Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Measurement of stenotic carotid arterial compliance with MRI

Arterial compliance has been shown to correlate well with overall cardiovascular outcome and it may also be a potential risk factor for the development of atheromatous disease. This study assesses the utility of 2-D phase contrast Magnetic Resonance (MR) imaging with intra-sequence blood pressure measurement to determine carotid compliance and distensibility. 20 patients underwent 2-D phase contrast MR imaging and also ultrasound-based wall tracking measurements. Values for carotid compliance and distensibility were derived from the two different modalities and compared. Linear regression analysis was utilised to determine the extent of correlation between MR and ultrasound derived parameters. In those variables that could be directly compared, an agreement analysis was undertaken. MR measures of compliance showed a good correlation with measures based on ultrasound wall-tracking (r=0.61, 95% CI 0.34 to 0.81 p=0.0003). Vessels that had undergone carotid endarterectomy previously were significantly less compliant than either diseased or normal contralateral vessels (p=0.04). Agreement studies showed a relatively poor intra-class correlation coefficient (ICC) between diameter-based measures of compliance through either MR or ultrasound (ICC=0.14). MRI based assessment of local carotid compliance appears to be both robust and technically feasible in most subjects. Measures of compliance correlate well with ultrasound-based values and correlate best when cross-sectional area change is used rather than derived diameter changes. If validated by further larger studies, 2-D phase contrast imaging with intra-sequence blood pressure monitoring and off-line radial artery tonometry may provide a useful tool in further assessment of patients with carotid atheroma.

Theoretical-Studies on the Modes of Binding of Some of the Beta-Glycosidically Linked Glucobioses to Concanavalin-A

The probable modes of binding for methyl-α-d-sophoroside, methyl-β-d-sophoroside, laminariboise and cellobiose to concanavalin A have been determined using theoretical methods. Methyl-d-sophorosides can bind to concanavalin A in two modes, i.e. by placing their reducing as well as non-reducing sugar units in the carbohydrate specific binding site, whereas laminaribiose and cellobiose can reach the binding site only with their non-reducing glucose units. However, the probability for methyl-α-d-sophoroside to bind to concanavalin A with its reducing sugar residue as the occupant of the binding site is much higher than it is with its non-reducing sugar residue as the occupant of the sugar binding site. A few of the probable conformers of methyl-β-d-sophoroside can bind to concanavalin A with either the reducing or non-reducing glucose unit. Higher energy conformers of cellobiose or laminaribiose can reach the binding site with their non-reducing residues alone. The relative differences in the binding affinities of these disaccharides are mainly due to the differences in the availability of proper conformers which can reach the binding site and to non-covalent interactions between the sugar and the protein. This study also suggests that though the sugar binding site of concanavalin A accommodates a single sugar residue, the residue outwards from the binding site also interacts with concanavalin A, indicating the existence of extended concanavalin A carbohydrate interactions.

Left-handed helices for DNA: studies on poly[d(I-C)]

Earlier, we showed that, for the D form (n = 8 and h = 3.03 A, where n is number of nucleotide units per turn and h is height per nucleotide unit) of poly[d(A-T)], both right- and left-handed double helical models are stereochemically satisfactory and give good agreement with the observed fiber diffraction data. It was also noted that the conformations of the right- and left-handed D-DNA models are very similar to those of the right- and left-handed B-DNA models. This observation was consistent with the D leads to B transition in the solid phase. As a continuation of our earlier studies, we have carried out similar experiments with poly[d(I-C)]. We could obtain a crystalline D-form pattern (n = 8, h = 3.13 A) of the fiber at 75% relative humidity (r.h.); the hydrated (r.h. approximately equal to 95%) form of the same fiber gave the classical B-form pattern (n = 10, h = 3.40 A). In the present report, we show that both right- and left-handed double-helical models are consistent with the fiber diffraction data of poly[d(I-C)] in the D-form. Theoretical energy calculations also suggest that the right- and left-handed B- and D-DNA models are almost equally stable. Hence, we conclude that the right- and left-handed double-helical models of poly[d(I-C)] in a given form (B or D) are equally likely and that the fiber diffraction data do not permit discrimination.

Electron Mean Energy, Secondary Ionization Coefficients And (E/P)Crit In Binary-Mixtures Of Sf6-N2 And Ccl2f2-N2

Measurements of the ratio of diffusion coefficient to mobility (D/ mu ) of electrons in SF6-N2 and CCl2F2-N2 mixtures over the range 80d in V cm-1 and p is the pressure in Torr reduced to 20 degrees C) are reported. Values of (E/p)c.mix (the critical E/p of the mixture, where alpha = eta ), and the electron mean energies epsilon c.mix corresponding to (E/p)c.mix, are found to vary with the percentage of the electronegative gas in the mixture (F) according to the following relationship: (E/p)c.mix=(E/p)c.N(2)+((E/p)c.A-(E/p)c.N(2)) (1-exp(- beta F/100-F)) and epsilon c.mix= epsilon c.N(2)+( epsilon c.A- epsilon c.N(2)) (1-exp(- beta F/100-F)) where A refers to the attaching gas, either SF6 or CCl2F2 and beta is a constant, equal to 2.43 for SF6 mixtures and 5.12 for CCl2F2 mixtures. In the present study, it has been possible to show that beta is indeed to a factor of synergism. Estimated gamma values (secondary ionisation coefficients) did not show any significant variation with F for F<50.

Breakdown voltage and V-Z characteristics of sodium vapour using coaxial cylindrical electrodes

Experimental results for breakdown voltage of sodium vapour measured for the first time using coaxial cylindrical electrodes of fixed gap distance (5 mm) and pressure (corrected to2 0 "C) in the range2 1 to 652 Pa are reported, and are founfdo l ltoow Paschen's Law. The investigations also reveal that V th-Ie characteristics are pressure dependent; the current during the breakdown and the buoifl dc-uurpre nt after a breakdoiws nei ther positive or negative. in spite of the central cylinder being always maintained at a positive potential

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiff ened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Ionisation and attachment in binary mixtures of SF6-N2 and CCl2F2-N2

Experimental results are presented of ionisation (a)a nd electron attachment ( v ) coefficients evaluated from the steady-state Townsend curregnrto wth curves for SFsN2 and CC12FrN2 mixtures over the range 60 S E/P 6 240 (where E is the electric field in V cm" and P is the pressure in Torr reduced to 20'C). In both the mixtures the attachment coefficients (vmu) evaluated were found to follow the relationship; where 7 is the attachment coefficient of pure electronegative gas, F is the fraction of the electronegative gas in the mixture and /3 is a constant. The ionisation coefficients (amlx) generally obeyed the relationship where w2a nd aAa re thei onisation coefficients of nitrogen and the attachinggraess pectively. However, in case of CC12FrN2 mixtures, there were maxima in the a,,,v,a,l ues for CCI2F2 concentrations varying between 10% and 30% at all values of E/P investigated. Effective ionisation coefficients (a - p)/P obtained in these binary mixtures show that the critical E/P (corresponding to (a - q)/P = 0) increases with increase in the concentration of the electronegative gas up to 40%. Further increase in the electronegative gas content does not seem to alter the critical E/P.

05-ions in a low pressure glow discharge of oxygen

0:- ions have been detected and measured in a positive column of glow discharge in oxygen between 0.04 and 0.17 Torr. A suitable ion-molecule reaction has been proposed, which appears to be supported by the mass spectrometer measurements.

Depth profile composition studies of thin film CdS: Cu,S solar cells using XPS and AES

Surface composition and depth profile studies of hemiplated thin film CdS:CuzS solar cells have been carried out using x-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) techniques. These studies indicate that the junction is fairly diffused in the as-prepared cell. However, heat treatment of the cell at 210°C in air relatively sharpens the junction and improves the cell performance. Using the Cu(2p3p)/S(2p) ratio as well as the Cu(LVV)/(LMM) Auger intensity ratio, it can be inferred that the nominal valency of copper in the layers above the junction is Cut and it is essentially in the CUSS form. Copper signals are observed from layers deep down in the cell. These seem to appear mostly from the grain boundary region. From the observed concentration of Cd, Cu and S in these deeper layers and the Cu(LVV)/(LMM) ratio it appears that the signals from copper essentially originate partly from copper in CuS and partly from Cu2t trapped in the lattice. It is significant to note that the nominal valence state of copper changes rather abruptly from Cut to Cuz+ across the junction.

ESR Studies of Phase Transitions in Double Propionates: Dicalcium Barium Propionate Ca2Ba(C2H5COO)6

Single crystal [(111) and (100) planes], and powder ESR of Mn2+ (substituting for Ca2+) in Ca2Ba(C2H5COO)6 in the temperature range 220°C to -160°C shows (i) a doubling of both the physically and chemically inequivalent sites, and a change in the magnitude (150 G at -6°C to 170 G at -8°C) as well as the orientation of the D tensor across the -6°C transition and (ii) an inflection point in the D vs T plot across the -75°C transition. The oxygen octahedra around the Ca2+ sites are inferred to undergo alternate rotations, showing the participation of the carboxyl oxygens in the -6°C transition. A relation of the type D=D0(1+αT+βT2) seems to fit the D variation satisfactorily.

Isänmaamme keisari : Eliitin kansallisen identiteetin murros ja suomalaisen isänmaan rakentuminen autonomian ajan alussa

The emperor of our fatherland The changing national identity of the elite and the construction of the Finnish fatherland at the beginning of the autonomy This study addresses the question of changing national identity of the elite at the beginning of the autonomy (1808 1814) in Finland. Russia had conquered Finland from Sweden, but Finland was not incorporated into the Russian Empire. Instead, it was governed as separately administered area, and Finland retained its own (laws of the realm of Sweden) laws. The inclusion in the Russian Empire compelled the elite of Finland to deliberate their national identity; they had to determine whether they remained Swedes or became Finns or Russians. The elite chose to become Finns, which may seem obvious from the nowadays perspective, but it cannot be taken for granted that the Swedish speaking and noble elite converted their local Finnish identity into a new national identity. The basis of this study is constructive in a sense that identity is not seen as stable and constant. Theoretical background lies on Stuart Hall s writings on national identity, which offer good practical methods to study national identity. According to Hall identity is based mainly on difference , difference to others . In practice this means how elite began to define themselves in contrast to Swedes and Russians. The Finnish national identity was constructed in contrast to Swedes due to the political reasons. In order to avoid Russians suspicions Finns had to diverge from Sweden. Sweden had also gone trough coup d état, which was disliked by the elite of Finland. However, the attitudes of the elite towards Sweden remained somewhat ambiguous. Even if it was politically and rationally thinking wisest to draw away from Sweden, emotionally it was difficult. Russia, on the other hand, had been for centuries the archenemy of the Finns as well as all the Swedes. The fear of the Russians was mainly imaginary. Russians were seen as cruel barbarians who hated and resented Finns. The Finnish national identity was constructed above all in contrast to the Russians, for the difference to Russia was seen as a precondition for the existence of Finland. Respectively, the new position of Finland also required approaching towards Russia, which was in its nature very pragmatic. The elite contrived to get rid off its prejudice against Russians on intellectual level, but not on emotional level. At the beginning of the autonomy the primary loyalty of the elite was directed into the Finnish fatherland and its habitants. This was a radical ideological change, because traditionally the loyalty of the elite had focused on monarch and monarch s realm. However, the role of Alexander I was crucial. According to the elite the emperor had granted them a new fatherland. The former native country (Finland) was seen as a new fatherland instead of Sweden. The loyalty of the elite to the emperor generated from the reciprocal gratitude; Alexander I had treated their native country so mercifully. The elite felt strong personal responsibility for Finland s existence. The elite believed that the future of Finland rested on their shoulders. Alexander I had given them fatherland, but it was in the hands of the elite to construct the Finnish state and national spirit. The study of the Finnish national identity brings forth also that the national identity was constructed by emphasizing Finns civic rights. The civic rights were essential part of the construction of the Finnish national identity, for the difference between Finns and Russians was based on Finns own laws and privileges, which the emperor of the Russia had ensured.

(Z)-11-Hexadecenal and (3Z,6Z,9Z)-Tricosatriene: Sex Pheromone Components of the Red Banded Mango Caterpillar Deanolis sublimbalis

The sex pheromone of the red banded mango caterpillar, Deanolis sublimbalis (Lepidoptera: Crambidae), a serious pest of the mango Mangifera indica (Anacardiaceae) in India and Southeast Asia and a recent invader into northern Australia, has been identified. Three candidate compounds were identified from pheromone gland extracts of female moths, using gas chromatography (GC), GC-electroantennographic detection and GC-mass spectrometric analyses, in conjunction with dimethyldisulfide derivatization. Field bioassays established that both (Z)-11-hexadecenal (Z11-16:Ald) and (3Z,6Z,9Z)-tricosatriene (3Z,6Z,9Z-23:Hy) were required for attraction of male D. sublimbalis moths, and 1,000 μg of a 1:1 mix of Z11-16:Ald and 3Z,6Z,9Z-23:Hy was more attractive to male moths than caged virgin females. However, the binary blend was only attractive when the isomeric purity of the monounsaturated aldehyde was >99%, suggesting that the (E)-isomer was inhibitory. Although (Z)-11-hexadecen-1-ol (Z11-16:OH) was tentatively identified in gland extracts, the addition of this compound to the binary blend did not increase the numbers of moths captured. The pheromone can now be used in integrated pest management strategies.

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE). These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.

Conformations of the amino aterminal tetrapeptide of emerimicins and antiamoebins in solution and in the solid state

The conformations of Boc-l-Phe-(AiB)3-OH (1) and Boc-l-Phe-(Aib)3-OMe (2) which correspond to the amino terminal sequence of the emerimicins and antiamoebins have been studied in solution using 270 MHz 1H n.m.r. In dimethyl sulphoxide solution both peptides show the presence of two strongly solvent shielded Aib NH groups, consistent with a consecutive β-turn conformation, involving the Aib(3) and Aib(4) NH groups in intramolecular 4 → I hydrogen bonds. This folded conformation is maintained for 2 in chloroform solution. Nuclear Overhauser effect studies provide evidence for a Type II Phe-Aib β-turn. An X-ray diffraction study of Boc-(d,l)-Phe-(Aib)3-OH establishes a single type III(III′) β-turn conformation with Aib(2)-Aib(3) as the corner residues. A single intramolecular 4 → I hydrogen bond between Phe(I) CO and Aib(4) NH groups is observed in the crystal. The solution conformation may incorporate a consecutive type II-III′ structure for the Phe(1)-Aib(2)-Aib(3) segment, with the initial type II β-turn being destabilized by intermolecular interactions in the solid state.