TRIPLE POSITIVE SOLUTIONS TO A CLASS OF m-POINT BOUNDARY VALUE PROBLEM OF SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATION

By a fixed point theorem,some new results on the multiplicity of positive solutions to some m-point boundary value problems of second-order functional differential equations are obtained. The associated Green's functions of the problems are also given.     

On the positive nonoscillatory solutions of the difference equation x_(n+1)= α +(x_(n-K)/x_(n-m))~p

The aim of this paper is to show that the following difference equation:xn+1=α+(xn-k/xn-m)p,n=0,1,2…,where α＞-1,p＞0,k,m ∈ N are fixed, 0≤m＜k,x-k,x-k+1,…,x-m,…,x-1,x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α+1.It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.     

Existence,uniqueness and stability of positive steady states to a prey-predator diffusion system

In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semi-trivial solution to the unique positive solution of the limiting system. This work was supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032) and Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)     

Circular neighbor-balanced designs using cyclic shifts

In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-...     

A Perron-Frobenius theorem for positive polynomial operators in Banach lattices

In this paper, we extend the Perron-Frobenius theorem for positive polynomial operators in Banach lattices. The result obtained is applied to derive necessary and sufficient conditions for the stability of positive polynomial operators. Then we study stability radii: complex, real and positive radii of positive polynomial operators and show that in this case the three radii coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results.     

Diatropicity of tetraazanaphthalenes

Tetraazanaphthalenes are diatropic molecules, whose magnetic response to a magnetic field perpendicular to the molecular plane closely resembles that of naphthalene. The out-of-plane component of the magnetic susceptibility tensor and its strong anisotropy can be used as quantifiers of magnetic aromaticity. Maps showing streamlines and modulus of the current density field provide clear evidence for diatropicity of these systems. They also explain the strong anisotropy of carbon and nitrogen magnetic shielding, which is determined by the big out-of-plane component of the nuclear shielding tensor. The electronic ring currents observed in the map deshield the nuclei of ring hydrogens by enforcing the local magnetic field and diminishing the out-of-plane component of proton shielding.     

Optimized 1D double quantum filter NMR experiments

We propose and demonstrate a 1D pulse sequence to convert double quantum coherence (DQC) of y phase with optimal efficiency, relying on single transition selection. Our sequence has a larger high-sensitivity bandwidth with respect to the coupling, compared to other reconversion strategies. A modified version of the new pulse sequence provides the missing chemical shift and coupling information, at minor cost in sensitivity. Application to 1D 13C INADEQUATE is demonstrated.Our new sequence is also applied to quadrupole coupled spin-1 systems, such as 2H in lyotropic phase. Performance of the sequence may be fine-tuned by pulse flip angle optimization, taking into account relaxation effects.     

1H, 13C and 15N NMR spectral characterization of twenty-seven 1,2-diaryl-(4E)-arylidene-2-imidazolin-5-ones

1H, 13C and 15N NMR chemical shifts and couplings (n)J(H,C) in DMSO-d(6) at 30 degrees C have been determined for 1,2-diaryl-(4E)-arylidene-2-imidazolin-5-one derivatives 1-27. Their chemical shift assignments are based on PFG DQF 1H,1H COSY, PFG 1H,13C HMQC as well as PFG 1H,13C and 1H,15N HMBC experiments. For compounds 1-10 including aryl fluorine substituent(s) also the couplings (n)J(F,C) (n = 1 - 4) are reported.     

Stereoelectronic and inductive effects on 1H and 13C NMR chemical shifts of some cis-1,3-disubstituted cyclohexanes

This work presents the substituent effects on the 1H and 13C NMR chemical shifts in the cis-isomer of 3-Y-cyclohexanols (Y = Cl, Br, I, CH3, N(CH3)2 and OCH3) and 3-Y-1-methoxycyclohexanes (Y = F, Cl, Br, I, CH3, N(CH3)2 and OCH3). It was observed that the H-3 chemical shift, due to the substituent alpha-effect, increases with the increase of substituent electronegativity when Y is from the second row of the periodic table of elements, (CH3 *sigma(C3--H3a) interaction energy. This interaction energy, for the halogenated compounds, decreases with an increase in size of the halogen, and this is a possible reason for the largest measured chemical shift for H-3 of the iodo-derivatives. The beta-effect of the analyzed compounds showed that the chemical shift of hydrogens at C-2 and C-4 increases with the decrease of n(Y) --> *sigma(C2-C3) and n(Y) --> *sigma(C3-C4) interaction energies, respectively, showing a behavior similar to H-3. The alpha-effect on 13C chemical shifts correlates well with substituent electronegativity, while the beta-effect is inversely related to electronegativity in halogenated compounds. NBO analysis indicated that the substituent inductive effect is the predominant effect on 13C NMR chemical shift changes for the alpha-carbon. It was also observed that C-2 and C-4 chemical shifts for compounds with N(CH3)2, OCH3 and F are more shielded in comparison to the compounds having a halogen, most probably because of the larger interaction of the lone pair of more electronegative atoms (n(N) > n(O) > n(F)) with *sigma(C2-C3), *sigma(C3-C4) and *sigma(C3-H3a) in comparison with the same type of interaction with the lone pair of the other halogens.     

15N NMR chemical shifts of ring substituted benzonitriles

15N chemical shifts in an extensive series of para (15) and meta (15) as well as ortho (8) substituted benzonitriles, X-C6H4-CN, were measured in deuteriochloroform solutions, using three different methods of referencing. The standard error of the average chemical shift was less than 0.03 ppm in most cases. The results are discussed for both empirical correlations with substituent parameters and quantum chemical calculations. The 15N chemical shifts calculated at the GIAO/B3LYP/6-31 + G*//B3LYP/6-31 + G* level reproduce the experimental values well, and include nitrogen atoms in the substituent groups (range of 300 ppm with slope 0.98 and R = 0.998, n = 43). The 15N shifts in hydroxybenzonitriles are affected by interaction with the OH group. Therefore, these derivatives are excluded from the correlation analysis. The resultant 15N chemical shift correlates well with substituent constants, both in the simple Hammett or DSP relationships and the 13C substituent-induced chemical shifts of the CN carbon.