iResum: a new paradigm for resumming gravitational wave amplitudes

We introduce a new, resummed, analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections $f_{\ell m}$ of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform multipoles, both for a test-mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much closer to the corresponding "exact" functions (obtained solving numerically the Teukolsky equation) up to the light-ring, than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical/analytical agreement at the last-stable-orbit, and a well-controlled behavior up to the light-ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with Numerical Relativity (NR) data shows that the analytical/numerical fractional disagreement at merger, without NR-calibration of the EOB waveform, is generically reduced by iResum, from a $40\%$ of the usual approach to just a few percents. This suggests that EOBNR waveform models for coalescing BBHs may be improved using iResum amplitudes.Comment: 6 pages, 7 figures. Improved discussion for the comparable-mass cas

Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order

Using black hole perturbation theory and arbitrary-precision computer algebra, we obtain the post-Newtonian (pN) expansions of the linear-in-mass-ratio corrections to the spin-precession angle and tidal invariants for a particle in circular orbit around a Schwarzschild black hole. We extract coefficients up to 20pN order from numerical results that are calculated with an accuracy greater than 1 part in $10^{500}$. These results can be used to calibrate parameters in effective-one-body models of compact binaries, specifically the spin-orbit part of the effective Hamiltonian and the dynamically significant tidal part of the main radial potential of the effective metric. Our calculations are performed in a radiation gauge, which is known to be singular away from the particle. To overcome this irregularity, we define suitable Detweiler-Whiting singular and regular fields in this gauge, and we devise a rigorous mode-sum regularization method to compute the invariants constructed from the regular field

Raising and Lowering operators of spin-weighted spheroidal harmonics

In this paper we generalize the spin-raising and lowering operators of spin-weighted spherical harmonics to linear-in-$\gamma$ spin-weighted spheroidal harmonics where $\gamma$ is an additional parameter present in the second order ordinary differential equation governing these harmonics. One can then generalize these operators to higher powers in $\gamma$. Constructing these operators required calculating the $\ell$-, $s$- and $m$-raising and lowering operators (and various combinations of them) of spin-weighted spherical harmonics which have been calculated and shown explicitly in this paper

High-Low Pricing (HL) vs. Every Day Low Pricing (EDLP) Strategy: The Consequence of JC Penney’s Move from HL to EDLP

Retailers follow one of two pricing strategies – high-low (HL) and every-day low pricing (EDLP). The HL strategy is where the retailer will start with a higher price and give deep discounts in order to attract customers. On the other hand, retailers that follow the EDLP strategy keep prices very low and rarely giving price discounts. Not too long ago, JC Penney changed its strategy from HL to EDLP that had a very negative impact on its performance. The study hypothesizes that retailers who change their strategy (from HL to EDLP or EDLP to HL) will not be successful if they do not change their entire marketing mix, and if its customers do not accept the change in strategy. This study has two parts, each part testing five hypotheses. The first part tests five hypotheses investigating the effects of JC Penney’s change in strategy on its financial performance and finds support for all of the five hypotheses, i.e., JC Penney’s financial performance worsened because of its move from a HL strategy to an EDLP strategy. This study contends that a firm’s change in strategy is going to be successful only if its customers (consumers) accept the new strategy. The second part of the study tests five more hypotheses to find whether consumers accepted JC Penney’s change in strategy. The findings of the study support the hypotheses that consumers do not accept the change in strategy. This is because consumers perceive JC Penney to be a medium-price department store that sells homogeneous and heterogeneous shopping goods using a HL strategy, not EDLP strategy. It is very likely that JC Penney’s change in strategy was not very successful because consumers still perceive JC Penney as a department store with a HL strategy. For a change in strategy to be successful, customers of the firm have to accept the change in strategy

Product Line Extension: Does Upward Line Extension Hurt or Benefit Competitive Advantage? The Case of Honda’s Acura, Nissan’s Infiniti, and Toyota’s Lexus Brands

Caldieraro, Kao, and Cunha Jr. (2015) report that when a company extends its product line (and brand name) upwards to premium products, it hurts the company’s overall demand, market share, and competitive advantage. However, evidence from the auto industry contradicts their findings. The three most successful line extensions in the luxury segment in the auto industry are Honda’s Acura, Toyota’s Lexus, and Nissan’s Infiniti. Line extensions are categorized as follows: extensions where a firm extends its brand horizontally (similar quality) or vertically (upward or downward) using the current brand name, and line extensions, where a firm extends its product line horizontally or vertically (upward or downward) using a different brand name. This study investigates upward line extensions of three companies – Toyota (Lexus), Nissan (Infiniti), and Honda (Acura). The study proposes that if a company pursues upward or downward line extension strategy, it can gain a big competitive advantage in the marketplace only if the line extension is systematic and the marketing mix is consistent with its target market. The firm will have to use a different brand name, different product offerings, different pricing, different distribution, and different promotion. The following propositions are proposed for upward line extension: P1a: Upward line extension into a luxury segment will increase a firm’s revenue if the company picks and markets to a segment (different from its current segment) that is compatible to its new product (brand) offering. P1b: Upward line extension into a luxury segment will increase a firm’s profits if the company picks and markets to a segment (different from its current segment) that is compatible to its new product offering. The profile of the target market of Acura, Infiniti and Lexus were very different from the profile of the target market of Honda, Nissan and Toyota when the three auto manufacturers were manufacturing and marketing cars to the lower to middle price segment. The target market profile for Acura, Infiniti, and Lexus were the younger, higher income professionals, upwardly mobile, and higher educated people. P2a: A company’s revenue (market share) will increase if it extends its product line upwards to a luxury segment using a new brand name that is different from its current (parent) brand name. P2b: A company’s profits will increase if it extends its product line upwards to a luxury segment using a brand name that is different from its current (parent) brand name. Acura’s unit sales increased from 52,869 in its debut year of 1985 to 177,165 in 2015. Infiniti’s unit sales from 88,351 in 2000 (unit sales for its debut year, 1989 were not available) to 133,498 in 2015. Lexus’ unit sales increased from 16,302 in its debut year of 1989 to 344,601 in 2015. Acura’s, market share increased from 0 in 1985 to 8.4% in 2015. Infiniti’s market share increased from zero in 1998 to 6.3% in 2015. Finally, Lexus’ market share increased from zero in 1998 to16.4% in 2015. P3a: A company’s sales (market share) will increase if it extends its product line upwards to a luxury segment charging a higher price than its current brand. P3b: A company’s profitability will increase if it extends its product line upwards to a luxury segment charging a higher price than its current brand. Average price of Honda, Nissan and Toyota before they ventured into the luxury segment was around $20,000. The average price of their luxury fleet was around$50,000. P4a: A company’s market revenue (share) will increase if it extends its product line upwards to a luxury segment using a different distribution system than its current (parent) brand name. P4b: A company’s profits will increase if it extends its product line upwards to a luxury segment using a different distribution system than its current (parent) brand name. When Honda, Nissan and Toyota ventured into the luxury segment, they did not use the same distribution/dealerships that they used for their lower to mid-priced segment. Their new dealers were very exclusive to their Acura, Infiniti and Lexus brand of cars. P5a: A company’s market revenue (share) will increase if it extends its product line upwards to a luxury segment using a different promotion (advertising) than its current (parent) brand name. P5b: A company’s profits will increase if it extends its product line upwards to a luxury segment using a promotion (advertising) than its current (parent) brand name. Acura, Infiniti, & Lexus’ advertising were completely different than the advertising of the parent companies. The new ads targeted the wealthier and upwardly mobile segments while the original ads targeted the lower to mid-priced segments