Ultrasonic extraction of oil from tobacco (Nicotiana tabacum L.) seeds

The ultrasonic extraction (UE) of oil from the seeds of a semi-oriental tobacco (Nicotiana tabacum L.) plant strain by using n-hexane and petroleum ether was studied at different temperatures and seeds-to-solvent ratios. The oil yield depended on the seed comminution, the extraction temperature, the seeds-to-solvent ratio and the type of solvent. The oil yield was much higher if the seeds were ground before extraction. The oil yield increased with increasing the extraction temperature and with decreasing the seeds-to-solvent ratio. n-Hexane was somewhat more efficient in the oil extraction than petroleum ether. In recovering the tobacco seed oil (TSO), the UE was less efficient than the Soxhlet extraction. The advantage of the UE was a relatively high oil yield at 25 degrees C in a shorter time. The kinetics of UE of TSO was described using the model of unsteady diffusion through plant material.     

Mechanism of hopping transport in disordered mott insulators

By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca2-xSrxRuO4 near the metal-insulator transition. The hopping exponent alpha shows a systematic evolution from a value of alpha=1/2 deeper in the insulator to the conventional Mott value alpha=1/3 closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induced localized electronic states populating the Mott-Hubbard gap.     

A single closed formula for the general three-denominator Dalitz integral

We examine a general Dalitz integral containing the usual Feynman-type two-denominator term together with the Fourier transform \(\tilde \phi _{nlm} (q)\) of the hydrogenlike wave-function. A single closed formula is obtained for an arbitrary set {nlm} of quantum numbers, which is expressed in terms of the multivariable Lauricella hypergeometric functionF _D . The result is useful in a variety of calculations within the second Born approximation.     

Renormalisation group calculation of the interfacial tension for the three-dimensional Ising model

The interfacial tension of a three-dimensional Ising model in the whole temperature region is calculated by the real-space renormalisation group methods. The cumulant and the finite-cluster approximations with different projection rules are used. The results are consistent with expected low-temperature and global behaviour of the interfacial tension in the three-dimensional model.     

A wave-packet formulation of multiparticle production at high energies

Starting from a free boson gas in a box, we formulate a statistical approach to multi-particle production. The specific feature of the small box quantization is the fact that one-particle wave functions are wave packets instead of plane waves. In this context we investigate the jet model with Bose-Einstein (BE) statistics. The transverse cut-off function is naturally related to the size of the box (production region). We compare our results with experimental data.     

Some results on starlike trees and sunlike graphs

A tree is called starlike if it has exactly one vertex of degree greater than two. In [4] it was proved that two starlike treesG andH are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, letG be a simple graph of ordern with vertex setV(G)={1,2, …,n} and letH={H ₁,H ₂, ...H _n } be a family of rooted graphs. According to [2], the rooted productG(H) is the graph obtained by identifying the root ofH _i with thei-th vertex ofG. In particular, ifH is the family of the paths $P_{k_1 } , P_{k_2 } , ..., P_{k_n } $ with the rooted vertices of degree one, in this paper the corresponding graphG(H) is called the sunlike graph and is denoted byG(k ₁,k ₂, …,k _n ). For any (x ₁,x ₂, …,x _n ) ∈I _* ⁿ , whereI _*={0,1}, letG(x ₁,x ₂, …,x _n ) be the subgraph ofG which is obtained by deleting the verticesi ₁, i₂, …,i _j ∈ V(G) (0≤j≤n), provided that $x_{i_1 } = x_{i_2 } = ... = x_{i_j } = 0$ . LetG(x ₁,x ₂,…, x _n] be the characteristic polynomial ofG(x ₁,x ₂,…, x _n ), understanding thatG[0, 0, …, 0] ≡ 1. We prove that $$G[k_1 , k_2 ,..., k_n ] = \Sigma _{x \in ^{I_ * ^n } } \left[ {\Pi _{i = 1}^n P_{k_i + x_i - 2} (\lambda )} \right]( - 1)^{n - (\mathop \Sigma \limits_{i = 1}^n x_i )} G[x_1 , x_2 , ..., x_n ]$$ where x=(x ₁,x ₂,…,x _n );G[k ₁,k ₂,…,k _n ] andP _n (γ) denote the characteristic polynomial ofG(k ₁,k ₂,…,k _n ) andP _n , respectively. Besides, ifG is a graph with λ₁(G)≥1 we show that λ₁(G)≤λ₁(G(k ₁,k ₂, ...,k _n )) < for all positive integersk ₁,k ₂,…,k _n , where λ₁ denotes the largest eigenvalue.     

Two Hadamard matrices of order 956 of Goethals-Seidel type

No Hadamard matrices of order 956 appear in the literature. In this note we construct two such matrices. They are both of Goethals-Seidel type. As a consequence of this and of a result of Seberry and Yamada, we conclude that there exist 4-Williamson type matrices of order 1913.This work was supported by NSERC of Canada Grants A-5285 and EQP0107539.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.