Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x¨=f(x,t)\ddot{x}=f(x,t)

In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\'e II, Sitnikov and Hill-Schr\"odinger equation. We emphasize in Painlev\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.Comment: 15 pages without figures (19 pages and 6 figures in the published version

Analytic Non-integrability in String Theory

Using analytic techniques developed for Hamiltonian dynamical systems we show that a certain classical string configurations in AdS_5 x X_5 with X_5 in a large class of Einstein spaces, is non-integrable. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles in the manifold X_5.Comment: 14 page

The Market Orientation and Customer Orientation Continuum: A Literature Review for Service Marketing

The purpose of this study is to disclose a drawback in the literature of the constructs of market orientation (MO) and customer orientation (CO). This flaw is indeed the lack of a systematic literature review of both concepts. This literature review should serve not only to collect all the literature regarding both constructs, but also to identify and classify the different relationships between MO and CO suggested by academics. The methodology is therefore divided in two, a first stage where a systematic literature review is conducted and a second stage where each study would be classified according to their positioning relative to the MO-CO relationship. The preliminary results suggest that there are three research streams regarding the MO-CO relationship: (1) MO and CO are analogous, (2) CO is part of MO, and (3) MO and CO are independent constructs. This conclusion must still be confirmed with the systematic literature review and used to catalogue the eventually collected studies. A key contribution of this research is to help academics to have access to the main literature about MO and CO and provide them with an adequate reference to frame their studies in one of the three research streams that have been identified. A potential contribution for professionals is the synthesis of several theories regarding MO and CO that could facilitate their implementation in companies and eventually improve their performance

New Perspective on Customer Orientation of Service Employees: A Conceptual Framework

Customer orientation of service employees (COSE) refers to the capacity and skills of employees to (1) identify, understand and satisfy their clients’ needs, and (2) act to that end. The COSE model has been used extensively to assess customer orientation of service employees within different settings. However, minimal modifications from the original have been presented so far, and the proposed settings were unrelated to highly relational services such as private banking (PB). PB is defined as the services specifically designed to satisfy the financial needs of high net worth individuals (HNWI); they are usually delivered by only one contact person – the private banker. Thus, PB is based on a personal and long-lasting relationship between the private banker and the client. Drawing on the literature regarding customer orientation and PB, trust, loyalty and word of mouth are identified as the potential consequences of COSE, improving on previous models. These new propositions are accompanied by a conceptual framework of COSE that is able to address the PB particularities by considering some moderating variables that are inherent to the PB service (customer segment and type of banking firm). Further avenues for research are then charted in light of the new conceptual framework developed

Customer Orientation in Highly Relational Services

Purpose – The purpose of this article is to investigate the antecedents, importance, and consequences of the customer orientation of service employees (COSE) in highly relational services (HRS). This study challenges the traditional vision of COSE and its sole focus on transactional services. The paper also examines and confirms new outcomes of COSE. Then, a revised COSE model adapted to HRS is proposed. Design/methodology/approach – The private banking (PB) service is chosen to represent a HRS setting. The qualitative study is comprised of 25 semi-structured interviews with PB practitioners. The results are analysed using NVivo 11. Findings – This study confirms the validity of the construct. COSE is proven to have notable importance in HRS. Various dimensions of COSE have different grades of importance. New consequences are elicited for HRS, including trust, loyalty, and co-creation. Practical implications – The results show that most private banking firms do not have standardised processes in place to measure COSE. This study proves how COSE can be used for several purposes by practitioners as a means of customer relationship management and in co-creation strategies. Originality/value – This study expands on the potential of the COSE construct by the use of HRS for the first time and introduces new consequences from the original COSE model

A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta

We searched integrable 2D homogeneous polynomial potential with a polynomial first integral by using the so-called direct method of searching for first integrals. We proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than 4.Comment: 22 pages, no figures, to appear in J. Phys. A: Math. Ge

Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom

We consider natural complex Hamiltonian systems with $n$ degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial potential $V$ of degree $k>2$. The well known Morales-Ramis theorem gives the strongest known necessary conditions for the Liouville integrability of such systems. It states that for each $k$ there exists an explicitly known infinite set \scM_k\subset\Q such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) calculated at a non-zero \vd\in\C^n satisfying V'(\vd)=\vd, belong to \scM_k. The aim of this paper is, among others, to sharpen this result. Under certain genericity assumption concerning $V$ we prove the following fact. For each $k$ and $n$ there exists a finite set \scI_{n,k}\subset\scM_k such that if the system is integrable, then all eigenvalues of the Hessian matrix V''(\vd) belong to \scI_{n,k}. We give an algorithm which allows to find sets \scI_{n,k}. We applied this results for the case $n=k=3$ and we found all integrable potentials satisfying the genericity assumption. Among them several are new and they are integrable in a highly non-trivial way. We found three potentials for which the additional first integrals are of degree 4 and 6 with respect to the momenta.Comment: 54 pages, 1 figur

Servitization and co-opetition in the pharmaceutical distribution: Back to Basics?

This paper discusses how the pharmaceutical distribution sector has evolved in the past decades and the role of servitization in an ever changing market led by big players. An empirical analysis was conducted on Portuguese and Spanish distributors which enabled the identification of a detailed portfolio of services currently offered by the industry. These companies were compared in terms of current service provision, levels of implementation of added-value services, main reasons for implementation and levels of co-opetion within the sector. Some differences between both countries have been found in terms of their level and reasons for the implementation of value adding services. Major findings refer to the tendency of distributors to further develop their base services provision in the future aiming at achieving increased competitive advantage and loyalty. This raises concerns given that it can be interpreted as a “back to basics” strategy of low differentiation which may not be consistent with long term competitiveness

Servitization and Co-opetition in pharmaceutical industry

Purpose: The present paper aims at providing an outlook of the portfolio of services developed by the pharmaceutical distribution in Spain and Portugal by looking at the different types and levels of implementation. This paper also provides the research framework that is currently the base for the ongoing data collection, exploring the rationale behind the implementation of different types of services and co-opetitive relationships in relation to the pursuit of profit, the creation of barriers with competitors and the reinforcement of customer loyalty. The impact of these factors on the intention to increase the delivery of services in the future will also be analysed. Design/methodology/approach: In order to address the research framework presented, a quantitative research methodology is suggested through the use of web-based questionnaires. After the identification and categorization of services in this industry, a questionnaire was developed in order to measure the presence of the identified services and their impact on the pursuit of profit, the creation of competitive advantages the improvement of customer loyalty, willingness to further develop these services and co-opetitive relationships. The sample includes Portuguese and Spanish pharmaceutical cooperatives and private companies, operating as wholesalers. Findings: The empirical data is currently being collected therefore the present paper provides solely the analysis of the pharmaceutical industry in both countries and the classification of the services offered in this industry which was used as the basis to develop the questionnaire. The paper discusses how the pharmaceutical distribution sector has evolved in the past decades and how the concentration process has changed the rules of the market owned by big players who are taking the lead. Additionally, the portfolio of new services that have recently been developed throughout the industry are identified. Some differences between both countries have been found mainly in IT services. The recent establishment of second degree cooperatives generates new perspectives to the suggested influence of co-opetitive relationships. Originality/value: The present paper is part of an ongoing research project which aims at providing both theoretical and practical implications: 1) The analysis of pharmaceutical wholesalers from a servitization perspective; 2) Application of Baines et al. (2013) classification to the pharmaceutical sector; 3) The adaptation and measurement of co-opetitive relationships within the servitization delivery; 4) Development of instruments to measure the level of implementation and the type of services which can be used in the future to make compared studies in other countries

Integrability of natural Hamiltonian systems with homogeneous potentials of degree zero

We derive necessary conditions for integrability in the Liouville sense of natural Hamiltonian systems with homogeneous potential of degree zero. We derive these conditions through an analysis of the differential Galois group of variational equations along a particular solution generated by a non-zero solution \vd\in\C^n of nonlinear equations \grad V(\vd)=\vd. We proved that if the system integrable then the Hessian matrix V''(\vd) has only integer eigenvalues and is semi-simple.Comment: 13 page