On circular designs

Summary A general method of analysis of circular designs (Das [3]) is suggested. Average efficiency factors of these designs have been tabulated.A-optimality of circular designs has been studied in comparison to group divisible incomplete block designs.     

Binding energy of finite nuclei in Jastrow-Factor-Cluster method with applications in helium

A general expression for the binding energy of finite nuclei in the Jastrow-Factor-Cluster method is developed upto the three-body cluster term with centre of mass correction. It is applied in massA=3 and 4 with the standard Chakkalakal function and the average Pauli condition. Compared to the previous work of Afnan (1969) better saturation properties are obtained for two- and three-body truncation. Convergence is also better.     

Chelate formation of ammonium aurintricarboxy-late with bivalent copper : Physico-chemical investigation of the composition,structure and stability

The formation of a coloured chelate, having λmax at 540 mμ, between cupric ions and ammonium aurintricarboxylate has been reported. It has been concluded that only one complex having metal : reagent ratio of 1:2 is formed in solution. The method adopted for investigation has been the continuous variation method, using spectrophotometric and electrical conductance measurements. It has been observed that there is an increase in acidity on mixing the reactants, which shows that hydrogen ions are liberated as a result of chelation It has been suggested that chelation occurs between the phenolic oxygen and the adjacent carboxylic oxygen.A method has been presented for the calculation of formation constant from spectrophotometric data and the value of K in the case of the chelate investigated has been calculated to be 6.45.10⁸. The free energy of formation works out to be —14.6 kcal at 25°C.     

The strength of multi-row aggregation cuts for sign-pattern integer programs

Sign-pattern IPs are a generalization of packing IPs, where for a given column all coefficients are either non-negative or non-positive. We show that the aggregation closure for such sign-pattern IPs can be 2-approximated by the original 1-row closure. This generalizes a result for packing IPs. On the other hand, unlike in the case of packing IPs, we show that the multi-row aggregation closure cannot be well approximated by the original multi-row closure.     

Relations between facets of low- and high-dimensional group problems

One-dimensional infinite group problems have been extensively studied and have yielded strong cutting planes for mixed integer programs. Although numerical and theoretical studies suggest that group cuts can be significantly improved by considering higher-dimensional groups, there are no known facets for infinite group problems whose dimension is larger than two. In this paper, we introduce an operation that we call sequential-merge. We prove that the sequential-merge operator creates a very large family of facet-defining inequalities for high-dimensional infinite group problems using facet-defining inequalities of lower-dimensional group problems. Further, they exhibit two properties that reflect the benefits of using facets of high-dimensional group problems: they have continuous variables’ coefficients that are not dominated by those of the constituent low-dimensional cuts and they can produce cutting planes that do not belong to the first split closure of MIPs. Further, we introduce a general scheme for generating valid inequalities for lower-dimensional group problems using valid inequalities of higher-dimensional group problems. We present conditions under which this construction generates facet-defining inequalities when applied to sequential-merge inequalities. We show that this procedure yields some two-step MIR inequalities of Dash and Günlük.     

Stabilizing a Flexible Beam on a Cart: A Distributed Port-Hamiltonian Approach

Motion planning and stabilization of the inverted pendulum on a cart is a much-studied problem in the control community. We focus our attention on asymptotically stabilizing a vertically upright flexible beam fixed on a moving cart. The flexibility of the beam is restricted only to the direction along the traverse of the cart. The control objective is to attenuate the effect of disturbances on the vertically upright profile of the beam. The control action available is the motion of the cart. By regulating this motion, we seek to regulate the shape of the beam. The problem presents a combination of a system described by a partial differential equation (PDE) and a cart modeled as an ordinary differential equation (ODE) as well as a controller which we restrict to an ODE. We set our problem in the port-controlled Hamiltonian framework. The interconnection of the flexible beam to the cart is viewed as a power-conserving interconnection of an infinite-dimensional system to a finite-dimensional system. The energy-Casimir method is employed to obtain the controller. In this method, we look for some constants of motion that are invariant of the choice of controller Hamiltonian. These Casimirs relate the controller states to the states of the system. We finally prove the stability of the equilibrium configuration of the closed-loop system.     

Disordered bcc γ-phase to δ-phase transformation in Zr-rich U-Zr alloy

The transformation mechanism of hexagonal delta phase from the disordered bcc gamma phase has not been reported before in the Zr-rich U–Zr alloy system. With the help of X-ray diffraction, transmission electron microscopy (TEM) and high-resolution TEM analyses it was shown that the gamma to delta conversion takes place by the lattice collapse mechanism of omega transformation. It was also ascertained that a higher aging temperature or time promotes the growth of all four variants of the delta phase within a parent gamma grain. In addition, ab initio electronic structure calculations showed that the bcc to hexagonal transformation, involving partial ordering of the parent bcc phase followed by (111) plane collapse, is energetically favorable.     

SERS‐based detection of barcoded gold nanoparticle assemblies from within animal tissue

We have explored the potential of deep Raman spectroscopy, specifically surface‐enhanced spatially offset Raman spectroscopy (SESORS), for non‐invasive detection from within animal tissue, by employing SERS‐barcoded nanoparticle (NP) assemblies as the diagnostic agent. This concept has been experimentally verified in a clinically‐relevant backscattered Raman system with an excitation line of 785 nm under ex vivo conditions. We have shown that our SORS system, with a fixed offset of 2–3 mm, offered sensitive probing of injected 2‐quinolinethiol‐barcoded NP assemblies through animal tissue containing both protein and lipid. In comparison with that of non‐aggregated SERS‐barcoded gold NPs, we have demonstrated that the tailored SERS‐barcoded aggregated NP assemblies have significantly higher detection sensitivity. We report that these NP assemblies can be readily detected at depths of 7–8 mm from within animal proteinaceous tissue with high signal‐to‐noise ratio. In addition, they could also be detected from beneath 1–2 mm of animal tissue with high lipid content, which generally poses a challenge because of high absorption of lipids in the near‐infrared region. We have also shown that the signal intensity and signal‐to‐noise ratio at a particular depth is a function of the SERS tag concentration used and that our SORS system has a 2‐quinolinethiol detection limit of 10⁻⁶ M. Higher detection depths may possibly be obtained with optimization of the NP assemblies, along with improvements in the instrumentation. Such NP assemblies offer prospects for in vivo, non‐invasive detection of tumours along with scope for incorporation of drugs and their targeted and controlled release at tumour sites. These diagnostic agents combined with drug delivery systems could serve as a ‘theranostic agent’, an integration of diagnostics and therapeutics into a single platform. Copyright © 2013 John Wiley & Sons, Ltd.     

Porosity Switching in Polymorphic Porous Organic Cages with Exceptional Chemical Stability

Porous solids that can be switched between different forms with distinct physical properties are appealing candidates for separation, catalysis, and host–guest chemistry. In this regard, porous organic cages (POCs) are of profound interest because of their solution‐state accessibility. However, the application of POCs is limited by poor chemical stability. Synthesis of an exceptionally stable imine‐linked (4+6) porous organic cage ( TpOMe‐CDA ) is reported using 2,4,6‐trimethoxy‐1,3,5‐triformyl benzene (TpOMe) as a precursor aldehyde. Introduction of the ‐OMe functional group to the aldehyde creates significant steric and hydrophobic characteristics in the environment around the imine bonds that protects the cage molecules from hydrolysis in the presence of acids or bases. The electronic effect of the ‐OMe group also plays an important role in enhancing the stability of the reported POCs. As a consequence, TpOMe‐CDA reveals exceptional chemical stability in neutral, acidic and basic conditions, even in 12 m NaOH. Interestingly, TpOMe‐CDA exists in three different porous and non‐porous polymorphic forms (α, β, and γ) with respect to differences in crystallographic packing and the orientation of the flexible methoxy groups. All of the polymorphs retain their crystallinity even after treatment with acids and bases. All the polymorphs of TpOMe‐CDA differ significantly in their properties as well as morphology and could be reversibly switched in the presence of an external stimulus.     

An [FeIII34] Molecular Metal Oxide

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe₃₄] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral Fe^III ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe‐O‐Fe angles and Fe?O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe₃₄], bulk iron oxides, previous Fe^III–oxo cages, and polyoxometalates (POMs), hints that much larger molecular Fe^III oxides can be made.