Zeta-Functions and Star-Products
Antonsen, Frank
1998-01-01
We use the definition of a star (or Moyal or twisted) product to give a phasespace definition of the $\\zeta$-function. This allows us to derive new closed expressions for the coefficients of the heat kernel in an asymptotic expansion for operators of the form $\\alpha p^2+v(q)$. For the particular case of the harmonic oscillator we furthermore find a closed form for the Green's function. We also find a relationship between star exponentials, path integrals and Wigner functions, which in a simp...
Zeta Pup: the merger of at least two massive stars
Vanbeveren, Dany
2011-01-01
We first discuss the stellar and wind parameters of zeta Pup resulting from detailed UV diagnostics. These parameters together with the runaway nature of the star can most easily be explained by dynamical binary-binary or binary-single star interactions in dense stellar clusters. In this case zeta Pup is most likely the merger of at least two massive stars.
The white dwarf companion of the B a 2 star zeta Cap
Boehm-Vitense, E.
1981-01-01
The Ba II star zeta Cap has a white dwarf companion. Its T (sub eff) is determined to be 22000 K, its mass is approximately one solar mass. The importance of this finding for the explanation of abundance peculiarities is discussed.
Giants of eclipse the ζ [Zeta] Aurigae stars and other binary systems
Griffin, Elizabeth
2015-01-01
The zeta Aurigae stars are the rare but illustrious sub-group of binary stars that undergo the dramatic phenomenon of "chromospheric eclipse". This book provides detailed descriptions of the ten known systems, illustrates them richly with examples of new spectra, and places them in the context of stellar structure and evolution. Comprised of a large cool giant plus a small hot dwarf, these key eclipsing binaries reveal fascinating changes in their spectra very close to total eclipse, when the hot star shines through differing heights of the "chromosphere", or outer atmosphere, of the giant star. The phenomenon provides astrophysics with the means of analyzing the outer atmosphere of a giant star and how that material is shed into space. The physics of these critical events can be explained qualitatively, but it is more challenging to extract hard facts from the observations, and tough to model the chromosphere in any detail. The book offers current thinking on mechanisms for heating a star's chromosphere an...
Time-series photometry of the O4 I(n)fp star zeta Puppis
Howarth, Ian D
2014-01-01
We report a time-series analysis of the O4 I(n)fp star zeta Pup, based on optical photometry obtained with the SMEI instrument on the Coriolis satellite, 2003--2006. A single astrophysical signal is found, with P = (1.780938 \\pm 0.000093) d and a mean semi-amplitude of (6.9 \\pm 0.3) mmag. There is no evidence for persistent coherent signals with semi-amplitudes in excess of ca. 2~mmag on any of the timescales previously reported in the literature. In particular, there is no evidence for a signature of the proposed rotation period, ca. 5.1~days; zeta Pup is therefore probably not an oblique magnetic rotator. The 1.8-day signal varies in amplitude by a factor ca. 2 on timescales of 10--100d (and probably by more on longer timescales), and exhibits modest excursions in phase, but there is no evidence for systematic changes in period over the 1000-d span of our observations. Rotational modulation and stellar-wind variability appear to be unlikely candidates for the underlying mechanism; we suggest that the physic...
The Structural Evolution of Milky-Way-Like Star-Forming Galaxies zeta is approximately 1.3
Patel, Shannon G.; Fumagalli, Mattia; Franx, Marun; VanDokkum, Pieter G.; VanDerWel, Arjen; Leja, Joel; Labbe, Ivo; Brammr, Gabriel; Whitaker, Katherine E.; Skelton, Rosalind E.; Momcheva, Ivelina; Lundgren, Britt; Muzzin, Adam; Quadri, Ryan F.; Nelson, Erica June; Wake, David A.; Rix, Hans-Walter
2013-01-01
We follow the structural evolution of star-forming galaxies (SFGs) like the Milky Way by selecting progenitors to zeta is approx. 1.3 based on the stellar mass growth inferred from the evolution of the star-forming sequence. We select our sample from the 3D-HT survey, which utilizes spectroscopy from the HST-WFC3 G141 near-IR grism and enables precise redshift measurements for our sample of SFGs. Structural properties are obtained from Sersic profile fits to CANDELS WFC3 imaging. The progenitors of zeta = 0 SFGs with stellar mass M = 10(exp 10.5) solar mass are typically half as massive at zeta is approx. 1. This late-time stellar mass grow is consistent with recent studies that employ abundance matching techniques. The descendant SFGs at zeta is approx. 0 have grown in half-light radius by a factor of approx. 1.4 zeta is approx. 1. The half-light radius grows with stellar mass as r(sub e) alpha stellar mass(exp 0.29). While most of the stellar mass is clearly assembling at large radii, the mass surface density profiles reveal ongoing mass growth also in the central regions where bulges and pseudobulges are common features in present day late-type galaxies. Some portion of this growth in the central regions is due to star formation as recent observations of H(a) maps for SFGs at zeta approx. are found to be extended but centrally peaked. Connecting our lookback study with galactic archeology, we find the stellar mass surface density at R - 8 kkpc to have increased by a factor of approx. 2 since zeta is approx. 1, in good agreement with measurements derived for the solar neighborhood of the Milky Way.
X-ray Observations of Bow Shocks around Runaway O Stars. The case of $\\zeta$ Oph and BD+433654
Toalá, J A; González-Gaán, A; Guerrero, M A; Ignace, R; Pohl, M
2016-01-01
Non-thermal radiation has been predicted within bow shocks around runaway stars by recent theoretical works. We present X-ray observations towards the runaway stars $\\zeta$ Oph (Chandra and Suzaku) and BD+433654 (XMM-Newton) to search for the presence of non-thermal X-ray emission. We found no evidence of non-thermal emission spatially coincident with the bow shocks, nonetheless, diffuse emission is detected in the vicinity of $\\zeta$ Oph. After a careful analysis of its spectral characteristics we conclude that this emission has a thermal nature with a plasma temperature of $T \\approx 2 \\times10^{6}$ K. The cometary shape of this emission seems to be in line with recent predictions of radiation-hydrodynamic models of runaway stars. The case of BD+433654 is puzzling as non-thermal emission has been reported in a previous work for this source.
Briquet, M; Petit, P; Leroy, B; de Batz, B
2016-01-01
Aims. The main-sequence B-type star $\\zeta$ Cassiopeiae is known as a N-rich star with a magnetic field discovered with the Musicos spectropolarimeter. We model the magnetic field of the star by means of 82 new spectropolarimetric observations of higher precision to investigate the field strength, topology, and effect. Methods. We gathered data with the Narval spectropolarimeter installed at T\\'elescope Bernard Lyot (TBL, Pic du Midi, France) and applied the least-squares deconvolution technique to measure the circular polarisation of the light emitted from $\\zeta$ Cas. We used a dipole oblique rotator model to determine the field configuration by fitting the longitudinal field measurements and by synthesizing the measured Stokes V profiles. We also made use of the Zeeman-Doppler Imaging technique to map the stellar surface and to deduce the difference in rotation rate between the pole and equator. Results. $\\zeta$ Cas exhibits a polar field strength $B_{\\rm pol}$ of 100-150 G, which is the weakest polar fiel...
Leutenegger, Maurice A.; Owocki, Stanley P.; Kahn, Steven M.; Paerels, Frits B. S.
2006-01-01
We fit the Doppler profiles of the He-like triplet complexes of \\ion{O}{7} and \\ion{N}{6} in the X-ray spectrum of the O star $\\zeta$ Puppis, using XMM-Newton RGS data collected over $\\sim 400$ ks of exposure. We find that they cannot be well fit if the resonance and intercombination lines are constrained to have the same profile shape. However, a significantly better fit is achieved with a model incorporating the effects of resonance scattering, which causes the resonance line to become more...
Leutenegger, M.A.; /Columbia U.; Owocki, S.P.; /Bartol Research Inst.; Kahn, S.M.; /KIPAC, Menlo Park; Paerels, F.B.S.; /Columbia U.
2006-10-10
We fit the Doppler profiles of the He-like triplet complexes of O VII and N VI in the X-ray spectrum of the O star {zeta} Pup, using XMM-Newton RGS data collected over {approx} 400 ks of exposure. We find that they cannot be well fit if the resonance and intercombination lines are constrained to have the same profile shape. However, a significantly better fit is achieved with a model incorporating the effects of resonance scattering, which causes the resonance line to become more symmetric than the intercombination line for a given characteristic continuum optical depth {tau}{sub *}. We discuss the plausibility of this hypothesis, as well as its significance for our understanding of Doppler profiles of X-ray emission lines in O stars.
Carciofi, A C; Bouquin, J-B le; Štefl, S; Rivinius, Th; Baade, D; Björkman, J E; Hummel, C A
2009-01-01
Aims. In this paper we model, in a self-consistent way, polarimetric, photometric, spectrophotometric and interferometric observations of the classical Be star $\\zeta$ Tauri. Our primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. We have carried out detailed three-dimensional, NLTE radiative transfer calculations using the radiative transfer code HDUST. For the input for the code we have used the most up-to-date research on Be stars to include a physically realistic description for the central star and the circumstellar disc. We adopt a rotationally deformed, gravity darkened central star, surrounded by a disc whose unperturbed state is given by a steady-state viscous decretion disc model. We further assume that disc is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disc model for $\\zeta$ Tauri and a rigorous solution of the radiative transfer, we have obtained a very good fit of the time-average properties of the disc. This prov...
Leutenegger, M A; Kahn, S M; Paerels, F B S; Leutenegger, Maurice A.; Owocki, Stanley P.; Kahn, Steven M.; Paerels, Frits B. S.
2006-01-01
We fit the Doppler profiles of the He-like triplet complexes of \\ion{O}{7} and \\ion{N}{6} in the X-ray spectrum of the O star $\\zeta$ Puppis, using XMM-Newton RGS data collected over $\\sim 400$ ks of exposure. We find that they cannot be well fit if the resonance and intercombination lines are constrained to have the same profile shape. However, a significantly better fit is achieved with a model incorporating the effects of resonance scattering, which causes the resonance line to become more symmetric than the intercombination line for a given characteristic continuum optical depth $\\tau_*$. We discuss the plausibility of this hypothesis, as well as its significance for our understanding of Doppler profiles of X-ray emission lines in O stars.
Zeta functions of quantum graphs
Harrison, J M
2009-01-01
Spectral problems on quantum graphs are a topic of current interest. Progress has been made with questions of spectral statistics, the spectral determinant, inverse problems, the relationship with operators on thin manifolds, Anderson localization, manipulation of the graph spectrum and many other important areas. In this article, however, we turn to a relatively untouched area of the spectral theory of quantum graphs and construct and analyze the spectral zeta function. Understanding the spectral zeta function has been a notable omission from the analysis of quantum graphs which is particularly striking as the Ihara-Selberg zeta function is known to play a fundamental role in the understanding of the spectral theory of combinatorial graphs and it is known that quantum and combinatorial graph spectra are related. In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neuma...
The magnetic field of $\\zeta$ Ori A
Blazère, A; Bouret, J-C; Tkachenko, A
2014-01-01
Magnetic fields play a significant role in the evolution of massive stars. About 7% of massive stars are found to be magnetic at a level detectable with current instrumentation and only a few magnetic O stars are known. Detecting magnetic field in O stars is particularly challenging because they only have few, often broad, lines to measure the field, which leads to a deficit in the knowledge of the basic magnetic properties of O stars. We present new spectropolarimetric Narval observations of $\\zeta$ Ori A. We also provide a new analysis of both the new and older data taking binarity into account. The aim of this study was to confirm the presence of a magnetic field in $\\zeta$ Ori A. We identify that it belongs to $\\zeta$ Ori Aa and characterize it.
Zeta functions of quantum graphs
Harrison, J. M.; Kirsten, K.
2011-06-01
In this paper, we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process, it is convenient to work with new forms for the secular equation of a quantum graph that extend the well-known secular equation of the Neumann star graph. In the second half of this paper, we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.
The magnetic field of zeta Orionis A
Blazère, A.; Neiner, C.; Tkachenko, A.; Bouret, J. -C.; Rivinius, Th.; collaboration, the MiMeS
2015-01-01
Zeta Ori A is a hot star claimed to host a weak magnetic field, but no clear magnetic detection was obtained so far. In addition, it was recently shown to be a binary system composed of a O9.5I supergiant and a B1IV star. We aim at verifying the presence of a magnetic field in zeta Ori A, identifying to which of the two binary components it belongs (or whether both stars are magnetic), and characterizing the field.Very high signal-to-noise spectropolarimetric data were obtained with Narval at...
The triple system Zeta Aquarii
Tokovinin, Andrei
2016-01-01
Zeta Aquarii is a bright and nearby (28 pc) triple star with a 26-year astrometric subsystem. Almost a half of the outer 540-year visual orbit has been covered in 238 years of its observations. Both inner and outer orbits are revised here taking into account recent direct resolution of the inner pair Aa,Ab. The inner orbit has a high eccentricity of 0.87 and is inclined to the outer orbit by 140+-10 degrees, suggesting that Kozai-Lidov cycles take place. The masses of the stars Aa, B, and Ab are 1.4, 1.4, and 0.6 solar. The age of the system is about 3 Gyr, and the two main components have just left the main sequence. Hypothetically, this system could have formed by a dynamical capture of the small star Ab in the twin binary Aa,B.
Kargın, Levent; Kurt, Veli
2015-01-01
In this study, obtaining the matrix analog of the Euler's reflection formula for the classical gamma function we expand the domain of the gamma matrix function and give a infinite product expansion of sinπxP. Furthermore we define Riemann zeta matrix function and evaluate some other matrix integrals. We prove a functional equation for Riemann zeta matrix function.
The magnetic field of zeta Orionis A
Blazère, A; Tkachenko, A; Bouret, J -C; Rivinius, Th
2015-01-01
Zeta Ori A is a hot star claimed to host a weak magnetic field, but no clear magnetic detection was obtained so far. In addition, it was recently shown to be a binary system composed of a O9.5I supergiant and a B1IV star. We aim at verifying the presence of a magnetic field in zeta Ori A, identifying to which of the two binary components it belongs (or whether both stars are magnetic), and characterizing the field.Very high signal-to-noise spectropolarimetric data were obtained with Narval at the Bernard Lyot Telescope (TBL) in France. Archival HEROS, FEROS and UVES spectroscopic data were also used. The data were first disentangled to separate the two components. We then analyzed them with the Least-Squares Deconvolution (LSD) technique to extract the magnetic information. We confirm that zeta Ori A is magnetic. We find that the supergiant component zeta Ori Aa is the magnetic component: Zeeman signatures are observed and rotational modulation of the longitudinal magnetic field is clearly detected with a per...
Kurkov, Maxim A; Sakellariadou, Mairi; Watcharangkool, Apimook
2014-01-01
In this paper we propose a novel definition of the bosonic spectral action using zeta function regularization, in order to address the issues of renormalizability, ultraviolet completeness and spectral dimensions. We compare the zeta spectral action with the usual (cutoff based) spectral action and discuss its purely spectral origin, predictive power, stressing the importance of the issue of the three dimensionful fundamental constants, namely the cosmological constant, the Higgs vacuum expectation value, and the gravitational constant. We emphasize the fundamental role of the neutrino Majorana mass term for the structure of the bosonic action.
Conditional estimates on small distances between ordinates of zeros of $\\zeta(s)$ and $\\zeta'(s)$
Ge, Fan
2016-01-01
Let $\\beta'+i\\gamma'$ be a zero of $\\zeta'(s)$. In \\cite{GYi} Garaev and Y{\\i}ld{\\i}r{\\i}m proved that there is a zero $\\beta+i\\gamma$ of $\\zeta(s)$ with $ \\gamma'-\\gamma \\ll \\sqrt{|\\beta'-1/2|} $. Assuming RH, we improve this bound by saving a factor $\\sqrt{\\log\\log\\gamma'}$.
A new integral-series identity of multiple zeta values and regularizations
KANEKO, Masanobu; Yamamoto, Shuji
2016-01-01
We present a new "integral=series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over Q. We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima's relation is discussed as well.
GENERALIZED THERMAL ZETA-FUNCTIONS
Boschi-Filho, H.; C. Farina
1995-01-01
We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as particular cases. We give an alternative prescription for the analytic extension of the generalized Epstein function involved in the calculation of the generalized thermal zeta-functions. We also conjecture about the relation of our calculation to anyonic ...
Shuffle product formulas of multiple zeta values
Li, Zhonghua; Chen QIN
2016-01-01
Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of $n$ multiple zeta values.
Finite Mordell-Tornheim multiple zeta values
Kamano, Ken
2016-01-01
We investigate a finite analogue of the Mordell-Tornheim multiple zeta values (the finite Mordell-Tornheim multiple zeta values). These values can be expressed by a linear combination of finite multiple zeta values, and its rules are described by the shuffle product. As a~corollary, we give a certain relation among finite multiple zeta values.
Deitmar, Anton
2002-01-01
In this essay I will give a strictly subjective selection of different types of zeta functions. Instead of providing a complete list, I will rather try to give the central concepts and ideas underlying the theory. This article is going to appear in the collected works of Erich K\\"ahler.
On multiple zeta values of even arguments
Hoffmann, Michael E. [U.S. Naval Academy, Annapolis, MD (United States). Dept. of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2012-06-15
For k {<=} n, let E(2n,k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. Of course E(2n,1) is the value {zeta}(2n) of the Riemann zeta function at 2n, and it is well known that E(2n,2)=(3)/(4){zeta}(2n). Recently Z. Shen and T. Cai gave formulas for E(2n,3) and E(2n,4) in terms {zeta}(2n) and {zeta}(2){zeta}(2n-2). We give two formulas form E(2n,k), both valid for arbitrary k{<=}n, one of which generalizes the Shen-Cai results; by comparing the two we obtain a Bernoulli-number identity. We also give an explicit generating function for the numbers E(2n,k).
Wadim Zudilin
2015-01-01
The multiple zeta values (MZVs) possess a rich algebraic structure of algebraic relations, which is conjecturally determined by two different (shuffle and stuffle) products of a certain algebra of noncommutative words. In a recent work, Bachmann constructed a $q$-analogue of the MZVs -- the so-called bi-brackets -- for which the two products are dual to each other, in a very natural way. We overview Bachmann's construction and discuss the radial asymptotics of the bi-brackets, its links to th...
Wadim Zudilin
2015-03-01
Full Text Available The multiple zeta values (MZVs possess a rich algebraic structure of algebraic relations, which is conjecturally determined by two different (shuffle and stuffle products of a certain algebra of noncommutative words. In a recent work, Bachmann constructed a q-analogue of the MZVs—the so-called bi-brackets—for which the two products are dual to each other, in a very natural way. We overview Bachmann’s construction and discuss the radial asymptotics of the bi-brackets, its links to the MZVs, and related linear (independence questions of the q-analogue.
Spectral symmetries of zeta functions
Paugam, Frederic
2008-01-01
We define, answering a question of Sarnak in his letter to Bombieri, a symplectic pairing on the spectral interpretation (due to Connes and Meyer) of the zeroes of Riemann's zeta function. This pairing gives a purely spectral formulation of the proof of the functional equation due to Tate, Weil and Iwasawa, which, in the case of a curve over a finite field, corresponds to the usual geometric proof by the use of the Frobenius-equivariant Poincar\\'e duality pairing in etale cohomology. We give ...
VizieR Online Data Catalog: Chemical abundances of zeta Reticuly (Adibekyan+, 2016)
Adibekyan, V.; Delgado-Mena, E.; Figueira, P.; Sousa, S. G.; Santos, N. C.; Faria, J. P.; Gonzalez Hernandez, J. I.; Israelian, G.; Harutyunyan, G.; Suarez-Andres, L.; Hakobyan, A. A.
2016-05-01
The file table1.dat lists stellar parameters, S/N, and observation dates of zeta1 Ret and zeta2 Ret derived from individual and combined spectra The file ew.dat lists the equivalent widths (EW) of all the spectral lines. The file s_lines.dat lists the lines that were used in this study. The file abund.dat lists the derived abundances of the elements for each star and spectra. (4 data files).
Apparent wavelength dependence of v sin i for Zeta Tauri
Heap, S. R.
1977-01-01
It was previously reported that the derived projected rotational velocity (v sin i) of the B shell star, Zeta Tau, appeared to depend on the wavelength of the line used in the analysis. This letter documents the apparent wavelength dependence of v sin i for Zeta Tau in order to provide an observational basis against which quantitative explanations can be tested. A value of 300 km/s is adopted for v sin i on the basis of an examination of the visual line spectrum, particularly the lines of He I at 4026 and 4471 A and Mg II at 4481 A. Analysis of the far-UV resonance lines of Si III at 1206 A and Si IV at 1393 and 1463 A in Copernicus spectrograms of Zeta Tau yields a representative value of no more than 150 km/s for v sin i. Gravity darkening of the star's atmosphere and distention of the atmosphere by rapid differential rotation are considered as possible explanations for the discrepancy between the v sin i values determined from the UV and visual lines.
Joint discrete universality of Hurwitz zeta functions
Laurinčikas, A.
2014-11-01
We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.
The angular diameter and distance of the Cepheid Zeta Geminorum
Kervella, P; Perrin, G; Schöller, M; Traub, W A; Lacasse, M D
2001-01-01
Cepheids are the primary distance indicators for extragalactic astronomy and therefore are of very high astrophysical interest. Unfortunately, they are rare stars, situated very far from Earth.Though they are supergiants, their typical angular diameter is only a few milliarcseconds, making them very challenging targets even for long-baseline interferometers. We report observations that were obtained in the K prime band (2-2.3 microns), on the Cepheid Zeta Geminorum with the FLUOR beam combiner, installed at the IOTA interferometer. The mean uniform disk angular diameter was measured to be 1.64 +0.14 -0.16 mas. Pulsational variations are not detected at a significant statistical level, but future observations with longer baselines should allow a much better estimation of their amplitude. The distance to Zeta Gem is evaluated using Baade-Wesselink diameter determinations, giving a distance of 502 +/- 88 pc.
Adibekyan, V; Figueira, P; Sousa, S G; Santos, N C; Faria, J P; Hernandez, J I Gonzalez; Israelian, G; Harutyunyan, G; Suarez-Andres, L; Hakobyan, A A
2016-01-01
Several studies have reported a correlation between the chemical abundances of stars and condensation temperature (known as Tc trend). Very recently, a strong Tc trend was reported for the $\\zeta$ Reticuli binary system, which consists of two solar analogs. The observed trend in $\\zeta^2$ Ret relative to its companion was explained by the presence of a debris disk around $\\zeta^2$ Ret. Our goal is to re-evaluate the presence and variability of the Tc trend in the $\\zeta$ Reticuli system and to understand the impact of the presence of the debris disk on a star. We used very high-quality spectra of the two stars retrieved from the HARPS archive to derive very precise stellar parameters and chemical abundances. We derived the stellar parameters with the classical (nondifferential) method, while we applied a differential line-by-line analysis to achieve the highest possible precision in abundances, which are fundamental to explore for very tiny differences in the abundances between the stars. We confirm that the ...
Height $\\zeta$ functions of toric varieties
Batyrev, V V; Batyrev, Victor V; Tschinkel, Yuri
1996-01-01
We investigate analytic properties of height zeta functions of toric varieties. Using the height zeta functions, we prove an asymptotic formula for the number of rational points of bounded height with respect to an arbitrary line bundle whose first Chern class is contained in the interior of the cone of effective divisors
Rational convex cones and cyclotomic multiple zeta values
TERASOMA, Tomohide
2004-01-01
In this paper, we introduce zeta values of rational convex cones, which is a generalization of cyclotomic multiple zeta values. These zeta values have integral expressions. The main theorem asserts that zeta values of cones can be expressed as linear combinations of cyclotomic multiple zeta values over some cyclotomic field.
Statistical properties of zeta functions' zeros
Kargin, Vladislav
2013-01-01
The paper reviews existing results about the statistical distribution of zeros for three main types of zeta functions: number-theoretical, geometrical, and dynamical. It provides necessary background and some details about the proofs of the main results.
Integrals of products of Hurwitz zeta functions
Shpot, M A; Paris, R B
2016-01-01
We evaluate two integrals over $x\\in [0,1]$ involving products of the function $\\zeta_1(a,x)\\equiv \\zeta(a,x)-x^{-a}$ for $\\Re (a)>1$, where $\\zeta(a,x)$ is the Hurwitz zeta function. The evaluation of these integrals for the particular case of integer $a\\geq 2$ is also presented. As an application we calculate the $O(g)$ weak-coupling expansion coefficient $c_{1}(\\varepsilon)$ of the Casimir energy for a film with Dirichlet-Dirichlet boundary conditions, first stated by Symanzik [Schr\\"odinger representation and Casimir effect in renormalizable quantum field theory, Nucl. Phys. B 190 (1981) 1-44] in the framework of $g\\phi^4_{4-\\varepsilon}$ theory.
Mean-periodicity and zeta functions
Suzuki, Masatoshi; Ricotta, Guillaume; Fesenko, Ivan
2008-01-01
This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of arithmetic scheme with its expected analytic shape is shown to correspond to mea...
Fractal Geography of the Riemann Zeta Function
King, Chris
2011-01-01
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space.
Renormalization of Multiple q-Zeta Values
Jianqiang ZHAO
2008-01-01
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV)which are special values of multiple q-zeta functions ζq(S1,..., sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv:math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(S1,..., Sd) (i.e., S1≤1). Moreover, when q 1 our renormalizations agree with those of Guo and Zhang.
The zeta potential of mineral fibres.
Pollastri, Simone; Gualtieri, Alessandro F; Gualtieri, Magdalena Lassinantti; Hanuskova, Miriam; Cavallo, Alessandro; Gaudino, Giovanni
2014-07-15
For the first time, the zeta (ξ) potential of pathogenic mineral fibres (chrysotiles, amphiboles and erionite) was systematically investigated to shed light on the relationship between surface reactivity and fibre pathogenicity. A general model explaining the zeta potential of chrysotile, amphiboles and erionite has been postulated. In double distilled water, chrysotiles showed positive values while crocidolite and erionite showed negative values. In contact with organic solutions, all fibres exhibited negative values of zeta potential. The decrease of the surface potential is deemed to be a defensive chemical response of the macrophage cells to minimize hemolytic damage. Negatively charged surfaces favour the binding of collagen and redox activated Fe-rich proteins, to form the so-called asbestos bodies and prompt the formation of HO via the reaction with peroxide (H2O2+e(-)→HO+HO(-)). An additional mechanism accounting for higher carcinogenicity is possibly related to the Ca(2+) sequestration by the fibres with surface negative potential, impairing the mitochondrial apoptotic pathway. It was also found that with a negative zeta potential, the attractive forces prevailed over repulsions and favoured processes such as agglomeration responsible of a tumorigenic chronic inflammation. PMID:24929786
Testing the surrogate zeta-function method
Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza-Klein theories. We establish the validity of this method for the case that the background metric is (Euclidean space)x(N-sphere). Our techniques do not apply to the case where the background is (Minkowski-space)x(N-sphere)
The magnetic field of $\\zeta$ Ori A
Blazère, A.; Neiner, C.; Bouret, J-C.; Tkachenko, A.; MiMeS collaboration
2014-01-01
Magnetic fields play a significant role in the evolution of massive stars. About 7% of massive stars are found to be magnetic at a level detectable with current instrumentation and only a few magnetic O stars are known. Detecting magnetic field in O stars is particularly challenging because they only have few, often broad, lines to measure the field, which leads to a deficit in the knowledge of the basic magnetic properties of O stars. We present new spectropolarimetric Narval observations of...
Motivic multiple zeta values and superstring amplitudes
The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows one to disentangle its α′-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α′-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the α′-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the α′-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form. (paper)
Functional equations for zeta functions of groups and rings
Voll, Christopher
2010-01-01
We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or $\\T$-)groups, and the normal zeta functions of $\\T$-groups of class 2. In particular w...
Functional equations for local normal zeta functions of nilpotent groups
Voll, Christopher
2003-01-01
We give explicit formulae for the local normal zeta functions of torsion-free, class-2-nilpotent groups, subject to conditions on the associated Pfaffian hypersurface which are generically satisfied by groups with small centre and sufficiently large abelianization. We show how the functional equations of two types of zeta functions - the Weil zeta function associated to an algebraic variety and zeta functions of algebraic groups introduced by Igusa - match up to give a functional equation for...
Zeta potential in colloid science principles and applications
Hunter, Robert J; Rowell, R L
2013-01-01
Zeta Potential in Colloid Science: Principles and Applications covers the concept of the zeta potential in colloid chemical theory. The book discusses the charge and potential distribution at interfaces; the calculation of the zeta potential; and the experimental techniques used in the measurement of electrokinetic parameters. The text also describes the electroviscous and viscoelectric effects; applications of the zeta potential to areas of colloid science; and the influence of simple inorganic ions or more complex adsorbates on zeta potential. Physical chemists and people involved in the stu
The first spectropolarimetric monitoring of the peculiar O4Ief supergiant zeta Puppis
Hubrig, S; Ilyin, I; Schöller, M; Oskinova, L M
2016-01-01
The origin of the magnetic field in massive O-type stars is still under debate. To model the physical processes responsible for the generation of O star magnetic fields, it is important to understand whether correlations between the presence of a magnetic field and stellar evolutionary state, rotation velocity, kinematical status, and surface composition can be identified. The O4Ief supergiant zeta Pup is a fast rotator and a runaway star, which may be a product of a past binary interaction, possibly having had an encounter with the cluster Trumper 10 some 2Myr ago. The currently available observational material suggests that certain observed phenomena in this star may be related to the presence of a magnetic field. We acquired spectropolarimetric observations of zeta Pup with FORS2 mounted on the 8-m Antu telescope of the VLT to investigate if a magnetic field is indeed present in this star. We show that many spectral lines are highly variable and probably vary with the recently detected period of 1.78d. No ...
Gatewood, George; Kiewiet De Jonge, Joost; Stephenson, Bruce
1993-01-01
Improved trigonometric parallaxes are reported for stars in the regions of Groombridge 1618, Zeta Bootis, and Sigma Draconis which differ from generally accepted parallaxes by two to five standard deviations. The weighted mean parallax of Groombridge 1618 becomes 0.2079 +/- 0.0013 arcsec, indicating a distance modulus of -1.59 +/- 0.014 and yielding an absolute magnitude of this K7 V star of 8.20 +/- 0.017. The parallax determined for the visual binary Zeta Bootis is 0.0202 +/- 0.0010 arcsec and implies an average absolute visual magnitude of 1.067 +/- 0.12 for the spectroscopically similar components. The weighted mean parallax of Sigma Draconis becomes 0.1747 +/- 0.0010 arcsec, indicating a distance modulus of -1.210 +/- 0.012 and yielding an absolute visual magnitude of 5.90 +/- 0.012 for this K0 V star. The absolute visual magnitudes of the high velocity star Roman 336 and of the subdwarf star AO 1187 are found to be + 4.0 +/- 0.13 and + 5.9 +/- 0.17, respectively.
Los Zetas and Proprietary Radio Network Development
James Halverson
2016-01-01
The years from 2006 through 2011 were very active years for a number of Mexican drug trafficking organizations. However, the group that probably saw the most meteoric rise in this period, Los Zetas, had a unique and innovative tool at their disposal. It was during these years that the group constructed and utilized a proprietary encrypted radio network that grew to span from Texas to Guatemala through the Gulf States of Mexico and across much of the rest of the country. This network gave the ...
Dedekind zeta-functions and Dedekind sums
陆洪文; 焦荣政; 纪春岗
2002-01-01
In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel's. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =1/45(26n3-41n±9), n ≡±2(mod 5), where K=Q( q),prime q=4n2+1, and the class number of quadratic number field K2=Q(q) is 1.
Wettability Studies Using Zeta Potential Measurements
Ghada Bassioni
2015-01-01
Full Text Available Wettability studies have been carried out on reservoir rocks using different techniques such as the Amott-Harvey method, the USBM method, and the contact angle method, all with limitations. In this study, the wettability is studied by discussing the surface charge using zeta potential measurements. The study relies on the finding that carbonated reservoir rocks, consisting of CaCO3 mainly, are positively charged and their surface has the potential to adsorb significant quantities of anions. Moreover, heavy fractions such as asphaltenes are reported to remain afloat depending on dispersive forces present in the oil and its various fractions. Experiments are carried out on aqueous limestone suspension with the addition of crude oil. The experiment is repeated with the use of polymeric inhibitors, A and B. The zeta potential is found to alter depending on the sequence of polymeric inhibitor in oil/water addition. The inhibitor is found to adsorb on the limestone surface, with a net negative charge, causing repulsion between crude oil and the inhibitor and, hence, preventing the deposition of heavy fractions and particularly asphaltenes. This study gives a comprehensive insight on the mechanism of polymeric inhibitor interaction with the surface and the effect of wettability on its performance.
Los Zetas and Proprietary Radio Network Development
James Halverson
2016-03-01
Full Text Available The years from 2006 through 2011 were very active years for a number of Mexican drug trafficking organizations. However, the group that probably saw the most meteoric rise in this period, Los Zetas, had a unique and innovative tool at their disposal. It was during these years that the group constructed and utilized a proprietary encrypted radio network that grew to span from Texas to Guatemala through the Gulf States of Mexico and across much of the rest of the country. This network gave the group an operational edge. It also stood as a symbol of the latitude the group enjoyed across vast areas, as this extensive illicit infrastructure stood, in the face of the government and rival cartels, for six years. This investigation explicates the process by which Los Zetas constructed, concealed and utilized this network and attempts to draw conclusions about the motivations and organizational dynamics that brought the network to be, with attention paid to what this case says about the complex engineering capabilities of non-state entities in general.
Distinguishing graphs with zeta functions and generalized spectra
Durfee, Christina; Martin, Kimball
2014-01-01
Conjecturally, almost all graphs are determined by their spectra. This problem has also been studied for variants such as the spectra of the Laplacian and signless Laplacian. Here we consider the problem of determining graphs with Ihara and Bartholdi zeta functions, which are also computable in polynomial time. These zeta functions are geometrically motivated, but can be viewed as certain generalizations of characteristic polynomials. After discussing some graph properties determined by zeta ...
The November 1987 eclipse of the zeta-Aur system HR 2554
Ake, Thomas B., III; Parsons, Sidney B.
1988-01-01
It is confirmed that HR 2554 (G6 II + A0 V) is an atmospheric eclipsing system of the zeta-Aur type. The IUE observations of the Nov. 1987 eclipse indicate that the eclipse of the A star lasts 4 days and is not total. Absorption lines due to the extended atmosphere of the primary can be seen a day before and after the eclipse and are missing 2 days from first and 4th contact. Thus the outer envelope of the primary extends to less than 1 stellar radius beyond the photosphere. Compared to 22 Vul (G3 Ib-II + B9 V), where the absorption can be traced to a few stellar radii, HR 2554 is a more moderate case of mass outflow, which implies there is reduced interaction of the secondary within the wind from the primary as is seen in the other zeta-Aur systems.
Computational Derivation to Zeta Zeros and Prime Numbers
Chalmers, Gordon
2005-01-01
A route to the derivation of the numbers $s$ to the transcendental equation $\\zeta(s)=0$ is presented. The solutions to this equation require the solving of a geodesic flow in an infinite dimensional manifold. These solutions enable one approach to a formula generating the prime numbers.
The multiple zeta value data mine
Buemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Broadhurst, D.J. [Open Univ., Milton Keynes (United Kingdom). Physics and Astronomy Dept.; Vermaseren, J.A.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); NIKHEF, Amsterdam (Netherlands)
2009-07-15
We provide a data mine of proven results for multiple zeta values (MZVs) of the form {zeta}(s{sub 1},s{sub 2},..,s{sub k}) = sum {sup {infinity}}{sub n{sub 1}}{sub >n{sub 2}}{sub >...>n{sub k}}{sub >0} {l_brace}1/(n{sub 1}{sup s{sub 1}}..n{sub k}{sup s{sub k}}){r_brace} with weight w = sum {sup K}{sub i=1}s{sub i} and depth k and for Euler sums of the form sum {sup {infinity}}{sub n{sub 1}}{sub >n{sub 2}}{sub >...>n{sub k}}{sub >0} {l_brace}({epsilon}{sub 1}{sup n{sub 1}}..{epsilon}{sub 1}{sup n{sub k}})/(n{sub 1}{sup s{sub 1}}..n{sub k}{sup s{sub k}}){r_brace} with signs {epsilon}{sub i} = {+-} 1. Notably, we achieve explicit proven reductions of all MZVs with weights w{<=}22, and all Euler sums with weights w{<=}12, to bases whose dimensions, bigraded by weight and depth, have sizes in precise agreement with the Broadhurst. Kreimer and Broadhurst conjectures. Moreover, we lend further support to these conjectures by studying even greater weights (w{<=}30), using modular arithmetic. To obtain these results we derive a new type of relation for Euler sums, the Generalized Doubling Relations. We elucidate the ''pushdown'' mechanism, whereby the ornate enumeration of primitive MZVs, by weight and depth, is reconciled with the far simpler enumeration of primitive Euler sums. There is some evidence that this pushdown mechanism finds its origin in doubling relations. We hope that our data mine, obtained by exploiting the unique power of the computer algebra language FORM, will enable the study of many more such consequences of the double-shuffle algebra of MZVs, and their Euler cousins, which are already the subject of keen interest, to practitioners of quantum field theory, and to mathematicians alike. (orig.)
Zeta Functions for Elliptic Curves I. Counting Bundles
Weng, Lin
2012-01-01
To count bundles on curves, we study zetas of elliptic curves and their zeros. There are two types, i.e., the pure non-abelian zetas defined using moduli spaces of semi-stable bundles, and the group zetas defined for special linear groups. In lower ranks, we show that these two types of zetas coincide and satisfy the Riemann Hypothesis. For general cases, exposed is an intrinsic relation on automorphism groups of semi-stable bundles over elliptic curves, the so-called counting miracle. All this, together with Harder-Narasimhan, Desale-Ramanan and Zagier's result, gives an effective way to count semi-stable bundles on elliptic curves not only in terms of automorphism groups but more essentially in terms of their $h^0$'s. Distributions of zeros of high rank zetas are also discussed.
The Riemann {zeta}-function in phase space
Feiler, Cornelia; Mack, Ruediger; Schleich, Wolfgang P. [Institute of Quantum Physics, Ulm University (Germany)
2009-07-01
The Riemann hypothesis, a conjecture about the distribution of the so called non-trivial zeros of the Riemann {zeta}-function, is at the very heart of number theory. The distribution of these zeros is strongly connected with the distribution of primes. Prime numbers, on the other hand, play a crucial role for example in cryptography or factorization. We propose a new physical approach to the Riemann {zeta}-function. We consider the states of an harmonic oscillator with a logarithmic coupling to an external field. With an appropriate projection we obtain the values {zeta}(s) for Re s>1. With the help of an entangled system, similar to the Jaynes-Cummings-Model, we managed to reach into the critical strip, where the non-trivial zeros of the {zeta}-function are expected to be.
Fundamental stellar parameters of $\\zeta$ Pup and $\\gamma^2$ Vel from HIPPARCOS data
Schärer, D; Grenon, Michel; Schaerer, Daniel; Schmutz, Werner; Grenon, Michel
1997-01-01
We report parallax measurements by the HIPPARCOS satellite of zeta Puppis and gamma^2 Velorum. The distance of zeta Pup is d=429 (+120/ -77) pc, in agreement with the commonly adopted value to Vela OB2. However, a significantly smaller distance is found for the gamma^2 Vel system: d=258 (+41/-31) pc. The total mass of gamma^2 Vel derived from its parallax, the angular size of the semi-major axis as measured with intensity interferometry, and the period is M(WR+O)=29.5 (+/-15.9) Msun. This result favors the orbital solution of Pike et al. (1983) over that of Moffat et al. (1986). The stellar parameters for the O star companion derived from line blanketed non-LTE atmosphere models are: Teff=34000 (+/-1500) K, log L/Lsun=5.3 (+/-0.15) from which an evolutionary mass of M=29 (+/-4) Msun and an age of 4.0 (+0.8/-0.5) Myr is obtained from single star evolutionary models. With non-LTE model calculations including He and C we derive a luminosity log L/Lsun~4.7 (+/-0.2) for the WR star. The mass-luminosity relation of...
Resonance scattering in the X-ray emission line profiles of Zeta Puppis
Leutenegger, M. A.; Cohen, D. H.; Kahn, S. M.; Owocki, S. P.; Paerels, F. B. S.
2007-01-01
We present XMM-Newton Reflection Grating Spectrometer observations of pairs of X-ray emission line profiles from the O star Zeta Pup that originate from the same He-like ion. The two profiles in each pair have different shapes and cannot both be consistently fit by models assuming the same wind parameters. We show that the differences in profile shape can be accounted for in a model including the effects of resonance scattering, which affects the resonance line in the pair but not the interco...
The multiple zeta value data mine
We provide a data mine of proven results for multiple zeta values (MZVs) of the form ζ(s1,s2,..,sk) = sum ∞n1>n2>...>nk>0 {1/(n1s1..nksk)} with weight w = sum Ki=1si and depth k and for Euler sums of the form sum ∞n1>n2>...>nk>0 {(ε1n1..ε1nk)/(n1s1..nksk)} with signs εi = ± 1. Notably, we achieve explicit proven reductions of all MZVs with weights w≤22, and all Euler sums with weights w≤12, to bases whose dimensions, bigraded by weight and depth, have sizes in precise agreement with the Broadhurst. Kreimer and Broadhurst conjectures. Moreover, we lend further support to these conjectures by studying even greater weights (w≤30), using modular arithmetic. To obtain these results we derive a new type of relation for Euler sums, the Generalized Doubling Relations. We elucidate the ''pushdown'' mechanism, whereby the ornate enumeration of primitive MZVs, by weight and depth, is reconciled with the far simpler enumeration of primitive Euler sums. There is some evidence that this pushdown mechanism finds its origin in doubling relations. We hope that our data mine, obtained by exploiting the unique power of the computer algebra language FORM, will enable the study of many more such consequences of the double-shuffle algebra of MZVs, and their Euler cousins, which are already the subject of keen interest, to practitioners of quantum field theory, and to mathematicians alike. (orig.)
Zeta Functions of the Dirac Operator on Quantum Graphs
Harrison, J M; Kirsten, K
2016-01-01
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general energy independent matching conditions at the vertices. The regularized spectral determinant of the Dirac operator is also obtained as the derivative of the zeta function at a special value. In each case the zeta function is formulated using a contour integral method, which extends results obtained for Laplace and Schrodinger operators on graphs.
Pure red cell aplasia induced by epoetin zeta.
Panichi, Vincenzo; Ricchiuti, Guido; Scatena, Alessia; Del Vecchio, Lucia; Locatelli, Francesco
2016-08-01
Pure red cell aplasia (PRCA) may develop in patients with chronic kidney disease receiving erythropoiesis-stimulating agents (ESA). We report on a 72-year-old patient who developed hypo-proliferative anaemia unresponsive to ESA following the administration of epoetin zeta subcutaneously for 7 months. On the basis of severe isolated hypoplasia of the erythroid line in the bone marrow and high-titre neutralizing anti-erythropoietin antibodies (Ab), a diagnosis of Ab-mediated PRCA was made. Epoetin zeta was discontinued and the patient was given steroids. This was associated with anaemia recovery. To our knowledge this is the first PRCA case related to epoetin zeta. PMID:27478604
Higgs interpretation of zeta (8.3 GeV)
We interpret the recently observed zeta (8.3 GeV) to be a Higgs boson of the SU(2) x U(1) model with two Higgs doublets. If zeta is a Nambu-Goldstone boson of a new approximate symmetry, then a second light neutral Higgs of mass less than 25 GeV is expected. Our fermion couplings enhance the rate for UPSILON → γ + zeta by approx. 100 compared to the standard one Higgs model. Other experimental tests are suggested
Functional equations for zeta functions of $\\mathbb{F}_1$-schemes
Lorscheid, Oliver
2010-01-01
For a scheme $X$ whose $\\mathbb F_q$-rational points are counted by a polynomial $N(q)=\\sum a_iq^i$, the $\\mathbb{F}_1$-zeta function is defined as $\\zeta(s)=\\prod(s-i)^{-a_i}$. Define $\\chi=N(1)$. In this paper we show that if $X$ is a smooth projective scheme, then its $\\mathbb{F}_1$-zeta function satisfies the functional equation $\\zeta(n-s) = (-1)^\\chi \\zeta(s)$. We further show that the $\\mathbb{F}_1$-zeta function $\\zeta(s)$ of a split reductive group scheme $G$ of rank $r$ with $N$ positive roots satisfies the functional equation $\\zeta(r+N-s) = (-1)^\\chi ( \\zeta(s) )^{(-1)^r}$.
Functional equations of prehomogeneous zeta functions and intertwining operators
Sato, Fumihiro
2006-01-01
We establish a relation between the gamma matrices of the functional equations satisfied by zeta functions associated with prehomogeneous vector spaces and certain integrals related to the intertwining operator of degenerate principal series representations of general linear groups.
The problem of the barium stars
Bohm-Vitense, E.; Nemec, J.; Proffitt, C.
1984-01-01
Ultraviolet observations of barium stars and other cool stars with peculiar element abundances are reported. Those observations attempted to find hot white dwarf companions. Among six real barium stars studied, only Zeta Cap was found to have a white dwarf companion. Among seven mild, or marginal, barium stars studied, at least three were found to have hot subluminous companions. It is likely that all of them have white dwarf companions.
Two-parametric zeta function regularization in superstring theory
Motl, Lubos
1995-01-01
In this paper some quite simple examples of applications of the zeta-function regularization to superstring theories are presented. It is shown that the Virasoro anomaly in the BRST formulation of (super)strings can be directly computed from the original expressions of the operators as well as normal ordering constants and masses of ground levels. Hawking's zeta regularization is recognized as an efficient tool for direct calculations, bringing no ambiguities. Possible implications for global...
Linear differential equations and multiple zeta-values. III. Zeta(3)
Zakrzewski, Michał; Żoładek, Henryk
2012-01-01
We consider the hypergeometric equation (1 - t)∂t∂t∂g + x3g = 0, whose unique analytic solution φ1(t; x) = 1 + O(t) near t = 0 for t = 1 becomes a generating function for multiple zeta values φ1(1; x) = f3(x) = 1 - ζ(3)x3 + ζ(3, 3)x6 - …. We apply the so-called WKB method to study solutions of the hypergeometric equation for large x and we calculate corresponding Stokes matrices. We prove that the function f3(x) near x = ∞ is also expressed via WKB type functions which subject to some Stokes phenomenon. This implies that f3(x) satisfies a sixth order linear differential equation with irregular singularity at infinity.
On the rate of accumulation of $\\alpha\\zeta^{n}$ mod 1 to 0
Schleischitz, Johannes
2014-01-01
In this paper we study the distribution of the sequence $(\\alpha \\zeta^{n})_{n\\geq 1}$ mod $1$, where $\\alpha,\\zeta$ are fixed positive real numbers, with special focus on the accumulation point $0$. For this purpose we introduce approximation constants $\\underline{\\sigma}(\\alpha,\\zeta),\\overline{\\sigma}(\\alpha, \\zeta)$ and study their properties in dependence of $\\alpha,\\zeta$, distinguishing in particular the cases of Pisot numbers, algebraic non Pisot numbers and transcendental values of $...
Two-parametric $\\zeta$ function regularization in superstring theory
Motl, L
1995-01-01
In this paper some quite simple examples of applications of the zeta-function regularization to superstring theories are presented. It is shown that the Virasoro anomaly in the BRST formulation of (super)strings can be directly computed from the original expressions of the operators as well as normal ordering constants and masses of ground levels. Hawking's zeta regularization is recognized as an efficient tool for direct calculations, bringing no ambiguities. Possible implications for global GSO operators' phases definitions (maybe ensuring modular invariance) will be discussed elsewhere.
Elliptic multiple zeta values and one-loop superstring amplitudes
Broedel, Johannes; Mafra, Carlos R.; Matthes, Nils; Schlotterer, Oliver
2015-07-01
We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.
Elliptic multiple zeta values and one-loop superstring amplitudes
Broedel, Johannes; Matthes, Nils; Schlotterer, Oliver
2014-01-01
We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.
Some bounds and limits in the theory of Riemann's zeta function
de Reyna, J Arias
2011-01-01
For any real a>0 we determine the supremum of the real \\sigma\\ such that \\zeta(\\sigma+it) = a for some real t. For 0 1 the results turn out to be quite different.} We also determine the supremum E of the real parts of the `turning points', that is points \\sigma+it where a curve Im \\zeta(\\sigma+it) = 0 has a vertical tangent. This supremum E (also considered by Titchmarsh) coincides with the supremum of the real \\sigma\\ such that \\zeta'(\\sigma+it) = 0 for some real t. We find a surprising connection between the three indicated problems: \\zeta(s) = 1, \\zeta'(s) = 0 and turning points of \\zeta(s). The almost extremal values for these three problems appear to be located at approximately the same height.
Zeta functional equation on Jordan algebras of type II
Kayoya, J. B.
2005-02-01
Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II.
Riemann zeta function from wave-packet dynamics
Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.;
2010-01-01
Maslov index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms in...
ZETA-POTENTIAL OF CONCRETE IN PRESENCE OF CHELATING AGENTS
Contamination of concrete surfaces at Nuclear Power Plants (NPP) and reprocessing facilities by radionuclides/heavy metals is a significant and widespread problem throughout the world’s Nuclear Power Industries. The current study of the zeta-potentials (') of concrete particles in the presence of va...
Zeta function regularization and effective action in curved spacetime. 16
This article expounds on a sophisticated regularization technique for quantum field theories in arbitrary gravitational fields: the zeta function regularization. The effective action in curved spacetime is obtained and used to discuss phase transitions in the De Sitter Universe. (author). 5 refs.; 6 figs.; 1 tab
Renormdynamics, multiparticle production, negative binomial distribution, and Riemann zeta function
Makhaldiani, N. V.
2013-09-01
After short introduction, we consider different aspects of the renormdynamics. Then scaling functions of the multiparticle production processes and corresponding stochastic dynamics are considered. Nonperturbative quasi-particle dynamics is considered on the base of the toy QCD- O( N)-sigma model. Last section concerns to the NBD-Riemann zeta function connection.
Mayer Transfer Operator Approach to Selberg Zeta Function
Momeni, Arash; Venkov, Alexei
These notes are based on three lectures given by the second author at Copenhagen University (October 2009) and at Aarhus University, Denmark (December 2009). We mostly present here a survey of results of Dieter Mayer on relations between Selberg and Smale-Ruelle dynamical zeta functions. In a spe...
On calculation of zeta function of integral matrix
Janáček, Jiří
2009-01-01
Roč. 134, č. 1 (2009), s. 49-58. ISSN 0862-7959 R&D Projects: GA AV ČR(CZ) IAA100110502 Institutional research plan: CEZ:AV0Z50110509 Keywords : Epstein zeta function * integral lattice * Riemann theta function Subject RIV: BA - General Mathematics
Crossing the entropy barrier of dynamical zeta functions
Dynamical zeta functions are an important tool to quantize chaotic dynamical systems. The basic quantization rules require the computation of the zeta functions on the real energy axis, where the Euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so-called entropy barrier determined by the topological entropy of the classical system. We shown that the convergence properties of the dynamical zeta functions rewritten as Dirichlet series are governed not only by the well-known topological and metric entropy, but depend crucially on subtle statistical properties of the Maslow indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy. If and only if the third entropy is nonvanishing, one can cross the entropy barrier; if it exceeds a certain value, one can even compute the zeta function in the physical region by means of a convergent Dirichlet series. A simple statistical model is presented which allows to compute the third entropy. Four examples of chaotic systems are studied in detail to test the model numerically. (orig.)
Renormdynamics, multiparticle production, negative binomial distribution, and Riemann zeta function
Makhaldiani, N. V., E-mail: mnv@jinr.ru [Joint Institute for Nuclear Research (Russian Federation)
2013-09-15
After short introduction, we consider different aspects of the renormdynamics. Then scaling functions of the multiparticle production processes and corresponding stochastic dynamics are considered. Nonperturbative quasi-particle dynamics is considered on the base of the toy QCD-O(N)-sigma model. Last section concerns to the NBD-Riemann zeta function connection.
From Fourier Series to Rapidly Convergent Series for Zeta(3)
Scheufens, Ernst E
2011-01-01
The article presents a mathematical study which investigates the exact values of the Riemann zeta (ζ) function. It states that exact values can be determined from Fourier series for periodic versions of even power functions. It notes that using power series for logarithmic functions on this such...
Cardelli, Jason A.; Savage, Blair D.; Ebbets, Dennis C.
1991-01-01
An analysis of weak (less than 10 mA) UV interstellar absorption line data obtained for the line of sight to the O9.5 IV star Zeta Oph is presented. Measurements of weak semiforbidden lines of N I, O I, Cu II, and a new UV detection of Na I are reported along with a small upper limit for C II. Interstellar detections of Ga II, Ge II, and Kr I are also presented. Ga, Ge, and Kr represent the heaviest elements detected in the ISM. A comparison of the derived column densities to cosmic abundances shows Ga to be depleted by about -1.2 dex while Ge is overabundant by +0.2 dex. Assuming Kr to be undepleted, a logarithmic cosmic abundance of Kr/H = 2.95 is obtained on the scale where H = 12.00.
Evidence for Resonance Scattering in the X-ray Spectrum of Zeta Puppis
Leutenegger, Maurice
2008-01-01
We present XMM-Newton Reflection Grating Spectrometer observations of pairs of X-ray emission line profiles from the 0 star Zeta Pup that originate from the same He-like ion. The two profiles in each pair have different shapes and cannot both be consistently fit by models assuming the same wind parameters. We show that the differences in profile shape can be accounted for in a model including the effects of resonance scattering, which affects the resonance line in the pair but not the intercombination line. This implies that resonance scattering is also important in single resonance lines, where its effect is difficult to distinguish from a low effective continuum optical depth in the wind. Thus, resonance scattering may help reconcile X-ray line profile shapes with literature mass-loss rates.
Resonance scattering in the X-ray emission line profiles of Zeta Puppis
Leutenegger, M A; Kahn, S M; Owocki, S P; Paerels, F B S
2007-01-01
We present XMM-Newton Reflection Grating Spectrometer observations of pairs of X-ray emission line profiles from the O star Zeta Pup that originate from the same He-like ion. The two profiles in each pair have different shapes and cannot both be consistently fit by models assuming the same wind parameters. We show that the differences in profile shape can be accounted for in a model including the effects of resonance scattering, which affects the resonance line in the pair but not the intercombination line. This implies that resonance scattering is also important in single resonance lines, where its effect is difficult to distinguish from a low effective continuum optical depth in the wind. Thus, resonance scattering may help reconcile X-ray line profile shapes with literature mass-loss rates.
A note on the real part of the Riemann zeta-function
de Reyna, Juan Arias; van de Lune, Jan
2011-01-01
We consider the real part Re(zeta(s)) of the Riemann zeta-function zeta(s) in the half-plane Re(s) >= 1. We show how to compute accurately the constant sigma_0 = 1.19... which is defined to be the supremum of sigma such that Re(zeta(sigma+it)) can be negative (or zero) for some real t. We also consider intervals where Re(zeta(1+it)) <= 0 and show that they are rare. The first occurs for t approximately 682112.9, and has length about 0.05. We list the first fifty such intervals.
Kahn, S. M.; Leutenegger, M. A.; Cottam, J.; Rauw, G.; Vreux, J. -M.; Boggende, A.J.F. den; Mewe, R.; Guedel, M.
2000-01-01
We present the first high resolution X-ray spectrum of the bright O4Ief supergiant star Zeta Puppis, obtained with the Reflection Grating Spectrometer on-board XMM-Newton. The spectrum exhibits bright emission lines of hydrogen-like and helium-like ions of nitrogen, oxygen, neon, magnesium, and silicon, as well as neon-like ions of iron. The lines are all significantly resolved, with characteristic velocity widths of order 1000-1500 km s^{-1}. The nitrogen lines are especially strong, and ind...
Avdispahic, Muharem; Gusic, Dzenan
2014-01-01
We derive approximate formulas for the logarithmic de- rivative of the Selberg and Ruelle zeta functions over compact, even- dimensional, locally symmetric spaces of rank one. The obtained for- mulas are given in terms of the zeta-singularities.
Riemann zeta zeros and zero-point energy
Dueñas, J G
2013-01-01
We postulate the existence of a self-adjoint operator associated to a system with countably infinite number of degrees of freedom whose spectrum is the sequence of the nontrivial zeros of the Riemann zeta function. We assume that it describes a massive scalar field coupled to a background field in a $(d+1)$-dimensional flat space-time. The scalar field is confined to the interval $[0,a]$ in one dimension and is not restricted in the other dimensions. The renormalized zero-point energy of this system is presented using techniques of dimensional and analytic regularization. In even dimensional space-time, the series that defines the regularized vacuum energy is finite. For the odd-dimensional case, to obtain a finite vacuum energy per unit area we are forced to introduce mass counterterms. A Riemann mass appears, which is the correction to the mass of the field generated by the nontrivial zeros of the Riemann zeta function.
Consistency relations and conservation of $\\zeta$ in holographic inflation
Garriga, Jaume
2016-01-01
It is well known that, in single clock inflation, the curvature perturbation $\\zeta$ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of $\\zeta$ follows from the cut-off independence of correlators of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.
Lecture notes: string theory and zeta-function
These lecture notes are based on a revised and LaTexed version of the Master thesis defended at ISAS. The research part being omitted, they included a review of the bosonic closed string a la Polyakov and of the one-loop background field method of quantisation defined through the zeta-function. In an appendix some basic features of the Riemann zeta-function are also reviewed. The pedagogical aspects of the material here presented are particularly emphasized. These notes are used, together with the Scherk's article in Rev. Mod. Phys. and the first volume of the Polchinski book, for the mini-course on String Theory (16-hours of lectures) held at CBPF. In this course the Green-Schwarz-Witten two-volumes book is also used for consultative purposes. (author)
The velocity distribution of interstellar titanium toward Zeta Persei
Hobbs, L. M.
1979-01-01
Observations of the interstellar 3384-A line of Ti II toward Zeta Persei are reported at a resolution of 1.4 km/s. This resolution exceeds by a factor of almost 3 that used in any previous observations of ions that are dominant stages of ionization in H I regions. Toward Zeta Per, two resolved line components of Ti II having widths generally comparable to those of the corresponding line components of trace ions K I, Ca II, and Na I are seen. For any other ions along this line of sight which have velocity distributions similar to that observed for Ti II, the critical equivalent width above which line saturation must be significant therefore does not exceed 14 mA for ultraviolet lines lying near 1200 A.
Velocity distribution of interstellar titanium toward zeta Persei
Observations of the interstellar lambda3384 line of Ti II toward zeta Persei are reported at a resolution of 1.4 km s-1. This resolution exceeds by a factor of almost 3 that used in any previous observations of ions which are dominant stages of ionization in HI regions. Toward zeta Per, two resolved line components of Ti II having widths generally comparable to those of the corresponding line components of trace ions K I, Ca II, and Na I are seen. For any other ions along this line of sight which have velocity distributions similar to that observed for Ti II, the critical equivalent width above which line saturation must be significant therefore does not exceed 14 mA, for ultraviolet lines lying near 1200 A
Lecture notes: string theory and zeta-function
Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: toppan@cbpf.br
2001-11-01
These lecture notes are based on a revised and LaTexed version of the Master thesis defended at ISAS. The research part being omitted, they included a review of the bosonic closed string a la Polyakov and of the one-loop background field method of quantisation defined through the zeta-function. In an appendix some basic features of the Riemann zeta-function are also reviewed. The pedagogical aspects of the material here presented are particularly emphasized. These notes are used, together with the Scherk's article in Rev. Mod. Phys. and the first volume of the Polchinski book, for the mini-course on String Theory (16-hours of lectures) held at CBPF. In this course the Green-Schwarz-Witten two-volumes book is also used for consultative purposes. (author)
A zeta function approach to the semiclassical quantization of maps
The quantum analogue of an area preserving map on a compact phase space is a unitary (evolution) operator which can be represented by a matrix of dimension L∝ℎ-1. The semiclassical theory for spectrum of the evolution operator will be reviewed with special emphasize on developing a dynamical zeta function approach, similar to the one introduced recently for a semiclassical quantization of hamiltonian systems. (author)
Zeta functions of regular arithmetic schemes at s=0
Morin, Baptiste
2011-01-01
Lichtenbaum conjectured in \\cite{Lichtenbaum} the existence of a Weil-\\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme $\\mathcal{X}$ at $s=0$ in terms of Euler-Poincar\\'e characteristics. Assuming the (conjectured) finite generation of some motivic cohomology groups we construct such a cohomology theory for regular schemes proper over $\\mathrm{Spec}(\\mathbb{Z})$. In particular, we compute (unconditionally) the right Weil-\\'etale cohomology of number rings and projective spaces over number rings. We state a precise version of Lichtenbaum's conjecture, which expresses the vanishing order (resp. the special value) of the Zeta function $\\zeta(\\mathcal{X},s)$ at $s=0$ as the rank (resp. the determinant) of a single perfect complex of abelian groups $R\\Gamma_{W,c}(\\mathcal{X},\\mathbb{Z})$. Then we relate this conjecture to Soul\\'e's conjecture and to the Tamagawa Number Conjecture. Lichtenbaum's conjecture for projective spaces over the r...
Fouling mitigation of anion exchange membrane by zeta potential control.
Park, Jin-Soo; Lee, Hong-Joo; Choi, Seok-Ju; Geckeler, Kurt E; Cho, Jaeweon; Moon, Seung-Hyeon
2003-03-15
The feasibility of fouling mitigation of anion exchange membranes (AEMs) in the presence of humate was studied by adding three different types of water-soluble polymers, i.e., poly(acrylic acid) (PAA), poly(vinyl alcohol) (PVA), and poly(ethylene imine) (PEI), during electrodialysis (ED) desalination. Measurement of zeta potential of the humate used in this study showed highly negative potential (about -30 mV), implying that the humate had a strong fouling potential on the AEMs in ED. Of the three water-soluble polymers, PEI showed a positive zeta potential (about +14 mV) and is able to form an interpolymer complex with the humate. PAA and PVA hardly formed interpolymer complexes with humate due to electrostatic repulsion. The PEI-humate mixture with a volume ratio of 1:20 (PEI:humate) showed zero zeta potential, and a complexed humate with zero surface charge was formed, resulting in no fouling effects on the AEMs. Accordingly, the desalting ED experiments with PEI showed improved ED performance. Further, black colloids formed in the mixture did not cause the cell resistance to increase. PMID:16256509
Landau-Siegel zeros and zeros of the derivative of the Riemann zeta function
Farmer, David W
2010-01-01
We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.
Langer, William D.; Glassgold, Alfred E.; Wilson, Robert W.
1987-01-01
This paper presents a small-scale map of the molecular gas around the line of sight toward Zeta Oph made with measurements of the (C-12)O (1-0) emission obtained at high signal-to-noise ratio and high velocity resolution. In addition, a measurement of the (C-12)O (2-1) line emission and a detection of (C-13)O along the line of sight to the star are reported. The results show that the CO emission toward the star is composed from at least four components with peak velocities at -2.0, -0.7, 0.0, and +0.6 km/s. The radio observations yield a total CO column density of 1.4 x 10 to the 15th/sq cm, with about one-half of the total CO column density being in the main component at -0.7 km/s. The main cmponent is uniform over the map, but the other components are variable, suggesting that the cloud is clumpy. The data on the two CO transitions imply that the excitation temperature and the density of the main component are about 7 K and 800/cu cm, respectively.
Ros-Oton, Xavier
2012-01-01
Let $K$ be a quadratic field, and let $\\zeta_K$ its Dedekind zeta function. In this paper we introduce a factorization of $\\zeta_K$ into two functions, $L_1$ and $L_2$, defined as partial Euler products of $\\zeta_K$, which lead to a factorization of Riemann's $\\zeta$ function into two functions, $p_1$ and $p_2$. We prove that these functions satisfy a functional equation which has a unique solution, and we give series of very fast convergence to them. Moreover, when $\\Delta_K>0$ the general t...
Detection of Doppler Shifted X-ray Line Profiles from the Wind of Zeta Puppis (O4f)
Cassinelli, J P; Waldron, W L; MacFarlane, J J; Cohen, D H
2001-01-01
We report on a 67 ks HETG observation of the optically brightest early O-star, Zeta Pup (O4 f). Many resolved X-ray lines are seen in the spectra over a wavelength range of 5 to 25 A. Chandra has sufficient spectral resolution to study the velocity structure of isolated X-ray line profiles, and to distinguish the individual forbidden, intercombination, and resonance (fir) emission lines in several He-like ions even where the individual components are strongly Doppler broadened. In contrast with X-ray line profiles in other hot stars, Zeta Pup shows blue-shifted and skewed line profiles, providing the clearest and most direct evidence that the X-ray sources are embedded in the stellar wind. The broader the line, the greater the blueward centroid shift tends to be. The N VII line at 24.78 A is a special case, showing a flat-topped profile. This indicates it is formed in regions beyond most of the wind attenuation. The sensitivity of the He-like ion fir lines to a strong UV radiation field is used to derive the ...
High moments of the Riemann zeta-function
Conrey, J. Brian; Gonek, Steven M.
1999-01-01
In 1918 G. Hardy and J. Littlewood proved an asymptotic estimate for the Second moment of the modulus of the Riemann zeta-function on the segment [1/2,1/2+iT] in the complex plane, as T tends to infinity. In 1926 Ingham proved an asymptotic estimate for the fourth moment. However, since Ingham's result, nobody has proved an asymptotic formula for any higher moment. Recently J. Conrey and A. Ghosh conjectured a formula for the sixth moment. We develop a new heuristic metho...
Justification of the zeta function renormalization in rigid string model
A consistent procedure for regularization of divergences and for subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov endash Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein endash Hurwitz zeta functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy. copyright 1997 American Institute of Physics
The Stokes phenomenon and the Lerch zeta function
R. B. Paris
2016-05-01
Full Text Available We examine the exponentially improved asymptotic expansion of the Lerch zeta function $L(\\lambda,a,s=\\sum_{n=0}^\\infty \\exp (2\\pi ni\\lambda/(n+a^s$ for large complex values of $a$, with $\\lambda$ and $s$ regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines $\\arg\\,a=\\pm\\fs\\pi$. In addition, it is found that the transition across the upper and lower imaginary $a$-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.
On the Riemann zeta-function, Part III
Csizmazia, Anthony
2007-01-01
An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. The partial fraction expansion, p(s), of f(s) is obtained using the conjunction of the Riemann hypothesis and hypotheses advanced by the author. That compound hypothesis and the expansion p(s) are employed in Part IV to derive the two-sided Laplace transform representation of f(s) on the open vertical strip of all s with real part between zero and four.
The semi-simple zeta function of quaternionic Shimura varieties
Reimann, Harry
1997-01-01
This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.
The Riemann zeta-function theory and applications
Ivic, Aleksandar
2003-01-01
""A thorough and easily accessible account.""-MathSciNet, Mathematical Reviews on the Web, American Mathematical Society. This extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estim
Logarithmic Fourier integrals for the Riemann Zeta Function
Kunik, Matthias
2008-01-01
We use symmetric Poisson-Schwarz formulas for analytic functions $f$ in the half-plane ${Re}(s)>\\frac12$ with $\\bar{f(\\bar{s})}=f(s)$ in order to derive factorisation theorems for the Riemann zeta function. We prove a variant of the Balazard-Saias-Yor theorem and obtain explicit formulas for functions which are important for the distribution of prime numbers. In contrast to Riemann's classical explicit formula, these representations use integrals along the critical line ${Re}(s)=\\frac12$ and ...
Zeta potential of soils with surfactants and its relevance to electrokinetic remediation.
Kaya, Abidin; Yukselen, Yeliz
2005-04-11
There are numerous studies on the application of electrokinetic decontamination technique to remediate heavy metal contaminated fine-grained soils. In recent studies, surfactants have been used to increase the efficiency of contaminant removal. However, there is limited data available on how physicochemical parameters such as zeta potential (zeta) of soils changes in the presence of surfactants. Understanding the zeta potential variations of soils with surfactant addition is important because it controls the direction and magnitude of electro-osmotic permeability, which plays important role on the efficiency of electrokinetic remediation. In this study, zeta potentials of kaolinite, montmorillonite and quartz powder with Li+, Ca+2, Cu+2, Pb+2 and Al+3 in the presence of anionic, cationic and non-ionic surfactants were determined. The results indicate that anionic surfactants produce negative zeta potentials. The other surfactants produce both positive and negative zeta potentials depending on soil type and ion present in the system. The results also indicate that the zeta potential of kaolinite and quartz powder with surfactants showed similar trends; however, the absolute magnitude of the zeta potential of quartz powder is higher than that of kaolinite. The zeta potential of montmorillonite commonly shows a different trend from those of kaolinite and quartz powder. Based on the test results, it is recommended that zeta potential of soils be determined before the electrokinetic decontamination in order to maximize the efficiency of the technique. PMID:15811672
Abramovici, Hanan; Hogan, Angela B; Obagi, Christopher; Topham, Matthew K; Gee, Stephen H
2003-11-01
Syntrophins are scaffolding proteins that link signaling molecules to dystrophin and the cytoskeleton. We previously reported that syntrophins interact with diacylglycerol kinase-zeta (DGK-zeta), which phosphorylates diacylglycerol to yield phosphatidic acid. Here, we show syntrophins and DGK-zeta form a complex in skeletal muscle whose translocation from the cytosol to the plasma membrane is regulated by protein kinase C-dependent phosphorylation of the DGK-zeta MARCKS domain. DGK-zeta mutants that do not bind syntrophins were mislocalized, and an activated mutant of this sort induced atypical changes in the actin cytoskeleton, indicating syntrophins are important for localizing DGK-zeta and regulating its activity. Consistent with a role in actin organization, DGK-zeta and syntrophins were colocalized with filamentous (F)-actin and Rac in lamellipodia and ruffles. Moreover, extracellular signal-related kinase-dependent phosphorylation of DGK-zeta regulated its association with the cytoskeleton. In adult muscle, DGK-zeta was colocalized with syntrophins on the sarcolemma and was concentrated at neuromuscular junctions (NMJs), whereas in type IIB fibers it was found exclusively at NMJs. DGK-zeta was reduced at the sarcolemma of dystrophin-deficient mdx mouse myofibers but was specifically retained at NMJs, indicating that dystrophin is important for the sarcolemmal but not synaptic localization of DGK-zeta. Together, our findings suggest syntrophins localize DGK-zeta signaling complexes at specialized domains of muscle cells, which may be critical for the proper control of lipid-signaling pathways regulating actin organization. In dystrophic muscle, mislocalized DGK-zeta may cause abnormal cytoskeletal changes that contribute to disease pathogenesis. PMID:14551255
Measuring the zeta potential. The relationships with sandstone fineness
de Luxán, M. P.
1989-09-01
Full Text Available The application of the zeta potential technique in the area of construction materials and Portland cement is quite recent. The initial research work involved the study of cement suspensions or suspensions of one of the components of cement, such as alite, tricalcium alumínate, in the presence of additives and, more specifically, superplasticizers. The studies of this sort were extended with the mixing of active additions into cement (fly ashes, etc.. The present study discusses the application of siliceous materials (sandstone as a basis of the research into the behaviour of sandstone mortars containing repair products.
La aplicación de la técnica del potencial zeta en el campo de los materiales de construcción y del cemento portland es muy reciente. Las primeras investigaciones se refieren al estudio de suspensiones de cemento o de alguno de sus compuestos que lo forman como alita, aluminato tricálcico, en presencia de aditivos y, más concretamente, de superfluidificantes. Con la incorporación de adiciones activas al cemento (cenizas volantes,... se amplían los estudios de este tipo de cementos. En este trabajo se considera la aplicación a los materiales silíceos (arenisca como base para la investigación del comportamiento de los morteros de arenisca conteniendo productos de reparación.
Potencial zeta de sulfatos de de bario y de estroncio
Edgar Delgado M.
2010-06-01
Full Text Available Por medio de la electroforesis se determinó las movilidades electroforéticas y los potenciales zeta del sulfato de bario a 25,0 °C como función de la fuerza iónica de NaCI, así como del Sulfato de estroncio en función de la fuerza iónica del cloruro de sodio y del pH. Se encontró que el amento de la fuerza iónica de NaCI causa un cambio del Potencial Zeta negativo del sulfato de estroncio a positivo con valor cero a aprox. 0,06 de fuerza iónica. El P.Z. del sulfato de estroncio es positivo a pH inferiores a aprox. 2,5 y negativo a pH superiores. El sulfato de bario presenta P.Z. negativas a fuerza iónicas de NaCI inferiores a aprox. 0.06 y PZ positivos a fuerzas iónicas mayores
Riemann Hypothesis and Random Walks: the Zeta case
LeClair, André
2016-01-01
In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line $\\Re (s) > 1/2$, and the Riemann Hypothesis for this class of $L$-functions follows. Building on this work, here we propose how to extend this line of reasoning to the Riemann zeta function and other principal Dirichlet $L$-functions. We use our results to argue that $ S_\\delta (t) \\equiv \\lim_{\\delta \\to 0^+} \\dfrac{1}{\\pi} \\arg \\zeta (\\tfrac{1}{2}+ \\delta + i t ) = O(1)$, and that it is nearly always on the principal branch. We conjecture that a 1-point correlation function of the Riemann zeros has a normal distribution. This leads to the construction of a probabilistic model for the zeros. Based on these results we describe a new algorithm for computing very high Riemann zeros as a kind of stochastic process, and we calculate the $10^{100}$-th zero to over 1...
Moreira, A.; S. C. de Siqueira; A. A. da Silva
1995-01-01
Com o objetivo de estimar a dose do herbicida "Zeta" que inibe 50% I50) do crescimento de plantas bioindicadoras em solos com diferentes texturas e teores de matéria orgânica, podendo estes ter uma influência marcante sobre a bioatividade do herbicida testado, utilizou-se o delineamento experimental inteiramente casualizado com 7 tratamentos (0, 50, 100, 150, 200, 250 e 300 g i.a./ha) e 4 repetições, sendo os tratamentos dispostos em 5 tipos de texturas de solo. Os parâmetros avaliados foram:...
Hubrig, S; Schöller, M; De Cat, P; Mathys, G; Aerts, C
2006-01-01
We present the results of a magnetic survey of a sample of eight beta Cephei stars and 26 Slowly Pulsating B stars with FORS1 at the VLT. A weak mean longitudinal magnetic field of the order of a few hundred Gauss is detected in the beta Cephei star xi^1 CMa and in 13 SPB stars. The star xi^1 CMa becomes the third magnetic star among the beta Cephei stars. Before our study, the star zeta Cas was the only known magnetic SPB star. All magnetic SPB stars for which we gathered several magnetic field measurements show a field that varies in time. We do not find a relation between the evolution of the magnetic field with stellar age in our small sample. Our observations imply that beta Cephei stars and SPBs can no longer be considered as classes of non-magnetic pulsators, but the effect of the fields on the oscillation properties remains to be studied.
Where do the tedious products of zetas come from?
Broadhurst, D J
2003-01-01
Lamentably, the full analytical content of the epsilon-expansion of the master two-loop two-point function, with arbitrary self-energy insertions in 4-2epsilon dimensions, is still unknown. Here we show that multiple zeta values (MZVs) of weights up to 12 suffice through O(epsilon^9). Products of primitive MZVs are generated by a processes of "pseudo-exponentiation"" whose combinatorics faithfully accord with expectations based on Kreimer's modified shuffle product and on the Drinfeld-Deligne conjecture. The existence of such a mechanism, relating thousands of complicated rational numbers, enables us to identify precise and simple combinations of MZVs specific to quantum field theories in even numbers of spacetime dimensions.
Central Binomial Sums, Multiple Clausen Values and Zeta Values
Borwein, J M; Kamnitzer, J
2000-01-01
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.
Lima, F M S
2009-01-01
In a recent work [JNT \\textbf{118}, 192 (2006)], Dancs and He have found new "Euler-type" formulas for $ \\ln{2} $ and $ \\zeta{(2 n+1)}$, $ n $ being a positive integer, each containing a series that apparently can not be evaluated in closed form, providing some insight into why the odd case is more difficult than the even, for which the Euler's formula applies, showing that $ \\zeta{(2 n)} $ is a rational multiple of $\\pi^{2 n}$. There, however, the formulas are derived through certain series manipulations, by following Tsumura's strategy, which makes it unclear (\\emph{curious}, in the words of the authors themselves) the appearance of the numbers $ \\ln{2} $ and $ \\zeta{(2 n+1)}$. In this short paper, I show how some known $\\zeta$-series can be used to elucidate the origin of the Dancs' series for these numbers.
The genus zeta function of hereditary orders in central simple algebras over global fields
Denert, M.
1990-01-01
Louis Solomon introduced the notion of a zeta function {ζ_θ }(s) of an order θ in a finite-dimensional central simple K-algebra A, with K a number field or its completion {K_P} (P a non-Archimedean prime in K). In several papers, C. J. Bushnell and I. Reiner have developed the theory of zeta functions and they gave explicit formulae in some special cases. One important property of these zeta functions is the Euler product, which implies that in order to calculate {ζ_θ }(s) , it is sufficient to consider the zeta function of local orders {θ _P} . However, since these local orders {θ _P} are in general not principal ideal domains, their zeta function is a finite sum of so-called 'partial zeta functions'. The most complicated term is the 'genus zeta function', {Z_{{θ _P}}}(s) , which is related to the free {θ _P} -ideals. I. Reiner and C. J. Bushnell calculated the genus zeta function for hereditary orders in quaternion algebras (i.e., [A:K] = 4 ). The authors mention the general case but they remark that the calculations are cumbersome. In this paper we derive an explicit method to calculate the genus zeta function {Z_{{θ _P}}}(s) of any local hereditary order {θ _P} in a central simple algebra over a local field. We obtain {Z_{{θ _P}}}(s) as a finite sum of explicit terms which can be calculated with a computer. We make some remarks on the programming of the formula and give a short list of examples. The genus zeta function of the minimal hereditary orders (corresponding to the partition (1, 1, ... , 1) of n) seems to have a surprising property. In all examples, the nominator of this zeta function is a generating function for the q-Eulerian polynomials. We conclude with some remarks on a conjectured identity.
Adsorption of urinary components influences the zeta potential of uropathogen surfaces
Habash, MB; van der Mei, HC; Busscher, HJ; Reid, G
2000-01-01
Zeta potential distributions of five uropathogens were measured in urines collected after increased water intake, consumption of cranberry supplements, or intake of ascorbic acid by volunteers. Zeta potentials of bacteria in urine from ascorbic acid consumption shifted towards less negative values d
A Substitution to Bernoulli Numbers in easier computation of (\\zeta(2k))
Arunachalam, Srinivasan
2011-01-01
An alternative formulae for the evaluation of (\\zeta(2k)) without the need for Bernoulli numbers. This formula is a recursive formula and helps in the calculation with lesser mathematical computation of large value of zeta function with huge Bernoulli numbers.
Some relations involving the higher derivatives of the Riemann zeta function
Connon, Donal F.
2015-01-01
We show that the higher derivatives of the Riemann zeta function may be expressed in terms of integrals involving the digamma function. Related integrals for the Stieltjes constants are also shown. We also present a formula for the derivatives of the Riemann zeta function entirely in terms of the Lehmer constants.
Functional relations for zeta-functions of weight lattices of Lie groups of type $A_3$
Komori, Yasushi; Matsumoto, Kohji; Tsumura, Hirofumi
2012-01-01
We study zeta-functions of weight lattices of compact connected semisimple Lie groups of type $A_3$. Actually we consider zeta-functions of SU(4), SO(6) and PU(4), and give some functional relations and new classes of evaluation formulas for them.
Partition function on spheres: how (not) to use zeta function regularization
Monin, A
2016-01-01
It is known that not all summation methods are linear and stable. Zeta function regularization is in general non-linear. However, in some cases formal manipulations with "zeta function" regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.
A symbolic approach to multiple zeta values at the negative integers
Moll, V. H.; Jiu, L.; Vignat , C.
2015-01-01
Symbolic computation techniques are used to derive some closed form expressions for an analytic continuation of the Euler-Zagier zeta function evaluated at the negative integers as recently proposed by B. Sadaoui. This approach allows to compute explicitly some contiguity identities, recurrences on the depth of the zeta values and generating functions.
Zeta Function Expression of Spin Partition Functions on Thermal AdS3
Floyd L.Williams
2015-07-01
Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.
A multifractal zeta function for Gibbs measures supported on cookie-cutter sets
Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures. (paper)
Mean Values of the Logarithmic Derivative of the zeta Function and the GUE Hypothesis
Farmer, David W.
1994-01-01
The GUE Hypothesis, which concerns the distribution of zeros of the Riemann zeta-function, is used to evaluate some integrals involving the logarithmic derivative of the zeta-function. Some connections are shown between the GUE Hypothesis and other conjectures.
Kahn, S M; Cottam, J; Rauw, G; Vreux, J M; Den Boggende, A J F; Mewe, R; Güdel, M
2000-01-01
We present the first high resolution X-ray spectrum of the bright O4Ief supergiant star Zeta Puppis, obtained with the Reflection Grating Spectrometer on-board XMM-Newton. The spectrum exhibits bright emission lines of hydrogen-like and helium-like ions of nitrogen, oxygen, neon, magnesium, and silicon, as well as neon-like ions of iron. The lines are all significantly resolved, with characteristic velocity widths of order 1000-1500 km s^{-1}. The nitrogen lines are especially strong, and indicate that the shocked gas in the wind is mixed with CNO-burned material, as has been previously inferred for the atmosphere of this star from ultraviolet spectra. We find that the forbidden to intercombination line ratios within the helium-like triplets are anomalously low for N VI, O VII, and Ne IX. While this is sometimes indicative of high electron density, we show that in this case, it is instead caused by the intense ultraviolet radiation field of the star. We use this interpretation to derive constraints on the loc...
Zeta functions and regularized determinants related to the Selberg trace formula
Momeni, Arash
2011-01-01
For a general Fuchsian group of the first kind with an arbitrary unitary representation we define the zeta functions related to the contributions of the identity, hyperbolic, elliptic and parabolic conjugacy classes in Selberg's trace formula. We present Selberg's zeta function in terms of a regularized determinant of the automorphic Laplacian. We also present the zeta function for the identity contribution in terms of a regularized determinant of the Laplacian on the two dimensional sphere. We express the zeta functions for the elliptic and parabolic contributions in terms of certain regularized determinants of one dimensional Schroedinger operator for harmonic oscillator. We decompose the determinant of the automorphic Laplacian into a product of the determinants where each factor is a determinant representation of a zeta function related to Selberg's trace formula. Then we derive an identity connecting the determinants of the automorphic Laplacians on different Riemannian surfaces related to the arithmetic...
Influence of surface conductivity on the apparent zeta potential of calcite
Li, Shuai; Heberling, Frank; Devau, Nicolas; Jougnot, Damien; Chiaberge, Christophe
2016-01-01
Zeta potential is a physicochemical parameter of particular importance in describing the surface electrical properties of charged porous media. However, the zeta potential of calcite is still poorly known because of the difficulty to interpret streaming potential experiments. The Helmholtz-Smoluchowski (HS) equation is widely used to estimate the apparent zeta potential from these experiments. However, this equation neglects the influence of surface conductivity on streaming potential. We present streaming potential and electrical conductivity measurements on a calcite powder in contact with an aqueous NaCl electrolyte. Our streaming potential model corrects the apparent zeta potential of calcite by accounting for the influence of surface conductivity and flow regime. We show that the HS equation seriously underestimates the zeta potential of calcite, particularly when the electrolyte is diluted (ionic strength < 0.01 M) because of calcite surface conductivity. The basic Stern model successfully predicted ...
Loopy Belief Propagation, Bethe Free Energy and Graph Zeta Function
Watanabe, Yusuke
2011-01-01
We propose a new approach to the theoretical analysis of Loopy Belief Propagation (LBP) and the Bethe free energy (BFE) by establishing a formula to connect LBP and BFE with a graph zeta function. The proposed approach is applicable to a wide class of models including multinomial and Gaussian types. The connection derives a number of new theoretical results on LBP and BFE. This paper focuses two of such topics. One is the analysis of the region where the Hessian of the Bethe free energy is positive definite, which derives the non-convexity of BFE for graphs with multiple cycles, and a condition of convexity on a restricted set. This analysis also gives a new condition for the uniqueness of the LBP fixed point. The other result is to clarify the relation between the local stability of a fixed point of LBP and local minima of the BFE, which implies, for example, that a locally stable fixed point of the Gaussian LBP is a local minimum of the Gaussian Bethe free energy.
Zeta potentials in the flotation of oxide and silicate minerals.
Fuerstenau, D W; Pradip
2005-06-30
Adsorption of collectors and modifying reagents in the flotation of oxide and silicate minerals is controlled by the electrical double layer at the mineral-water interface. In systems where the collector is physically adsorbed, flotation with anionic or cationic collectors depends on the mineral surface being charged oppositely. Adjusting the pH of the system can enhance or prevent the flotation of a mineral. Thus, the point of zero charge (PZC) of the mineral is the most important property of a mineral in such systems. The length of the hydrocarbon chain of the collector is important because of chain-chain association enhances the adsorption once the surfactant ions aggregate to form hemimicelles at the surface. Strongly chemisorbing collectors are able to induce flotation even when collector and the mineral surface are charged similarly, but raising the pH sufficiently above the PZC can repel chemisorbing collectors from the mineral surface. Zeta potentials can be used to delineate interfacial phenomena in these various systems. PMID:16007737
DNA polymerase zeta (polζ) in higher eukaryotes
Gregory N Gan; John P Wittschieben; Birgitte φ Wittschieben; Richard D Wood
2008-01-01
Most current knowledge about DNA polymerase zeta (pol ζ) comes from studies of the enzyme in the budding yeast Saccharomyces cerevisiae, where polζ consists of a complex of the catalytic subunit Rev3 with Rev7, which associates with Rev1. Most spontaneous and induced mutagenesis in yeast is dependent on these gene products, and yeast pol can mediate translesion DNA synthesis past some adducts in DNA templates. Study of the homologous gene products in higher eukaryotes is in a relatively early stage, but additional functions for the eukaryotic proteins are already appar-ent. Suppression of vertebrate REV3L function not only reduces induced point mutagenesis but also causes larger-scale genuine instability by raising the frequency of spontaneous chromosome translocations. Disruption of Rev3L function is tolerated in Drosophila, Arabidopsis, and in vertebrate cell lines under some conditions, but is incompatible with mouse embryonic development. Functions for REV3L and REV7(MAD2B) in higher eukaryotes have been suggested not only in translesion DNA synthesis but also in some forms of homologous recombination, repair ofinterstrand DNA erosslinks, somatic hypermutation of immunoglobulin genes and cell-cycle control. This review discusses recent devel-opments in these areas.
Standard Model with extra dimensions and its zeta function regularization
García-Jiménez, I; Martínez-Pascual, E; Nápoles-Cañedo, G I; Novales-Sánchez, H; Toscano, J J
2016-01-01
We start from a field theory governed by the extra-dimensional $ISO(1,3+n)$ Poincar\\'e group and by the extended SM gauge group, $G({\\cal M}^{4+n})$. Then we construct an effective field theory whose symmetry groups are $ISO(1,3)$ and $G({\\cal M}^{4})$. The transition is carried out via two canonical transformations: a map that preserves, but it hides, the $SO(1,3+n)$ symmetry; and a transformation, given by Fourier series, that explicitly breaks $ISO(1,3+n)$ into $ISO(1,3)$, but conserves and hides the gauge symmetry $G({\\cal M}^{4+n})$, which manifests through nonstandard gauge transformations. From the 4-dimensional perspective, a particle that propagates in compact extra dimensions unfolds into a family of fields that reduces to the SM field if the size of the compact manifold is negligible. We include a full catalogue of Lagrangian terms that can be used to derive Feynman rules. The divergent character of the theory at one-loop is studied. A regularization scheme, based on the Epstein zeta function (EZF)...
Advances in random matrix theory, zeta functions, and sphere packing.
Hales, T C; Sarnak, P; Pugh, M C
2000-11-21
Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues ("the energy levels") follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks. PMID:11058156
Borwein, J M
1998-01-01
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $a/b vol(M)=(-D)^{3/2}/(2\\pi)^{2n-4} (\\zeta_K(2))/(2\\zeta(2))$ for a manifold M whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekind zeta value $\\zeta_K(2)$. The largest numerator of the 998 invariants of Hodgson-Weeks manifolds is, astoundingly, $a=2^4\\times23\\times37\\times691 =9,408,656$; the largest denominator is merely b=9. We also study the rational invariant a/b for single-complex-place cusped manifolds, complementary to knots and links, both within and beyond the Hildebrand-Weeks census. Within the censi, we identify 152 distinct Dedekind zetas rationally related to volumes. Moreover, 91 census manifolds have volumes reducible to pairs of these zeta values. Motivated by studies of Feynman diagrams, we find a 10-component 24-crossing link in the case n=2 and D=-20. It is one of 5 alternating platonic links,...
Factors Influencing the Period of Improved Stability in Zeta
Further experimental and theoretical studies have been made of the period of improved stability in Zeta. Measurements, by Thomson scattering, show that the electron temperature, Te , at the start of the period is about 100 eV. Studies have also been made of Te during this period. Detailed measurements have been made of the plasma parameters (Ne, Te) at the edge of the discharge. Measurements of the axial field at a pinch parameter of 1.8 show that this field is reversed by about 20% of the initial axial field B0 at the start of the period. This reversal disappears after 1 ms when the improved stability ceases. At a pinch parameter of 2.9 the reversal is 80% of B0 and the period is extended to 3 ms. The degree of reversal is constant round the major axis of the torus. A reversed axial electric field at the edge of the plasma is always observed during the period. The dependence of stability on this field has been studied further by modifying the machine so that the field can be controlled externally. The observations of the field configuration in the outer regions during the period of stability are consistent with the requirements of MHD theory. However, residual fluctuations are still observed and an analysis has been made of the possible instabilities which might cause these fluctuations. The MHD stability close to the magnetic axis for localized modes with vanishing pressure gradient has been studied and compared with experiment. Resistive instabilities, in particular the tearing mode and the possibility of stabilization by ion viscosity, have been analysed for the measured configurations. Estimates have been made of the growth times. The trapped particle modes are predicted not to be serious during this period and calculations have been made of the shear stabilization of drift modes. (author)
The phase of the Riemann zeta function and the inverted harmonic oscillator
Bhaduri, R K; Law, J; Avinash Khare
1994-01-01
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
The Phase of the Riemann Zeta Function and the Inverted Harmonic Oscillator
Bhaduri, R. K.; Khare, Avinash; Law, J.
1994-01-01
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram. This leads to the analogy with the scattering amplitude, and an approximate rule for the location of the zeros. The smooth phase of the Zeta function along the line of the zeros is related to the quantum density of states of an inverted oscillator.
Zeta functions related to the pro-p group SL1(Delta(p))
Klopsch, B.
2003-01-01
Let D-p be a central simple Q(p)-division algebra of index 2, with maximal Z(p)-order Delta(p). We give an explicit formula for the number of subalgebras of any given finite index in the Z(p) Lie algebra L := sl(1) (Delta(p)). From this we obtain a closed formula for the zeta function zeta(L)(s) := Sigma(M less than or equal to L) \\ L: M\\(-s). The results are extended to the p-power congruence subalgebras of L, and as an application we obtain the zeta functions of the corresponding congruence...
Demonstration of how the zeta function method for effective potential removes the divergences
Nogueira, J A
2002-01-01
The calculation of the minimum of the effective potential using the zeta function method is extremely advantagous, because the zeta function is regular at $s=0$ and we gain immediately a finite result for the effective potential without the necessity of subtratction of any pole or the addition of infinite counter-terms. The purpose of this paper is to explicitly point out how the cancellation of the divergences occurs and that the zeta function method implicitly uses the same procedure used by Bollini-Giambiagi and Salam-Strathdee in order to gain finite part of functions with a simple pole.
Lattice Dynamical Interpretation of the Structure of \\zeta-Phase AgZn
Yamada, Yasusada; Noda, Yukio
1988-04-01
The crystal structure of \\zeta-phase AgZn has been reconsidered. It is shown that the static structure of \\zeta-AgZn is expressible in terms of (i) two types of lattice waves (phonon modes) and (ii) one type of probability density wave of Zn atom site-occupation. It is noted that the relevant phonon modes are the soft modes existing commonly in bcc Hume-Rothery alloys. It is pointed out that \\zeta-AgZn shares the common origin of stabilization with 9R martensites and ω-phase.
zeta-COP, a subunit of coatomer, is required for COP-coated vesicle assembly
1993-01-01
cDNA encoding the 20-kD subunit of coatomer, zeta-COP, predicts a protein of 177-amino acid residues, similar in sequence to AP17 and AP19, subunits of the clathrin adaptor complexes. Polyclonal antibody directed to zeta-COP blocks the binding of coatomer to Golgi membranes and prevents the assembly of COP-coated vesicles on Golgi cisternae. Unlike other coatomer subunits (beta-, beta'-, gamma-, and epsilon- COP), zeta-COP exists in both coatomer bound and free pools.
Value-distribution of the Riemann zeta-function and related functions near the critical line
Christ, Thomas
2013-01-01
The Riemann zeta-function forms a central object in multiplicative number theory; its value-distribution encodes deep arithmetic properties of the prime numbers. Here, a crucial role is assigned to the analytic behavior of the zeta-function on the so called critical line. In this thesis we study the value-distribution of the Riemann zeta-function near and on the critical line. Amongst others we focus on the following. PART I: A modified concept of universality, a-points near the critical ...
On the sign of the real part of the Riemann zeta-function
de Reyna, Juan Arias; van de Lune, Jan
2012-01-01
We consider the distribution of $\\arg\\zeta(\\sigma+it)$ on fixed lines $\\sigma > \\frac12$, and in particular the density \\[d(\\sigma) = \\lim_{T \\rightarrow +\\infty} \\frac{1}{2T} |\\{t \\in [-T,+T]: |\\arg\\zeta(\\sigma+it)| > \\pi/2\\}|\\,,\\] and the closely related density \\[d_{-}(\\sigma) = \\lim_{T \\rightarrow +\\infty} \\frac{1}{2T} |\\{t \\in [-T,+T]: \\Re\\zeta(\\sigma+it) < 0\\}|\\,.\\] Using classical results of Bohr and Jessen, we obtain an explicit expression for the characteristic function $\\psi_\\sigma(x)$ associated with $\\arg\\zeta(\\sigma+it)$. We give explicit expressions for $d(\\sigma)$ and $d_{-}(\\sigma)$ in terms of $\\psi_\\sigma(x)$. Finally, we give a practical algorithm for evaluating these expressions to obtain accurate numerical values of $d(\\sigma)$ and $d_{-}(\\sigma)$.
New computations of the Riemann zeta function on the critical line
Bober, Jonathan W.; Hiary, Ghaith A.
2016-01-01
We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating quadratic exponential sums. In addition, we use a new simple multi-evaluation method to compute the zeta function in a very small range at little more than the cost of evaluation at a single point.
Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution
Elizalde, Emilio
2012-01-01
A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a nu...
Sharma Pushkar Raj; Lewis Shaila Angela
2011-01-01
The study was aimed at evaluating the stability of marketed albendazole suspension through electrokinetic characterization of the particles. The marketed brands of Albendazole suspension that were studied include AVIZOLE®, BENTAL®, BENDEX®, NOWORM® and ZENTAL®.Particle size, zeta potential, sedimentation volume, viscosity and pH of the suspension were the parameters determined and their correlation was established. ZENTAL® showed maximum sedimentation volume and its zeta potential was also f...
Effects of surface conductivity on the apparent zeta potential at the calcite-water interface
Li, Shuai; Leroy, Philippe; Devau, Nicolas
2015-01-01
International audience Carbonates are very reactive minerals that are used in many engineering applications like substance remediation and CO2 geological storage. Surface complexation reactions on calcite have significant effects on transport processes in carbonates. Zeta potential is a critical parameter to characterize the mineral surface electrochemical properties. The zeta potential is defined as the electrical potential at the shear plane between quasi immobile and mobile water at the...
Sembach, Kenneth R.; Savage, Blair D.; Jenkins, Edward B.
1994-01-01
We present Goddard High-Resolution Spectrograph observations at 3.5 km/s resolution and signal-to-noise ratios of 30 to 60 for the Al III, Si IV, and N V absorption lines in the far-ultraviolet spectrum of the O9.5 V star zeat Ophiuchi. The measurement reveal three types of highly ionized gas along the 140 pc line of sight. (1) Narrow components of Al III (b = 4.3 km/s, the mean value of (v(helio)) = -7.8 km/s; b = 3.2 km/s, the mean value of (v(sub helio)) = -14.4 km/s) and Si IV (b = 5.3 km/s, the mean value of (v(sub helio)) = -15.0 km/s) trace photionized gas in the expanding H II region surrounding zeta Oph. The observed magnitude and direction of the velocity offset between the Al III and Si IV profiles can be explained by models of H II regions that incorporate expansion. Narrow C IV absorption associated with the H II region is not detected. Predictions of the expected amounts of Si IV and C IV overestimate the column densities of these ions by factors of 30 and more than 10, respectively. The discrepancy may be due to the effects of elemental depletions in the gas and/or to the interaction of the stellar wind with surrounding matter. (2) Broad (b = 15 to 18 km/s) and weak Si IV and C IV absorption components are detected near the mean value of (v(sub helio)) = -26 km/s. The high-ionization species associated with these absorption components are probably produced by electron collisional ionization in a heated gas. This absorption may be physically related to the zeta Oph bow shock ot to a cloud complex situated within the local interstellar medium at d less than 60 pc. The C IV to Si IV column density ratio in this gas is 8, a factor of 6 less than conductive interface models predict, but this discrepancy may be removed by considering the effects of self-photoionization within the cooling gas in the model calculations. (3) A broad (b = 13 km/s) and weak C IV absorption feature detected at the mean value of (v(sub helio)) = -61 km/s is not seen in other
The electrophoretic mobility of montmorillonite. Zeta potential and surface conductivity effects.
Leroy, Philippe; Tournassat, Christophe; Bernard, Olivier; Devau, Nicolas; Azaroual, Mohamed
2015-08-01
Clay minerals have remarkable adsorption properties because of their high specific surface area and surface charge density, which give rise to high electrochemical properties. These electrochemical properties cannot be directly measured, and models must be developed to estimate the electrostatic potential at the vicinity of clay mineral surfaces. In this context, an important model prediction is the zeta potential, which is thought to be representative of the electrostatic potential at the plane of shear. The zeta potential is usually deduced from electrophoretic measurements but for clay minerals, high surface conductivity decreases their mobility, thereby impeding straightforward interpretation of these measurements. By combining a surface complexation, conductivity and electrophoretic mobility model, we were able to reconcile zeta potential predictions with electrophoretic measurements on montmorillonite immersed in NaCl aqueous solutions. The electrochemical properties of the Stern and diffuse layers of the basal surfaces were computed by a triple-layer model. Computed zeta potentials have considerably higher amplitudes than measured zeta potentials calculated with the Smoluchowski equation. Our model successfully reproduced measured electrophoretic mobilities. This confirmed our assumptions that surface conductivity may be responsible for montmorillonite's low electrophoretic mobility and that the zeta potential may be located at the beginning of the diffuse layer. PMID:25875489
Protein kinase C-zeta inhibition exerts cardioprotective effects in ischemia-reperfusion injury.
Phillipson, Aisha; Peterman, Ellen E; Taormina, Philip; Harvey, Margaret; Brue, Richard J; Atkinson, Norrell; Omiyi, Didi; Chukwu, Uchenna; Young, Lindon H
2005-08-01
Ischemia followed by reperfusion (I/R) in the presence of polymorphonuclear leukocytes (PMNs) results in marked cardiac contractile dysfunction. A cell-permeable PKC-zeta peptide inhibitor was used to test the hypothesis that PKC-zeta inhibition could attenuate PMN-induced cardiac contractile dysfunction by suppression of superoxide production from PMNs and increase nitric oxide (NO) release from vascular endothelium. The effects of the PKC-zeta peptide inhibitor were examined in isolated ischemic (20 min) and reperfused (45 min) rat hearts reperfused with PMNs. The PKC-zeta inhibitor (2.5 or 5 microM, n = 6) significantly attenuated PMN-induced cardiac dysfunction compared with I/R hearts (n = 6) receiving PMNs alone in left ventricular developed pressure (LVDP) and the maximal rate of LVDP (+dP/dt(max)) cardiac function indexes (P < 0.01), and these cardioprotective effects were blocked by the NO synthase inhibitor, N(G)-nitro-L-arginine methyl ester (50 microM). Furthermore, the PKC-zeta inhibitor significantly increased endothelial NO release 47 +/- 2% (2.5 microM, P < 0.05) and 54 +/- 5% (5 microM, P < 0.01) over basal values from the rat aorta and significantly inhibited superoxide release from phorbol-12-myristate-13-acetate-stimulated rat PMNs by 33 +/- 12% (2.5 microM) and 40 +/- 8% (5 microM) (P < 0.01). The PKC-zeta inhibitor significantly attenuated PMN infiltration into the myocardium by 46-48 +/- 4% (P < 0.01) at 2.5 and 5 microM, respectively. In conclusion, these results suggest that the PKC-zeta peptide inhibitor attenuates PMN-induced post-I/R cardiac contractile dysfunction by increasing endothelial NO release and by inhibiting superoxide release from PMNs thereby attenuating PMN infiltration into I/R myocardium. PMID:15792991
Gravitational vacuum polarization around static spherical stars
The gravitational vacuum polarization of conformally coupled quantum fields in the spacetime of a uniform-density, static, spherical star is studied using the approximation developed by Page, Brown, and Ottewill. Approximate vacuum stress-energy tensors are calculated for conformal massless scalar, spinor, and vector fields; in the case of vector fields, both dimensionally regularized and zeta-function results are given. Explicit algebraic forms for the stress-energy tensors are given for the interior of the star and for the exterior Schwarzschild region. If the vacuum stress energy is to be conserved and have the correct trace anomaly at the surface of the star, it is necessary that there be distributional terms in the vacuum stress energy at the surface. The nature and magnitude of these terms are determined. The semiclassical Einstein equations are solved in the exterior region of the star to first order in (h/2π), and the first quantum corrections to Kepler's third law are found
An approach to the Selberg trace formula via the Selberg zeta-function
Fischer, Jürgen
1987-01-01
The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea is to compute the trace of the iterated resolvent kernel of the hyperbolic Laplacian in order to arrive at the logarithmic derivative of the Selberg zeta-function. Previous knowledge of the Selberg trace formula is not assumed. The theory is developed for arbitrary real weights and for arbitrary multiplier systems permitting an approach to known results on classical automorphic forms without the Riemann-Roch theorem. The author's discussion of the Selberg trace formula stresses the analogy with the Riemann zeta-function. For example, the canonical factorization theorem involves an analogue of the Euler constant. Finally the general Selberg trace formula is deduced easily from the properties of the Selberg zeta-function: this is similar to the procedure in analytic number theory where the explicit formulae are deduced from the properties of the Riemann zeta-f...
Effects of heavy metals and oxalate on the zeta potential of magnetite.
Erdemoğlu, Murat; Sarikaya, Musa
2006-08-15
Zeta potential is a function of surface coverage by charged species at a given pH, and it is theoretically determined by the activity of the species in solution. The zeta potentials of particles occurring in soils, such as clay and iron oxide minerals, directly affect the efficiency of the electrokinetic soil remediation. In this study, zeta potential of natural magnetite was studied by conducting electrophoretic mobility measurements in single and binary solution systems. It was shown that adsorption of charged species of Co(2+), Ni(2+), Cu(2+), Zn(2+), Pb(2+), and Cd(2+) and precipitation of their hydroxides at the mineral surface are dominant processes in the charging of the surface in high alkaline suspensions. Taking Pb(2+) as an example, three different mechanisms were proposed for its effect on the surface charge: if pH6, precipitation of heavy metal hydroxides prevails. Oxalate anion changed the associated surface charge by neutralizing surface positive charges by complexing with iron at the surface, and ultimately reversed the surface to a negative zeta potential. Therefore the adsorption ability of heavy metal ions ultimately changed in the presence of oxalate ion. The changes in the zeta potentials of the magnetite suspensions with solution pH before and after adsorption were utilized to estimate the adsorption ability of heavy metal ions. The mechanisms for heavy metals and oxalate adsorption on magnetite were discussed in the view of the experimental results and published data. PMID:16707134
Proof of Analytic Extension Theorem for Zeta Function Using Abel Transformation and Euler Product
Mbaitiga Zacharie
2010-01-01
Full Text Available Problem statement: In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important questions in mathematics whose many researchers are still trying to find answer to some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function. Approach: Abel transformation was used to prove that the extension theorem is true for the real part of the complex variable that is strictly greater than one and consequently provides the required analytic extension of the zeta function to the real part greater than zero and Euler product was used to prove the real part of the complex that are less than zero and greater or equal to one. Results: From this proposed study we noted that the real values of the complex variable are lying between zero and one which may help to understand the relation between zeta function and its properties and consequently can pay the way to solve some complex arithmetic problems including the Riemann Hypothesis. Conclusion: The combination of Abel transformation and Euler product is a powerful tool for proving theorems and functions related to Zeta function including other subjects such as radio atmospheric occultation.
Uniform asymptotics for the full moment conjecture of the Riemann zeta function
Hiary, Ghaith A
2011-01-01
Conrey, Farmer, Keating, Rubinstein, and Snaith recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of zeta on the critical line is asymptotically given by a certain $2k$-fold residue integral. This residue integral can be expressed as a polynomial of degree $k^2$, whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first $k$ coefficients of the moment polynomial are derived. Numerical data to support our asymptotic formula are presented. An application to bounding the maximal size of the zeta function is considered.
Sharma Pushkar Raj
2011-03-01
Full Text Available The study was aimed at evaluating the stability of marketed albendazole suspension through electrokinetic characterization of the particles. The marketed brands of Albendazole suspension that were studied include AVIZOLE®, BENTAL®, BENDEX®, NOWORM® and ZENTAL®.Particle size, zeta potential, sedimentation volume, viscosity and pH of the suspension were the parameters determined and their correlation was established. ZENTAL® showed maximum sedimentation volume and its zeta potential was also found to be the highest. Rheological studies of the suspension displayed maximum viscosity with ZENTAL®. Particle size analysis showed that ZENTAL® had least size. From the study it is evident that particle size, zeta potential and sedimentation volume have an influence on the suspension stability.
Frydecka, I; Boćko, D; Kosmaczewska, A; Ciszak, L; Morilla, R
2001-01-01
It has been reported that peripheral blood T cells and NK cells express reduced levels of the T-cell receptor signal-transducing zeta chain in Hodgkin's disease (HD). The zeta chain has emerged as a key subunit of the T-cell antigen receptor, which plays a central role in the signal-transducing events leading to T and NK-cell activation. We were interested in determining whether the low zeta chain expression in HD could be corrected by anti-CD3, anti-CD3-rIL-2 ex vivo stimulation. Zeta chain expression was analysed by dual immunofluorescence on permeabilized cells before and after 72 hours of culture. The IL-2 concentration in the culture supernatants was measured by ELISA. Zeta chain was significantly reduced on unstimulated CD4+, CD8+ and CD56+ cells from patients in active disease compared with normal subjects. In patients in complete remission, the values were normal except for CD8+ cells, on which zeta expression remained significantly reduced. Stimulation with anti-CD3 did not change zeta expression. Co-stimulation with rIL-2 increased but did not normalize the proportions of CD4+/zeta+, CD8+/zeta+and CD56+/zeta+cells and IL-2 production in active disease. Stimulation of cells from patients in clinical remission with anti-CD3+rIL-2 increased the proportion of CD8+zeta+cells and normalized IL-2 production levels. Considering the pivotal role of CD3-zeta in immune response, our data suggest that successful immunotherapy approaches in active HD should consider inclusion of other potent cytokines, as well as genetically engineered tumour vaccines. © 2001 Cancer Research Campaign www.bjcancer.com PMID:11355944
A3V2(PO4)3 (A = Na or Li) probed by in situ X-ray absorption spectroscopy
Pivko, Maja; Arcon, Iztok; Bele, Marjan; Dominko, Robert; Gaberscek, Miran
2012-10-01
Two stable modifications of A3V2(PO4)3 (A = Na or Li) were synthesized by citric acid assisted modified sol-gel synthesis. The obtained samples were phase pure Li3V2(PO4)3 and Na3V2(PO4)3 materials embedded in a carbon matrix. The samples were tested as half cells against lithium or sodium metal. Both samples delivered about 90 mAh g-1 at a C/10 cycling rate. The change of vanadium oxidation state and changes in the local environment of redox center for both materials were probed by in-situ X-ray absorption spectroscopy. Oxidation state of vanadium was determined by energy shift of the absorption edge. The reversible change of valence from trivalent to tetravalent oxidation state was determined in the potential window used in our experiments. Small reversible changes in the interatomic distances due to the relaxation of the structure in the process of alkali metal extraction and insertion were observed. Local environment (vanadium-oxygen bond distances) after 1st cycle were found to be the same as in the starting material. Both structures have been found very rigid without significant changes during alkali metal extraction.
Dynamic interaction between 14-3-3zeta and bax during TNF-α-induced apoptosis in living cells
Gao, Xuejuan; Xing, Da; Chen, Tongsheng
2006-09-01
Bax, a proapoptotic member of the Bcl-2 family, localizes largely in the cytoplasm but redistributes to mitochondria and undergoes oligomerization to induce the release of apoptogenic factors such as cytochrome c in response to apoptotic stimuli. Cytoplasmic protein 14-3-3zeta binds to Bax and, upon apoptotic stimulation, releases Bax by a caspase-independent mechanism. However, the direct interaction of the cytoplasmic 14-3-3zeta and Bax in living cells has not been observed. In present study, to monitor the dynamic interaction between 14-3-3zeta and Bax in living cells in real time during apoptosis induced by tumor necrosis factor (TNF-α), DsRed-14-3-3zeta plasmid is constructed. By cotransfecting DsRed- 14-3-3zeta and GFP-Bax plasmids into human lung adenocarcinoma cells (ASTC-a-1), we observe the dynamic interaction between Bax and 14-3-3zeta using fluorescence resonance energy transfer (FRET) technique on laser scanning confocal microscope. The results show that 14-3-3zeta remains in the cytoplasm but GFP-Bax translocates to mitochondria completely after TNF-α stimulation. These results reveal that 14-3-3zeta binds directly to Bax in healthy cells, and that 14-3-3zeta negatively regulates Bax translocation to mitochondria during TNF-α-induced apoptosis.
Roots of the derivative of the Riemann zeta function and of characteristic polynomials
Dueñez, Eduardo; Froehlich, Sara; Hughes, Chris; Mezzadri, Francesco; Phan, Toan
2010-01-01
We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both cases show a surprising bimodal distribution which has yet to be explained. We show by example that the bimodality is a general phenomenon. For the unitary matrix case we prove a conjecture of Mezzadri concerning the leading order behavior, and we show that the same follows from the random matrix conjectures for the zeros of the zeta function.
Zeta Function Regularization in Casimir Effect Calculations and J. S. Dowker's Contribution
Elizalde, Emilio
2012-07-01
A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker and collaborators, considered by many authors as the actual starting point of the introduction of zeta function regularization methods in theoretical physics, in particular, for quantum vacuum fluctuation and Casimir effect calculations. After recalling a number of the strengths of this powerful and elegant method, some of its limitations are discussed. Finally, recent results of the so called operator regularization procedure are presented.
Zeta functions of Dirac and Laplace-type operators over finite cylinders
In this paper, a complete description of the zeta functions and corresponding zeta determinants for Dirac and Laplace-type operators over finite cylinders using the contour integration method, for example described in [K. Kirsten, Spectral Functions in Mathematics and Physics, Chapman and Hall/CRC Press, Boca Raton, 2001] is given. Different boundary conditions, local and non-local ones, are considered. The method is shown to be very powerful in that it is easily adapted to each situation and in that answers are very elegantly obtained
On the Singularities of the Zeta and Eta functions of an Elliptic Operator
Loya, Paul; Moroianu, Sergiu; Ponge, Raphaël
2010-01-01
Let P be a selfadjoint elliptic operator of order m>0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s=k/m, where k ranges over all non-zero integers less than or equal to n. In this paper, we construct elementary and explicit examples of perturbations of P which make the zeta and eta functions be singular at all the points at which they are ...
XMM-Newton observations of Zeta Orionis (O9.7 Ib): A Collisional Ionization Equilibrium model
Raassen, A J J; Miller, N A; Cassinelli, J P
2008-01-01
We present XMM-Newton observations of the O supergiant Zeta Orionis (O9.7 Ib). The spectra are rich in emission lines over a wide range of ionization stages. The RGS-spectra show for the first time lines of low ion stages such as C VI, N VI, N VII, and O VII. The line profiles are symmetric and rather broad (FWHM approximately 1500 km/s) and show only a slight blue shift. With the XMM-epic spectrometer several high ions are detected in this star for the first time including Ar XVII and S XV. Simultaneous multi-temperature fits and DEM-modeling were applied to the RGS and EPIC spectra to obtain emission measures, elemental abundances and plasma temperatures. The calculations show temperatures in the range of about 0.07-0.6 keV. According to the derived models the intrinsic source X-ray luminosity at a distance of 251 pc Lx=1.37(.03) times 10^{32} ergs/s, in the energy range 0.3-10 keV. In the best multi-temperature model fit, the abundances of C, N, O, and Fe are near their solar values, while the abundances o...
Eason, Oliver
Myths and tales from around the world about constellations and facts about stars in the constellations are presented. Most of the stories are from Greek and Roman mythology; however, a few Chinese, Japanese, Polynesian, Arabian, Jewish, and American Indian tales are also included. Following an introduction, myths are presented for the following 32…
Fractals of the Julia and Mandelbrot sets of the Riemann Zeta Function
Woon, S. C.
1998-01-01
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in Goldbach conjecture is conjectured.
Fractals of the Julia and Mandelbrot sets of the Riemann $zeta$ Function
Woon, S C
1998-01-01
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in Goldbach conjecture is conjectured.
On the Distribution of the Argument of the Riemann Zeta-Function on the Critical Line
Selin Selen Özbek
2015-12-01
Full Text Available We investigate the distribution of the argument of the Riemann zeta-function on arithmetic progressions on the critical line. We prove uniform distribution modulo ${\\pi\\over 2}$ and we show uniform distribution modulo $\\pi$ under certain restrictions. We also discuss continuous uniform distribution.
"Armastuse retsepti" tippkokk Zeta Jones ei oska muna keeta / Triin Tael
Tael, Triin
2007-01-01
Scott Hicksi romantiline komöödiafilm "Armastuse retsept" ("No Reservations"), mille peaosas Walesist pärit näitlejanna Catherine Zeta Jones. Näitlejanna muljeid oma rolliks ettevalmistustest, mille hulka käis ka praktika pärisrestoranis
Indivisibility of special values of zeta functions associated to real quadratic fields
Kimura, Iwao
2007-01-01
We discuss some aspects of indivisibility of the special values of Dedekind zeta functions at negative odd integers associated to real quadratic fields. These values are closely related to the orders of certain cohomology groups and algebraic $\\mathrm{K}$-groups.\
Broadway teatrites näeb Denzel Washingtoni ja Catherine Zeta-Jonesi / Andres Laasik
Laasik, Andres, 1960-2016
2010-01-01
New Yorgis välja antud Tony teatriauhinna pälvisid filminäitlejad Denzel Washington, Catherine Zeta-Jones ja Scarlett Johansson. Parim lavale naasnud näidend - "Piirdeaed", parim uus näidend - draama "Punane", mis räägib läti päritolu maalikunstnikust Mark Rothkost. Parim muusikal - "Memphis"
The 2-ideal class groups of {$\\Bbb Q(\\zeta\\sb l)$}
Cornacchia, Pietro
2001-01-01
For prime $l$ we study the structure of the $2$-part of the ideal class group $\\Cl$ of ${\\smallBbb Q}(\\zeta_l)$. We prove that $\\Cl \\otimes {\\smallBbb Z}_2$ is a cyclic Galois module for all $l < 10000$ with one exception and compute the explicit structure in several cases.
Double zeta values, double Eisenstein series, and modular forms of level 2
Kaneko, Masanobu; Tasaka, Koji
2011-01-01
We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms of level 2.
Certain Subclasses of Analytic and Bi-Univalent Functions Involving Double Zeta Functions
Saibah Siregar
2012-01-01
Full Text Available In the present paper, we introduce two new subclasses of the functions class Σ of bi-univalent functions involving double zeta functions in the open unit disc U={z:zEC, |z|<1}. The estimates on the coefficients |a2| and |a3| for functions in these new subclasses of the function class Σ are obtained in our investigation.
14-3-3-zeta participates in TLR3-mediated TICAM-1 signal-platform formation.
Funami, Kenji; Matsumoto, Misako; Obuse, Chikashi; Seya, Tsukasa
2016-05-01
Recognition of pathogen-associated molecular patterns (PAMPs) by pattern-recognition receptors (PRRs) is important in innate immune signaling. Toll-like receptors (TLRs) are well-characterized PRRs and are pivotal in antiviral and antitumor host defense. TIR domain-containing adaptor molecule 1 (TICAM-1, also called TRIF) is an adapter molecule in TLR3- and TLR4-mediated IRF3 activation, late-phase NF-κB activation and MAPK-mediated AP-1 activation. When a TLR3 ligand is added to TLR3-positive cells, TICAM-1 transiently interacts with TLR3 and forms multimers in the cytosol. However, the precise mechanism of TICAM-1 multimer formation remains unknown. In this study, we identified 14-3-3-zeta as a molecule that functions in TLR3-mediated signaling. Knockdown of 14-3-3-zeta reduced production of type I interferon and inflammatory cytokines, nuclear translocation of IRF3 and phosphorylation of IκB via the TLR3-TICAM-1 pathway. Furthermore, TICAM-1 multimerization by ligand stimulation was prohibited by 14-3-3-zeta knockdown. These results suggest that 14-3-3-zeta is involved in the TLR3-TICAM-1 pathway in promoting multimerization of TICAM-1 for the formation of a TICAM-1 signalosome. PMID:27058640
Molecular characterization of zeta class glutathione S-transferases from Pinus brutia Ten.
E. Oztetik; F. Kockar; M. Alper; M. Iscan
2015-09-01
Glutathione transferases (GSTs; EC 2.5.1.18) play important roles in stress tolerance and metabolic detoxification in plants. In higher plants, studies on GSTs have focussed largely on agricultural plants. There is restricted information about molecular characterization of GSTs in gymnosperms. To date, only tau class GST enzymes have been characterized from some pinus species. For the first time, the present study reports cloning and molecular characterization of two zeta class GST genes, namely PbGSTZ1 and PbGSTZ2 from Pinus brutia Ten., which is an economically important pine native to the eastern Mediterranean region and have to cope with several environmental stress conditions. The PbGSTZ1 gene was isolated from cDNA, whereas PbGSTZ2 was isolated from genomic DNA. Sequence analysis of PbGSTZ1 and PbGSTZ2 revealed the presence of an open reading frame of 226 amino acids with typical consensus sequences of the zeta class plant GSTs. Protein and secondary structure prediction analysis of two zeta class PbGSTZs have shared common features of other plant zeta class GSTs. Genomic clone, PbGSTZ2 gene, is unexpectedly intronless. Extensive sequence analysis of PbGSTZ2, with cDNA clone, PbGSTZ1, revealed 87% identity at nucleotide and 81% identity at amino acid levels with 41 amino acids differences suggesting that genomic PbGSTZ2 gene might be an allelic or a paralogue version of PbGSTZ1.
Lopez, Henrique Fioravanti Miguel
2009-08-15
This work presents the study and development of a processing power system that could be used in the connection of renewable energy sources to commercial power grid. The system consists of a ZETA converter associated with a bridge inverter operating at low frequency. The Zeta converter, operating in discontinuous conduction mode (DCM), plays the main role in this arrangement, producing a rectified sinusoidal current waveform synchronized with the electric grid. The function of the full-bridge inverter, connected in cascade with the Zeta converter, is to reverse every 180 deg the current generated by the Zeta converter. Initially it presents the analysis of the Zeta converter operating in DCM, as well as a design criterion. Following by the control strategy and the experimental results for the proposed system are presented and discussed. (author)
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star.......Denne rapport beskriver numeriske beregninger af forskellige flydergeometrier for bølgeenergianlæget Wave Star....
Non-Commutative Integration, Zeta Functions and the Haar State for SUq(2)
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SUq(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SUq(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SUq(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension
Non-Commutative Integration, Zeta Functions and the Haar State for SU{sub q}(2)
Matassa, Marco, E-mail: marco.matassa@gmail.com [SISSA (Italy)
2015-12-15
We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group SU{sub q}(2). In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of SU{sub q}(2). We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of SU{sub q}(2). Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.
Michallet, Mauricette; Losem, Christoph
2016-01-01
Chemotherapy-induced anaemia is frequent in cancer patients, with severity depending on the extent of the disease and intensity of treatment. Clinical guidelines recommend erythropoietin therapy to treat or prevent anaemia in some oncology/haematology patients being treated with chemotherapy. The patent expiry of the first-generation erythropoietins has led to the development of biosimilar products, i.e. therapeutic proteins exhibiting comparable quality, safety and efficacy to an existing reference biological medicine, the patent of which has expired. This review summarises the available data set supporting the use of one such biosimilar product, epoetin zeta (Retacrit™) in oncology/haematology. The body of evidence supporting the use of epoetin zeta continues to grow, with post-marketing clinical studies underway to evaluate its longer-term clinical efficacy and safety. Biosimilar medicines have the potential to offer cost savings to health care providers, with the assurance of ongoing risk management programmes to ensure patient safety. PMID:26426164
Nyren-Erickson, Erin K; Haldar, Manas K.; Totzauer, Jessica R.; Ceglowski, Riley; Patel, Dilipkumar S.; Daniel L. Friesner; Srivastava, D. K.; Mallik, Sanku
2012-01-01
Though the aggregation of glycosaminoglycans (GAGs) in the presence of liposomes and divalent cations has been previously reported, the effect of different GAG species, as well as minor changes in GAG composition on the aggregates formed is yet unknown. If minor changes in GAG composition produce observable changes in liposome aggregate diameter or zeta potential, such a phenomenon may be used to detect potentially dangerous over-sulfated contaminants in heparin. We studied the mechanism of t...
Nyren-Erickson, Erin K; Haldar, Manas K; Totzauer, Jessica R; Ceglowski, Riley; Patel, Dilipkumar S; Friesner, Daniel L; Srivastava, D K; Mallik, Sanku
2012-11-20
Though the aggregation of glycosaminoglycans (GAGs) in the presence of liposomes and divalent cations has been previously reported, the effects of different GAG species and minor changes in GAG composition on the aggregates that are formed are yet unknown. If minor changes in GAG composition produce observable changes in the liposome aggregate diameter or zeta potential, such a phenomenon may be used to detect potentially dangerous oversulfated contaminants in heparin. We studied the mechanism of the interactions between heparin and its oversulfated glycosaminoglycan contaminants with liposomes. Herein, we demonstrate that Mg(2+) acts to shield the incoming glycosaminoglycans from the negatively charged phosphate groups of the phospholipids and that changes in the aggregate diameter and zeta potential are a function of the glycosaminoglycan species and concentration as well as the liposome bilayer composition. These observations are supported by TEM studies. We have shown that the organizational states of the liposome bilayers are influenced by the presence of GAG and excess Mg(2+), resulting in a stabilizing effect that increases the T(m) value of DSPC liposomes; the magnitude of this effect is also dependent on the GAG species and concentration present. There is an inverse relationship between the percent change in aggregate diameter and the percent change in aggregate zeta potential as a function of GAG concentration in solution. Finally, we demonstrate that the diameter and zeta potential changes in POPC liposome aggregates in the presence of different oversulfated heparin contaminants at low concentrations allow for an accurate detection of oversulfated chondroitin sulfate at concentrations of as low as 1 mol %. PMID:23102026
Single-valued multiple zeta values in genus 1 superstring amplitudes
Zerbini, Federico
2015-01-01
We study the functions $D_{\\underline{l}}$ introduced by Green, Russo, Vanhove in the context of type II superstring scattering amplitudes of 4 gravitons on a torus. In particular we describe a method to algorithmically compute the coefficients in their expansion at the cusp in terms of conical sums. We perform explicit computations for 3-graviton functions, which naturally suggest to conjecture that only single-valued multiple zeta values appear.
Variations of the Ramanujan polynomials and remarks on $\\zeta(2j+1)/\\pi^{2j+1}$
Lalin, Matilde
2011-01-01
We observe that five polynomial families have all of their zeros on the unit circle. We prove the statements explicitly for four of the polynomial families. The polynomials have coefficients which involve Bernoulli numbers, Euler numbers, and the odd values of the Riemann zeta function. These polynomials are closely related to the Ramanujan polynomials, which were recently introduced by Murty, Smyth and Wang. Our proofs rely upon theorems of Schinzel, and Lakatos and Losonczi and some generalizations.
Long-Term Radial Velocity Monitoring of the HeI 6678 Line of zeta Tau
Pollmann, E.
2016-06-01
With our investigation period of approximately 15 years we have been able to calculate a new long-term period of the HeI 6678 radial velocity (RV) of the binary system zeta Tau. Such a long investigation period was possible because we were able to combine RV data from Ruzdjak et al. (2009) with our own data of the ARAS group (http://www.astrosurf.com/aras/).
Highlights: ► Natural and relatively pure hydroxyapatite particles can be obtained from bovine bone. ► A Complete characterization of bone-derived HA particles was carried out. ► Bone-derived HA particles reveal a negative zeta potential in physiological saline at 37 °C. - Abstract: Animal bone-derived calcium hydroxyapatite (HA) particles were produced and characterized. Adult bovine femoral bone was boiled, washed, cleaned and heated in air at 700 °C for 2 h. The resulting macro-porous solid was ground, crushed and sieved into particles −1 (MgCO3 or CaCO3) and 874 cm−1 (CaHPO4). Main elements by EDXRF were Ca and P (molar ratio 1.93 vs. theoretical ratio 1.67). Minor amounts of Si, Mg and Na were detected, plus traces of K, Sr, Zn, Ba, V, Al, Mn, Pb, Cu and Fe. EDX detected Ca, P, Na and Mg. BET gas adsorption surface area was ∼2.23 m2 g−1 and theoretical particle size ∼857 nm. Laser DLS indicated ∼40% of particles were ∼952 nm in diameter, plus ∼50% were ∼760 nm – in close agreement with BET calculations. By laser Doppler electrophoresis (LDE) the zeta potential of the bone-derived HA particles suspended in 0.154 M NaCl was negative for pH 6–11 and −9.25 ± 0.9 mV at pH 7.4. Negative zeta potential is reported to favor attachment and proliferation of bone cells. HA particles produced synthetically are reported to have positive zeta potentials. The source of the negative potential was not determined but may stem from factors peculiar to producing HA particles from bone. The results suggest further investigation for biomedical use.
Effects of fermion-vacuum polarization by a singular magnetic vortex: zeta function and energy
The influence of the configuration of an external static magnetic field in the form of a singular vortex on the vacuum of quantized spinor field in (2 + 1)-dimensional space-time is studied. The expression for the zeta function, heat kernel, densities of the vacuum energy and effective action under the most general (compatible with self-adjointness of the Hamiltonian) boundary condition at the point singularity are obtained
The Stability of Electron Orbital Shells based on a Model of the Riemann-Zeta Function
Harney M.
2008-01-01
Full Text Available It is shown that the atomic number Z is prime at the beginning of the each s1, p1, d1, and f1 energy levels of electrons, with some fluctuation in the actinide and lanthanide series. The periodic prime number boundary of s1, p1, d1, and f1 is postulated to occur because of stability of Schrodinger's wave equation due to a fundamental relationship with the Riemann-Zeta function.
The Stability of Electron Orbital Shells based on a Model of the Riemann-Zeta Function
Harney M.
2008-01-01
Full Text Available It is shown that the atomic number Z is prime at the beginning of the each s1, p1, d1, and f1 energy levels of electrons, with some fluctuation in the actinide and lanthanide series. The periodic prime number boundary of s1, p1, d1, and f1 is postulated to occur because of stability of Schrodinger’s wave equation due to a fundamental relationship with the Riemann-Zeta function.
Fontes, Adriana; Fernandes, Heloise P.; Barjas-Castro, Maria L.; de Thomaz, André A.; de Ysasa Pozzo, Liliana; Barbosa, Luiz C.; Cesar, Carlos L.
2006-02-01
The red blood cell (RBC) viscoelastic membrane contains proteins and glycolproteins embedded in, or attached, to a fluid lipid bilayer and are negatively charged, which creates a repulsive electric (zeta) potential between the cells and prevents their aggregation in the blood stream. There are techniques, however, to decrease the zeta potential to allow cell agglutination which are the basis of most of the tests of antigen-antibody interactions in blood banks. This report shows the use of a double optical tweezers to measure RBC membrane viscosity, agglutination and zeta potential. In our technique one of the optical tweezers trap a silica bead that binds strongly to a RBC at the end of a RBCs rouleaux and, at the same time, acts as a pico-Newton force transducer, after calibration through its displacement from the equilibrium position. The other optical tweezers trap the RBC at the other end. To measure the membrane viscosity the optical force is measured as a function of the velocity between the RBCs. To measure the adhesion the tweezers are slowly displaced apart until the RBCs disagglutination happens. The RBC zeta potential is measured in two complimentary ways, by the force on the silica bead attached to a single RBC in response to an applied electric field, and the conventional way, by the measurement of terminal velocity of the RBC after released from the optical trap. These two measurements provide information about the RBC charges and, also, electrolytic solution properties. We believe this can improve the methods of diagnosis in blood banks.
Chun, Myung-Suk; Lee, Sang-Yup; Yang, Seung-Man
2003-10-01
The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel. PMID:12957590
A perturbative approach to the spectral zeta functions of strings, drums, and quantum billiards
We show that the spectral zeta functions of inhomogeneous strings and drums can be calculated using Rayleigh-Schrödinger perturbation theory. The inhomogeneities that can be treated with this method are small but otherwise arbitrary and include the previously studied case of a piecewise constant density. In two dimensions the method can be used to derive the spectral zeta function of a domain obtained from the small deformation of a square. We also obtain exact sum rules that are valid for arbitrary densities and that correspond to the values taken by the spectral zeta function at integer positive values; we have tested numerically these sum rules in specific examples. We show that the Dirichlet or Neumann Casimir energies of an inhomogeneous string, evaluated to first order in perturbation theory, contain in some cases an irremovable divergence, but that the combination of the two is always free of divergences. Finally, our calculation of the Casimir energies of a string with piecewise constant density and of two perfectly conducting concentric cylinders, of similar radius, reproduce the results previously published.
On the Singularities of the Zeta and Eta functions of an Elliptic Operator
Loya, Paul; Ponge, Raphaël
2010-01-01
Let P be a selfadjoint elliptic operator of order m>0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s=k/m, where k ranges over all non-zero integers less than or equal to n. In this paper, we construct elementary and explicit examples of perturbations of P which make the zeta and eta functions be singular at all the points at which they are allowed to have singularities. We proceed within three classes of operators: Dirac-type operators, selfadjoint first-order differential operators, and selfadjoint elliptic pseudodifferential operators. As a result, we obtain genericity results for the singularities of the zeta and eta functions in those settings. In particular, in the setting of Dirac-type operators we obtain a new proof of a well known result of Branson-Gilkey.
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of ''non-perturbative'' poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
Hatsuda, Yasuyuki
2015-01-01
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example as...
Influence of particle/solid surface zeta potential on particle adsorption kinetics.
Savaji, Kunal V; Niitsoo, Olivia; Couzis, Alexander
2014-10-01
In this paper we attempt to understand monolayer formation of spherical particles on a solid surface immersed in a suspension and driven by electrostatic interaction force. The study focuses on the theoretical aspects of the particle adsorption and modeling work based on the random sequential adsorption (RSA) approach is done in order to describe the particle adsorption kinetics and the saturation coverage. The theoretical model is then compared with experimental data obtained under conditions similar to those of the modeling work. Studying the adsorption of polystyrene particles on a silicon wafer in an aqueous system was employed to experimentally validate the theoretical framework. It has been shown both theoretically and experimentally that the particle and solid surface zeta potential values do influence the adsorption kinetics but the effect is too negligible to be of any use in accelerating the kinetics. We have shown that the electrostatically driven particle adsorption is a transport limited process and the rate of transport is not a major function of the zeta potential values of the particle and the solid surface. The faster kinetics seen when the ionic concentration of the suspension is increased is because of the blocking effects and not due to faster approach of particles towards the solid surface. Finally, we have made an important addition to the existing models by incorporating the variation in the flux as a function of particle/solid surface zeta potentials, surface coverage and the randomized position of incidence of an incoming particle on the solid surface. PMID:24996026
T-cell receptor downregulation by ceramide-induced caspase activation and cleavage of the zeta chain
Menné, C; Lauritsen, Jens Peter Holst; Dietrich, J;
2001-01-01
gamma L-based motif-dependent and the tyrosine kinase-dependent pathways. This pathway is dependent on ceramide-induced activation of caspases and correlate with caspase-mediated cleavage of the zeta chain. Thus, a 10--15% downregulation of the TCR was induced following the treatment of the T cells with...... ceramide for 4 h. A close correlation between TCR downregulation, caspase activation, and cleavage of the zeta chain was found. Furthermore, the caspase inhibitors abolished the cleavage of the zeta chain and TCR downregulation in parallel with the inhibition of the caspase activity....
Do all barium stars have a white dwarf companion?
Dominy, J. F.; Lambert, D. L.
1983-01-01
International Ultraviolet Explorer short-wavelength, low-dispersion spectra were analyzed for four barium, two mild barium, and one R-type carbon star in order to test the hypothesis that the barium and related giants are produced by mass transfer from a companion now present as a white dwarf. An earlier tentative identification of a white dwarf companion to the mild barium star Zeta Cyg is confirmed. For the other stars, no ultraviolet excess attributable to a white dwarf is seen. Limits are set on the bolometric magnitude and age of a possible white dwarf companion. Since the barium stars do not have obvious progenitors among main-sequence and subgiant stars, mass transfer must be presumed to occur when the mass-gaining star is already on the giant branch. This restriction, and the white dwarf's minimum age, which is greater than 8 x 10 to the 8th yr, determined for several stars, effectively eliminates the hypothesis that mass transfer from an asymptotic giant branch star creates a barium star. Speculations are presented on alternative methods of producing a barium star in a binary system.
Li, Dan; Yu, Long; Wu, Hai; Shan, Yuxi; Guo, Jinhu; Dang, Yongjun; Wei, Youheng; Zhao, Shouyuan
2003-01-01
Lysophosphatidic acid (LPA) is a naturally occurring component of phospholipid and plays a critical role in the regulation of many physiological and pathophysiological processes including cell growth, survival, and pro-angiogenesis. LPA is converted to phosphatidic acid by the action of lysophosphatidic acid acyltransferase (LPAAT). Five members of the LPAAT gene family have been detected in humans to date. Here, we report the identification of a novel LPAAT member, which is designated as LPAAT-zeta. LPAAT-zeta was predicted to encode a protein consisting of 456 amino acid residues with a signal peptide sequence and the acyltransferase domain. Northern blot analysis showed that LPAAT-zeta was ubiquitously expressed in all 16 human tissues examined, with levels in the skeletal muscle, heart, and testis being relatively high and in the lung being relatively low. The human LPAAT-zeta gene consisted of 13 exons and is positioned at chromosome 8p11.21. PMID:12938015
Moretti, Valter
2010-01-01
This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy tensor and the field fluctuations.
Moretti, Valter
2011-01-01
This is a quick review on some technology concerning the local zeta function applied to Quantum Field Theory in curved static (thermal) spacetime to regularize the stress-energy tensor and the field fluctuations.
The Zeta method for the calibration of fission-track dating against other radiometric dating techniques has been described by Hurford and Green (1983). In this paper, the data for the Zeta calibration were obtained using 4π -Conversion Procedure (Suzuki et. al., 1984). The preliminary Zeta value determined from this work was found to be 224.52 ± 38.73, showing significant difference from values obtained by workers elsewhere using equivalent standard glass dosimeter. Factors that might have contributed to such discrepancy are discussed. From this study and work done by other fission-track workers, it is obvious that a wide range of Zeta values are in common use. However consistency in track-counting remains the prime factor for getting reliable ages for unknown samples
Maurette, M.; Hammer, C.
A shooting star passage -even a star shower- can be sometimes easily seen during moonless black night. They represent the partial volatilization in earth atmosphere of meteorites or micrometeorites reduced in cosmic dusts. Everywhere on earth, these star dusts are searched to be gathered. This research made one year ago on the Greenland ice-cap is the object of this article; orbit gathering projects are also presented.
Eduardo Alberto López-Maldonado; Mercedes Teresita Oropeza-Guzmán; Adrián Ochoa-Terán
2014-01-01
Efficiency of coagulation-flocculation process used for semiconductor wastewater treatment was improved by selecting suitable conditions (pH, polyelectrolyte type, and concentration) through zeta potential measurements. Under this scenario the zeta potential, ζ, is the right parameter that allows studying and predicting the interactions at the molecular level between the contaminants in the wastewater and polyelectrolytes used for coagulation-flocculation. Additionally, this parameter is a k...
A Derivation of $pi(n$ Based on a Stability Analysis of the Riemann-Zeta Function
Harney M.
2010-04-01
Full Text Available The prime-number counting function $pi(n$, which is significant in the prime number theorem, is derived by analyzing the region of convergence of the real-part of the Riemann-Zeta function using the unilateral $z$-transform. In order to satisfy the stability criteria of the $z$-transform, it is found that the real part of the Riemann-Zeta function must converge to the prime-counting function.
Archimedean zeta integrals on $GL_n \\times GL_m$ and $SO_{2n+1} \\times GL_m$
Ishii, Taku; Stade, Eric
2011-01-01
In this paper, we evaluate archimedean zeta integrals for automorphic $L$-functions on $GL_n \\times GL_{n-1+\\ell}$ and on $ SO_{2n+1} \\times GL_{n+\\ell}$, for $\\ell=-1$, $0$, and $1$. In each of these cases, the zeta integrals in question may be expressed as Mellin transforms of products of class one Whittaker functions. Here, we obtain explicit expressions for these Mellin transforms in terms of Gamma functions and Barnes integrals.
A Derivation of π(n Based on a Stability Analysis of the Riemann-Zeta Function
Harney M.
2010-04-01
Full Text Available The prime-number counting function ( n , which is significant in the prime number the- orem, is derived by analyzing the region of convergence of the real-part of the Riemann- Zeta function using the unilateral z -transform. In order to satisfy the stability criteria of the z -transform, it is found that the real part of the Riemann-Zeta function must con- verge to the prime-counting function.
Hjellming, R M; Wade, C M
1971-09-17
Up to the present time six classes of radio stars have been established. The signals are almost always very faint and drastically variable. Hence their discovery has owed as much to serendipity as to the highly sophisticated equipment and techniques that have been used. When the variations are regular, as with the pulsars, this characteristic can be exploited very successfully in the search for new objects as well as in the detailed study of those that are already known. The detection of the most erratically variable radio stars, the flare stars and the x-ray stars, is primarily a matter of luck and patience. In the case of the novas, one at least knows where and oughly when to look for radio emission. A very sensitive interferometer is clearly the best instrument to use in the initial detection of a radio star. The fact that weak background sources are frequently present makes it essential to prove that the position of a radio source agrees with that of a star to within a few arc seconds. The potential of radio astronomy for the study of radio stars will not be realized until more powerful instruments than those that are available today can be utilized. So far, we have been able to see only the most luminous of the radio stars. PMID:17836594
Kramer, Morten; Brorsen, Michael; Frigaard, Peter
Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star.......Nærværende rapport beskriver numeriske beregninger af den hydrodynamiske interaktion mellem 5 flydere i bølgeenergianlægget Wave Star....
Madsen, Peter Buch; Jørgensen, John Leif; Thuesen, Gøsta; Paulsen, Thomas Eide
1997-01-01
The version of the star imager developed for Astrid II is described. All functions and features are described as well as the operations and the software protocol.......The version of the star imager developed for Astrid II is described. All functions and features are described as well as the operations and the software protocol....
Ren, Jing M; McKenzie, Thomas G; Fu, Qiang; Wong, Edgar H H; Xu, Jiangtao; An, Zesheng; Shanmugam, Sivaprakash; Davis, Thomas P; Boyer, Cyrille; Qiao, Greg G
2016-06-22
Recent advances in controlled/living polymerization techniques and highly efficient coupling chemistries have enabled the facile synthesis of complex polymer architectures with controlled dimensions and functionality. As an example, star polymers consist of many linear polymers fused at a central point with a large number of chain end functionalities. Owing to this exclusive structure, star polymers exhibit some remarkable characteristics and properties unattainable by simple linear polymers. Hence, they constitute a unique class of technologically important nanomaterials that have been utilized or are currently under audition for many applications in life sciences and nanotechnologies. This article first provides a comprehensive summary of synthetic strategies towards star polymers, then reviews the latest developments in the synthesis and characterization methods of star macromolecules, and lastly outlines emerging applications and current commercial use of star-shaped polymers. The aim of this work is to promote star polymer research, generate new avenues of scientific investigation, and provide contemporary perspectives on chemical innovation that may expedite the commercialization of new star nanomaterials. We envision in the not-too-distant future star polymers will play an increasingly important role in materials science and nanotechnology in both academic and industrial settings. PMID:27299693
Doostmohammadi, Ali, E-mail: alidm14@ma.iut.ac.ir [Biomaterials Research Center, Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Isfahan University of Medical Sciences, Isfahan 81746-73461 (Iran, Islamic Republic of); Monshi, Ahmad [Biomaterials Research Center, Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Salehi, Rasoul [Department of Genetics and Molecular Biology, School of Medicine, Isfahan University of Medical Sciences, Isfahan 81746-73461 (Iran, Islamic Republic of); Fathi, M.H. [Biomaterials Research Center, Department of Materials Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Karbasi, Saeed [Medical Physics and Biomedical Engineering Group, School of Medicine, Isfahan University of Medical Sciences, Isfahan (Iran, Islamic Republic of); Pieles, Uwe [Institute for Chemistry and Bioanalytics, School of Life Sciences, University of Applied Sciences of Northwestern Switzerland, Muttenz (Switzerland); Daniels, A.U. [Laboratory of Biomechanics and Biocalorimetry, Coaltion for Clinical Morphology and Biomedical Engineering, University of Basel Faculty of Medicine, Basel (Switzerland)
2012-02-15
Highlights: Black-Right-Pointing-Pointer Natural and relatively pure hydroxyapatite particles can be obtained from bovine bone. Black-Right-Pointing-Pointer A Complete characterization of bone-derived HA particles was carried out. Black-Right-Pointing-Pointer Bone-derived HA particles reveal a negative zeta potential in physiological saline at 37 Degree-Sign C. - Abstract: Animal bone-derived calcium hydroxyapatite (HA) particles were produced and characterized. Adult bovine femoral bone was boiled, washed, cleaned and heated in air at 700 Degree-Sign C for 2 h. The resulting macro-porous solid was ground, crushed and sieved into particles <50 {mu}m. SEM showed the particles were agglomerations of crystals {approx}50-500 nm across. XRD showed highly crystalline HA with nominal MgO and no detectable CaO. FTIR spectroscopy yielded typical HA absorptions, plus absorptions at 1457 and 1412 cm{sup -1} (MgCO{sub 3} or CaCO{sub 3}) and 874 cm{sup -1} (CaHPO{sub 4}). Main elements by EDXRF were Ca and P (molar ratio 1.93 vs. theoretical ratio 1.67). Minor amounts of Si, Mg and Na were detected, plus traces of K, Sr, Zn, Ba, V, Al, Mn, Pb, Cu and Fe. EDX detected Ca, P, Na and Mg. BET gas adsorption surface area was {approx}2.23 m{sup 2} g{sup -1} and theoretical particle size {approx}857 nm. Laser DLS indicated {approx}40% of particles were {approx}952 nm in diameter, plus {approx}50% were {approx}760 nm - in close agreement with BET calculations. By laser Doppler electrophoresis (LDE) the zeta potential of the bone-derived HA particles suspended in 0.154 M NaCl was negative for pH 6-11 and -9.25 {+-} 0.9 mV at pH 7.4. Negative zeta potential is reported to favor attachment and proliferation of bone cells. HA particles produced synthetically are reported to have positive zeta potentials. The source of the negative potential was not determined but may stem from factors peculiar to producing HA particles from bone. The results suggest further investigation for biomedical use.
Chan, L C; So, J C; Chui, D H
1995-01-01
AIMS--To compare the haemoglobin (Hb) H inclusion test with immunocytochemical detection of embryonic zeta chains in screening for alpha thalassaemia. METHODS--Blood samples from 115 patients with relevant clinical history and hypochromic microcytic indexes were screened using the HbH inclusion test and the Variant Hemoglobin Testing System (BioRad, Hercules, CA, USA). RESULTS--The HbH inclusion test was positive in 61 of 115 cases, three of whom had HbH disease confirmed by electrophoresis. ...
Modeling of Zeta converter based DVR system for power quality improvement
P.Velmurugan
2014-05-01
Full Text Available A new development of voltage control scheme for power quality improvement such as voltage sag, swell, harmonics, and transient conditions in three-phase power systems has been proposed. Faults occurring in power distribution systems or amenities can inject the voltage sag or swell. This fault can damage or affect the power transmission and distribution. For sensitive loads, the short duration of voltage sags also cause huge problems in the entire power system. In order to reduce power interruptions, this work proposes a novel Zeta converter based DVR system. This proposed scheme can quickly access the voltage sag and swell under transient condition.
Hearing the music of the primes: auditory complementarity and the siren song of zeta
A counting function for the primes can be rendered as a sound signal whose harmonies, spanning the gamut of musical notes, are the Riemann zeros. But the individual primes cannot be discriminated as singularities in this ‘music’, because the intervals between them are too short. Conversely, if the prime singularities are detected as a series of clicks, the Riemann zeros correspond to frequencies too low to be heard. The sound generated by the Riemann zeta function itself is very different: a rising siren howl, which can be understood in detail from the Riemann–Siegel formula. (fast track communication)
La medida del potencial zeta. Relaciones con la finura en arenisca
Luxán, María Pilar de; Sánchez de Rojas, María Isabel; Frías Rojas, Moisés; Martín Patiño, M. T.
1989-01-01
[ES] Con el fin de ampliar y mejorar las posibilidades de empleo del cemento y de su colocación se ha buscado la incorporación de aditivos que modifiquen sus propiedades reológicas. Con ello se abre un campo de investigación, en el que la estabilidad del sistema coloidal está en función del potencial zeta, por lo que la medida del mismo contribuye al conocimiento del mecanismo de las reacciones de hidratación del cemento. La aparición de trabajos de investigación...
Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and $q$-zeta functions
Komori, Yasushi; Tsumura, Hirofumi
2010-01-01
We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we evaluate those double series. Our main results can be regarded as a certain generalization of well-known results of Hurwitz, Herglotz, Katayama and so on. Our results also include recent formulas of the third-named author which are double analogues of the formulas of Cauchy, Mellin, Ramanujan, Berndt and so on, about certain Dirichlet series involving hyperbolic functions. As an application, we give some evaluation formulas for $q$-zeta functions at positive integers.
Relations between elliptic multiple zeta values and a special derivation algebra
Broedel, Johannes; Matthes, Nils; Schlotterer, Oliver
2016-04-01
We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths.
Bass-Ihara Zeta functions for non-uniform tree lattices and class number asymptotics
Deitmar, Antonius; Kang, Ming-Hsuan
2014-01-01
It is shown that the Euler product giving the Bass-Ihara zeta function of a finite graph also converges in the case of a non-compact arith- metic quotient graph. Despite the infinite-dimensional setting, it turns out to be a rational function, generally with zeros and poles, in contrast to the compact case. The determinant formulas of Bass and Ihara hold true if one defines the determinant as limit of all finite principal minors. From this analysis, a prime geodesic theorem is derived, which,...
Statistical properties of the zeros of zeta functions - beyond the Riemann case
The statistical distribution of the zeros of Dirichlet L-functions is investigated both analytically and numerically. Using the Hardy-Littlewood conjecture about the distribution of primes it is shown that the two-point correlation function of these zeros coincides with that for eigenvalues of the Gaussian unitary ensemble of random matrices, and that the distributions of zeros of different L-functions are statistically independent. Applications of these results to Epstein's zeta functions are shortly discussed. (authors) 30 refs., 3 figs., 1 tab
Primality Testing and Factorization by using Fourier Spectrum of the Riemann Zeta Function
Musha Takaaki
2015-11-01
Full Text Available In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers, for which there is not known efficient algorithm. In this article, the author tries to make primality testing and factorization of integers by using Fourier transform of a correlation function generated from the Riemann zeta function. From the theoretical analysis, we can see that prime factorization for the integer composed of two different primes can be conducted within a polynomial time and it can be seen that this special case belongs to the P class.
Abramovici, Hanan; Gee, Stephen H
2007-07-01
The fusion of mononuclear myoblasts into multinucleated myofibers is essential for the formation and growth of skeletal muscle. Myoblast fusion follows a well-defined sequence of cellular events, from initial recognition and adhesion, to alignment, and finally plasma membrane fusion. These processes depend upon coordinated remodeling of the actin cytoskeleton. Our recent studies suggest diacylglycerol kinase-zeta (DGK-zeta), an enzyme that metabolizes diacylglycerol to yield phosphatidic acid, plays an important role in actin reorganization. Here, we investigated whether DGK-zeta has a role in the fusion of cultured C2C12 myoblasts. We show that DGK-zeta and syntrophins, scaffold proteins of the dystrophin glycoprotein complex that bind directly to DGK-zeta, are spatially regulated during fusion. Both proteins accumulated with the GTPase Rac1 at sites where fine filopodia mediate the initial contact between myoblasts. In addition, DGK-zeta codistributed with the Ca(2+)-dependent cell adhesion molecule N-cadherin at nascent, but not previously established cell contacts. We provide evidence that C2 cells are pulled together at cell-cell junctions by N-cadherin-containing filopodia reminiscent of epithelial adhesion zippers, which guide the advance of lamellipodia from apposing cells. At later times, vesicles with properties of macropinosomes formed close to cell-cell junctions. Reconstruction of confocal optical sections showed these form dome-like protrusions from the dorsal surface of contacting cells. Collectively, these results suggest DGK-zeta and syntrophins play a role at multiple stages of the fusion process. Moreover, our findings provide a potential link between changes in the lipid content of the membrane bilayer and reorganization of the actin cytoskeleton during myoblast fusion. PMID:17410543
Casimir force in brane worlds: Coinciding results from Green's and zeta function approaches
Casimir force encodes the structure of the field modes as vacuum fluctuations and so it is sensitive to the extra dimensions of brane worlds. Now, in flat spacetimes of arbitrary dimension the two standard approaches to the Casimir force, Green's function, and zeta function yield the same result, but for brane world models this was only assumed. In this work we show that both approaches yield the same Casimir force in the case of universal extra dimensions and Randall-Sundrum scenarios with one and two branes added by p compact dimensions. Essentially, the details of the mode eigenfunctions that enter the Casimir force in the Green's function approach get removed due to their orthogonality relations with a measure involving the right hypervolume of the plates, and this leaves just the contribution coming from the zeta function approach. The present analysis corrects previous results showing a difference between the two approaches for the single brane Randall-Sundrum; this was due to an erroneous hypervolume of the plates introduced by the authors when using the Green's function. For all the models we discuss here, the resulting Casimir force can be neatly expressed in terms of two four-dimensional Casimir force contributions: one for the massless mode and the other for a tower of massive modes associated with the extra dimensions.
Remarks on non-gaussian fluctuations of the inflaton and constancy of \\zeta outside the horizon
Mahajan, Namit
2010-01-01
We point out that the non-gaussianity arising from cubic self interactions of the inflaton field is proportional to \\xi N_e where \\xi ~ V''' and N_e is the number of e-foldings from horizon exit till the end of inflation. For scales of interest N_e = 60, and for models of inflation such as new inflation, natural inflation and running mass inflation \\xi is large compared to the slow roll parameter \\epsilon ~ V'^{2}. Therefore the contribution from self interactions should not be outrightly ignored while retaining other terms in the non-gaussianity parameter f_{NL}. But the N_e dependent term seems to imply the growth of non-gaussianities outside the horizon. Therefore we briefly discuss the issue of the constancy of correlations of the curvature perturbation \\zeta outside the horizon. We then calculate the 3-point function of the inflaton fluctuations using the canonical formalism and further obtain the 3-point function of \\zeta_k. We find that the N_e dependent contribution to f_{NL} from self interactions of...
Dust-correlated cm-wavelength continuum emission on translucent clouds {\\zeta} Oph and LDN 1780
Vidal, M; Dickinson, C; Witt, A N; Castellanos, P; Davies, R D; Davis, R J; Cabrera, G; Cleary, K; Allison, J R; Bond, J R; Bronfman, L; Bustos, R; Jones, M E; Paladini, R; Pearson, T J; Readhead, A C S; Reeves, R; Sievers, J L; Taylor, A C
2011-01-01
The diffuse cm-wave IR-correlated signal, the "anomalous" CMB foreground, is thought to arise in the dust in cirrus clouds. We present Cosmic Background Imager (CBI) cm-wave data of two translucent clouds, {\\zeta} Oph and LDN 1780 with the aim of characterising the anomalous emission in the translucent cloud environment. In {\\zeta} Oph, the measured brightness at 31 GHz is 2.4{\\sigma} higher than an extrapolation from 5 GHz measurements assuming a free-free spectrum on 8 arcmin scales. The SED of this cloud on angular scales of 1{\\odot} is dominated by free-free emission in the cm-range. In LDN 1780 we detected a 3 {\\sigma} excess in the SED on angular scales of 1{\\odot} that can be fitted using a spinning dust model. In this cloud, there is a spatial correlation between the CBI data and IR images, which trace dust. The correlation is better with near-IR templates (IRAS 12 and 25 {\\mu}m) than with IRAS 100 {\\mu}m, which suggests a very small grain origin for the emission at 31 GHz. We calculated the 31 GHz em...
Electroosmotic fluid motion and late-time solute transport at non-negligible zeta potentials
S. K. Griffiths; R. H. Nilson
1999-12-01
Analytical and numerical methods are employed to determine the electric potential, fluid velocity and late-time solute distribution for electroosmotic flow in a tube and channel when the zeta potential is not small. The electric potential and fluid velocity are in general obtained by numerical means. In addition, new analytical solutions are presented for the velocity in a tube and channel in the extremes of large and small Debye layer thickness. The electroosmotic fluid velocity is used to analyze late-time transport of a neutral non-reacting solute. Zeroth and first-order solutions describing axial variation of the solute concentration are determined analytically. The resulting expressions contain eigenvalues representing the dispersion and skewness of the axial concentration profiles. These eigenvalues and the functions describing transverse variation of the concentration field are determined numerically using a shooting technique. Results are presented for both tube and channel geometries over a wide range of the normalized Debye layer thickness and zeta potential. Simple analytical approximations to the eigenvalues are also provided for the limiting cases of large and small values of the Debye layer thickness. The methodology developed here for electroosmotic flow is also applied to the Taylor problem of late-time transport and dispersion in pressure-driven flows.
Zeta potential control in decontamination with inorganic membranes and inorganic adsorbents
The application of some advanced separation processes such as microfiltration and ultrafiltration, electroosmosis and electrodialysis for treating nuclear waste from different aqueous streams is under examination at the Chilean Commission for Nuclear Energy. The application of these techniques can be extended to regular industrial wastes when economically advisable. This report deals mainly with electrodialysis, electroosmosis and adsorption with inorganic materials. Special attention is paid to zeta potential control as a driving factor to electroosmosis. For radioactive contaminants that are present in the form of cations, anions, non-ionic solutions, colloids and suspended matter, appropriate combination of the processes may considerably increase the efficiency of processes used. As an example, colloids and suspended particles may be retained in porous ceramic membranes by nanofiltration, ultrafiltration or microfiltration depending on the particle size of the particles. The control of zeta potential by acting in the solid phase or else on the liquid phase has been studied; a mathematical model to predict electrodialysis data has been developed, and finally, the use of a home-made inorganic adsorbent illustrated. The effect of gamma irradiation on the membranes has also been studied. Properties such as salt retention, water flux and pore size diameter determined on both organic and inorganic membranes before and after irradiation indicate deterioration of the organic membrane. (author). 13 refs, 15 figs, 2 tabs
Cisterna, Adolfo; Rinaldi, Massimiliano
2015-01-01
We consider the sector of Horndeski's gravity characterized by a coupling between the kinetic scalar field term and the Einstein tensor. Our goal is to find realistic neutron star configurations in this framework. We show that, in a certain limit, there exist solutions that are identical to the Schwarzschild metric outside the star but change considerably inside, where the scalar field is not trivial. We study numerically the equations and find the region of the parameter space where neutron stars exist. We determine their internal pressure and mass-radius relation, and we compare them with standard general relativity models.
Zhang, Lixia; Huang, Li; Zeng, Zehua; Qian, Jun; Hua, Daoben
2016-05-14
Uranium(vi) is one of the main sources in nuclear energy but can cause severe effects to human health and the environment, therefore it is important to develop a new method and materials for uranium capture. A novel approach is reported here for efficient uranium sorption by polyamidoxime-functionalized colloids with zeta potential-assistance. Specifically, colloidal particles were prepared via emulsion polymerization with (3-acrylamidopropyl)trimethyl-ammonium chloride (MAPTAC). The zeta potential of the colloids could be controlled by the concentration of MAPTAC. The effects of pH, the sorbent dose and competing ions on uranium(vi) sorption were investigated. The sorption process followed a pseudo-second-order kinetics and could reach equilibrium within 3.5 h at pH 7.8. The colloidal particles with high zeta potentials showed higher selectivity, faster kinetics and larger capacity for the sorption of uranium(vi) in comparison with that of negative zeta potential particles. This work may provide a new method for efficient uranium(vi) capture from aqueous solution through zeta potential-assisted sorption. PMID:27109739
张国平
2000-01-01
Around the world young people are spending unbelievable sums of money to listen to rock music. Forbes Magazine reports that at least fifty rock stars have incomes between two million and six million dollars per year.
The number of stars counted along a particular line of sight depends on the spatial distribution of stars, the luminosity function, and the absorption. Thus star count programs designed to constrain or determine one or more of these functions. Early efforts to understand the structure of our Galaxy, including the fundamentals of stellar statistics, were largely based on work that involved star counts. Since then a growing appreciation has developed for the variety of forms the density function and the luminosity function can take, especially the recognition of different stellar populations, each with different density and luminosity functions. In the simplest formulation two distinct populations are considered: disk and halo. This suggests two distinct formation histories, but uncertainty in the picture remains. (Auth.)
Theoretical models of star formation are discussed beginning with the earliest stages and ending in the formation of rotating, self-gravitating disks or rings. First a model of the implosion of very diffuse gas clouds is presented which relies upon a shock at the edge of a galactic spiral arm to drive the implosion. Second, models are presented for the formation of a second generation of massive stars in such a cloud once a first generation has formed. These models rely on the ionizing radiation from massive stars or on the supernova shocks produced when these stars explode. Finally, calculations of the gravitational collapse of rotating clouds are discussed with special focus on the question of whether rotating disks or rings are the result of such a collapse. 65 references
T. Lloyd Evans
2010-12-01
In this paper, the present state of knowledge of the carbon stars is discussed. Particular attention is given to issues of classification, evolution, variability, populations in our own and other galaxies, and circumstellar material.
Kramer, Morten; Frigaard, Peter
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Byggeri og Anlæg med bølgeenergianlæget Wave Star....
Kramer, Morten; Andersen, Thomas Lykke
Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star.......Nærværende rapport beskriver modelforsøg udført på Aalborg Universitet, Institut for Vand, Jord og Miljøteknik med bølgeenergianlægget Wave Star....
Korhonen, H.; Wittkowski, M.; Kovari, Zs.; Granzer, Th.; Hackman, T.; Strassmeier, K. G.
2010-01-01
We have obtained high-resolution spectroscopy, optical interferometry, and long-term broad band photometry of the ellipsoidal primary of the RS CVn-type binary system zeta And. Based on the optical interferometry the apparent limb darkened diameter of zeta And is 2.55 +/- 0.09 mas using a uniform disk fit. The Hipparcos distance and the limb-darkened diameter obtained with a uniform disk fit give stellar radius of 15.9 +/- 0.8 Rsolar, and combined with bolometric luminosity, it implies an eff...
Extended Fermi-Dirac and Bose-Einstein functions with applications to the family of zeta functions
Chaudhry, M Aslam; Tassaddiq, Asifa
2010-01-01
Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relation to the family of zeta functions. These extensions are "dual" to each other in a sense that is explained. Some identities are proved for them and the relation between them and the general Hurwitz-Lerch zeta function (\\phi(z,s,v) is exploited to deduce new identities.
Provirnina, E. V.; Barbin, M. B.
1984-01-01
The value of the zeta-potential does not have an explicit effect, which is expressed by a simple math correlation, on filtration rate when a solution of the tested collector is filtered through a cake prepared under standard conditions from the examined particulate material. The zeta-potential measurements and filtration tests were carried out on silica and galena with solutions contg. a cationic container ANP and Et xanthane, resp. at PH = 6.5, varying concentration of the agent (0-2500 g/ton), and under a vacuum of 100 to 600 mm Hg.
Combinatorics of lower order terms in the moment conjectures for the Riemann zeta function
Dehaye, Paul-Olivier
2012-01-01
Conrey, Farmer, Keating, Rubinstein and Snaith have given a recipe that conjecturally produces, among others, the full moment polynomial for the Riemann zeta function. The leading term of this polynomial is given as a product of a factor explained by arithmetic and a factor explained by combinatorics (or, alternatively, random matrices). We explain how the lower order terms arise, and clarify the dependency of each factor on the exponent $k$ that is considered. We use extensively the theory of symmetric functions and representations of symmetric groups, ideas of Lascoux on manipulations of alphabets, and a key lemma, due in a basic version to Bump and Gamburd. Our main result ends up involving dimensions of partitions, as studied by Olshanski, Regev, Vershik, Ivanov and others.
Measuring differential rotation of the K-giant $\\zeta$\\,And
K\\Hovári, Zs; Kriskovics, L; Vida, K; Donati, J -F; Coroller, H Le; Pedretti, J D Monnier E; Petit, P
2012-01-01
We investigate the temporal spot evolution of the K-giant component in the RS CVn-type binary system $\\zeta$\\,Andromedae to establish its surface differential rotation. Doppler imaging is used to study three slightly overlapping spectroscopic datasets, obtained independently at three different observing sites. Each dataset covers one full stellar rotation with good phase coverage, and in total, results in a continuous coverage of almost three stellar rotations ($P_{\\rm rot}=$17.8\\,d). Therefore, these data are well suited for reconstructing surface temperature maps and studying temporal evolution in spot configurations. Surface differential rotation is measured by the means of cross-correlation of all the possible image pairs. The individual Doppler reconstructions well agree in the revealed spot pattern, recovering numerous low latitude spots with temperature contrasts of up to $\\approx$1000\\,K with respect to the unspotted photosphere, and also an asymmetric polar cap which is diminishing with time. Our det...
Relations between elliptic multiple zeta values and a special derivation algebra
We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths. (paper)