Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

On the solvability of second kind integral equations on the real line

This paper considers general second kind integral equations of the form(in operator form φ − kφ = ψ), where the functions k and ψ are assumed known, with ψ ∈ Y, the space of bounded continuous functions on R, and k such that the mapping s → k(s, · ), from R to L1(R), is bounded and continuous. The function φ ∈ Y is the solution to be determined. Conditions on a set W ⊂ BC(R, L1(R)) are obtained such that a generalised Fredholm alternative holds: If W satisfies these conditions and I − k is injective for all k ∈ W then I − k is also surjective for all k ∈ W and, moreover, the inverse operators (I − k) − 1 on Y are uniformly bounded for k ∈ W. The approximation of the kernel in the integral equation by a sequence (kn) converging in a weak sense to k is also considered and results on stability and convergence are obtained. These general theorems are used to establish results for two special classes of kernels: k(s, t) = κ(s − t)z(t) and k(s, t) = κ(s − t)λ(s − t, t), where κ ∈ L1(R), z ∈ L∞(R), and λ ∈ BC((R\{0}) × R). Kernels of both classes arise in problems of time harmonic wave scattering by unbounded surfaces. The general integral equation results are here applied to prove the existence of a solution for a boundary integral equation formulation of scattering by an infinite rough surface and to consider the stability and convergence of approximation of the rough surface problem by a sequence of diffraction grating problems of increasingly large period.

On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Modelling the Knowledge Interface between Sales and Production Functions of a Company. Case: New Service Development Process.

Yrityksen sisäisten rajapintojen tunteminen mahdollistaa tiedonvaihdon hallinnan läpi organisaation. Idean muokkaaminen kannattavaksi innovaatioksi edellyttää organisaation eri osien läpi kulkevaa saumatonta prosessiketjua sekä tietovirtaa. Tutkielman tavoitteena oli mallintaa organisaation kahden toiminnallisesti erilaisen osan välinen tiedon vaihto. Tiedon vaihto kuvattiin rajapintana, tietoliittymänä. Kolmiulotteinen organisaatiomalli muodosti tutkimuksen pääteorian. Se kytkettiin yrityksen tuotanto- ja myyntiosiin, kuten myös BestServ-projektin kehittämään uuteen palvelujen kehittämisen prosessiin. Uutta palvelujen kehittämisen prosessia laajennettiin ISO/IEC 15288 standardin kuvaamalla prosessimallilla. Yritysarkkitehtuurikehikoita käytettiin mallintamisen perustana. Tietoliittymä nimenä kuvastaa näkemystä siitä, että tieto [tietämys] on olemukseltaan yksilöiden tai ryhmien välistä. Mallinnusmenetelmät eivät kuitenkaan vielä mahdollista tietoon [tietämykseen] liittyvien kaikkien ominaisuuksien mallintamista. Tietoliittymän malli koostuu kolmesta osasta, joista kaksi esitetään graafisessa muodossa ja yksi taulukkona. Mallia voidaan käyttää itsenäisesti tai osana yritysarkkitehtuuria. Teollisessa palveluliiketoiminnassa sekä tietoliittymän mallinnusmenetelmä että sillä luotu malli voivat auttaa konepajateollisuuden yritystä ymmärtämään yrityksen kehittämistarpeet ja -kohteet, kun se haluaa palvelujen tuottamisella suuremman roolin asiakasyrityksen liiketoiminnassa. Tietoliittymän mallia voidaan käyttää apuna organisaation tietovarannon ja tietämyksen mallintamisessa sekä hallinnassa ja näin pyrkiä yhdistämään ne yrityksen strategiaa palvelevaksi kokonaisuudeksi. Tietoliittymän mallinnus tarjoaa tietojohtamisen kauppatieteelliselle tutkimukselle menetelmällisyyden tutkia innovaatioiden hallintaa sekä organisaation uudistumiskykyä. Kumpikin tutkimusalue tarvitsevat tarkempaa tietoa ja mahdollisuuksia hallita tietovirtoja, tiedon vaihtoa sekä organisaation tietovarannon käyttöä.

Nitric oxide synthesis and biological functions of nitric oxide released from ruthenium compounds

During three decades, an enormous number of studies have demonstrated the critical role of nitric oxide (NO) as a second messenger engaged in the activation of many systems including vascular smooth muscle relaxation. The underlying cellular mechanisms involved in vasodilatation are essentially due to soluble guanylyl-cyclase (sGC) modulation in the cytoplasm of vascular smooth cells. sGC activation culminates in cyclic GMP (cGMP) production, which in turn leads to protein kinase G (PKG) activation. NO binds to the sGC heme moiety, thereby activating this enzyme. Activation of the NO-sGC-cGMP-PKG pathway entails Ca2+ signaling reduction and vasodilatation. Endothelium dysfunction leads to decreased production or bioavailability of endogenous NO that could contribute to vascular diseases. Nitrosyl ruthenium complexes have been studied as a new class of NO donors with potential therapeutic use in order to supply the NO deficiency. In this context, this article shall provide a brief review of the effects exerted by the NO that is enzymatically produced via endothelial NO-synthase (eNOS) activation and by the NO released from NO donor compounds in the vascular smooth muscle cells on both conduit and resistance arteries, as well as veins. In addition, the involvement of the nitrite molecule as an endogenous NO reservoir engaged in vasodilatation will be described.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.

Differential orthogonality: Laguerre and Hermite cases with applications

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Unique and conserved functions of B cell-activating factor of the TNF family (BAFF) in the chicken.

The chicken represents the best-characterized animal model for B cell development in the so-called gut-associated lymphoid tissue (GALT) and the molecular processes leading to B cell receptor diversification in this species are well investigated. However, the mechanisms regulating B cell development and homeostasis in GALT species are largely unknown. Here we investigate the role played by the avian homologue of B cell-activating factor of the tumor necrosis factor family (BAFF). Flow cytometric analysis showed that the receptor for chicken B cell-activating factor of the tumor necrosis factor family (chBAFF) is expressed by mature and immature B cells. Unlike murine and human BAFF, chBAFF is primarily produced by B cells both in peripheral lymphoid organs and in the bursa of Fabricius, the chicken's unique primary lymphoid organ. In vitro and in vivo studies revealed that chBAFF is required for mature B cell survival. In addition, in vivo neutralization with a decoy receptor led to a reduction of the size and number of B cell follicles in the bursa, demonstrating that, in contrast to humans and mice, in chickens BAFF is also required for the development of immature B cells. Collectively, we show that chBAFF has phylogenetically conserved functions in mature B cell homeostasis but displays unique and thus far unknown properties in the regulation of B cell development in birds.

Adapter and enzymatic functions of proteases in T-cell activation.

Proteases control many vital aspects of humoral and cellular immune responses, including the maturation of cytokines and the killing of target cells. Recently, it has become evident that triggering of the T-cell receptor controls T-cell proliferation through proteases such as mucosa-associated lymphoid tissue 1 (MALT1) and Caspase-8 that act both as adapters and enzymes. Here, we discuss the role of these and other proteases that are relevant to the control of the T-cell response and represent interesting targets of therapeutic immunomodulation.

Evolution of a polymineralic mantle shear zone and the role of second phases in the localization of deformation

The influence of second phases (e.g., pyroxenes) on olivine grain size was studied by quantitative microfabric analyses of samples of the Hilti massif mantle shear zone (Semail ophiolite, Oman). The microstructures range from porphyroclastic tectonites to ultramylonites, from outside to the center of the shear zone. Starting at conditions of ridge-related flow, they formed under continuous cooling leading to progressive strain localization. The dependence of the average olivine grain size on the second-phase content can be split into a second-phase controlled and a dynamic recrystallization-controlled field. In the former, the olivine grain size is related to the ratio between the second-phase grain size and volume fraction (Zener parameter). In the latter, dynamic recrystallization manifested by a balance between grain growth and grain size reduction processes yields a stable olivine grain size. In both fields the average olivine and second-phase grain size decreases with decreasing temperature. Combining the microstructural information with deformation mechanism maps suggests that the porphyroclastic tectonites (similar to 1100 degrees C) and mylonites (similar to 800 degrees C) formed under the predominance of dislocation creep. Since olivine-rich layers are intercalated with layer parallel, polymineralic bands in the mylonites, nearly equiviscous conditions can be assumed. In the ultramylonites, diffusion creep represents the major deformation mechanism in the polymineralic layers. It is this switch in deformation mechanism from dislocation creep to diffusion creep that forces strain to localize in the fine-grained polymineralic domains at low temperatures (<similar to 700 degrees C), underlining the role of the second phases on strain localization in cooling mantle rocks.

Desmin: molecular interactions and putative functions of the muscle intermediate filament protein

Desmin is the intermediate filament (IF) protein occurring exclusively in muscle and endothelial cells. There are other IF proteins in muscle such as nestin, peripherin, and vimentin, besides the ubiquitous lamins, but they are not unique to muscle. Desmin was purified in 1977, the desmin gene was characterized in 1989, and knock-out animals were generated in 1996. Several isoforms have been described. Desmin IFs are present throughout smooth, cardiac and skeletal muscle cells, but can be more concentrated in some particular structures, such as dense bodies, around the nuclei, around the Z-line or in costameres. Desmin is up-regulated in muscle-derived cellular adaptations, including conductive fibers in the heart, electric organs, some myopathies, and experimental treatments with drugs that induce muscle degeneration, like phorbol esters. Many molecules have been reported to associate with desmin, such as other IF proteins (including members of the membrane dystroglycan complex), nebulin, the actin and tubulin binding protein plectin, the molecular motor dynein, the gene regulatory protein MyoD, DNA, the chaperone alphaB-crystallin, and proteases such as calpain and caspase. Desmin has an important medical role, since it is used as a marker of tumors' origin. More recently, several myopathies have been described, with accumulation of desmin deposits. Yet, after almost 30 years since its identification, the function of desmin is still unclear. Suggested functions include myofibrillogenesis, mechanical support for the muscle, mitochondrial localization, gene expression regulation, and intracellular signaling. This review focuses on the biochemical interactions of desmin, with a discussion of its putative functions.

Silencing HIF-1α reduces the adhesion and secretion functions of acute leukemia hBMSCs

Hypoxia inducible factor-1α (HIF-1α) is an important transcription factor, which plays a critical role in the formation of solid tumor and its microenviroment. The objective of the present study was to evaluate the expression and function of HIF-1α in human leukemia bone marrow stromal cells (BMSCs) and to identify the downstream targets of HIF-1α. HIF-1α expression was detected at both the RNA and protein levels using real-time PCR and immunohistochemistry, respectively. Vascular endothelial growth factor (VEGF) and stromal cell-derived factor-1α (SDF-1α) were detected in stromal cells by enzyme-linked immunosorbent assay. HIF-1α was blocked by constructing the lentiviral RNAi vector system and infecting the BMSCs. The Jurkat cell/BMSC co-cultured system was constructed by putting the two cells into the same suitable cultured media and conditions. Cell adhesion and secretion functions of stromal cells were evaluated after transfection with the lentiviral RNAi vector of HIF-1α. Increased HIF-1α mRNA and protein was detected in the nucleus of the acute myeloblastic and acute lymphoblastic leukemia compared with normal BMSCs. The lentiviral RANi vector for HIF-1α was successfully constructed and was applied to block the expression of HIF-1α. When HIF-1α of BMSCs was blocked, the expression of VEGF and SDF-1 secreted by stromal cells were decreased. When HIF-1α was blocked, the co-cultured Jurkat cell’s adhesion and migration functions were also decreased. Taken together, these results suggest that HIF-1α acts as an important transcription factor and can significantly affect the secretion and adhesion functions of leukemia BMSCs.

Techno-economic modelling and cost functions of CO2 capture processes

The paper presents the techno-economic modelling of CO2 capture process in coal-fired power plants. An overall model is being developed to compare carbon capture and sequestration options at locations within the UK, and for studies of the sensitivity of the cost of disposal to changes in the major parameters of the most promising solutions identified. Technological options of CO2 capture have been studied and cost estimation relationships (CERs) for the chosen options calculated. Created models are related to the capital, operation and maintenance cost. A total annualised cost of plant electricity output and amount of CO2 avoided have been developed. The influence of interest rates and plant life has been analysed as well. The CERs are included as an integral part of the overall model.