Disjoint NP-pairs from propositional proof systems

For a proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P. We exhibit structural properties of proof systems which make the previously defined canonical NP-pairs of these proof systems hard or complete for DNPP(P). Moreover we demonstrate that non-equivalent proof systems can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for DNPP(P) and the reductions between the canonical pairs exist

A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions

[EN] In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.The research of the authors was partially supported by MEC and FEDER Project MTM2013-43540-P and the work of of Bonet by the Grant GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. DEC-2013/10/A/ST1/00091.Bonet Solves, JA.; Domanski, P. (2017). A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions. Complex Analysis and Operator Theory. 11(1):161-174. https://doi.org/10.1007/s11785-016-0589-5S161174111Belitskii, G., Lyubich, Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81–97 (1998)Belitskii, G., Lyubich, Y.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135–141 (1999)Belitskii, G., Tkachenko, V.: One-Dimensional Functional Equations. Springer, Basel (2003)Belitskii, G., Tkachenko, V.: Functional equations in real analytic functions. Studia Math. 143, 153–174 (2000)Bonet, J., Domański, P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69–83 (2011)Bonet, J., Domański, P.: Hypercyclic composition operators on spaces of real analytic fucntions. Math. Proc. Cambridge Phil. Soc. 153, 489–503 (2012)Bonet, J., Domański, P.: Abel’s functional equation and eigenvalues of composition operators on spaces of real analytic functions. Integr. Equ. Oper. Theor. 81, 455–482 (2015). doi: 10.1007/s00020-014-2175-4Cartan, H.: Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. France 85, 77–99 (1957)Domański, P.: Notes on real analytic functions and classical operators, Topics in Complex Analysis and Operator Theory (Winter School in Complex Analysis and Operator Theory, Valencia, February 2010), Contemporary Math. 561 (2012) 3–47. Amer. Math. Soc, Providence (2012)Domański, P., Goliński, M., Langenbruch, M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Mat. 103, 209–216 (2012)Domański, P., Langenbruch, M.: Composition operators on spaces of real analytic functions. Math. Nachr. 254–255, 68–86 (2003)Domański, P., Langenbruch, M.: Coherent analytic sets and composition of real analytic functions. J. reine angew. Math. 582, 41–59 (2005)Domański, P., Langenbruch, M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636–646 (2006)Domański, P., Vogt, D.: The space of real analytic functions has no basis. Studia Math. 142, 187–200 (2000)Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North Holland, Amsterdam (1986)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon, Oxford (1997)Smajdor, W.: On the existence and uniqueness of analytic solutions of the functional equation $$\varphi (z)=h(z,\varphi [f(z)])$$ φ ( z ) = h ( z , φ [ f ( z ) ] ) . Ann. Polon. Math. 19, 37–45 (1967

The Deduction Theorem for Strong Propositional Proof Systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NPUnknown control sequence '\mathsf' -pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NPUnknown control sequence '\mathsf' -pairs

The deduction theorem for strong propositional proof systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs

STM and ab initio study of holmium nanowires on a Ge(111) Surface

A nanorod structure has been observed on the Ho/Ge(111) surface using scanning tunneling microscopy (STM). The rods do not require patterning of the surface or defects such as step edges in order to grow as is the case for nanorods on Si(111). At low holmium coverage the nanorods exist as isolated nanostructures while at high coverage they form a periodic 5x1 structure. We propose a structural model for the 5x1 unit cell and show using an ab initio calculation that the STM profile of our model structure compares favorably to that obtained experimentally for both filled and empty states sampling. The calculated local density of states shows that the nanorod is metallic in character.Comment: 4 pages, 12 figures (inc. subfigures). Presented at the the APS March meeting, Baltimore MD, 200

Spectra of weighted algebras of holomorphic functions

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.Comment: 25 pages Corrected typo

Kinetics of Particles Adsorption Processes Driven by Diffusion

The kinetics of the deposition of colloidal particles onto a solid surface is analytically studied. We take into account both the diffusion of particles from the bulk as well as the geometrical aspects of the layer of adsorbed particles. We derive the first kinetic equation for the coverage of the surface (a generalized Langmuir equation) whose predictions are in agreement with recent simulation results where diffusion of particles from the bulk is explicitly considered.Comment: 4 page

Particle-Based Mesoscale Hydrodynamic Techniques

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC -- DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl

Holography and Variable Cosmological Constant

An effective local quantum field theory with UV and IR cutoffs correlated in accordance with holographic entropy bounds is capable of rendering the cosmological constant (CC) stable against quantum corrections. By setting an IR cutoff to length scales relevant to cosmology, one easily obtains the currently observed rho_Lambda ~ 10^{-47} GeV^4, thus alleviating the CC problem. It is argued that scaling behavior of the CC in these scenarios implies an interaction of the CC with matter sector or a time-dependent gravitational constant, to accommodate the observational data.Comment: 7 pages, final version accepted by PR

Histogram Reweighting Method for Dynamic Properties

The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from Molecular Dynamics simulations. The theory presented here is based on the fact that the correlation functions in systems in thermodynamic equilibrium are averages over initial conditions of functions of the trajectory of the system in phase-space, the latter depending on the volume, the total number of particles and the classical Hamiltonian. Thus, the well-known histogram reweighting method can almost straightforwardly be applied to reconstruct the probability distribution of initial states at different thermodynamic conditions, without extra computational effort. Correlation functions and transport coefficients are obtained with this method from few simulation data sets.Comment: 4 pages, 3 figure