Vibration of simply-supported trapezoidal plates I. Symmetric trapezoids

A detailed investigation of the natural frequencies and mode shapes of simply supported symmetric trapezoidal plates is undertaken in this paper. For numerical calculations, the relationship that exists between the eigenvalue problem of a polygonal simply supported plate and the eigenvalue problem of polygonal membrane of the same shape is utilized with advantage. The deflection surface is expressed in terms of a Fourier sine series in transformed coordinates and the Galerkin method is used. Results are presented in the form of tables and graphs. Several features like the crossing of frequency curves and the metamorphosis of some of the nodal patterns are observed. By a suitable interpretation of the modes of those symmetric trapezoidal plates which have the median as the nodal line, the results for some of the modes of unsymmetrical trapezoidal plates are also deduced.

On self-interacting oligoribonucleotides. I. Absorption and optical rotatory dispersion of 2′-5′- and 3′-5′-oligoguanylic acids

A series of 2′-5′-oligoguanylic acids are prepared by reacting G(cyclic)p with takadiastase T1 ribonuclease and separating the products chromatographically. The 3′-5′-oligoguanylic acids are obtained by separating the products of alkaline degradation of 3′-5′-poly(G). The optical rotatory dispersion and hypochromism of both 2′-5′- and 3′-5′-oligoguanylic acids are studied at two different pH. The optical rotatory dispersion spectrum of 2′-5′-GpG is significantly different from that of 3′-5′-GpG. The magnitude of rotation of the long-wavelength peak of 2′-5′-GpG is larger than that of 3′-5′-GpG. This finding contradicts the explanation that the extra stability and more intense circular dichroism band of other 3′-5′-dinucleoside monophosphates is due to H-bond formation between 2′-OH and either the base or the phosphate oxygen. The end phosphate group has a marked effect on the spectrum of GpG between 230 and 250 mμ. In addition the optical rotatory dispersion spectra of 2′-5′ exhibit strong pH, temperature, and solvent dependence between 230 and 250 mμ. ΔH and AS for order ⇌ disorder transition is estimated to be 9.7 kcal/mole and 35.2 eu, respectively. The optical rotatory dispersion spectra of guanine-rich oligoribonucleotides, GpGpC, GpGpU, GpGpGpC, and GpGpGpU are compared to the calculated optical rotatory dispersion from the semiempirical expression of Cantor and Tinoco, using measured optical rotatory dispersion of dimers. Contrary to previous studies, agreement is found not at all satisfactory. However, optical rotatory dispersion of 3′-5′-GpGpGpC and GpGpGpU can be estimated from the semiempirical expression, if a next-nearest interaction parameter is introduced empirically. Such interaction parameter can be calculated from the measured properties of trinucleotide sequences like GpGpG, GpGpC, and GpGpU, assuming that only the nearest-neighbor interaction is important. The optical rotatory dispersion of single-stranded poly(G) is also predicted. The importance of syn-anti equilibrium and next-nearest-neighbor interaction in oligoguanylic acids is suggested as a probable explanation.

Studies on the structure of the chromosomes - I. Allium cepa-Stain fixatives and their utility

The structure of the mitotic chromosomes of Allium cepa has been elucidated by controlling the temperature and time of exposure of fresh roots to stain fixatives. The details seen in material stained in N HCl-orcein for 8 min. at 60° C. and squashed after varying intervals of storage at room temperature were essentially similar to pictures obtained with 1% aceto-orcein and 1% aceto-orcein-N HCl (10:1) under identical conditions of handling. The chromosomes appear quadri-partite at metaphase and bi-partite at anaphase. A rare instance of the precocious assumption of a quadri-partite condition by two anaphase chromosomes is illustrated. Caduceus coiling of chromonemata was seen in chromosome bridges also. Chromosomes have material easily dissociable from the chromonemata and their removal does not affect the structural integrity of the chromosome.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part I. Copper(I and II)-ammonia and methylamine complexes

The equilibrium between cuprous ion, cupric ion and metallic copper has been studied using polarographic and redox potential measurements, by reducing cupric ion with copper gauze until equilibrium. Using the well-defined anodic diffusion current plateau, an amperometric method for estimating cuprous copper based on the titration of cuprous ion with dichromate or permanganate has been developed. The diffusion current constant and the disproportionation constant of cuprous ion and the standard potential for the reduction reaction of Cu2+ → Cu+ have been determined. Polarograms have been taken after reducing cupric complexes of ammonia and methylamine with copper until equilibrium. In the case of the copper-ammonia system, reduction to the cuprous state is practically complete while in the case of the cupric-methylamine system, the first cathodic wave occurs to some extent. A new method, called the polarographic-redox potential method, for determining the stability constants of cuprous and cupric complexes has been developed. The method depends upon the determination of the concentration of complexes by polarographic wave heights, and free cupric anc cuprous ions by redox potentials. The stability constants of the following complexes have been obtained: Cu(NH3)2+4, Cu(NH3)+2, Cu(CH3NH2)2(OH)2, Cu(CH3NH2)+2. The stability constants determined by the new method and the half-wave potential shift method agree and the value for the cupric-ammonia complex is in good agreement with Bjerrum method, indicating the reliability of this method.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

The Raman spectra of organic compounds -Part I. Methyl, ethyl, n-propyl and n-butyl alcohols

The Raman spectra of methyl alcohol, ethyl alcohol, n-propyl alcohol and n-butyl alcohol have been recorded using λ 2537 excitation. 35, 49, 45 and 51 Raman lines respectively have been identified in the spectra of these alcohols, in addition to the rotational 'wings'. In each case, a large number of additional lines have been recorded. The existence of Raman lines with frequency shifts greater than 3800 cm.-1, first reported by Bolla in the spectrum of ethyl alcohol, has been confirmed. Similar high-frequency shift Raman lines have also been recorded in the spectrum of methyl alcohol. They have been assigned as combinations. Proper assignments have been given for the prominent Raman lines appearing in the spectra of these alcohols.

Raman spectra of single crystals of dicarboxylic acids - Part I. β-malonic acid and β-succinic acid

Raman spectra of single crystals of β-malonic acid and β-succinic acid have been photographed using λ 2536·5 radiation. 32 Raman lines have been recorded in the case of β-malonic acid. Of these 21 lines have been recorded for the first time. The three intense lattice lines at 52, 90 and 144 cm.-1 have been attributed to rotational lattice oscillations. 29 Raman lines in the case of β-succinic acid have been recorded. The entire lattice spectrum and many internal frequencies have been recorded for the first time. The three intense lattice lines at 80, 135 and 160 cm.-1 have been assigned to the rotational oscillations of the two molecules of the succinic acid in the unit cell.

Polarisation studies on the Raman spectra of cubic crystals - Part I. Sodium chlorate

neral expressions have been derived for the intensities of the three classes of Raman lines namely totally symmetric A, doubly degenerate E and triply degenerate F, in the case of cubic crystals under the following conditions. The direction of the incident beam which is polarised with its electric vector inclined at an angle α to the normal to the scattering plane makes an angle Θ with one of the cubic axes of the crystal. The transversely scattered light is analysed by a double image prism with its principal axes inclined at angle β to the normal to the scattering plane, which is horizontal. For incident unpolarised light and Θ=22 1/2°, and the scattered light being analysed by a double image prism rotated through 45° from the position when its principal axes are vertical and horizontal ρ{variant} for A lines is equal to one, for E lines >1 and for F lines <1. This gives a method of classifying the Raman lines of a cubic crystal in a single setting. The results have been experimentally verified in sodium chlorate.

Studies on nucleotide pyrophosphatase I. Partial purification and properties of a sheep liver enzyme that catalyzes the hydrolysis of dinucleotides

A partially purified sheep liver enzyme that hydrolyzed dinucleotides at the pyrophosphate bond was obtained by solubilizing the 18,000g sediment with n-butanol and fractionating the solubilized enzyme with acetone. The enzyme activity when measured using FAD as substrate, (FAD → FMN + AMP), was optimal at pH 9.7 and temperatures between 30 °–36 ° and at 60 °. The rate of release of FMN with time occurred with an initial lag of 30 sec, a linear increase for 1 min, and a subsequent irregular rate. In the presence of orthophosphate (Pi; 10 μImage ), FMN was released at an uniformly continuous and enhanced rate. 32Pi was not incorporated into the substrate or products. Sodium arsenate counteracted the effects of Pi. The apparent Km and Vmax were 0.133 mImage and 100 units; and 0.133 mImage and 200 units, in the absence and presence of Pi, respectively. The temperature optimum was 42 ° in the presence of Pi.Negative cooperative interactions observed at low concentrations of FAD were abolished by the addition of Pi. The inhibition by AMP was sigmoid and Pi abolished this sigmoidal response. The enzyme hydrolyzed in addition to FAD, NAD+ and NADP+. Nucleoside triphosphates were potent inhibitors of the enzyme activity. The partial inhibition of the enzyme by o-phenanthroline and by p-hydroxymercuribenzoate could be reversed by Fe2+ ions and by reduced glutathione, respectively.

Japanese Encephalitis Virus Utilizes the Canonical Pathway To Activate NF-kappa B but It Utilizes the Type I Interferon Pathway To Induce Major Histocompatibility Complex Class I Expression in Mouse Embryonic Fibroblasts

Flaviviruses have been shown to induce cell surface expression of major histocompatibility complex class I (MHC-I) through the activation of NF-kappa B. Using IKK1(-/-), IKK2(-/-), NEMO-/-, and IKK1-/- IKK2-/- double mutant as well as p50(-/-) RelA(-/-) cRel(-/-) triple mutant mouse embryonic fibroblasts infected with Japanese encephalitis virus (JEV), we show that this flavivirus utilizes the canonical pathway to activate NF-kappa B in an IKK2- and NEMO-, but not IKK1-, dependent manner. NF-kappa B DNA binding activity induced upon virus infection was shown to be composed of RelA: p50 dimers in these fibroblasts. Type I interferon (IFN) production was significantly decreased but not completely abolished upon virus infection in cells defective in NF-kappa B activation. In contrast, induction of classical MHC-I (class 1a) genes and their cell surface expression remained unaffected in these NF-kappa B-defective cells. However, MHC-I induction was impaired in IFNAR(-/-) cells that lack the alpha/beta IFN receptor, indicating a dominant role of type I IFNs but not NF-kappa B for the induction of MHC-I molecules by Japanese encephalitis virus. Our further analysis revealed that the residual type I IFN signaling in NF-kappa B-deficient cells is sufficient to drive MHC-I gene expression upon virus infection in mouse embryonic fibroblasts. However, NF-kappa B could indirectly regulate MHC-I expression, since JEV-induced type I IFN expression was found to be critically dependent on it.

Structural stability of slender aerospace vehicles: Part I Mathematical modeling

A detailed mechanics based model is developed to analyze the problem of structural instability in slender aerospace vehicles. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic pressure and the propulsive thrust of the vehicle. The model is one-dimensional, and it can be employed to idealized slender vehicles with complex shapes. Condition under which a flexible body with internal stress waves behaves like a perfect rigid body is derived. Two methods are developed for finite element discretization of the system: (1) A time-frequency Fourier spectral finite element method and (2) h-p finite element method. Numerical results using the above methods are presented in Part II of this paper. (C) 2010 Elsevier Ltd. All rights reserved.