The Case n ≥ 2 — 1 226
The Case sk = sp = sq In this case and Q ∼ kq(k — p)(q — p) , (3.31) |gkpq |2 2 |gkpq |2 2x = —2 |Usp| [kq +(k — p)(q — p)] — 2 |Bsp| [k(k — p) + q(q — p)] . (3.32)√For k < p < q we obtain Q < 0 and thus x + x2 — Q ≥ 0, leading to exponentially growing solutions independent of Hc(p) and the ratio|Usp|/|Bsp|. In the present case both velocity and magnetic field modes have positive and negative contributions to the sign of x. For both local (k ' p ' q) and nonlocal (k << p ' q) interactions Q = 0 and the sign of x determines whether unstable solutions occur. For the nonlocal case onlythe magnetic field term is positive, and x has the form |gkpq|2 2 2x ' 2 kq(|Bsp| — |Usp| ) . (3.33)leading to unstable solutions if |Bsp| > |Usp|, while for local interactions no instability occurs as the only term in x that does not vanish isp—|gkpq|2|Us |2kq < 0.For k < q < p, the possibility of exponentially growing solutions depends on the ratio |Usp|/|Bsp| and on the relative magnitudes of the wavenumbers k,p and q, as now Q > 0. Since the magnetic field term in x is now positive, instabilities occur for |Usp|/|Bsp| < 1. If |Usp|/|Bsp| > 1 it depends also on the cross-helicity whether instabilities occur. For maximal Hc(p) one obtains x2 — Q > 0, hence the perturbations cannot grow exponentially. If Hc(p) = 0 and |Usp|/|Bsp| is not too small, instabilities will occur, depending also on the shape of the triad (see appendix B.2 for further details). In general, the smaller |Usp|/|Bsp| the more unstable is the solution.For p < k < q we obtain x < 0 and Q > 0, furthermore x2 — Q > 0 independent of |Usp|/|Bsp| and Hc(p) (see appendix B.1), thus no linear instabilities occur. Nonlocal interactions (p << k ' q) do not lead to instabilities, since p px ' —|gkpq|2[k2 — kp](|Us |2 + |Bs |2) < 0 . (3.34)
The Case. G| = pIn this section we fix a Galois extension of number fields L/K of degree p and set G := Gal(L/K). We also fix a finite set of places of K that contains all archimedean places, all that ramify in L/K and all that divide p.In this case there are three isomorphism classes of indecomposable Zp[G]-lattices and there basic properties are given by the following table (taken from ) in which we write TrG forthe element Σg∈G g of Zp[G]. Table I MH0(G, M )Hˆ—1(G, M ) rkZ (M )pZp[G]Zp0pOp := Zp[G]/TrG0Z /p Zp − 1ZpZp01By using this classification, the following result gives a complete description of the Galois structure of the Zp[G]-lattice AΣ in terms of the finite group T Σdefined at the beginningLof Chapter 4.L/K Proposition 5.1.1. Let p be an odd prime, assume that Leopoldt’s Conjecture is valid forL at p and set d := dimF (T Σ ). Then there is an isomorphism of Zp[G]-modulesp L/K LppAΣ ~= Zp[G]rK—d ⊕ Od ⊕ Zd+1. Proof. The Krull-Schmidt theorem combines with Table I to imply that for suitable non-negative integers a, b and c there is an isomorphism of Zp[G]-modules LppAΣ ~= Zp[G]a ⊕ Ob ⊕ Zc. (5.1) We therefore need to show that the integers a, b and c are uniquely determined by the integer d.To see this we use the decomposition (5.1) in conjunction with the fourth column of Table
The Case. Located in Southeast Asia region, Vietnam is a low-income country with annual GDP per capital equivalent to approximately 2000 USD. As a tropical country, Vietnam faces high risks of deadly infectious diseases such as dengue fever, malaria, tuberculosis etc. The recent economic reform has significantly increased the people’s income and thus drastically changed their nutrition regimes and life styles especially in urban areas. These changes, however, results in a surge of non-communicable diseases such as diabetes, hypertension, and heart problems. All these factors have tremendously overburdened the country’s weak and vulnerable healthcare system. Overall, chronic problems such as fatal epidemics, hospital overloading and errors, bribery, and corruption, health professional neglects and incompetence are rampant and seemly out of control [13-17].In an effort towards strengthening and upgrading the healthcare sector, a law on medical treatment and examination was passed by the Vietnam Assembly in 2009. The process of building the law involved support and wide participation of international aid agencies and other social civil institutions. To effectively implement the law, a computer- based information system was required as it could resolve the following issues related to medical health professionals management: a) Only qualified persons with sufficient training and internship are allowed to practice independently b) Continuous Medicine Education (CME) is a prerequisite for license lifetime validity c) To ensure that each medical practitioner has no more than one license.The support from the international aid organization to health human resource development also included financial resources and expertise to build a software system. Originally, an international tender was planned to opt a qualified software firm for this task.However, as the bidding process took too long and to fill the urgent need for licensing offices across the country, a local team was founded to build a prototype of licensing management system by adapting an open source platform specially designed for health care. The construction of this software system had followed the bootstrapping  and participation approach, targeting firstly one provincial licensing office. The system was well received by the community of licensing officers in the country. Its implementation was rapidly expanded and reached national scale in a short time. The geographical expansion of the implementation we...
The Case. • At the November 24 hearing before Judge Seraphim, testimony was given by one of the police officers and three physicians and Miss Lessard was ordered committed for thirty additional days. Judge Seraphim gave no reasons for his order except to state that he found Miss Lessard to be "mentally ill."
The Case. In the case-based reasoning approach, one of the most important parts is the represen- tation of a case. A case consists of the following three components: • A primary slot for the main problem description and some additional informative fields, for example the creation date. • Many different slots that hold the case description. 1He is the author of the book , an Adjunct Professor at the University of New Hampshire and Director of Research in a high-tech company. • One or many solutions that are related to the case. This solution(s) can be com- puted by the values provided by the slots or entered manually by the user. There exist two possibilities of representing a case. One approach is to define all the possible slots (fields) in advance. This is much easier but only possible if all the fields used to describe a case are known beforehand. The other possibility is more flexible because the slots are not explicitly named when implementing the system. The big challenge for this approach is, that the calculation of the similarity between two cases is much more difficult. This calculation is one of the most important things in a case-based reasoning system. If the comparison of two cases does not return results as expected by the user, the system will be unusable. In the network environment there are many changes over the time. There may be new protocols or new technologies that demand for new slots. If the first way of describing a case is used, the addition of new slots requires the system developer to change the way the similarity of two cases is calculated. In addition, the system developer most likely has to change the database structures and some code in the implementation. To avoid such maintenance intensive tasks, the second approach was used for the concept and implementation. It should provide an as flexible as possible case description as well as an adaptable behavior of the system to new situations. Such new situations can be changes in the network protocols, new categories, or other changes that results in a change of the case description.
The Case. The problem of operating and handling working vessels is illustrated by a case describing a single voyage for an offshore supply vessel. The vessel is on a time charter contract covering voyages between the shore base in a harbour and a number of fixed offshore oil and gas production installations. The voyage starts alongside the harbour, the ship is fully loaded and ready to let go of the mooring lines. The planned tasks for the voyage are as follows: Cargo transfer from the harbour to installation A, cargo transfer from installation A to installation B, be standby vessel at installation B for a shorter period, cargo transfer from installation B to installation A and then returning to port with empty containers and garbage. An unplanned activity occurs during the voyage where a broken pump from installation A is sent ashore for repair.
The Case. M = kπ. The E1-term of the I-adic spectral sequence of X with coefficients in kπ,E1(X, kπ) = gr(kπ) ⊗k H∗(X, k),SPECTRAL SEQUENCE OF AN EQUIVARIANT CHAIN COMPLEX 2697 ⊗is a left gr(kπ)-module, freely generated by a k-basis for 1 H∗(X, k). We want to show(22) d1 = (gr(µkπ) ⊗ id) ◦ (id ⊗∇X ).Clearly, the map on the right side is gr(kπ)-linear. In the next lemma, we verify that d1 is gr(kπ)-linear, too (a more general result will be proved in Lemma 6.2).(X, kπ) → ELemma 4.3. The differential d1 : E1−p,p+q
The Case. This will be a problem based upon an area of EEA substantive and/or procedural law, containing a referral to the EFTA Court from a EFTA EEA national court under Article 34 of the Agreement between the EFTA States on the establishment of a Surveillance Authority and a Court of Justice (“SCA”). Both written and oral pleadings on the part of applicant and respondent will be required from each competing team.