The Effect of Economic and Relational Direct Marketing Communication on Buying Behavior in B2B Markets

Business to Business (B2B) firms spend significant resources managing close relationships with their customers, yet there is limited understanding of how the customers perceive the relationship based on the customer management efforts initiated by the firm. Specifically, studies on how firms communicate different values to B2B customers and how they perceive the values the firm offers by consistently evaluating the direct marketing communication which ultimately affect their buying behaviors have been largely overlooked. Typically, the direct marketing communication efforts are geared towards explicitly featuring economic values or relational values. To implement an effective communication strategy catering to customers’ preferences, firms should understand how these organizational marketing communications dynamically influence the perceived importance of different values offered by the firm. Therefore, using data from a Fortune 500 B2B service firm and employing a content analysis and a robust econometric model, we find that (i) the effect of economic and relational marketing communication on customer purchase behavior vary by customers and change overtime (ii) the latent stock variable of direct marketing communication affect the customer purchase behaviors and (iii) the evolution of customers’ perceived importance can be recovered using the transaction data. Overall, we provide a marketing resource reallocation strategy that enables marketers to customize marketing communication and improve a firm’s financial performance

Sharp universal rate for stable blow-up of corotational wave maps

We consider the energy-critical (corotational) 1-equivariant wave maps into the two-sphere. By the seminal work [53] of Rapha\"el and Rodnianski, there is an open set of initial data whose forward-in-time development blows up in finite time with the blow-up rate $\lambda(t)=(T-t)e^{-\sqrt{|\log(T-t)|}+O(1)}$. In this paper, we show that this $e^{O(1)}$-factor in fact converges to the universal constant $2e^{-1}$, and hence these solutions contract at the universal rate $\lambda(t)=2e^{-1}(T-t)e^{-\sqrt{|\log(T-t)|}}(1+o_{t\to T}(1))$. Our proof is inspired by recent works on type-II blow-up dynamics for parabolic equations. The key improvement is in the construction of an explicit invariant subspace decomposition for the linearized operator perturbed by the scaling generator in the dispersive case, from which we obtain a more precise ODE system determining $\lambda(t)$.Comment: 66 page

Cross Layer Based Cooperative Communication Protocol for Improving Network Performance in Underwater Sensor Networks

For underwater sensor networks (USNs), cooperative communications have been introduced to improve network performance with the help of relay nodes. The previous cooperative communications select the best relay node on a hop-by-hop basis. Therefore, they have limitations in improving performance. In order to get better performance, a cooperative communication protocol based on  the cross layer is proposed in this paper. The proposed protocol uses the information provided by a routing protocol at the network layer for the erroneous data packet delivery. It selects one with the minimum routing cost among relay candidate nodes. The routing protocol in the selected relay node provides the MAC layer with the address of the next hop node on the path to the sink node. Then, the MAC layer in the selected relay node forwards the erroneous data packet to the next hop node rather than a receiver node. Performance studies are carried out through simulation. Simulation results show that the proposed protocol has about 21.8% lower average delay and about 14.4% lower average number of nodes passed than the previous protocol, regardless of the maximum transmission range

Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schr\"odinger equation

We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariance symmetry. Among others, (CSS) has a static solution $Q$ and pseudoconformal symmetry. We study the conditional stability of pseudoconformal blow-up solutions $u$ such that $$u(t,r)-\frac{e^{i\gamma_{\ast}}}{T-t}Q\Big(\frac{r}{T-t}\Big)\to u^{\ast}\quad\text{as }t\to T^{-}.$$ When the equivariance index $m\geq1$, we construct a codimension one blow-up manifold, i.e. a codimension one set of initial data yielding pseudoconformal blow-up solutions. Moreover, when $m\geq3$, we establish the Lipschitz regularity of the constructed blow-up manifold (the conditional stability). This is a forward construction of blow-up solutions, as opposed to authors' previous work [25] (arXiv:1909.01055), which is a backward construction of blow-up solutions with prescribed asymptotic profiles. In view of the instability result of [25], the codimension one condition is expected to be optimal. We perform the modulation analysis with a robust energy method developed by Merle, Rapha\"el, Rodnianski, and others. One of our crucial inputs is a remarkable conjugation identity, which enables the method of supersymmetric conjugates as like Schr\"odinger maps and wave maps. It suggests how we define adapted derivatives. More interestingly, it shows a deep connection with the Schr\"odinger maps at the linearized level and allows us to find a repulsivity structure. The nonlocal nonlinearities become obstacles in many places. For instance, we need to capture non-perturbative contributions from the nonlocal nonlinearities and absorb them into phase corrections in a spirit of [25]. More importantly, we need to take a nonlinear pathway to construct modified profiles. This is suggested from [25] and becomes available thanks to the self-duality. From this, we also recognize the stable modes and unstable modes.Comment: 95 page

Low regularity well-posedness for generalized Benjamin–Ono equations on the circle

New low regularity well-posedness results for the generalized Benjamin-Ono equations with quartic or higher nonlinearity and periodic boundary conditions are shown. We use the short-time Fourier transform restriction method and modified energies to overcome the derivative loss. Previously, Molinet–Ribaud established local well-posedness in $H^1(\mathbb{T},\mathbb{R})$ via gauge transforms. We show local existence and a priori estimates in $H^s(\mathbb{T},\mathbb{R}),$ $s>1/2$, and local well-posedness in $H^s(\mathbb{T},\mathbb{R})$, $s\ge3/4$ without using gauge transforms. In case of quartic nonlinearity we prove global existence of solutions conditional upon small initial data

Low regularity well-posedness for generalized Benjamin-Ono equations on the circle

New low regularity well-posedness results for the generalized Benjamin-Ono equations with quartic or higher nonlinearity and periodic boundary conditions are shown. We use the short-time Fourier transform restriction method and modified energies to overcome the derivative loss. Previously, Molinet--Ribaud established local well-posedness in $H^{1}(\mathbb{T},\mathbb{R})$ via gauge transforms. We show local existence and a priori estimates in $H^{s}(\mathbb{T},\mathbb{R})$, $s>1/2$, and local well-posedness in $H^{s}(\mathbb{T},\mathbb{R})$, $s\geq3/4$ without using gauge transforms. In case of quartic nonlinearity we prove global existence of solutions conditional upon small initial data.Comment: 46 pages, accepted to JHD

On classification of global dynamics for energy-critical equivariant harmonic map heat flows and radial nonlinear heat equation

We consider the global dynamics of finite energy solutions to energy-critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the maximal time of existence. Our main result for (HMHF) gives a complete classification of their dynamics for equivariance indices $D\geq3$; (i) they exist globally in time, (ii) the number of bubbles and signs are determined by the energy class of the initial data, and (iii) the scales of bubbles are asymptotically given by a universal sequence of rates up to scaling symmetry. In parallel, we also obtain a complete classification of $\dot{H}^{1}$-bounded radial solutions to (NLH) in dimensions $N\geq7$, building upon soliton resolution for such solutions. To our knowledge, this provides the first rigorous classification of bubble tree dynamics within symmetry. We introduce a new approach based on the energy method that does not rely on maximum principle. The key ingredient of the proof is a monotonicity estimate near any bubble tree configurations, which in turn requires a delicate construction of modified multi-bubble profiles also.Comment: 44 page