Metal-organic framework structures - how closely are they related to classical inorganic structures?

Metal-organic frameworks (MOFs) have emerged as an important family of compounds for which new properties are increasingly being found. The potential for such compounds appears to be immense, especially in catalysis, sorption and separation processes. In order to appreciate the properties and to design newer frameworks it is necessary to understand the structures from a fundamental perspective. The use of node, net and vertex symbols has helped in simplifying some of the complex MOF structures. Many MOF structures are beginning to be described as derived from inorganic structures. In this tutorial review, we have provided the basics of the node, the net and the vertex symbols and have explained some of the MOF structures. In addition, we have also attempted to provide some leads towards designing newer structures/topologies.

Spectral analysis of finite section normal integral operators

Some continuity and differentiability properties of the eigenvalues and eigenfunctions of finite section normal integral operators are proved. These are the extension of corresponding results for symmetric operators ([4.], 554–566; K. B. Athreya and R. Vittal Rao, to appear; [10.], 463–471.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

On solitons with half integral charge

Can certain soliton states, with half integral expectation value of charge, be also eigenstates of charge X with half integral eigenvalue? It can be so only with a somewhat sophisticated definition of charge.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the "unbroken" symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)C×U(1)em, a consequence is that color multiplets are not globally defined, while if H is SU(3)C×SU(2)WS×U(1)Y, the same is the case for both color and electroweak multiplets. There are, however, several subgroups KT, KT′,… of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H=SU(3)C×U(1)em, a choice for KT is SU(2)C×U(1)em, while for H=SU(3)C×SU(2)WS×U(1)Y, a choice is SU(2)C×U(1)×U(1)×U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations.

Assessing the potential of the rust fungus Puccinia spegazzinii as a classical biological control agent for the invasive weed Mikania micrantha in Papua New Guinea

The rust fungus Puccinia spegazzinii was introduced into Papua New Guinea (PNG) in 2008 as a classical biological control agent of the invasive weed Mikania micrantha (Asteraceae), following its earlier release in India, mainland China and Taiwan. Prior to implementing field releases in PNG, assessments were conducted to determine the most suitable rust pathotype for the country, potential for damage to non-target species, most efficient culturing method and potential impact to M. micrantha. The pathotype from eastern Ecuador was selected from the seven pathotypes tested, since all the plant populations evaluated from PNG were highly susceptible to it. None of the 11 plant species (representing eight families) tested to confirm host specificity showed symptoms of infection, supporting previous host range determination. A method of mass-producing inoculum of the rust fungus, using a simple technology which can be readily replicated in other countries, was developed. Comparative growth trials over one rust generation showed that M. micrantha plants infected with the rust generally had both lower growth rates and lower final dry weights, and produced fewer nodes than uninfected plants. There were significant correlations between the number of pustules and (a) the growth rate, (b) number of new nodes and (c) final total dry weight of single-stemmed plants placed in open sunlight and between the number of pustules and number of new nodes of multi-stemmed plants placed under cocoa trees. The trials suggest that field densities of M. micrantha could be reduced if the rust populations are sufficiently high. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

Prospects for the classical biological control of Calotropis procera (Apocynaceae) using co-evolved insects

Calotropis procera (Apocynaceae), a native of tropical Africa, the Middle East and the Indian subcontinent, is a serious environmental and rangeland weed of Australia and Brazil. It is also a weed in Hawaii in USA, the Caribbean Islands, the Seychelles, Mexico, Thailand, Vietnam and many Pacific Islands. In the native range C. procera has many natural enemies, thus classical biological control could be the most cost-effective option for its long-term management. Based on field surveys in India and a literature search, some 65 species of insects and five species of mites have been documented on C. procera and another congeneric-invador C. gigantea in the native range. All the leaf-feeding and stem-boring agents recorded on Calotropis spp. have wide host range. Three pre-dispersal seed predators,the Aak weevil Paramecops farinosus and the Aak fruit fly Dacuspersicus in the Indian subcontinent, and the Sodom apple fruit fly Dacus longistylus in the Middle East have been identified as prospective biological control agents based on their field host range. In Australia and Brazil, where C. procera has the potential to spread across vast areas, pre-dispersal seed predators would help to limit the spread of the weed. While the fruits of C. procera vary in size and shape across its range, those from India are similar to the ones in Australia and Brazil. Hence, seed-feeding insects from India are more likely to be suitable due to adaptation to fruit size and morphology. Future survey efforts for potential biological control agents should focus on North Africa.

Classical solitons with no quantum counterparts and their supersymmetric revival

We demonstrate the phenomenon stated in the title, using for illustration a two-dimensional scalar-field model with a triple-well potential {fx837-1}. At the classical level, this system supports static topological solitons with finite energy. Upon quantisation, however, these solitons develop infinite energy, which cannot be renormalised away. Thus this quantised model has no soliton sector, even though classical solitons exist. Finally when the model is extended supersymmetrically by adding a Majorana field, finiteness of the soliton energy is recovered.

On the Solution of Certain Simultaneous Pairs of Dual Integral Equations

Mit einer direkten Methode, bei der der Erdelyi-Kober- und der modifizierte Hankel-Operator Anwendung finden, werden gewisse Systeme aus zwei bzw. drei Paaren dualer Integralgleichungen mit Bessel-Kernen in geschlossener Form gelöst. Für bestimmte Funktionenklassen und Ordnungen der Bessel-Funktionen ist die Vorgehensweise angebrachter und geeigneter als die bereits existierenden Methoden.

Overcoming barriers to the successful implementation of a classical biological control strategy for the exotic invasive weed Mikania micrantha in the Asia-Pacific region

Mikania micrantha (Asteraceae) commonly known as mikania, is a major invasive alien plant (IAP) in the tropical humid agricultural and forest zones of the Asia-Pacific region. This fast-growing Neotropical vine is able to smother plants in agricultural ecosystems, agroforestry and natural habitats, reducing productivity and biodiversity. Fungal pathogens were first investigated for the classical biological control of this weed in 1996. This resulted in the selection and screening of the highly host-specific and damaging rust pathogen, Puccinia spegazzinii (Pucciniales). It was first released in India and China in 2005/6, although it is not believed to have established. Since then, it has been released successfully in Taiwan, Papua New Guinea (PNG), Fiji and most recently Vanuatu. The rust has established and is spreading rapidly after applying lessons learned from the first releases on the best rust pathotype and release strategy. In PNG, direct monitoring of vegetation change has demonstrated that the rust is having a significant impact on M. micrantha, with no unpredicted non-target impacts. Despite this, the authorities in many countries where mikania is a problem remain cautious about releasing the rust. In Western Samoa, introduction of the rust was not pursued because of a conflict of interest, and the perception that mikania suppresses even worse weeds. For some, ‘pathophobia’ is still a major obstacle. In Indonesia, where insects for weed CBC have been introduced, pathogens will currently not be considered. In other countries such as Bhutan and Myanmar, there are no baseline data on the presence and impact of IAPs and, with no history of CBC, no institutional framework for implementing this approach. Malaysia has a well-developed framework, but capacity needs to be built in the country. Overall, it remains critical to have champions at decision making levels. Hence, even with an effective ‘off-the-shelf’ agent available, implementation of mikania CBC still requires significant inputs tailored to the countries’ specific needs.

Determination of integral fringe order in photoelasticity

The paper describes a method to determine the integral fringe order associated with a fractional fringe value that is measured using Tardy or other similar compensators. The method makes use of two different wavelengths of light to determine the fractional fringe values. Further, it does not assume the independence of the material fringe constant on the wavelength of light used. From these measured fractional fringe values, the associated integral fringe order is determined. A method to construct a ready-reckoner table is also described which helps to identify the integral fringe order from any two measured fractional fringe values.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.