Set Of New Functions Research Articles

Stratigraphic sequence map for groundwater assessment and protection of unconsolidated aquifers: A case example in the Abitibi-Témiscamingue region, Québec, Canada

Quantifying water resources at various scales is crucial for ensuring safe access to potable water for present and future generations. Fitting into this framework, this study presents a GIS-based approach aimed at allowing the evaluation of available groundwater resources within unconsolidated aquifers set in vast and heterogeneous shield regions. The approach was developed in a 19,397 km2 region located in Abitibi-Témiscamingue (Québec, Canada) where unconsolidated aquifers are set in an irregular geologic framework owing to the rugged Canadian Shield topography and to the diversity of glacial and post-glacial events that shaped the landscape. Sparse and unevenly distributed stratigraphic borehole data were used for constructing a GIS-based model representing the total overburden thickness (unconsolidated sediments covering the bedrock), as well as the thickness and extent of the fine-grained deep-water sediments (silt-clay) of the Barlow-Ojibway proglacial Lake on a 100 m × 100 m mesh at the regional scale. The study suggests a new set of functions to map drift thickness in areas of highly discontinuous drift cover, using GIS tools. These data were used jointly with surficial deposits maps in order to develop a regional-scale two-dimensional model where 15 distinct stratigraphic sequences allow representation of the architecture of unconsolidated geological units. The approach allows simplifying data representation and ensuring the consistency between various regional-scale hydrogeological maps. The data is used to produce a stratigraphic sequence map for representing the architecture of aquifer– aquitard systems at the regional scale in a manner that is intelligible to non-specialists. The map and related data are first discussed for documenting the extent and volume of regional aquifers. The stratigraphic sequence map is subsequently discussed as a tool for supporting political decision makers dealing with issues related to groundwater resource assessment, protection and sustainable development.

Fractional-order Bernoulli functions and their applications in solving fractional Fredholem–Volterra integro-differential equations

In this paper, we define a new set of functions called fractional-order Bernoulli functions (FBFs) to obtain the numerical solution of linear and nonlinear fractional integro-differential equations. The properties of these functions are employed to construct the operational matrix of the fractional integration. By using this matrix and the least square approximation method the fractional integro-differential equations are reduced to systems of algebraic equations which are solved through the Newton's iterative method. The convergence of the method is extensively discussed and finally, some numerical examples are shown to illustrate the efficiency and accuracy of the method.

Érzékelt tér, elgondolt tér, megélt tér: A térbeliség trialektikája egy budapesti barnamező-rehabilitációs beruházás példáján

A tanulmány egy budapesti barnamező-rehabilitációs beruházás, a Millenáris lakossági percepcióját, az azzal kapcsolatos ismereteket és attitűdöket, valamint a helyszínhez kötődő társadalmi térhasználatot vizsgálja. A kérdőíves felmérés elméleti alapjául Henri Lefebvre és Edward Soja térelméleti koncepciója, a térbeliség trialektikája szolgált, mely a térbeliség három szemléleti módját különbözteti meg: a tér, ahogy azt érzékeljük (érzékelt tér), a tér, ahogy arról gondolkodunk (elgondolt tér), illetve a tér, ahogy azt megéljük, használjuk (megélt tér). A kutatás tapasztalatai alapján kijelenthető, hogy a vizsgált helyszín azért válhatott sikeres barnamező-rehabilitációs beruházássá, mert a kilátogatók érzékelt, elgondolt és megélt terében egyaránt markánsan jelen van. Az épített környezet újraértelmezésének sikerességét az építészeti-örökségvédelmi szakma által is nagyra értékelt építészeti kulisszák jelzik, ugyanakkor kétségtelen, hogy a Millenárist létrehozó érdekcsoport a terület „jelentéseit” (vagyis a tér reprezentációit) is a számára megfelelő módon tudta pozicionálni. Mindössze ezek által azonban nem válhatott volna sikeressé a helyszín: a lakosság az erőteljes hatalmi-politikai konnotációk ellenére is elfogadja és aktívan használja a területet, azonban ehhez olyan napi rutinokra épülő új funkciókra volt szükség, amelyek a performativitás révén folyamatosan megélt kapcsolatot teremtenek a környező lakosság és a megújult egykori ipari helyszín között.

Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems

In this paper, a new set of functions called fractional-order Boubaker functions is defined for solving the delay fractional optimal control problems with a quadratic performance index. To solve the problem, first we obtain the operational matrix of the Caputo fractional derivative of these functions and the operational matrix of multiplication to solve the nonlinear problems for the first time. Also, a general formulation for the delay operational matrix of these functions has been achieved. Then we utilized these matrices to solve delay fractional optimal control problems directly. In fact, the delay fractional optimal control problem converts to an optimization problem, which can then be easily solved with the aid of the Gauss–Legendre integration formula and Newton’s iterative method. Convergence of the algorithm is proved. The applicability of the method is shown by some examples; moreover, a comparison with the existing results shows the preference of this method.

Sector magnets or transverse electromagnetic fields in cylindrical coordinates

The Laplace's equations for the scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates with translational invariance along azimuthal coordinate are considered. The series of special functions which, when expanded in power series in radial and vertical coordinates, in lowest order replicate the harmonic homogeneous polynomials of two variables are found. These functions are based on radial harmonics found by Edwin~M.~McMillan in his more-than-40-years "forgotten" article, which will be discussed. In addition to McMillan's harmonics, second family of adjoint radial harmonics is introduced, in order to provide symmetric description between electric and magnetic fields and to describe fields and potentials in terms of same special functions. Formulas to relate any transverse fields specified by the coefficients in the power series expansion in radial or vertical planes in cylindrical coordinates with the set of new functions are provided. This result is no doubt important for potential theory while also critical for theoretical studies, design and proper modeling of sector dipoles, combined function dipoles and any general sector element for accelerator physics. All results are presented in connection with these problems.

Upgrade of the Automatic Measurement System for the Electrical Verification of the LHC Superconducting Circuits

Electrical quality assurance (ELQA) of the superconducting electrical circuits in the LHC requires an advanced test equipment accompanied by the dedicated software, data storage system, and analysis toolset. In 2007, the measurement system was built to carry out the Test Procedure 4 (TP4), namely the qualification of the whole superconducting circuits in terms of instrumentation routing, insulation quality, resistance, and impedance of the circuit components. This measurement system has become the main ELQA tool at the LHC. During the testing campaign at LHC from 2007 to 2009, a set of new functionalities was proposed. For the Long Shutdown 1 of the LHC that was planned for 2013-2015, the number of the measurement systems had to be increased from the existing four to eight units. In view of these facts, in 2010, the decision was made to perform the upgrade of the TP4 system. In this paper, we describe the requirements, the upgrade process, the architecture, and parameters of the upgraded system, including the maintainability improvements. We also present examples of the automated electrical tests of the LHC superconducting circuits performed with the upgraded TP4 system during LHC Long Shutdown 1, which show high flexibility and extendibility of the implemented solution.

Surface functionalization of semiconductor and oxide nanocrystals with small inorganic oxoanions (PO4(3-), MoO4(2-)) and polyoxometalate ligands.

In this work, we study the functionalization of the nanocrystal (NC) surface with inorganic oxo ligands, which bring a new set of functionalities to all-inorganic colloidal nanomaterials. We show that simple inorganic oxoanions, such as PO4(3-) and MoO4(2-), exhibit strong binding affinity to the surface of various II-VI and III-V semiconductor and metal oxide NCs. ζ-Potential titration offered a useful tool to differentiate the binding affinities of inorganic ligands toward different NCs. Direct comparison of the binding affinity of oxo and chalcogenidometallate ligands revealed that the former ligands form a stronger bond with oxide NCs (e.g., Fe2O3, ZnO, and TiO2), while the latter prefer binding to metal chalcogenide NCs (e.g., CdSe). The binding between NCs and oxo ligands strengthens when moving from small oxoanions to polyoxometallates (POMs). We also show that small oxo ligands and POMs make it possible to tailor NC properties. For example, we observed improved stability upon Li(+)-ion intercalation into the films of Fe2O3 hollow NCs when capped with MoO4(2-) ligands. We also observed lower overpotential and enhanced exchange current density for water oxidation using Fe2O3 NCs capped with [P2Mo18O62](6-) ligands and even more so for [{Ru4O4(OH)2(H2O)4}(γ-SiW10O36)2] with POM as the capping ligand.

Modelado de la singularidad de borde libre en grietas 3D mediante XFEM y armónicos esféricos

One type of singularity that may appear in a three-dimensional fracture problem under elastic behavior is the free corner singularity, which occurs at the intersection of the crack with a free boundary and whose effect is usually ignored. The extended finite element method (XFEM) is a technique that allows the efficient numerical modeling of fracture problems, by using enrichment functions within a finite element model that incorporate the geometry and effect of the crack. However, when applied to the study of a problem with corner singularity, the singular behavior is not properly captured. The reason is that the usual enrichment in the XFEM only describes the typical crack front singularity. Hence, in order to include the effect of the free border singularity, the enrichment has to be modified. In this work, we present a new set of functions which relies on spherical harmonics and is able to capture the behavior of the free border singularity.

Using quantum technologies to improve fiber optic communication systems

We discuss the near future impact that recent developments of quantum technologies can have in the field of fiber optic communication systems. The ability to generate, manipulate, transmit, and detect a single or very few photon(s) may open new routes that can trigger a completely new generation of communication systems. We show that quantum technologies can address two of the more challenging problems communication engineers face nowadays: capacity and security. Indeed, by radically decreasing the number of photons used to encode each bit of information, we can more efficiently explore the full capacity to carry information of optical fibers. Moreover, by encoding information in individual or very few photons, we can take advantage of the quantum laws to add new functionalities to communication systems. Secrecy is the more obvious one, but a completely new set of functionalities can be added at the physical layer considering the peculiarities of quantum laws that rule transmission and detection.

An interacting multiple model filter‐based autofocus strategy for confocal time‐lapse microscopy

Gene expression and other cellular processes are stochastic, thus their study requires observing multiple events in multiple cells. Therefore, confocal microscopy cell imaging has recently gained much interest. In time-lapse imaging, adjustments are needed at short intervals to compensate for focus drift. There are several automated methods for this purpose. In general, before acquiring higher resolution images, software-based autofocus algorithms require a set of low-resolution images along the z-axis to determine the plane for which a predefined focusing function is maximized. These algorithms require 10-100 z-slices each time, and there is no fixed number or upper limit of required z-slices that ensures optimal focusing. The higher is this number, the stronger is photo bleaching, hampering the feasibility of long-time series measurements. We propose a new focusing strategy in time-lapse imaging. The algorithm relies on the nature and predictability of the focus drift. We first show that the focus drift curve is predictable within a small error bound in standard experimental setups. We, then, exploit the interacting multiple model filter algorithm to predict the drift at time, t, based on the measurement at time t-1. This allows a drastic reduction of the number of required z-slices for focus drift correction, largely overcoming the problem of photo bleaching. In addition, we propose a new set of functions for focusing in time-lapse imaging, derived from preexisting ones. We demonstrate the method's efficiency in time-lapse imaging of Escherichia coli cells expressing MS2d-GFP tagged RNA molecules.

A new Chebyshev family with applications to Abel equations

We prove that a family of functions defined through some definite integrals forms an extended complete Chebyshev system. The key point of our proof consists of reducing the study of certain Wronskians to the Gram determinants of a suitable set of new functions. Our result is then applied to give upper bounds for the number of isolated periodic solutions of some perturbed Abel equations.

Vibration analysis of rectangular plates with side cracks via the Ritz method

This analysis deals with free vibrations of a rectangular plate with a side crack by using the famous Ritz method with special displacement functions. To appropriately describe the stress singularities at the crack tip and show the discontinuities of displacement and slope crossing the crack, previously used corner functions, as well as a new set of functions, are added to the well known admissible functions consisting of regular polynomials. Comprehensive convergence studies on the vibrations of simply supported rectangular plates with horizontal cracks at the symmetry axis are carried out and show that both the corner functions and the proposed new set of functions indeed accelerate the convergence of numerical solutions. Furthermore, the new set of functions is found to be particularly capable in improving convergence of solutions, especially when there is a large crack. Convergence studies also demonstrate that the present approach gives more accurate results than previously published approaches using the Ritz method combined with various domain composition techniques. Finally, the present approach is applied to investigate the effects of location, length and orientation of side cracks on the free vibration frequencies and mode shapes of simply supported and completely free square plates with side cracks, including cracks which are not along a symmetry axis, are skewed. Most of the results shown are novel.

Covering symmetric semi-monotone functions

We define a new set of functions called semi-monotone, a subclass of skew-supermodular functions. We show that the problem of augmenting a given graph to cover a symmetric semi-monotone function is NP-complete if all the values of the function are in { 0 , 1 } and we provide a minimax theorem if all the values of the function are different from 1. Our problem is equivalent to the node to area augmentation problem. Our contribution is to provide a significantly simpler and shorter proof.

OneChannelGUI: a graphical interface to Bioconductor tools, designed for life scientists who are not familiar with R language

OneChannelGUI is an add-on Bioconductor package providing a new set of functions extending the capability of the affylmGUI package. This library provides a graphical interface (GUI) for Bioconductor libraries to be used for quality control, normalization, filtering, statistical validation and data mining for single channel microarrays. Affymetrix 3' expression (IVT) arrays as well as the new whole transcript expression arrays, i.e. gene/exon 1.0 ST, are actually implemented. oneChannelGUI is available for most platforms on which R runs, i.e. Windows and Unix-like machines. http://www.bioconductor.org/packages/2.0/bioc/html/oneChannelGUI.html

Impact of the pion mass on nonpower expansion for QCD observables

A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the π meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the π meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower expansion persist in the considered case of the nonvanishing pion mass.

Solution of Poisson's equation using spectral forms

A new technique is presented for the solution of Poisson's equation in spherical coordinates. The method employs an expansion of the solution in a new set of functions defined herein for the first time, called ‘spectral forms’. The spectral forms have spherical harmonics as their angular part, but use a new set of radial functions that automatically statisfy the boundary conditions, up to a multiplicative constant, on the Poisson solution. The resultant problem reduces to a set of simultaneous equations for the expansion coefficients . The matrix A is block diagonal in the spherical harmonic indices l,m and is independent of any parameters. The simultaneous equations may be solved by LU decomposition. The LU decomposition only needs to be done once and multiple right hand sides (B-vectors) can be treated by a matrix-vector multiply. For a parallel computing platform, each such B-vector may be dealt with on a separate processor. Thus the algorithm is highly parallel. This technique may be used to calculate Coulomb energy integrals efficiently on a parallel computer.

Acceptance of the Kober Medal It only gets better

As all of you know, the New England Journal of Medicine embargoes its presentations until the date of public release. I deeply appreciate Jeff’s generous remarks. We have enjoyed a wonderful collaboration over several decades. My choice to study inflammation, an area that was not popular, was guided by wonderful early mentors. These individuals included Walter Bauer at the Massachusetts General Hospital (MGH), who emphasized the importance of acknowledging what one did not know when providing patient care, specifically to patients with inflammatory arthritis; Elmer Becker at the Walter Reed Army Institute of Research, who directed me to the study of the biologic consequences rather than the exquisite specificity of an immune reaction and arranged for me to move on to John Humphrey’s program at Mill Hill, England; Walter Brocklehurst, who taught me how to generate and bioassay slow-reacting substance of anaphylaxis (cysteinyl leukotrienes) using smooth-muscle preparations; Manfred Mayer of Johns Hopkins, who emphasized that serious research was characterized by “deep mining,” not “surface mining”; and Bob Ebert, who as Dean of Harvard Medical School conceived my move from the MGH to the Robert B. Brigham Hospital and the complex now known as the Brigham and Women’s Hospital to expand the effort in studying the inflammatory response. The composite outcome of their guidance has been my 45 years of focused research in inflammation, directed to the alternative complement pathway, the cysteinyl leukotrienes, and the mast cell. The inflammatory process is now dignified by the term “innate immunity.” Irrespective of nomenclature, inflammation precedes and primes an adaptive immune response and then follows that response to provide biologic meaning. Inflammation/pattern recognition is the big arena within which adaptive immunity operates as one of the controls. Importantly, there is increasing evidence of counter-regulatory or attenuating signals for both the innate and adaptive components of immunity. “Turn-off” mechanisms are as important as activation pathways, regardless of specificity; without them, we would be consumed by our inflammatory responses. My submitted title for my response to receiving the Kober Medal from the Association of American Physicians was It only gets better with age and experience. Experience and focus provide a context to which new technology is easily and strategically added. Only this year, 2004, after studying slow-reacting substance of anaphylaxis for 45 years did we unexpectedly find a new set of functions. Through a second receptor, cysteinyl leukotrienes have a role in chronic inflammation. By chronic inflammation, I mean the accumulation of macrophages and fibroblasts with the laying down of extracellular matrix such as collagen. Although the acute effects of the cysteinyl leukotrienes were revealed in pharmacologic studies of animals and humans, the role of these mediators in chronic inflammation was uncovered only through transgenic approaches in which inflammation was induced in strains with targeted disruption of individual receptors. Truly, it only gets better. Like many in academic medicine, I have benefited mightily by “reverse mentoring” from pre- and postdoctoral fellows. To choose to study inflammation rather than lymphocyte biology, these trainees were inherently a risk-taking group. They made certain that we explored the primitive area of host inflammatory responses with state-of-the-art technology. Happily, many were physicians who found it easy to relate this subject to their clinical work, which, in turn, reinforced and modulated our laboratory program. Another benefit of my career in biomedical science has been my interactions with other investigators in laboratories around the world. Together, we have reached shared goals that could not have been achieved in a single laboratory or through a single discipline. The unraveling of the cysteinyl leukotriene pathway and its functions derived from interdisciplinary research involving the biochemistry of Bengt Samuelsson in Sweden, the synthetic chemistry of E.J. Corey at Harvard, the physiologic expertise of Jeff Drazen, and numerous others. These friendships between laboratories and between families continue independently of any ongoing shared science. Finally, I am blessed with a most joyful and tolerant spouse, Joycelyn, who allowed my avocation and the accompanying need to live in five-year funding cycles. Similarly, our four children and now our son- and daughters-in-law share Joycelyn’s immunity to my shortcomings and amusement when I attempt to direct their activities in any fashion. Joycelyn is both the source and the glue of the wonderful family that I appreciate so very much. I thank the Association of American Physicians for allowing me to share in the honor of this medal with those who have preceded and those who will follow.

Supersymmetric quantum merchanics, orthogonal states and the Pauli exclusion principle

Starting from the orthonormal eigenfunctions which are the solutions of the Schrodinger equation for a given potential it is shown that sets of functions orthogonal to the eigenstates inside a region of varying radius R may be constructed. These sets of functions may in turn be used to construct a new set of functions which satisfy bound-state boundary conditions and are themselves solutions of the Schrodinger equation in a new potential. The bound-state spectrum of the new potential is related to the spectrum of the original potential in a definite manner. The relationship of this construction of a new potential to the inverse scattering theory approach based on the Gelfand–Levitan equation and the potentials constructed using supersymmetric quantum mechanics (SUSYQM) is explored. The connection of this approach to other approaches based on the implementation of orthogonality and their relation to Pauli exclusion principle is examined.

Phase Modulated Dark Solitons

We present a new simple and straightforward technique for solving the eigenvalue problem for initially phase modulated dark solitons in nonlinear dispersive media. Starting from the eigenvalue equations for the nonlinear Schrödinger equation which governs the dynamics of dark solitons, and introducing a set of new functions and a new variable for the phasor, we deduce an equation resembling the harmonic oscillator equation. The latter is solved for strong and weak modulations, and simple exact expressions for the amplitude and the generalized phase-shift of dark solitons are found.

A variable-stepsize variable-order multistep method for the integration of perturbed linear problems

In 1971 Scheifele wrote the solution of a perturbed oscillator as an expansion in terms of a new set of functions, which extends the monomials in the Taylor series of the solution. Recently, Martı́n and Ferrándiz constructed a multistep code based on the Scheifele technique, and it was generalized by López and Martı́n for perturbed linear problems. However, the remarked codes are constant steplength methods, and efficient integrators must be able to change the steplength. In this paper we extend the ideas of Krogh from Adams methods to the algorithm proposed by López and Martı́n, and we show the advantages of the new code in perturbed problems.