Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Finite Intersection Property and Dynamical Compactness

[EN] Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800-6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the -limit and the -limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics.Wen Huang and Sergii Kolyada acknowledge the hospitality of the School of Mathematical Sciences of the Fudan University, Shanghai. Sergii Kolyada also acknowledges the hospitality of the Max-Planck-Institute fur Mathematik (MPIM) in Bonn, the Departament de Matematica Aplicada of the Universitat Politecnica de Valencia, the partial support of Project MTM2013-47093-P, and the Department of Mathematics of the Chinese University of Hong Kong. We thank the referees for careful reading and constructive comments that have resulted in substantial improvements to this paper. Wen Huang was supported by NNSF of China (11225105, 11431012); Alfred Peris was supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by GVA, Project PROMETEOII/2013/013; and Guohua Zhang was supported by NNSF of China (11671094).Huang, W.; Khilko, D.; Kolyada, S.; Peris Manguillot, A.; Zhang, G. (2018). Finite Intersection Property and Dynamical Compactness. Journal of Dynamics and Differential Equations. 30(3):1221-1245. https://doi.org/10.1007/s10884-017-9600-8S12211245303Akin, E.: Recurrence in topological dynamics. The University Series in Mathematics, Plenum Press, New York, Furstenberg families and Ellis actions (1997)Akin, E., Auslander, J., Berg, K.: When is a transitive map chaotic Convergence in ergodic theory and probability (Columbus, OH, 1993), Ohio State Univ. Math. Res. Inst. Publ., vol. 5, pp. 25–40, de Gruyter, Berlin (1996)Akin, E., Glasner, E.: Residual properties and almost equicontinuity. J. Anal. Math. 84, 243–286 (2001)Akin, E., Kolyada, S.: Li–Yorke sensitivity. Nonlinearity 16(4), 1421–1433 (2003)Auslander, J.: Minimal flows and their extensions. North-Holland Mathematics Studies, vol. 153. North-Holland Publishing Co., Amsterdam, Notas de Matemática [Mathematical Notes], 122 (1988)Auslander, J., Yorke, J.A.: Interval maps, factors of maps, and chaos. Tôhoku Math. J. (2) 32(2), 177–188 (1980)Bayart, F., Matheron, É.: Dynamics of Linear Operators, Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167(1), 94–112 (1999)Blanchard, F., Huang, W.: Entropy sets, weakly mixing sets and entropy capacity. Discrete Contin. Dyn. Syst. 20(2), 275–311 (2008)de la Rosa, M., Read, C.: A hypercyclic operator whose direct sum $$T\oplus T$$ T ⊕ T is not hypercyclic. J. Oper. Theory 61(2), 369–380 (2009)Dowker, Y.N., Friedlander, F.G.: On limit sets in dynamical systems. Proc. Lond. Math. Soc. (3) 4, 168–176 (1954)Downarowicz, T.: Survey of odometers and Toeplitz flows. Algebraic and topological dynamics. Contemp. Math., vol. 385, Amer. Math. Soc., Providence, RI, pp. 7–37 (2005)Edwards, R.E.: Functional analysis. Dover Publications Inc, New York. Theory and applications. Corrected reprint of the 1965 original (1995)Furstenberg, H.: Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation. Math. Syst. Theory 1, 1–49 (1967)Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory. M. B. Porter Lectures. Princeton University Press, Princeton, NJ (1981)Furstenberg, H., Weiss, B.: Topological dynamics and combinatorial number theory. J. Anal. Math. 34(1978), 61–85 (1979)Glasner, E., Weiss, B.: Sensitive dependence on initial conditions. Nonlinearity 6(6), 1067–1075 (1993)Grosse-Erdmann, K.-G., Peris, A.: Weakly mixing operators on topological vector spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, vol. 104, no. 2, pp. 413–426 (2010)Grosse-Erdmann, K.-G., Peris-Manguillot, A.: Linear chaos, Universitext. Springer, London (2011)Guckenheimer, J.: Sensitive dependence to initial conditions for one-dimensional maps. Commun. Math. Phys. 70(2), 133–160 (1979)Halpern, J.D.: Bases in vector spaces and the axiom of choice. Proc. Am. Math. Soc. 17, 670–673 (1966)He, W.H., Zhou, Z.L.: A topologically mixing system whose measure center is a singleton. Acta Math. Sin. (Chin. Ser.) 45(5), 929–934 (2002)Huang, W., Khilko, D., Kolyada, S., Zhang, G.: Dynamical compactness and sensitivity. J. Differ. Equ. 260(9), 6800–6827 (2016)Huang, W., Kolyada, S., Zhang, G.: Analogues of Auslander–Yorke theorems for multi-sensitivity. Ergod. Theory Dyn. Syst. 22, 1–15 (2016). doi: 10.1017/etds.2016.48Huang, W., Ye, X.: Devaney’s chaos or 2-scattering implies Li–Yorke’s chaos. Topol. Appl. 117(3), 259–272 (2002)Kelley, J.L.: General topology. Graduate Texts in Mathematics, vol. 27. Springer, New York. Reprint of the 1955 edition [Van Nostrand, Toronto, ON] (1975)Kolyada, S., Snoha, L., Trofimchuk, S.: Noninvertible minimal maps. Fund. Math. 168(2), 141–163 (2001)Li, J.: Transitive points via Furstenberg family. Topol. Appl. 158(16), 2221–2231 (2011)Li, J., Ye, X.D.: Recent development of chaos theory in topological dynamics. Acta Math. Sin. (Engl. Ser.) 32(1), 83–114 (2016)Liu, H., Liao, L., Wang, L.: Thickly syndetical sensitivity of topological dynamical system. Discrete Dyn. Nat. Soc. (2014). Art. ID 583431, 4Moothathu, T.K.S.: Stronger forms of sensitivity for dynamical systems. Nonlinearity 20(9), 2115–2126 (2007)Mycielski, J.: Independent sets in topological algebras. Fund. Math. 55, 139–147 (1964)Oprocha, P., Zhang, G.: On local aspects of topological weak mixing in dimension one and beyond. Stud. Math. 202(3), 261–288 (2011)Oprocha, P., Zhang, G.: On local aspects of topological weak mixing, sequence entropy and chaos. Ergod. Theory Dyn. Syst. 34(5), 1615–1639 (2014)Petersen, K.E.: Disjointness and weak mixing of minimal sets. Proc. Am. Math. Soc. 24, 278–280 (1970)Read, C.J.: The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators. Isr. J. Math. 63(1), 1–40 (1988)Ruelle, D.: Dynamical systems with turbulent behavior. In: Mathematical problems in theoretical physics (Proc. Internat. Conf., Univ. Rome, Rome, 1977), Lecture Notes in Phys., vol. 80, pp. 341–360. Springer, Berlin (1978)Šarkovskiĭ, A.N.: Continuous mapping on the limit points of an iteration sequence. Ukrain. Mat. Ž. 18(5), 127–130 (1966)Weiss, B.: A survey of generic dynamics. Descriptive set theory and dynamical systems (Marseille-Luminy, 1996), London Math. Soc. Lecture Note Ser., vol. 277, pp. 273–291. Cambridge Univ. Press, Cambridge (2000

Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV

A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7 TeV is presented. The data were collected at the LHC, with the CMS detector, and correspond to an integrated luminosity of 4.6 inverse femtobarns. No significant excess is observed above the background expectation, and upper limits are set on the Higgs boson production cross section. The presence of the standard model Higgs boson with a mass in the 270-440 GeV range is excluded at 95% confidence level.Comment: Submitted to JHE

Combined search for the quarks of a sequential fourth generation

Results are presented from a search for a fourth generation of quarks produced singly or in pairs in a data set corresponding to an integrated luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in 2011. A novel strategy has been developed for a combined search for quarks of the up and down type in decay channels with at least one isolated muon or electron. Limits on the mass of the fourth-generation quarks and the relevant Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a simple extension of the standard model with a sequential fourth generation of fermions. The existence of mass-degenerate fourth-generation quarks with masses below 685 GeV is excluded at 95% confidence level for minimal off-diagonal mixing between the third- and the fourth-generation quarks. With a mass difference of 25 GeV between the quark masses, the obtained limit on the masses of the fourth-generation quarks shifts by about +/- 20 GeV. These results significantly reduce the allowed parameter space for a fourth generation of fermions.Comment: Replaced with published version. Added journal reference and DO

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV

The production of b jets in association with a Z/gamma* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7 TeV and recorded by the CMS detector. The inclusive cross section for Z/gamma* + b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 inverse femtobarns. The Z/gamma* + b-jet cross section with Z/gamma* to ll (where ll = ee or mu mu) for events with the invariant mass 60 < M(ll) < 120 GeV, at least one b jet at the hadron level with pT > 25 GeV and abs(eta) < 2.1, and a separation between the leptons and the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.) +(0.25)/-(0.55) (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with the predictions made by the MadGraph event generator with the parton shower and the hadronisation performed by PYTHIA.Comment: Submitted to the Journal of High Energy Physic

Measurement of the t t-bar production cross section in the dilepton channel in pp collisions at sqrt(s) = 7 TeV

The t t-bar production cross section (sigma[t t-bar]) is measured in proton-proton collisions at sqrt(s) = 7 TeV in data collected by the CMS experiment, corresponding to an integrated luminosity of 2.3 inverse femtobarns. The measurement is performed in events with two leptons (electrons or muons) in the final state, at least two jets identified as jets originating from b quarks, and the presence of an imbalance in transverse momentum. The measured value of sigma[t t-bar] for a top-quark mass of 172.5 GeV is 161.9 +/- 2.5 (stat.) +5.1/-5.0 (syst.) +/- 3.6(lumi.) pb, consistent with the prediction of the standard model.Comment: Replaced with published version. Included journal reference and DO

Search for New Physics with Jets and Missing Transverse Momentum in pp collisions at sqrt(s) = 7 TeV

A search for new physics is presented based on an event signature of at least three jets accompanied by large missing transverse momentum, using a data sample corresponding to an integrated luminosity of 36 inverse picobarns collected in proton--proton collisions at sqrt(s)=7 TeV with the CMS detector at the LHC. No excess of events is observed above the expected standard model backgrounds, which are all estimated from the data. Exclusion limits are presented for the constrained minimal supersymmetric extension of the standard model. Cross section limits are also presented using simplified models with new particles decaying to an undetected particle and one or two jets

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Search for anomalous t t-bar production in the highly-boosted all-hadronic final state

A search is presented for a massive particle, generically referred to as a Z', decaying into a t t-bar pair. The search focuses on Z' resonances that are sufficiently massive to produce highly Lorentz-boosted top quarks, which yield collimated decay products that are partially or fully merged into single jets. The analysis uses new methods to analyze jet substructure, providing suppression of the non-top multijet backgrounds. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 5 inverse femtobarns. Upper limits in the range of 1 pb are set on the product of the production cross section and branching fraction for a topcolor Z' modeled for several widths, as well as for a Randall--Sundrum Kaluza--Klein gluon. In addition, the results constrain any enhancement in t t-bar production beyond expectations of the standard model for t t-bar invariant masses larger than 1 TeV.Comment: Submitted to the Journal of High Energy Physics; this version includes a minor typo correction that will be submitted as an erratu