Surface remodeling of bones induced by intra-medullary nailing

The paper is devoted to a study on the surface remodeling of bones. Anisotropy and piezoelectricity of bone tissue (as per previous experimental studies) are incorporated in the analysis. Surface remodeling induced by intra-medullary nailing is of primary concern in the study.     

Iminodiacetic acid/ethylcellulose as a chelating ion exchanger: Part 2. Determination of trace metals by inductively-coupled plasma atomic emission spectrometry

A chelate-forming cellulose, iminodiacetic acid/ethylcellulose (IDAEC), is applied to the collection of metals from ammonium citrate and acetate solutions. A method is devised for the i.c.p./a.e.s. determination of metal contaminants in magnesium by separation and preconcentration of the metals with IDAEC.     

Bismuth triflate catalyzed prins‐type cyclization in ionic liquid: Synthesis of 4‐tetrahydropyranol derivatives

The reaction of aldehydes with homoallylic alcohols in the presence of catalytic amount of bismuth triflate in [bmim]PF₆generates 4‐tetrahydropyranol derivatives in excellent yield and with high diastereoselectivity. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:104–106, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20403     

Transcendental values of the digamma function

Let ψ(x) denote the digamma function, that is, the logarithmic derivative of Euler's Γ-function. Let q be a positive integer greater than 1 and γ denote Euler's constant. We show that all the numbers

     

A variant of Lehmer's conjecture

Lehmer's conjecture asserts that τ(p)≠0 where τ is the Ramanujan τ-function. This is equivalent to the assertion that τ(n)≠0 for any n. A related problem is to find the distribution of primes p for which . These are open problems. We show that the variant of estimating the number of integers n for which n and τ(n) do not have a non-trivial common factor is more amenable to study. In particular, we show that the number of such n?x is ?x/logloglogx. We prove a similar result for more general cusp forms. This may be seen as a modular analogue of an old result of Erd?s on the Euler ? function.     

Regioselective strategies mediated by lanthanide triflates for efficient assembly of oligomannans

Readily prepared mannosyl n-pentenylorthoesters (NPOEs) serve as donors in themselves and as convenient intermediates for other glycosyl donors, such as n-pentenyl glycosides (NPGs), thioglycosides, and trichloroacetimidates. These various donors are activated by different reagents, and are therefore amenable to versatile, discriminate use. Scandium and ytterbium triflates respond very differently to these donors, with the result that chemoselective discrimination between NPOEs, NPGs, trichloroacetimidates as well as ethyl and phenyl thioglycosides can be achieved. Appropriate NPOEs are also able to provide 2,6 and 3,6 diol acceptors via rearrangement or glycoside formation, and these can be used for one-pot, sequential glycosidations based on orthogonal donors, and in situ double differential glycosidations. Thus NPOEs activated by iodonium ion, specifically generated from ytterbium triflate/N-iodosuccinimide, can be used to monoglycosidate the diols rapidly, with exquisite regio, and sometimes chemo, selectivity. The residual NPOE is converted into disarmed NPG, which is refractory to the reaction conditions, and so poses no threat to the free-OH of the monoglycosidation product. Further glycosidation of the latter can then achieved by direct addition of a trichloroacetimidate or ethyl thioglycoside. This basic strategy has been used to prepare a branched chain pentadecamannan. The success is an example of the efficiency of donor/acceptor MATCH concept for regioselective glycosylation.     

Distribution of uranium in drinking/ground waters in Narsipatnam Revenue Division of Visakhapatnam District of Andhra Pradesh,India and consequent ingestion dose

Journal of Radioanalytical and Nuclear Chemistry - Uranium is a naturally occurring radioactive element. The higher concentrations of U in waters can cause chemical as well as radiological...     

Thermodynamic prediction of bulk metallic glass forming alloys in ternary Zr–Cu–X (X = Ag,Al, Ti,Ga) systems

Prediction of bulk metallic glass (BMG) forming compositions has always been a challenge due to thermodynamic and kinetic constraints. In the present investigation, a parameter based on the enthalpy of chemical mixing (?H_chem) and the mismatch entropy (?S_σ/k_B) has been used to correlate with glass forming ability in some Zr based BMGs. The new thermodynamic parameter, P_HS = ?H_chem × ?S_σ/k_B, is found to have strong correlation with glass forming ability in the configurational entropy (?S_config/R) range of 0.9–1.0. P_HS has been calculated for compositions in Zr–Cu–Ag, Zr–Cu–Al, Zr–Cu–Ti and Zr–Cu–Ga ternary systems. It is observed that in all the systems studied, the best BMG composition (highest critical diameter (Z_c) of glass formation) is the one that corresponds to the highest negative P_HS value. Present approach using P_HS could be road map to design new BMG forming compositions.     

A problem in enumerating extreme points, and an efficient algorithm for one class of polytopes

We consider the problem of developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints. Murty and Chung (Math Program 70:27–45, 1995) introduced the concept of a segment of a polytope, and used it to develop some steps for carrying out the enumeration efficiently until the convex hull of the set of known extreme points becomes a segment. That effort stops with a segment, other steps outlined in Murty and Chung (Math Program 70:27–45, 1995) for carrying out the enumeration after reaching a segment, or for checking whether the segment is equal to the original polytope, do not constitute an efficient algorithm. Here we describe the central problem in carrying out the enumeration efficiently after reaching a segment. We then discuss two procedures for enumerating extreme points, the mukkadvayam checking procedure, and the nearest point procedure. We divide polytopes into two classes: Class 1 polytopes have at least one extreme point satisfying the property that there is a hyperplane H through that extreme point such that every facet of the polytope incident at that extreme point has relative interior point intersections with both sides of H; Class 2 polytopes have the property that every hyperplane through any extreme point has at least one facet incident at that extreme point completely contained on one of its sides. We then prove that the procedures developed solve the problem efficiently when the polytope belongs to Class 2.