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)

Steady-State Response of Thick Rectangular Plates

The classical theory of plates neglects the effects of rotatory inertia and shear deformation, and due to this assumption it is applicable only for thin plates. Mindlin presented an improved plate theory which is fairly accurate.

Reinvestigation of the structure of Feist's acid 3-methylene-trans-1,2-cyclopropanedicarboxylic acid

C6H604, Mr = 142, triclinic, P[, a = 4.842(1), b = 7.607(1), c = 9.168 (3) A, ~ = 98.41(2), fl = 99.89(2), y = 77.74(1) ° , V = 320.9/k 3, Z = 2, Dm= 1.45 (flotation), D x = 1.470 g cm -3, p(Mo Ktt, 2 = 0.7107 A) = 0.63 cm -~, F(000) = 148. The structure was solved by direct methods and refined to an R value of 0.038 for 723 intensity measurements. The geometrical changes in the cyclopropane ring are discussed in the light of substituent effects. In the crystal structure the carboxylic groups are disordered.

Mandelic acid-4-hydroxylase, a new inducible entyme from Image

A soluble fraction of Image catalyzed the hydroxylation of mandelic acid to Image -hydroxymandelic acid. The enzyme had a pH optimum of 5.4 and showed an absolute requirement for Fe2+, tetrahydropteridine, NADPH. Image -Hydroxymandelate, the product of the enzyme reaction was identified by paper chromatography, thin layer chromatography, UV and IR-spectra.

Optical, dielectric and morphological studies of sol-gel derived nanocrystalline TiO2 films

Nanocrystalline TiO2 films have been synthesized on glass and silicon substrates by sol-gel technique. The films have been characterized with optical reflectance/transmittance in the wavelength range 300-1000nm and the optical constants (n, k) were estimated by using envelope technique as well as spectroscopic ellipsometry. Morphological studies have been carried Out using atomic force microscope (AFM). Metal-Oxide-Silicon (MOS) capacitor was fabricated using conducting coating on TiO2 film deposited on silicon. The C-V measurements show that the film annealed at 300 degrees C has a dielectric constant of 19.80. The high percentage of transmittance, low surface roughness and high dielectric constant suggests that it can be used as an efficient anti-reflection coating on silicon and other optical coating applications and also as a MOS capacitor.

Mechanism of failure in a free-standing Pt-aluminide bond coat during tensile testing at room temperature

The room temperature (RT) tensile behaviour of a free-standing high activity Pt-aluminide bond coat has been evaluated by microtensile testing technique. The coating had a typical three-layer microstructure. The stress-strain plot for the free-standing coating was linear, indicating the coating to be brittle at RT. Different fracture features were observed across the coating layers, namely quasi-cleavage in the outer layer and inner interdiffusion zone, and cleavage in the intermediate layer. By employing interrupted tensile test and observing the cross-sectional microstructure of the tested specimens, it was determined that failure of the microtensile samples occurred by the initiation of a single crack in the intermediate layer of the coating and its subsequent inside-out propagation. Such a mechanism of failure has been explained in terms of the fracture features observed across the sample thickness. This mechanism of failure is consistent with fracture toughness values of the individual coating layers. (C) 2009 Elsevier B.V. All rights reserved.

Mandelic Acid 4-Hydroxylase - New Inducible Enzyme From Pseudomonas-Convexa

A soluble fraction of catalyzed the hydroxylation of mandelic acid to -hydroxymandelic acid. The enzyme had a pH optimum of 5.4 and showed an absolute requirement for Fe2+, tetrahydropteridine, NADPH. -Hydroxymandelate, the product of the enzyme reaction was identified by paper chromatography, thin layer chromatography, UV and IR-spectra

On Using Projective Relations for Calibration and Estimation in a Structured-Light Scanner

For structured-light scanners, the projective geometry between a projector-camera pair is identical to that of a camera-camera pair. Consequently, in conjunction with calibration, a variety of geometric relations are available for three-dimensional Euclidean reconstruction. In this paper, we use projector-camera epipolar properties and the projective invariance of the cross-ratio to solve for 3D geometry. A key contribution of our approach is the use of homographies induced by reference planes, along with a calibrated camera, resulting in a simple parametric representation for projector and system calibration. Compared to existing solutions that require an elaborate calibration process, our method is simple while ensuring geometric consistency. Our formulation using the invariance of the cross-ratio is also extensible to multiple estimates of 3D geometry that can be analysed in a statistical sense. The performance of our system is demonstrated on some cultural artifacts and geometric surfaces.

Optical absorption and photoluminescence studies of Nd3 doped alkali boro germanate glasses

Optical absorption and photoluminescence studies have been carried out at room temperature in 25 R2O-25 GeO2-49.5 B2O3-0.5 Nd2O3 glass systems, (Composition in mol%, R= Li, Na, K and Rb). Judd Ofelt Intensity parameters and other parameters like Racah (E-1, E-2 and E-3), Slater-Condon-Shortley (F-2, F-4 and F-6) Spin-Orbit Coupling (xi(4f)) and Configuration Interaction (alpha,beta and gamma) for Nd3+ ion in the glass system are calculated. The variation of the 02 parameters are interpreted in terms of the covalency of the RE ion in the glass matrix. Further the hypersensitive transition I-4(9/2) -> (4)G(5/2), (2)G(7/2) is analyzed with respect to the intensity ratio I-L/I-S and is found to be dependent on the type of alkali in the glass matrix. The Photoluminescence studies do not show any appreciable shift in the peak emission wavelength of the F-4(3/2) to I-4(11/2) transition with the change in alkali type. (C) 2010 Elsevier B.V. All rights reserved.

C-H functionalization of tertiary amines by cross dehydrogenative coupling reactions: solvent-free synthesis of alpha-aminonitriles and beta-nitroamines under aerobic condition

A solvent-free synthesis of alpha-aminonitriles and beta-nitroamines by oxidative cross-dehydrogenative coupling under aerobic condition is reported. A catalytic amount of molybdenum(VI) acetylacetonoate was found to catalyze cyanation of tertiary amines to form alpha-aminonitriles, whereas vanadium pentoxide was found to promote aza-Henry reaction to furnish beta-nitroamines. Both of these environmentally benign reactions are performed in the absence of solvents using molecular oxygen as an oxidant.

A naturally occurring amino acid substitution in the voltage-dependent sodium channel selectivity filter affects channel gating

The pore of sodium channels contains a selectivity filter made of 4 amino acids, D/E/K/A. In voltage sensitive sodium channel (Nav) channels from jellyfish to human the fourth amino acid is Ala. This Ala, when mutated to Asp, promotes slow inactivation. In some Nav channels of pufferfishes, the Ala is replaced with Gly. We studied the biophysical properties of an Ala-to-Gly substitution (A1529G) in rat Nav1.4 channel expressed in Xenopus oocytes alone or with a beta 1 subunit. The Ala-to-Gly substitution does not affect monovalent cation selectivity and positively shifts the voltage-dependent inactivation curve, although co-expression with a beta 1 subunit eliminates the difference between A1529G and WT. There is almost no difference in channel fast inactivation, but the beta 1 subunit accelerates WT current inactivation significantly more than it does the A1529G channels. The Ala-to-Gly substitution mainly influences the rate of recovery from slow inactivation. Again, the beta 1 subunit is less effective on speeding recovery of A1529G than the WT. We searched Nav channels in numerous databases and noted at least four other independent Ala-to-Gly substitutions in Nav channels in teleost fishes. Thus, the Ala-to-Gly substitution occurs more frequently than previously realized, possibly under selection for alterations of channel gating.

Osteoprotective effect of propranolol in ovariectomized rats: a comparison with zoledronic acid and alfacalcidol

Currently beta-adrenergic receptor blockers are considered to be potential drugs under investigation for preventive or therapeutic effect in osteoporosis. However, there is no published data showing the comparative study of beta-blockers with well accepted agents for the treatment of osteoporosis. To address this question, we compared the effects of propranolol with well accepted treatments like zoledronic acid and alfacalcidol in an animal model of postmenopausal osteoporosis. Five days after ovariectomy, 36 ovariectomized (OVX) rats were divided into 6 equal groups, randomized to treatments zoledronic acid (100 mu g/kg, intravenous single dose); alfacalcidol (0.5 mu g/kg, oral gauge daily); propranolol (0.1 mg/kg, subcutaneously 5 days per week) for 12 weeks. Untreated OVX and sham OVX were used as controls. At the end of treatment serum calcium and alkaline phosphatase were assayed. Femurs were removed and tested for bone density, bone porosity, bone mechanical properties and trabecular micro-architecture. Propranolol showed a significant decrease in alkaline phosphatase levels and bone porosity in comparison to OVX control. Moreover, propranolol significantly improved bone density, bone mechanical properties and inhibited the deterioration of trabecular microarchitecture when compared with OVX control. The osteoprotective effect of propranolol was comparable with zoledronic acid and alfacalcidol. Based on this comparative study, the results strongly suggest that propranolol can be a candidate therapeutic drug for the management of postmenopausal osteoporosis.

Condition R and proper holomorphic maps between equidimensional product domains

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as a product of proper mappings between the factor domains. (C) 2013 Elsevier Inc. All rights reserved.