358,210 research outputs found

    S-Lemma with Equality and Its Applications

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    Let f(x)=xTAx+2aTx+cf(x)=x^TAx+2a^Tx+c and h(x)=xTBx+2bTx+dh(x)=x^TBx+2b^Tx+d be two quadratic functions having symmetric matrices AA and BB. The S-lemma with equality asks when the unsolvability of the system f(x)<0,h(x)=0f(x)<0, h(x)=0 implies the existence of a real number μ\mu such that f(x)+μh(x)0, xRnf(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n. The problem is much harder than the inequality version which asserts that, under Slater condition, f(x)<0,h(x)0f(x)<0, h(x)\le0 is unsolvable if and only if f(x)+μh(x)0, xRnf(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n for some μ0\mu\ge0. In this paper, we show that the S-lemma with equality does not hold only when the matrix AA has exactly one negative eigenvalue and h(x)h(x) is a non-constant linear function (B=0,b0B=0, b\not=0). As an application, we can globally solve inf{f(x)h(x)=0}\inf\{f(x)\vert h(x)=0\} as well as the two-sided generalized trust region subproblem inf{f(x)lh(x)u}\inf\{f(x)\vert l\le h(x)\le u\} without any condition. Moreover, the convexity of the joint numerical range {(f(x),h1(x),,hp(x)): xRn}\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\} where ff is a (possibly non-convex) quadratic function and h1(x),,hp(x)h_1(x),\ldots,h_p(x) are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

    Quantitative recurrence properties in conformal iterated function systems

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    Let Λ\Lambda be a countable index set and S={ϕi:iΛ}S=\{\phi_i: i\in \Lambda\} be a conformal iterated function system on [0,1]d[0,1]^d satisfying the open set condition. Denote by JJ the attractor of SS. With each sequence (w1,w2,...)ΛN(w_1,w_2,...)\in \Lambda^{\mathbb{N}} is associated a unique point x[0,1]dx\in [0,1]^d. Let JJ^\ast denote the set of points of JJ with unique coding, and define the mapping T:JJT:J^\ast \to J^\ast by Tx=T(w1,w2,w3...)=(w2,w3,...)Tx= T (w_1,w_2, w_3...) = (w_2,w_3,...). In this paper, we consider the quantitative recurrence properties related to the dynamical system (J,T)(J^\ast, T). More precisely, let f:[0,1]dR+f:[0,1]^d\to \mathbb{R}^+ be a positive function and R(f):={xJ:Tnxx<eSnf(x), for infinitely many nN},R(f):=\{x\in J^\ast: |T^nx-x|<e^{-S_n f(x)}, \ {\text{for infinitely many}}\ n\in \mathbb{N}\}, where Snf(x)S_n f(x) is the nnth Birkhoff sum associated with the potential ff. In other words, R(f)R(f) contains the points xx whose orbits return close to xx infinitely often, with a rate varying along time. Under some conditions, we prove that the Hausdorff dimension of R(f)R(f) is given by inf{s0:P(T,s(f+logT))0}\inf\{s\ge 0: P(T, -s(f+\log |T'|))\le 0\}, where PP is the pressure function and TT' is the derivative of TT. We present some applications of the main theorem to Diophantine approximation.Comment: 25 page

    Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

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    We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling f2(ϕ)FμνFμνf^{2}(\phi)F_{\mu\nu}F^{\mu\nu} of the electromagnetic field to the inflaton field ϕ\phi. We consider the case where the coupling function f(ϕ)f(\phi) decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter ϵ\epsilon and inflaton energy density, ρEϵρinf\rho_{E}\sim \epsilon \rho_{\rm inf}. It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index nB=2n_{B}=2 for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below 1022G10^{-22}\,{\rm G}. It is worth emphasizing that since the effective electric charge of particles eeff=e/fe_{\rm eff}=e/f is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike faαf\propto a^{\alpha} and Ratra-type f=exp(βϕ/Mp)f=\exp(\beta\phi/M_{p}) coupling functions.Comment: 21 pages, 8 figure

    Exploring reuse spaces of web services and contents

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    Development of commercial web systems is laborious, lengthy and costly. This is partly due to the fact that the methods of their development can hardly cope with the complexity of provided services. Such services may need to be distributed and collaborative, require sophisticated software architecture, be rich in f rm, c ntent and interactivity, and have a wide range f p tentially casual users. T impr ve this situati n, the auth rs pr p se a reuse space analysis (RSA) appr ach t web devel pment. Our appr ach f cuses n capturing d main and devel pment experience f all system stakeh lders and subsequently using this experience in making inf rmed design and reuse decisi ns acr ss the devel pment life cycle. As a result we managed t seamlessly integrate design and reuse processes, and reaching the balance between the development cost, system function and its quality

    Quantum codes from a new construction of self-orthogonal algebraic geometry codes

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    [EN] We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results demonstrate that there is a lot more scope for constructing self-orthogonal AG codes than was previously known.G. McGuire was partially supported by Science Foundation Ireland Grant 13/IA/1914. The remainder authors were partially supported by the Spanish Government and the EU funding program FEDER, Grants MTM2015-65764-C3-2-P and PGC2018-096446-B-C22. F. Hernando and J. J. Moyano-Fernandez are also partially supported by Universitat Jaume I, Grant UJI-B2018-10.Hernando, F.; Mcguire, G.; Monserrat Delpalillo, FJ.; Moyano-Fernández, JJ. (2020). Quantum codes from a new construction of self-orthogonal algebraic geometry codes. Quantum Information Processing. 19(4):1-25. https://doi.org/10.1007/s11128-020-2616-8S125194Abhyankar, S.S.: Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74, 190–257 (1989)Abhyankar, S.S.: Algebraic Geometry for Scientists and Engineers. Mathematical Surveys and Monographs, American Mathematical Society, Providence (1990)Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection I: statement of the problem. IEEE Trans. Inf. Theory 46, 778–788 (2000)Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.: Quantum error-detection II: bounds. IEEE Trans. Inf. Theory 46, 789–800 (2000)Ashikhmin, A., Knill, E.: Non-binary quantum stabilizer codes. IEEE Trans. Inf. Theory 47, 3065–3072 (2001)Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997)Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. 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    Evaluation codes defined by finite families of plane valuations at infinity

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    We construct evaluation codes given by weight functions defined over polynomial rings in m a parts per thousand yen 2 indeterminates. These weight functions are determined by sets of m-1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedureSupported by Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1B2009-03. The authors thank to the referees for their valuable suggestions.Galindo Pastor, C.; Monserrat Delpalillo, FJ. (2014). Evaluation codes defined by finite families of plane valuations at infinity. Designs, Codes and Cryptography. 70(1-2):189-213. https://doi.org/10.1007/s10623-012-9738-7S189213701-2Abhyankar S.S.: Local uniformization on algebraic surfaces over ground field of characteristic p ≠ 0. Ann. Math. 63, 491–526 (1956)Abhyankar S.S.: On the valuations centered in a local domain. Am. J. 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Theory 53, 1919–1924 (2007)Decker W., Greuel G.M., Pfister G., Schöenemann H.: Singular 3.1.3, a computer algebra system for polynomial computations (2011) http://www.singular.uni-kl.de .Feng G.L., Rao T.R.N.: Decoding of algebraic geometric codes up to the designed minimum distance. IEEE Trans. Inf. Theory 39, 37–45 (1993)Feng G.L., Rao T.R.N.: A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Trans. Inf. Theory 40, 1003–1012 (1994)Feng G.L., Rao T.R.N.: Improved geometric Goppa codes, part I: basic theory. IEEE Trans. Inf. Theory 41, 1678–1693 (1995)Fujimoto M., Suzuki M.: Construction of affine plane curves with one place at infinity. Osaka J. Math. 39(4), 1005–1027 (2002)Galindo C.: Plane valuations and their completions. Commun. Algebra 23(6), 2107–2123 (1995)Galindo C., Monserrat F.: δ-sequences and evaluation codes defined by plane valuations at infinity. Proc. Lond. Math. 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    What are the competences in information system required by managers? Curriculum development for management and public administration degrees

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    [EN] This paper analyzes the competences required by executives to manage information system, and consequently, the competences that must define the information system subjects in non-technical degrees, degrees, such as Public Administration or Business Management. This work reviews the literature about business managers competences on Information Technologies (IT) and compares the theory with the traditional body of knowledge about information systems taught at business schools. By analyzing the executives function, their role in the information system management, and, above, all the importance of their decisions in the effective integration of IT in business processes, this work proposes specific development in seven knowledge areas that facilitate the acquisition of these types of executive competencesDevece Carañana, CA.; Peris-Ortiz, M.; Rueda Armengot, C. (2016). What are the competences in information system required by managers? Curriculum development for management and public administration degrees. Technology, Innovation and Education. 2(10):1-9. doi:10.1186/s40660-016-0016-2S19210Bassellier G, Benbasat I (2004) Business competence of IT professionals: conceptual development and influence on IT-business partnerships. MIS Q 28(4):673–694Bassellier G, Reich BH, Benbasat I (2001) Information technology competence of business managers: a definition and research model. J Manag Inf Syst 17(4):159–182Bassellier G, Benbasat I, Reich BH (2003) The influence of business managers’ IT competence on championing IT. Inf Syst Res 14(4):317–336Bettiol M, Di Maria E, Finotto V (2012) Marketing in SMEs: the role of entrepreneurial sensemaking. Int Entrep Manag J 8(2):223–248Boyatzis RE (1982) The competent manager a model for effective performance. Wiley, New YorkBoynton AC, Zmud RW, Jacobs GC (1994) The influence of IT management practice on IT use in large organizations. 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    On the form of the large deviation rate function for the empirical measures of weakly interacting systems

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    A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by relative entropy with respect to the common distribution. Large deviation principles for the empirical measures are also known to hold for broad classes of weakly interacting systems. When the interaction through the empirical measure corresponds to an absolutely continuous change of measure, the rate function can be expressed as relative entropy of a distribution with respect to the law of the McKean-Vlasov limit with measure-variable frozen at that distribution. We discuss situations, beyond that of tilted distributions, in which a large deviation principle holds with rate function in relative entropy form.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ540 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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