Convolution Products in L1(R+), Integral Transforms and Fractional Calculus

Mathematics Subject Classification: 43A20, 26A33 (main), 44A10, 44A15

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

An Application of Convolution Integral

MSC 2010: 30C45

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

MSC 2010: 11B83, 05A19, 33C45

Weighted Sum of Correlated Lognormals: Convolution Integral Solution

Probability density function (pdf) for sum of n correlated lognormal variables is deducted as a special convolution integral. Pdf for weighted sums (where weights can be any real numbers) is also presented. The result for four dimensions was checked by Monte Carlo simulation.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Sistema de Informació i Gestió Integral de la Producció Pesquera Internacional (SIGIPPI)

Des de la ciència geogràfica combinada amb el coneixement biològic i comercial, aquest projecte pretén crear una eina basada en la biogeografia i les últimes tecnologies de la Informació Geogràfica, que permetrà a l’usuari disposar de informació actualitzada per cada espècie amb interès comercial. El projecte es basa en el desenvolupament d’una aplicació web de consulta, entrada i actualització de dades referents a la producció pesquera internacional. Les eines utilitzades són les bases de dades MySQL i PostgreSQL i programació web amb html, php i javacript. Aquesta aplicació està pensada per ser accessible des de qualsevol ordinador amb connexió a internet i es subdivideix en tres sub-aplicacions. La primera sub-aplicació es basa en l’entrada d’espècies a partir de l’estructura taxonòmica. Partint de l’arbre taxonòmic, l’usuari té la possibilitat d’entrar, eliminar o modificar qualsevol tàxon o espècie. La segona subaplicació és una eina de digitalització cartogràfica on-line on l’usuari podrà marcar, eliminar o modificar sobre un mapa les localitzacions de les espècies que estiguin entrades en la sub-aplicació anterior. Finalment, la tercera sub-aplicació és una eina d’entrada de dades quinzenals referent als comportaments pel que fa tan a les dimensions com a les disponibilitats de pesca per cada espècie i localització.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Transcriptome of a mouse kidney cortical collecting duct cell line: effects of aldosterone and vasopressin.

Aldosterone and vasopressin are responsible for the final adjustment of sodium and water reabsorption in the kidney. In principal cells of the kidney cortical collecting duct (CCD), the integral response to aldosterone and the long-term functional effects of vasopressin depend on transcription. In this study, we analyzed the transcriptome of a highly differentiated mouse clonal CCD principal cell line (mpkCCD(cl4)) and the changes in the transcriptome induced by aldosterone and vasopressin. Serial analysis of gene expression (SAGE) was performed on untreated cells and on cells treated with either aldosterone or vasopressin for 4 h. The transcriptomes in these three experimental conditions were determined by sequencing 169,721 transcript tags from the corresponding SAGE libraries. Limiting the analysis to tags that occurred twice or more in the data set, 14,654 different transcripts were identified, 3,642 of which do not match known mouse sequences. Statistical comparison (at P < 0.05 level) of the three SAGE libraries revealed 34 AITs (aldosterone-induced transcripts), 29 ARTs (aldosterone-repressed transcripts), 48 VITs (vasopressin-induced transcripts) and 11 VRTs (vasopressin-repressed transcripts). A selection of the differentially-expressed, hormone-specific transcripts (5 VITs, 2 AITs and 1 ART) has been validated in the mpkCCD(cl4) cell line either by Northern blot hybridization or reverse transcription-PCR. The hepatocyte nuclear transcription factor HNF-3-alpha (VIT39), the receptor activity modifying protein RAMP3 (VIT48), and the glucocorticoid-induced leucine zipper protein (GILZ) (AIT28) are candidate proteins playing a role in physiological responses of this cell line to vasopressin and aldosterone.

Field Testing of Integral Abutments, Interim Report, HR-399, 1998

Integral abutment bridges are constructed without an expansion joint in the superstructure of the bridge; therefore, the bridge girders, deck, abutment diaphragms, and abutments are monolithically constructed. The abutment piles in an integral abutment bridge are vertically orientated, and they are embedded into the pile cap. When this type of a bridge experiences thermal expansion or contraction, horizontal displacements are induced at the top of the abutment piles. The flexibility of the abutment piles eliminates the need to provide an expansion joint at the inside face to the abutments: Integral abutment bridge construction has been used in Iowa and other states for many years. This research is evaluating the performance of integral abutment bridges by investigating thermally induced displacements, strains, and temperatures in two Iowa bridges. Each bridge has a skewed alignment, contains five prestressed concrete girders that support a 30-ft wide roadway for three spans, and involves a water crossing. The bridges will be monitored for about two years. For each bridge, an instrumentation package includes measurement devices and hardware and software support systems. The measurement devices are displacement transducers, strain gages, and thermocouples. The hardware and software systems include a data-logger; multiplexers; directline telephone service and computer terminal modem; direct-line electrical power; lap-top computer; and an assortment of computer programs for monitoring, transmitting, and management of the data. Instrumentation has been installed on a bridge located in Guthrie County, and similar instrumentation is currently being installed on a bridge located in Story County. Preliminary test results for the bridge located in Guthrie County have revealed that temperature changes of the bridge deck and girders induce both longitudinal and transverse displacements of the abutments and significant flexural strains in the abutment piles. For an average temperature range of 73° F for the superstructure concrete in the bridge located in Guthrie County, the change in the bridge length was about 1 118 in. and the maximum, strong-axis, flexural-strain range for one of the abutment piles was about 400 micro-strains, which corresponds to a stress range of about 11,600 psi.

Lineamientos básicos para un plan de mejoramiento y sostenibilidad de la cátedra UNESCO Gestión Integral del Patrimonio.

La Cátedra UNESCO “Gestión Integral del Patrimonio” de la UniversidadNacional de Colombia es una cátedra de carácter cultural cuyo objetivo principal es“Promover un sistema integrado de actividades de investigación, formación ydocumentación de la gestión integral

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .