A note on the integral trace form in cyclotomic fields

Let m >= 3 be an integer, zeta(m) is an element of C a primitive mth root of unity, and K-m the cyclotomic field Q(zeta(m)). An explicit description of the integral trace form Tr-Km/Q(x (x) over bar)vertical bar Z[zeta(m)] where (x) over bar is the complex conjugate of x is presented. In the case where m is prime, a procedure for finding the minimum of the form subject to x being a nonzero element of a certain Z- module in Z[zeta(m)] is presented.

Torres de extensões abelianas de grau primo ímpar não ramificado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Birkhoff normal forms in semi-classical inverse problems

Iantchenko, A.; Sj?strand, J.; Zworski, M., (2002) 'Birkhoff normal forms in semi-classical inverse problems', Mathematical Research Letters 9(3) pp.337-362 RAE2008

Birkhoff normal forms for Fourier integral operators II

Iantchenko, A.; Sj?strand, J., (2001) 'Birkhoff normal forms for Fourier integral operators II', American Journal of Mathematics 124(4) pp.817-850 RAE2008

Consonance in urban form : morphogenetic analysis of architectural elements within urban forms

"By understanding how places have evolved, we are better able to guide development and change in the urban fabric and avoid the incongruity created by so much of the modern environment" (MacCormac, R (1996), An anatomy of London, Built Environment, Dec 1996 This paper proposes a theory on the relevance of mapping the evolutionary aspects of historical urban form in order to develop a measure of evaluating architectural elements within urban forms, through to deriving parameters for new buildings. By adopting Conzen's identification of the tripartite division of urban form; the consonance inurban form of a particular palce resides in the elements and measurable values tha makeup the fine grain aggregates of urban form. The paper will demonstrate throughthe case study of Brisbane in Australia, a method of conveying these essential components that constitute a cities continuity of form and active usage. By presenting the past as a repository of urban form characteristics, it is argued that concise architectural responses that stem from such knowledge should result in an engaged urban landscape. The essential proposition is that urban morphology is a missing constituent in the process of urban design, and that the approach of the geographical discipline to the study of urban morphology holds the key to providing the evidence of urban growth characteristics, and this methodology suggests possibilities for an architectural approach that can comprehensively determine qualitative aspects of urban buildings. The relevance of this research lies in a potential to breach the limitations of current urban analysis whilst continuing the evolving currency of urban morphology as an integral practice in the design of our cities.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

On some integral properties of hypergeometric functions

In this note certain integrals involving hypergeometric functions have been evaluated in convenient and elegant forms. © 1971 Indian Academy of Sciences.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

Site-specific N-Linked Glycosylation of Receptor Guanylyl Cyclase C Regulates Ligand Binding, Ligand-mediated Activation and Interaction with Vesicular Integral Membrane Protein 36, VIP36

Guanylyl cyclase C (GC-C) is a multidomain, membrane-associated receptor guanylyl cyclase. GC-C is primarily expressed in the gastrointestinal tract, where it mediates fluid-ion homeostasis, intestinal inflammation, and cell proliferation in a cGMP-dependent manner, following activation by its ligands guanylin, uroguanylin, or the heat-stable enterotoxin peptide (ST). GC-C is also expressed in neurons, where it plays a role in satiation and attention deficiency/hyperactive behavior. GC-C is glycosylated in the extracellular domain, and differentially glycosylated forms that are resident in the endoplasmic reticulum (130 kDa) and the plasma membrane (145 kDa) bind the ST peptide with equal affinity. When glycosylation of human GC-C was prevented, either by pharmacological intervention or by mutation of all of the 10 predicted glycosylation sites, ST binding and surface localization was abolished. Systematic mutagenesis of each of the 10 sites of glycosylation in GC-C, either singly or in combination, identified two sites that were critical for ligand binding and two that regulated ST-mediated activation. We also show that GC-C is the first identified receptor client of the lectin chaperone vesicular integral membrane protein, VIP36. Interaction with VIP36 is dependent on glycosylation at the same sites that allow GC-C to fold and bind ligand. Because glycosylation of proteins is altered in many diseases and in a tissue-dependent manner, the activity and/or glycan-mediated interactions of GC-C may have a crucial role to play in its functions in different cell types.

DEFINING alpha-HELIX GEOMETRY BY C-alpha ATOM TRACE vs (phi-psi) TORSION ANGLES: A COMPARATIVE ANALYSIS

A regular secondary structure is described by a well defined set of values for the backbone dihedral angles (phi,psi and omega) in a polypeptide chain. However in real protein structures small local variations give rise to distortions from the ideal structures, which can lead to considerable variation in higher order organization. Protein structure analysis and accurate assignment of various structural elements, especially their terminii, are important first step in protein structure prediction and design. Various algorithms are available for assigning secondary structure elements in proteins but some lacunae still exist. In this study, results of a recently developed in-house program ASSP have been compared with those from STRIDE, in identification of alpha-helical regions in both globular and membrane proteins. It is found that, while a combination of hydrogen bond patterns and backbone torsional angles (phi-psi) are generally used to define secondary structure elements, the geometry of the C-alpha atom trace by itself is sufficient to define the parameters of helical structures in proteins. It is also possible to differentiate the various helical structures by their C-alpha trace and identify the deviations occurring both at mid-positions as well as at the terminii of alpha-helices, which often lead to occurrence of 3(10) and pi-helical fragments in both globular and membrane proteins.

Two new integral transforms and their applications

This thesis is in two parts. In Part I the independent variable θ in the trigonometric form of Legendre's equation is extended to the range ( -∞, ∞). The associated spectral representation is an infinite integral transform whose kernel is the analytic continuation of the associated Legendre function of the second kind into the complex θ-plane. This new transform is applied to the problems of waves on a spherical shell, heat flow on a spherical shell, and the gravitational potential of a sphere. In each case the resulting alternative representation of the solution is more suited to direct physical interpretation than the standard forms.

In Part II separation of variables is applied to the initial-value problem of the propagation of acoustic waves in an underwater sound channel. The Epstein symmetric profile is taken to describe the variation of sound with depth. The spectral representation associated with the separated depth equation is found to contain an integral and a series. A point source is assumed to be located in the channel. The nature of the disturbance at a point in the vicinity of the channel far removed from the source is investigated.

Copper and manganese forms in Lake Edku sediments, Alexandria, Egypt

Lake Edku is one of the Nile Delta lakes. It is subjected to contaminations by several anthropogenic materials such as trace elements and other wastes. The distribution of the different chemical forms of copper and manganese has been studied using sequential extraction techniques. Chemical analysis of the sediments shows that CaCO sub(3) ranged from 3.7% to 9.6% and organic matter from 3.06% to 8.11%. The results indicate that the distribution of manganese among the six chemical forms in the sediments of the lake obeys the following order: Mn-residual>Mn-carbonate>Mn-moderately reducible>Mn-organic form>Mn-exchangeable > Mn-easily reducible fraction. Also, the data revealed that more than 50% of the total manganese was found in the residual form, while the remainder was distributed among the other forms. In contrast, more than 70% of the total copper content was associated with the five chemical forms (exchangeable, carbonate, easily and moderately reducible and organic forms). Generally, the enrichment of manganese in the residual form revealed the important role in building up of clay minerals, while the distribution of copper among the different forms reflects an important role in biological and biochemical processes.

Speciation of some trace metals (Fe, Cu, and Cd) in El-Mex Bay waters, Alexandria, Egypt

Surface- and bottom-water samples were collected from October 1996 to August 1997 to study levels of iron, copper, and cadmium species in their dissolved labile as well as non-labile and particulate forms in the waters of El-Mex Bay. The results showed that the non-labile concentration of the metals was generally more abundant than that of the labile form: its content reached more than 90% of the total dissolved metal for Cu and more than 80% for Fe. The particulate form was almost at the level of the labile form. The annual concentration of the trace metals of the labile form was 13 µglˉ¹ for Fe; 3µglˉ¹ for Cu, and 1.2 µglˉ¹ for Cd in the surface- and bottom-waters.

Effects of nitrogen forms on the production of cyanobacterial toxin microcystin-LR by an isolated Microcystis aeruginosa

A cyanobacterial strain, which produced high content of microcystin-LR (MC-LR) but no rnicrocystin-RR (MC-RR), was isolated from the hypertrophic Dianchi Lake in China and identified as Microcystis aeruginosa DC-1. Effects of nitrogen containing chemicals and trace elements on the growth and the production of MC-LR by this strain were Studied. In the presence of bicine, compared with urea and ammonium, nitrate greatly promoted the growth and the production of MC-LR. However, leucine and arginine, which were the constitutional components in the molecular structure of MC-LR or RR, inhibited the production of MC-LR. Iron and silicon up to 10mg/L had little effects on the growth of M. aeruginosa DC-1, but the production of MC-LR was apparently enhanced. Under all conditions studied here, only MC-LR but no RR was detected within the cells of M. aeruginosa DC-1. Thus, chemical forms of nitrogen, rather than the usually concerned the total nitrogen, Lind trace elements played important roles in the production of MC toxins during cyanobacterial blooms.