Some recent developments in the transmutation operator approach

This is a brief overviewof some recent developments in the transmutation operator approach to practical solution of mathematical physics problems. It introduces basic notions and results of transmutation theory, and gives a brief historical survey with some important references. Mainly applications to linear ordinary and partial differential equations and to related boundary value and spectral problems are discusse

Transmutation operators boundary value problems

Transmutation operators method is used to solve and study boundary value problems. In this paper several ways to obtain transformation operators are considered: the finite integral transforms, Neumann series, the Fourier transforms, and reflection techniques. The finite integral transform technique leads to solution in the form of a composition of the Fourier sine transform and inverse finite integral transfor

One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels

This paper consists of two parts. In the first part we give a brief survey of results on Buschman–Erdélyi operators, which are transmutations for the Bessel singular operator. Main properties and applications of Buschman–Erdélyi operators are outlined. In the second part of the paper we consider multi-dimensional integral transforms of Buschman–Erdélyi type with Legendre functions in kernels. Complete proofs are given in this part, main tools are based on Mellin transform properties and usage of Fox H-functions

Constraining noncommutative field theories with holography

An important window to quantum gravity phenomena in low energy noncommutative (NC) quantum field theories (QFTs) gets represented by a specific form of UV/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective QFTs as a distinct UV/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff $\Lambda_{\rm UV}$, the IR cutoff $\Lambda_{\rm IR}$ and the scale of noncommutativity $\Lambda_{\rm NC}$, can be obtained. We show that an effective QFT endowed with both principles may not be capable to fit disparate experimental bounds simultaneously, like the muon $g-2$ and the masslessness of the photon. Also, the constraints from the muon $g-2$ preclude any possibility to observe the birefringence of the vacuum coming from objects at cosmological distances. On the other hand, in NC theories without the UV completion, where the perturbative aspect of the theory (obtained by truncating a power series in $\Lambda_{\rm NC}^{-2}$) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined $E/ \Lambda_{\rm NC} \lesssim 1$, gets affected when holography is applied by providing the energy of the system $E$ a $\Lambda_{\rm NC}$-dependent lower limit. This may affect models which try to infer the scale $\Lambda_{\rm NC}$ by using data from low-energy experiments.Comment: 4 pages, version to be published in JHE

Lectin-like bacteriocins from pseudomonas spp. utilise D-rhamnose containing lipopolysaccharide as a cellular receptor

Lectin-like bacteriocins consist of tandem monocot mannose-binding domains and display a genus-specific killing activity. Here we show that pyocin L1, a novel member of this family from Pseudomonas aeruginosa, targets susceptible strains of this species through recognition of the common polysaccharide antigen (CPA) of P. aeruginosa lipopolysaccharide that is predominantly a homopolymer of d-rhamnose. Structural and biophysical analyses show that recognition of CPA occurs through the C-terminal carbohydrate-binding domain of pyocin L1 and that this interaction is a prerequisite for bactericidal activity. Further to this, we show that the previously described lectin-like bacteriocin putidacin L1 shows a similar carbohydrate-binding specificity, indicating that oligosaccharides containing d-rhamnose and not d-mannose, as was previously thought, are the physiologically relevant ligands for this group of bacteriocins. The widespread inclusion of d-rhamnose in the lipopolysaccharide of members of the genus Pseudomonas explains the unusual genus-specific activity of the lectin-like bacteriocins

On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show

A systematic review of primary care models for non-communicable disease interventions in Sub-Saharan Africa

Background Chronic diseases, primarily cardiovascular disease, respiratory disease, diabetes and cancer, are the leading cause of death and disability worldwide. In sub-Saharan Africa (SSA), where communicable disease prevalence still outweighs that of non-communicable disease (NCDs), rates of NCDs are rapidly rising and evidence for primary healthcare approaches for these emerging NCDs is needed. Methods A systematic review and evidence synthesis of primary care approaches for chronic disease in SSA. Quantitative and qualitative primary research studies were included that focused on priority NCDs interventions. The method used was best-fit framework synthesis. Results Three conceptual models of care for NCDs in low- and middle-income countries were identified and used to develop an a priori framework for the synthesis. The literature search for relevant primary research studies generated 3759 unique citations of which 12 satisfied the inclusion criteria. Eleven studies were quantitative and one used mixed methods. Three higher-level themes of screening, prevention and management of disease were derived. This synthesis permitted the development of a new evidence-based conceptual model of care for priority NCDs in SSA. Conclusions For this review there was a near-consensus that passive rather than active case-finding approaches are suitable in resource-poor settings. Modifying risk factors among existing patients through advice on diet and lifestyle was a common element of healthcare approaches. The priorities for disease management in primary care were identified as: availability of essential diagnostic tools and medications at local primary healthcare clinics and the use of standardized protocols for diagnosis, treatment, monitoring and referral to specialist care

Development of mandibular, hyoid and hypobranchial muscles in the zebrafish: homologies and evolution of these muscles within bony fishes and tetrapods

<p>Abstract</p> <p>Background</p> <p>During vertebrate head evolution, muscle changes accompanied radical modification of the skeleton. Recent studies have suggested that muscles and their innervation evolve less rapidly than cartilage. The freshwater teleostean zebrafish (<it>Danio rerio</it>) is the most studied actinopterygian model organism, and is sometimes taken to represent osteichthyans as a whole, which include bony fishes and tetrapods. Most work concerning zebrafish cranial muscles has focused on larval stages. We set out to describe the later development of zebrafish head muscles and compare muscle homologies across the Osteichthyes.</p> <p>Results</p> <p>We describe one new muscle and show that the number of mandibular, hyoid and hypobranchial muscles found in four day-old zebrafish larvae is similar to that found in the adult. However, the overall configuration and/or the number of divisions of these muscles change during development. For example, the undivided adductor mandibulae of early larvae gives rise to the adductor mandibulae sections A0, A1-OST, A2 and Aω, and the protractor hyoideus becomes divided into dorsal and ventral portions in adults. There is not always a correspondence between the ontogeny of these muscles in the zebrafish and their evolution within the Osteichthyes. All of the 13 mandibular, hyoid and hypobranchial muscles present in the adult zebrafish are found in at least some other living teleosts, and all except the protractor hyoideus are found in at least some extant non-teleost actinopterygians. Of these muscles, about a quarter (intermandibularis anterior, adductor mandibulae, sternohyoideus) are found in at least some living tetrapods, and a further quarter (levator arcus palatini, adductor arcus palatini, adductor operculi) in at least some extant sarcopterygian fish.</p> <p>Conclusion</p> <p>Although the zebrafish occupies a rather derived phylogenetic position within actinopterygians and even within teleosts, with respect to the mandibular, hyoid and hypobranchial muscles it seems justified to consider it an appropriate representative of these two groups. Among these muscles, the three with clear homologues in tetrapods and the further three identified in sarcopterygian fish are particularly appropriate for comparisons of results between the actinopterygian zebrafish and the sarcopterygians.</p

Azimuthal anisotropy and correlations at large transverse momenta in p+pp+p and Au+Au collisions at sNN\sqrt{s_{_{NN}}}= 200 GeV

Results on high transverse momentum charged particle emission with respect to the reaction plane are presented for Au+Au collisions at $\sqrt{s_{_{NN}}}$= 200 GeV. Two- and four-particle correlations results are presented as well as a comparison of azimuthal correlations in Au+Au collisions to those in $p+p$ at the same energy. Elliptic anisotropy, $v_2$, is found to reach its maximum at $p_t \sim 3$ GeV/c, then decrease slowly and remain significant up to $p_t\approx 7$ -- 10 GeV/c. Stronger suppression is found in the back-to-back high-$p_t$ particle correlations for particles emitted out-of-plane compared to those emitted in-plane. The centrality dependence of $v_2$ at intermediate $p_t$ is compared to simple models based on jet quenching.Comment: 4 figures. Published version as PRL 93, 252301 (2004