The Experts below are selected from a list of 40941 Experts worldwide ranked by ideXlab platform

Edwin Love - One of the best experts on this subject based on the ideXlab platform.

  • new product pricing strategy under customer asymmetric anchoring
    International Journal of Research in Marketing, 2011
    Co-Authors: Joo Heon Park, Douglas L Maclachlan, Edwin Love
    Abstract:

    Abstract Potential customers' willingness to pay (WTP) for a new product can be affected by their observing a posted price and this can be modeled in terms of an anchoring mechanism. A theoretical argument and Mathematical Proof are developed, showing that if customers use an asymmetric WTP anchoring mechanism, it will normally be optimal for firms to price higher than otherwise. Experimental evidence is provided supporting the notion that an asymmetric anchoring mechanism can be involved in purchase decisions.

  • new product pricing strategy under customer asymmetric anchoring
    Social Science Research Network, 2011
    Co-Authors: Joo Heon Park, Douglas L Maclachlan, Edwin Love
    Abstract:

    Potential customers’ willingness to pay (WTP) for a new product can be affected by their observing a posted price and this can be modeled in terms of an anchoring mechanism. A theoretical argument and Mathematical Proof is developed, showing that if customers use an asymmetric WTP anchoring mechanism, it will normally be optimal for firms to price higher than otherwise. Experimental evidence is provided supporting the notion that an asymmetric anchoring mechanism can be involved in purchase decisions.

Stanislav Smirnov - One of the best experts on this subject based on the ideXlab platform.

  • Universality in the 2D Ising model and conformal invariance of fermionic observables
    Inventiones mathematicae, 2012
    Co-Authors: Dmitry Chelkak, Stanislav Smirnov
    Abstract:

    It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no Mathematical Proof has ever been given, and even physics arguments support (a priori weaker) Möbius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.

  • the connective constant of the honeycomb lattice equals sqrt 2 sqrt2
    Annals of Mathematics, 2012
    Co-Authors: Hugo Duminilcopin, Stanislav Smirnov
    Abstract:

    We provide the first Mathematical Proof that the connective constant of the hexagonal lattice is equal to $\sqrt{2+\sqrt 2}$. This value has been derived non rigorously by B. Nienhuis in 1982, using Coulomb gas approach from theoretical physics. Our Proof uses a parafermionic observable for the self avoiding walk, which satisfies a half of the discrete Cauchy-Riemann relations. Establishing the other half of the relations (which conjecturally holds in the scaling limit) would also imply convergence of the self-avoiding walk to SLE(8/3).

  • universality in the 2d ising model and conformal invariance of fermionic observables
    arXiv: Mathematical Physics, 2009
    Co-Authors: Stanislav Smirnov, Dmitry Chelkak
    Abstract:

    It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no Mathematical Proof of universality and conformal invariance has ever been given, and even physics arguments support (a priori weaker) M\"obius invariance. We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs. We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.

Joo Heon Park - One of the best experts on this subject based on the ideXlab platform.

  • new product pricing strategy under customer asymmetric anchoring
    International Journal of Research in Marketing, 2011
    Co-Authors: Joo Heon Park, Douglas L Maclachlan, Edwin Love
    Abstract:

    Abstract Potential customers' willingness to pay (WTP) for a new product can be affected by their observing a posted price and this can be modeled in terms of an anchoring mechanism. A theoretical argument and Mathematical Proof are developed, showing that if customers use an asymmetric WTP anchoring mechanism, it will normally be optimal for firms to price higher than otherwise. Experimental evidence is provided supporting the notion that an asymmetric anchoring mechanism can be involved in purchase decisions.

  • new product pricing strategy under customer asymmetric anchoring
    Social Science Research Network, 2011
    Co-Authors: Joo Heon Park, Douglas L Maclachlan, Edwin Love
    Abstract:

    Potential customers’ willingness to pay (WTP) for a new product can be affected by their observing a posted price and this can be modeled in terms of an anchoring mechanism. A theoretical argument and Mathematical Proof is developed, showing that if customers use an asymmetric WTP anchoring mechanism, it will normally be optimal for firms to price higher than otherwise. Experimental evidence is provided supporting the notion that an asymmetric anchoring mechanism can be involved in purchase decisions.

Denis J. Evans - One of the best experts on this subject based on the ideXlab platform.

  • a Mathematical Proof of the zeroth law of thermodynamics and the nonlinear fourier law for heat flow
    Journal of Chemical Physics, 2012
    Co-Authors: Denis J. Evans, Stephen R. Williams, Lamberto Rondoni
    Abstract:

    What is now known as the zeroth “law” of thermodynamics was first stated by Maxwell in 1872: at equilibrium, “Bodies whose temperatures are equal to that of the same body have themselves equal temperatures.” In the present paper, we give an explicit Mathematical Proof of the zeroth “law” for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will in the course of time (subject to some simple conditions) relax to isothermal equilibrium where all parts of the system will have the same temperature in accord with the zeroth “law.” As part of the derivation we give for the first time, an exact expression for the far from equilibrium thermal conductivity. We also give a general Proof that the infinite-time integral, of transient and equilibrium autocorrelation functions of fluxes of non-conserved quantities vanish. This constitutes a Proof of what was called the “heat death of the Universe” as was widely discussed in the latter half of the 19th century.

  • A simple Mathematical Proof of Boltzmann's equal a priori probability hypothesis
    arXiv: Statistical Mechanics, 2009
    Co-Authors: Denis J. Evans, Debra J. Searles, Stephen R. Williams
    Abstract:

    Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. We show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.

  • A Simple Mathematical Proof of Boltzmann's Equal a priori Probability Hypothesis
    2009
    Co-Authors: Denis J. Evans, Debra J. Searles, Stephen R. Williams
    Abstract:

    Using the Fluctuation Theorem (FT), we give a first-principles derivation of Boltzmann’s postulate of equal a priori probability in phase space for the microcanonical ensemble. Using a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble. Most textbook discussions of the equilibrium microcanonical phase space distribution functions rely on Boltzmann’s postulate of equal a priori probability in phase space[2-5]. Arguments are then given for various microscopic expressions for the various macroscopic thermodynamic quantities. No attempt is made to prove the Boltzmann’s postulate. A second approach by-passes the microcanonical ensemble [1-3] and seeks to propose a microscopic definition for the entropy in the canonical ensemble and then attempts to show that the standard canonical distribution function can be obtained by maximising the entropy subject to the constraints that the distribution function should be normalized and that the average energy is constant. The choice of the second constraint is completely subjective due to the fact that at equilibrium, the average of every phase function is fixed. Why single out the energy? The relaxation of systems to equilibrium is also fraught with difficulties. The only reasonably general approach to this problem is summarized in the Boltzmann H-theorem. Beginning with the definition of the H-function, Boltzmann proved that the Boltzmann equation for the time evolution of the single particle probability density in an ideal gas, implies that in spatially uniform gases the H-function cannot increase [2, 4]. There are at least four problems with this. Firstly the Boltzmann equation is only valid for an ideal gas. Secondly and more problematically, unlike Newton’s equations the Boltzmann equation itself is not time reversal symmetric so there is no surprise that one can prove relaxation. Thirdly the Boltzmann H-theorem only allows a monotonic relaxation to equilibrium. Everyday experience of the behaviour of dense fluids and solids shows that

Stephen R. Williams - One of the best experts on this subject based on the ideXlab platform.

  • a Mathematical Proof of the zeroth law of thermodynamics and the nonlinear fourier law for heat flow
    Journal of Chemical Physics, 2012
    Co-Authors: Denis J. Evans, Stephen R. Williams, Lamberto Rondoni
    Abstract:

    What is now known as the zeroth “law” of thermodynamics was first stated by Maxwell in 1872: at equilibrium, “Bodies whose temperatures are equal to that of the same body have themselves equal temperatures.” In the present paper, we give an explicit Mathematical Proof of the zeroth “law” for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will in the course of time (subject to some simple conditions) relax to isothermal equilibrium where all parts of the system will have the same temperature in accord with the zeroth “law.” As part of the derivation we give for the first time, an exact expression for the far from equilibrium thermal conductivity. We also give a general Proof that the infinite-time integral, of transient and equilibrium autocorrelation functions of fluxes of non-conserved quantities vanish. This constitutes a Proof of what was called the “heat death of the Universe” as was widely discussed in the latter half of the 19th century.

  • A simple Mathematical Proof of Boltzmann's equal a priori probability hypothesis
    arXiv: Statistical Mechanics, 2009
    Co-Authors: Denis J. Evans, Debra J. Searles, Stephen R. Williams
    Abstract:

    Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. We show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.

  • A Simple Mathematical Proof of Boltzmann's Equal a priori Probability Hypothesis
    2009
    Co-Authors: Denis J. Evans, Debra J. Searles, Stephen R. Williams
    Abstract:

    Using the Fluctuation Theorem (FT), we give a first-principles derivation of Boltzmann’s postulate of equal a priori probability in phase space for the microcanonical ensemble. Using a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble. Most textbook discussions of the equilibrium microcanonical phase space distribution functions rely on Boltzmann’s postulate of equal a priori probability in phase space[2-5]. Arguments are then given for various microscopic expressions for the various macroscopic thermodynamic quantities. No attempt is made to prove the Boltzmann’s postulate. A second approach by-passes the microcanonical ensemble [1-3] and seeks to propose a microscopic definition for the entropy in the canonical ensemble and then attempts to show that the standard canonical distribution function can be obtained by maximising the entropy subject to the constraints that the distribution function should be normalized and that the average energy is constant. The choice of the second constraint is completely subjective due to the fact that at equilibrium, the average of every phase function is fixed. Why single out the energy? The relaxation of systems to equilibrium is also fraught with difficulties. The only reasonably general approach to this problem is summarized in the Boltzmann H-theorem. Beginning with the definition of the H-function, Boltzmann proved that the Boltzmann equation for the time evolution of the single particle probability density in an ideal gas, implies that in spatially uniform gases the H-function cannot increase [2, 4]. There are at least four problems with this. Firstly the Boltzmann equation is only valid for an ideal gas. Secondly and more problematically, unlike Newton’s equations the Boltzmann equation itself is not time reversal symmetric so there is no surprise that one can prove relaxation. Thirdly the Boltzmann H-theorem only allows a monotonic relaxation to equilibrium. Everyday experience of the behaviour of dense fluids and solids shows that