Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain C_c^\infty(\Omega) where the self-adjointness is defined relative to L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E. Segal and B. Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when \Omega=I\times\Omega_2 and I is an open interval. We then apply the results to the case when \Omega is a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that {e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km, 02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt, 61.44.B

VUCA and the future of the global mobile telco industry

The disruption global digitally based firms are imposing on the positions of established multinational telcos is not just in degree, but also in kind. As such, the telcos are entering a period of VUCA. Although digitally based competitors could suffer from liabilities of ‘outsidership’, employing the telco Telenor as a case, we argue that the physical presence of telcos in local markets will be insufficient to avoid a future as utilities or dumb-pipes. One significant issue as they confront VUCA is therefore whether telcos are able to develop and apply dynamic capabilities

The digital challenge for multinational mobile network operators. More marginalization or rejuvenation?

Multinational mobile network operators (MNOs) rapidly emerged in the early 1990s and for a decade and a half were the dominant actors in their industry. We analyze the development and competitiveness of a typical MNO, Telenor. With the introduction of 4G in 2010, we show that Telenor, like other MNOs largely failed to respond to the opportunity that connectivity provided to develop digital services. Instead, these were developed by technology platform companies such as Amazon, Google and Microsoft. Telenor became a marginalized supplier of standardized internet connectivity. We argue that the ‘decade of lost opportunity’ (2010-2020) for Telenor was a product of a lack of ‘recombinant firm-specific advantages’ (FSARs). With the launch of 5G, an emerging global digital infrastructure, this sidelining is set to intensify unless Telenor responds to this new opportunity by developing B2B digital services. We analyze the FSARs that are necessary for a successful transition of capturing the value that 5G provides and the degree to which they are present, or potentially present, in Telenor

Experimental and numerical study of error fields in the CNT stellarator

Sources of error fields were indirectly inferred in a stellarator by reconciling computed and numerical flux surfaces. Sources considered so far include the displacements and tilts (but not the deformations, yet) of the four circular coils featured in the simple CNT stellarator. The flux surfaces were measured by means of an electron beam and phosphor rod, and were computed by means of a Biot-Savart field-line tracing code. If the ideal coil locations and orientations are used in the computation, agreement with measurements is poor. Discrepancies are ascribed to errors in the positioning and orientation of the in-vessel interlocked coils. To that end, an iterative numerical method was developed. A Newton-Raphson algorithm searches for the coils' displacements and tilts that minimize the discrepancy between the measured and computed flux surfaces. This method was verified by misplacing and tilting the coils in a numerical model of CNT, calculating the flux surfaces that they generated, and testing the algorithm's ability to deduce the coils' displacements and tilts. Subsequently, the numerical method was applied to the experimental data, arriving at a set of coil displacements whose resulting field errors exhibited significantly improved quantitative and qualitative agreement with experimental results.Comment: Special Issue on the 20th International Stellarator-Heliotron Worksho

Synthesis and analysis of jet fuel from shale oil and coal syncrudes

Thirty-two jet fuel samples of varying properties were produced from shale oil and coal syncrudes, and analyzed to assess their suitability for use. TOSCO II shale oil and H-COAL and COED syncrudes were used as starting materials. The processes used were among those commonly in use in petroleum processing-distillation, hydrogenation and catalytic hydrocracking. The processing conditions required to meet two levels of specifications regarding aromatic, hydrogen, sulfur and nitrogen contents at two yield levels were determined and found to be more demanding than normally required in petroleum processing. Analysis of the samples produced indicated that if the more stringent specifications of 13.5% hydrogen (min.) and 0.02% nitrogen (max.) were met, products similar in properties to conventional jet fuels were obtained. In general, shale oil was easier to process (catalyst deactivation was seen when processing coal syncrudes), consumed less hydrogen and yielded superior products. Based on these considerations, shale oil appears to be preferred to coal as a petroleum substitute for jet fuel production

The effect of organizational separation on individuals' knowledge sharing in MNCs

The ability of an organization to apply knowledge globally has been conceptualized as critical for the existence of multinational corporations (MNCs). We argue for an organizational separation effect on knowledge sharing that challenges the view of the MNC as a latent social community. Using a unique data-set of more than 4.000 individual responses from an MNC, Telenor, we test how three types of drivers for individuals’ knowledge sharing –individuals’ motivation, and individuals’ perceptions of organizational values and organizational work practices- work differently within, as opposed to across, business units. Our analysis suggests that while intrinsic motivation, innovative values and job autonomy are relatively important drivers of knowledge sharing within the business units, extrinsic motivation, result-oriented values and participation in corporate employee development are relatively more important for knowledge sharing across business units

Einstein-Weyl structures corresponding to diagonal K\"ahler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal K\"ahler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in the family of biaxial K\"ahler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.Comment: 15 pages, Latex file, minor modifications, to be published in Class. Quant. Gra

Volume-energy correlations in the slow degrees of freedom of computer-simulated phospholipid membranes

Constant-pressure molecular-dynamics simulations of phospholipid membranes in the fluid phase reveal strong correlations between equilibrium fluctuations of volume and energy on the nanosecond time-scale. The existence of strong volume-energy correlations was previously deduced indirectly by Heimburg from experiments focusing on the phase transition between the fluid and the ordered gel phases. The correlations, which are reported here for three different membranes (DMPC, DMPS-Na, and DMPSH), have volume-energy correlation coefficients ranging from 0.81 to 0.89. The DMPC membrane was studied at two temperatures showing that the correlation coefficient increases as the phase transition is approached