Mappings preserving generalized and hyper-generalized projection operators

This paper is based on the lessons learned during the two recent expansions of the Southern LNG import terminal in Savannah GA. It shows how the Project Management team planned and executed the expansions, and particularly how the team interfaced with Operations. Possible applications of the information provided in this paper is for LNG terminal owners and operators who seek to perform similar expansions within an operating terminal, or similar mid-stream operating facility (gas processing, etc.). The paper concludes with 4 major findings that will benefit the reader:Project Management and Operations teams are significantly different in their goals, work practices, structure, culture, and scope, which affect expansion projects. Project engineers may lack operating experience and perspective, which can limit their ability to " Design for Operability??. Operations personnel can have less project management perspective, but are the true authorities on running the plant safely and efficiently. Leveraging both strengths is the key to a successful project.The greatest risk on the expansion project occurs at the Project - Operations interface. This interface is best managed through planned and structured communication systems (meetings, reviews, reports, golf), tailored for a mutual success.Contractor management is challenging when working within a live plant. Tie-ins, notices, permits, interference, slow downs, etc. must be planned for early, and thoroughly addressed in the contract.Commissioning and turnover of the expansion is crucial from the stand point of Operations interface. The phasing in of Operations personnel with Project personnel (training, spares, warranty work, lessons learned, and close out) must be thoroughly planned beforehand. Three major technical contributions to the knowledge base for the LNG industry are:The Post-Project Lessons-Learned exercise this project confirmed the effectiveness of our communications management approach.The Contracting strategy for the EPC contract included key contractor responsibilities and specified expectations and communications responsibilities that mitigated interface risks.The Project Team acquisition, development and leadership methods used were highly projectized to produce a purpose-built project organization. 1. INTRODUCTION Southern LNG owns and operates an LNG receiving terminal near Savannah GA. The terminal was built in the late 70s, operated for 3 years and was decommissioned for 18 years until being re-commissioned in 2000-2001. Shortly thereafter, the first expansion was planned. This expansion coincided with the initial years of operations of the newly reactivated plant, and had to be taken into account from a risk and scope standpoint. The project team worked closely with the Operations staff to plan and execute the expansion successfully. Lessons-learned from the first expansion has been applied to the subsequent expansion, now underway at Elba.

The chemisorption phenomenon has been studied for different chemisorption sites (``cage,'' ``bridge,'' and ``on top``) of ${\mathrm{Li}}_{8}$(6,2)-H, ${\mathrm{Li}}_{12}$(6,6)-H, ${\mathrm{Li}}_{14}$(6,6,2)-H, ${\mathrm{Li}}_{10}$(5,4,1)-H, and ${\mathrm{Li}}_{14}$(9,4,1)-H systems [the symbol ${\mathrm{Li}}_{\mathrm{n}}$(i,j, . . .), where i,j, . . . is the number of atoms in the first, second, . . . layer]. An alternative algorithm to the Whitten procedure based on the simple overlap criterion using a projection operator over L\"owdin orthogonalized orbitals (L\"owdin procedure) has been proposed for localization of the one-electron functions employed in the configuration-interaction (CI) treatments. The selected one-electron functions have very similar composition for different chemisorption model clusters. In this manner only a small group of valence electrons which mostly contribute to the substrate-adsorbate interaction is selected for the truncated CI. Local properties of the chemisorption bond have been clearly demonstrated, particularly for the cage and bridge chemisorption sites. The chemisorption energy does not increase with increasing nuclearity of the cluster. The results are independent of both localization procedures used (employing projection or exchange operator).

Analysis and Prediction of Differential Operation and Maintenance Cost of Power Transmission and Transformation

On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac–Pauli–Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends–Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends–Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends–Fronsdal projection operators for arbitrary space–time dimensions D>2.

A method, correct to order alpha 2, is suggested for the relativistic treatment of pair correlation. Projection operators for positive energy states are applied to the two-particle equation which describes the interaction between the electrons. After elimination of two of the four spatial components-each with four spin components-of a relativistic pair function, two coupled equations for the 'large-large' and 'small-small' components, rho LL and rho SS, remain. By neglecting certain terms in the coupled equations, the occurrence of homogeneous solutions with one electron in the positive and one electron in the negative energy continuum is avoided, and an equation for rho LL alone is obtained, which can be solved using numerical methods developed for the non-relativistic problem. For the Coulomb interaction, this procedure is found to be correct to O( alpha 2) even without the use of projection operators, whereas for the lowest-order Breit interaction (exchange of a single virtual transverse photon), projection operators give corrections to the pair function already in O( alpha 2), thereby removing the well known alpha 2 errors that occur if the Breit interaction is used in a higher-order calculation neglecting projection operators. If projection operators are included, the Breit interaction can be treated to higher orders without causing spurious alpha 2 terms. By means of an iterative procedure, pair correlation effects, due to the instantaneous Coulomb interaction and the exchange of single virtual transverse photons, can be evaluated to all orders.

In an $n$-dimensional crystal, an energy band is usually made of several branches which are connected with each other. Accordingly, the Bloch states of wave vector K which are eigenfunctions of a one-electron Hamiltonian $H=\ensuremath{-}\ensuremath{\Delta}+V$ and which belong to a given band $\mathcal{B}$, define a subspace $\mathcal{S}(\mathrm{K})$ of finite dimensionality. For a large class of potentials, two properties concerning the subspaces $\mathcal{S}(\mathrm{K})$ which are associated with a fixed band $\mathcal{B}$ have been proved for $n$-dimensional crystals. (1) The projection operator $P(\mathrm{K})$ on $\mathcal{S}(\mathrm{K})$ can be defined for complex values of K, and its matrix elements $〈\mathrm{r}|P(\mathrm{K})|{\mathrm{r}}^{\ensuremath{'}}〉$ are analytic in a strip of the complex K space; this strip is centered on the real K space and is independent of r and r'. (2) The projection operator $P=\ensuremath{\int}{d}^{h}\mathrm{K}P(\mathrm{K})$ (integration on the Brillouin zone) has matrix elements $〈\mathrm{r}|P|{\mathrm{r}}^{\ensuremath{'}}〉$ which decrease exponentially when the length|r-${\mathbf{r}}^{\ensuremath{'}}$| goes to infinity.

Collective coordinate theory for light pulses in fibers: The reduced projection operators

Second-order spectral line shift comparisons

The Columbia River and its tributaries are the primary water system in the Pacific Northwest, draining some 219,000 square miles in seven states and another 39,500 square miles in British Columbia. Beginning in the 1930`s, the Columbia River has been significantly modified by construction of 30 major dams on the river and its tributaries, along with dozens of non-Federal projects. Construction and subsequent operation of these water development projects have contributed to eight primary uses of the river system, including navigation, flood control, irrigation, electric power generation, fish migration, fish and wildlife habitat, recreation, and water supply and quality considerations. Increasing stress on the water development of the Columbia River and its tributaries has led primary Federal agencies to undertake intensive analysis and evaluation of the operation of these projects. These agencies are the U.S. Army Corps of Engineers and the Bureau of Reclamation, who operate the large Federal dams on the river, and the Bonneville Power Administration who sells the power generated at the dams. This review, termed the System Operation Review (SOR), has as its ultimate goal to define a strategy for future operation of the major Columbia River projects which effectively considers the needs of all river uses. This volume, Appendix D: Cultural resources appendix, Technical imput includes the following: Development of geomorphology based framework for cultural resources management, Dworshak Reservoir, Idaho; Impact profiles for SOR reservoirs; comments from the following Native American tribes: Burns Paiute Tribe; Coville Confederated Tribes; Confederated Tribes of the Warm Springs Indian Reservation; Confederated Tribes and bands of the Yakama Indian Nation (comments); Nez Perce Tribe; Coeur D`Alene Tribe; Spokane Tribe of Indians; The confederated Tribes of the Umatilla Indian Reservation.

We consider two versions of the relational algebra: (a) the attribute relational algebra, based on the natural join and relations with columns corresponding to attributes, and (b) the positional relational algebra, based on the cross product and relation with an order on the columns, and with any column identified by its position in that order. For the attribute relational algebra, we show that both the equivalence and the finite equivalence (i.e., equivalence over finite relations only) of expressions involving just one ternary relation and the operators of projection, selection, join and difference, are undecidable. For the positional relational algebra, we show that both the equivalence and finite equivalence of expressions involving just one binary relation and the operators of projection, selection, cross product, restriction and difference, are undecidable.

Objective To analyze the operation of water improvement projects in drinking water-borne fluorosis areas of Province and the trend of dental fluorosis in children aged 8 to 12 years, and to evaluate the effects of prevention and control measures comprehensively, so as to provide basis for improving prevention and control strategies. Methods In 2009 - 2017, according to the Qinghai Drinking Water Endemic Fluorosis Surveillance Program, four project counties of Huangyuan, Minhe, Hualong and Guide were selected in Province. Three villages in each project county were selected according to their mild, moderate and severe conditions, and monitored the operation of water improvement projects, water fluoride content and dental fluorosis among children aged 8 to 12-year-old in each diseased village. Results In 2009 - 2017, the normal operation rate of water improvement projects increased from 2/8 to 7/8; the batch operation rate of the projects decreased from 5/8 to 1/8; the number of abandoned projects decreased from 1 to 0; the number of people covered by qualified water fluoride increased from 9 962 to 80 760 people; there was no significant difference in water fluoride content between different years (F = 0.758, P > 0.05). The total detection rate of children′s dental fluorosis was 33.01% (1 812/5 489) from 2009 to 2017, the index of dental fluorosis was 0.65, and the epidemic intensity was slightly prevalent; the detection rate of children′s dental fluorosis was 30.02% (951/3 168) in villages with normal operation of water improvement projects and qualified water fluoride content, the index of dental fluorosis was 0.58, and the epidemic intensity was marginal; the detection rate of children′s dental fluorosis was 32.72% (583/1 782) in villages with abnormal operation of water improvement projects or excessive fluoride, the index of dental fluorosis was 0.66, and the epidemic intensity was slight; the detection rate of children′s dental fluorosis in villages without changing the water was 51.58% (278/539), and the index of dental fluorosis was 1.04, belonging to the moderate epidemic intensity; the detection rate of children′s dental fluorosis in villages without changing the water was significantly higher than that in villages with normal operation of water improvement projects and qualified water fluoride content (χ2 = 102.30, P < 0.01). Conclusions The water improvement project in drinking water-borne fluorosis areas is running well and the operation rate is increasing year by year. The detection rate of dental fluorosis in children aged 8 - 12 years old in villages with normal operation of water improvement projects and qualified water fluoride content was significantly lower than that in villages without changing the water. The monitoring of fluorosis and the maintenance of water-renovation projects should be strengthened, and the problem of drinking water for residents in villages without changing the water should be resolved as soon as possible. Key words: Fluorosis, dental; Drinking; Dental fluorosis index; Epidemic intensity

Sparse representation acts as a fundamental data science methodology for solving a wide range of problems in machine learning and engineering. In this paper, we respectively propose novel distributed continuous-time and discrete-time projection neurodynamic approaches for sparse recovery by seeking the minimum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm solution with the undetermined linear measurement <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Ax=b$</tex-math></inline-formula> in two cases over undirected networks. The proposed approaches only require the communication network to be undirected and connected, without the notion of central processing node, and no node visit the entire matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> , so some privacy preserving efficiencies are guaranteed based on our approaches. First, for the one case that the rows of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> are distributed, we propose a distributed continuous-time projection neurodynamic approach based on the projection operators and prove the global convergence and optimality of it. Then, a corresponding distributed discrete-time projection neurodynamic algorithm with a fixed step size is also presented, and the convergence and the scope of values of the step size of it are also analyzed. Second, for another case that the columns of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> are distributed, a distributed continuous-time projection neurodynamic approach based on the projection operators and its derivative feedback is proposed and its global convergence is rigorously analyzed. Immediately following, we discuss its corresponding distributed discrete-time projection neurodynamic algorithm with a discrete version of the differential feedback term. Finally, the effectiveness and superiority of the proposed neurodynamic method are verified by the experiments of sparse signal and image reconstruction.

Sum rules and the symmetry of the memory function in spectral line shape theories

Achimov deposits extend over 12,000 square kilometers around the city of Novy Urengoy. These deposits are characterized by high reservoir pressures, and a narrow range of drilling fluid densities that creates complicated conditions for drilling and completion of wells. Due to the high accident rate of drilling horizontal wells only S-shape wells were drilled for this formation. The first successful horizontal production well was drilled in 2013 in cooperation Arcticgaz, ERIELL, Schlumberger. The first well to drill a horizontal wellbore on Achimov formation, has been planned to open Ach3,4 and Ach5 layers of Achimov formation. In close cooperation with project operator - Arcticgaz company, engineering group of Schlumberger drilling contractor and drilling contractor developed and successfully implemented comprehensive solutions for drilling and completion of horizontal wells Achim. One of the key factors of success was the use of drilling muds Megadril-D with constant control of equivalent circulating density. Application of rotary steareable system with optimally balanced PDC bits, allowed to drill horizontal wells through Achimov deposits in record time. An additional factor for drilling risks reduction was implementation of geomechanic model, as in the preparation of the preliminary model and real-time control for wellbore stability with the latest technology logging measurements (LWD) – acoustic and density neutron formation properties. In the period for 2013 to the 2nd quarter of 2014 have been successfully constructed more than 10 similar wells. Esteblished new records: maximum closure – 2403 meters, the length of the longest subhorizontal section reached 1233 meters. Set a record duration of well construction time of 62 days vs 100 planned, which could not been reached before by anyone in the region (formerly similar wells with shorter intervals of subhorizontal sectionhave been constructed in evarage about 150 days). Recently were successfully run two completion liners for 3-stage hydraulic fracturing (MSF) and one of MSF was successfully done. For completion purposes was used OBM with the weighting agent of mikro size, provided an unprecedented stability to settlement for a long time. This article devoted to the description of technologies and solutions that have been used for the construction of sub-horizontal wells. Preliminary production index of subhorizontal wells shows that current PI higher than S-shape wells (even with frac). Positive experience in the construction of subhorizontal wells change plans to develop Achimov deposits and opens new perspectives of hydrocarbon production in the region.

This paper aims at providing a systematic treatment of the crystallographic point groups. Some well-known properties of them, in terms of the theory of the poles of finite rotations, are first discussed, so as to provide a simple way for recognizing their invariant subgroups. A definition of the semi-direct product is then given, and it is shown that all crystallographic point groups can be expressed as a semi-direct product of one of their invariant subgroups by a cyclic subgroup. Many useful relations between point groups can be obtained by exploiting the properties of the triple and mixed triple semi-direct products, which are defined. Much of the rest of the paper is devoted to the theory of the representations of semi-direct products. The treatment here parallels that given by Seitz (1936) for the reduction of space groups in terms of the representations of its invariant subgroups (the translation groups). The latter, however, are always Abelian and this is not always the case for point groups. The full treatment of the general case, such as given by McIntosh (1958), is laborious and it is shown that, if the emphasis is placed on the bases of the representations, rather than the representations themselves, it is possible to achieve the reduction of the point groups by a method hardly more involved than that required when the invariant subgroup is Abelian. It is also shown that, just as for space groups, the representations of the invariant subgroups can be denoted and visualized by means of a vector, which allows a very rapid classification of the representations, very much as the k vector as used by Bouckaert, Smoluchowski &amp; Wigner (1936) allows the formalism of the Seitz method for space groups to be carried out in a graphical fashion. One of the major consequences of this work is that it affords a substantial simplification in the use of the symmetrizing and projection operators that are required to obtain symmetry-adapted functions: a very systematic alternative to the method given by Melvin (1956) is therefore provided. In the last section of the paper all the techniques discussed are applied in detail, as an example, to the cubic groups. The projection operators are used to obtain symmetry-adapted spherical harmonics for these groups. The paper might be found useful as an introduction to the methods for the reduction of space groups.