly than the outer surface of the test.Using published dissolution rate measurements for foraminifera and deep-sea sediment, the effect of diffusional reduction of pore wall dissolution was quantitatively estimated with a one-dimensional model for the steady state condition where diffusional flux out of the foraminifer's pores is balanced by the dissolution flux from the encapsulated fines and pore walls. The diffusional effect is found to principally depend on the structural parametric ratioT_wd_T/f, whereT_w is the wall thickness,d_T the test diameter andf is the test porosity. In the case of adult planktonic foraminifera, the ratio of the pore wall to outer surface dissolution flux is predicted to vary between 60% for the thin-walled porous species and 30% for thick-walled tests.Incorporation of the predicted pore to outer surface flux ratios into the morphologic index equation of Adelseck (1978) results in a very good prediction (73% of the variation) of the solution index of Berger (1975) obtained from ranking species counts from core tops. A simple empirical equation which may be useful for prediction of the resistance of extinct microfossils was found as follows:

$R=\frac{T_w}{\lambda \{1+[A_w/(A_s?A_p)][.74?.27log?(T_w{d}_T/f)]\}}$

is the measured ratio of pore wall area to outer surface of the test, andT_wd_T/f is in units of 10⁴ μm².     

The effects of fasting on swimming performance in juvenile qingbo (Spinibarbus sinensis) at two temperatures

We measured the following variables to investigate the effects of fasting and temperature on swimming performance in juvenile qingbo (Spinibarbus sinensis): the critical swimming speed (U_crit), resting metabolic rate ${(\dot{\mathrm{M}}O}_{\mathrm{2rest}})$ and active metabolic rate ${(\dot{\mathrm{M}}O}_{2active})$ of fish fasting for 0 (control), 1, 2 and 4 weeks at low and high acclimation temperatures (15 and 25 °C). Both fasting treatment and temperature acclimation had significant effects on all parameters measured (P<0.05). Fasting at the higher temperature had a negative effect on all measured parameters after 1 week (P<0.05). However, when acclimated to the lower temperature, fasting had a negative effect on U_crit until week 2 and on ${(\dot{\mathrm{M}}O}_{\mathrm{2rest}})$, ${(\dot{\mathrm{M}}O}_{\mathrm{2active}})$ and metabolic scope (MS, ${(\dot{\mathrm{M}}O}_{\mathrm{2active}})$–${(\dot{\mathrm{M}}O}_{\mathrm{2rest}})$) until week 4 (P<0.05). The values of all parameters at the lower temperature were significantly lower than those at the higher temperature in the identical fasting period groups except for ${(\dot{\mathrm{M}}O}_{\mathrm{2rest}})$ of the fish that fasted for 2 weeks. The relationship between fasting time (T) and U_crit was described as U_crit(15)=−0.302T²−0.800T+35.877 (r=0.781, n=32, P<0.001) and U_crit(25)=0.471T²−3.781T+50.097 (r=0.766, n=32, P<0.001₎ at 15 and 25 °C, respectively. The swimming performance showed less decrease in the early stage of fasting but more decrease in the later stage at the low temperature compared to the high temperature, which might be related to thermal acclimation time, resting metabolism, respiratory capacity, energy stores, enzyme activity in muscle tissue and energy substrate utilization changes with fasting between low and high temperatures. The divergent response of the swimming performance to fasting in qingbo at different temperatures might be an adaptive strategy to seasonal temperature and food resource variation in their habitat.     

New chemistry based on reduction of homobinuclear bis(μ-phosphido) metal complexes

Studies are reported on the chemical reduction of the homobinuclear bis(μ-phosphido) metal complexes ${(CO)}_3\stackrel{︹}{Fe{(\mu -P{R}_2)}_{2}F}e{(CO)}_3$ (R = Ph or Me), ${(NO)}_2-\stackrel{︹}{Fe{(\mu -PP{h}_2)}_{2}F}e{(NO)}_2$ and ${(CO)}_4\stackrel{︹}{M{(\mu -PP{h}_2)}_{2}M}{(CO)}_4$ (M = Mo or W). Two reduction pathways have been observed which result in different two-electron transformations: (1) with Na or LiAlH₄, electron transfer to yield the corresponding symmetric dianions of the type L_nM(μ-PR₂)₂ML_n^2? without metalmetal bond and (2) with M′BR′₃H(M′ = Li, Na, or K; R′ = Et or sec-Bu), hydride transfer to give monoanionic complexes of the type $L_n\stackrel{︹}{M(\mu -P{R}_2)(\mu -L)M}{L}_{n?1}{(P{R}_{2}H)}^{?}$ or $L_n\stackrel{︹}{M(\mu -P{R}_2)M}{L}_n{(P{R}_{2}H)}^{?}$ (M = Fe, Mo, or W; L = CO or NO; R = Ph or Me). The monoanionic complexes can be deprotonated with n-BuLi at ?78 °C to the corresponding unsymmetric dianions $L_n\stackrel{︹}{M(\mu -P{R}_2)(\mu -L)M}{L}_{n?1}{(P{R}_2)}^{2?}$ (M = Fe; L = CO or NO; R = Ph) or symmetric dianions L_nM(μ-PR₂)₂ML_n^2? (M = Mo or W; L = CO; R = Ph). The unsymmetric dianions isomerize on slight warming to the symmetric dianions, which undergo protonation by CF₃COOH to yield the aforementioned monoanions. Reactions of several members of these three classes of binuclear anions with CF₃COOH, alkylating reagents, 1,1-diiodohydrocarbons and metal diiodo complexes have resulted in the synthesis of new binuclear and trinuclear compounds. Examples include ${(CO)}_3(H)\stackrel{︹}{Fe(\mu -PP{h}_2)Fe}{(CO)}_3(PP{H}_{2}H)$, ${(CO)}_3\stackrel{︹}{Fe(\mu -PP{h}_2)(\mu -C(R)O)Fe}{(CO)}_2(PP{h}_{2}R)$ (R = Me, Et, n-Pr, or i-Pr), ${(CO)}_4\stackrel{︹}{M{(\mu -PP{h}_2)}_{2}M}{(CO)}_3(C(R)Ome)$ (M = Mo or W; R = Me or Ph), ${(CO)}_2({\eta }^3?C_3{H}_5)\stackrel{︹}{Fe(\mu ?PP{h}_2)?F}e{(CO)}_3(PP{h}_2{C}_3{H}_5)$, ${(CO)}_4\stackrel{︹}{M{(\mu ?PP{h}_2)}_{2}M}{(CO)}_3(C(R)Ome)$, ${(NO)}_2\stackrel{︹}{Fe(\mu ?C{H}_2)(\mu ?P{h}_{2}PPP{h}_2)Fe}{(NO)}_2$, and Fe₂Co(η⁵-C₅H₅)(CO)(NO)₄(μ-PPh₂)₂. Synthetic and mechanistic studies on these reactions are presented.     

Stability enhancement and circular dichroism spectral anomaly as an indication of non-covalent interactions in histidine- and tyrosine-containing ternary copper(II)—amino acid systems

Visible absorption and CD spectral and potentiometric studies on the His- and Tyr-containing ternary copper(II) complexes Cu(A)(L-B), where A refers to L-His, D-His, or L-Tyr and B to Lys, Tyr, Trp, Phe, Ala, Val, Arg, Glu, Asn, Gln, Ser, or Thr, were made to study ligand-ligand interactions in the complexes. While the CD spectral magnitudes in the d—d region are additive in the absence of side chain interactions and can be estimated from the magnitudes for the ternary systems involving DL-A or DL-B, deviation from the additivity was observed for Cu(L-His)(L-B) (B = LysH, Tyr, Trp, or Phe) and Cu(L-Tyr)(L-Trp). From the stability constants determined at 25 °C and I = 0.1 M (KNO₃), the equilibrium constants, K, for the following hypothetical equilibria were calculated to be large (0.14–0.60) for formation of Cu(L-/D-His)(L-B)(B = Tyr or Trp) and Cu(D-His)(L-Phe) with Cu(en)(L-Ala) as standard: $Cu(A)(L?Ala)+Cu(en)(L?b)\stackrel{K}{?}Cu(A)(L?B)+Cu(en)(L?Ala)$ The positive values indicate the stabilization due to the stacking between the imidazole ring of His and the aromatic side chain of L-B. Solvent dependence of the CD spectra for Cu(L-His)(L-LysH) and Cu(L-His) L-Trp) further supported the existence of the intramolecular electrostatic and hydrophobic interactions.     

A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic X¯ control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic X¯ chart integrates the VSI X¯ chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic X¯ chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic X¯ chart and the existing X¯, synthetic X¯, VSI X¯ and EWMA X¯ charts, in terms of ATS, are made. The ATS results show that the VSI synthetic X¯ chart outperforms the other X¯ type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic X¯ chart.