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By: Y. Berek, M.B. B.CH., M.B.B.Ch., Ph.D.

Medical Instructor, Tufts University School of Medicine

And yet the mystery of scientific computing is that its new worlds over the water ombrello glass treatment purchase discount pepcid, wrought only of numbers and video images medicine 54 092 purchase pepcid 20 mg fast delivery, are as real as the furrowed brow of the first Cro-Magnon who was mystified by the stars medications j-tube safe pepcid 20mg, and looked for a story symptoms kidney disease buy pepcid amex. My sabbatical at Rutgers was supported by the Institute for Marine and Coastal Sciences and the hospitality of Dale Haidvogel. I am grateful for the comments and suggestions of William Schultz, George Delic, and the students of the course on which this book is based, especially Ahmet Selamet, Mark Storz, Sue Haupt, Mark Schumack, Hong Ma, Beth Wingate, Laila Guessous, Natasha Flyer and Jeff Hittinger. I thank Andreas Chaniotis for correcting a formula I am also appreciative of the following publishers and authors for permission to reproduce figures or tables. Orszag, Numerical Analysis of Spectral Methods (1977), Society for Industrial and Applied Mathematics. I also would like to acknowledge a debt to Paul Bamberg of the Harvard Physics department. His lecturing style strongly influenced mine, especially his heavy reliance on class notes both as text and transparencies. I thank Joel Primack, who directed my undergraduate research, for his many lessons. Another is the need to write quick-and-rough reports, summary sheets and annotations for even the most preliminary results. It is only too true that "otherwise, in six months all your computer output and all your algebra will seem the work of a stranger. Our joint venture on tides in the Martian atmosphere was scooped, but I found my calling. His running commentary on science, scientists, and the interplay of numerics and analysis was a treasured part of my education. I am appreciative of John Grafton and the staff of Dover Press for bringing this book back into print in an expanded and corrected form. Lastly, I am grateful for the support of the colleagues and staff of the University of Michigan, particularly Stan Jacobs for sharing his knowledge of nonlinear waves and perturbation theory, Bill Schultz for many fruitful collaborations in applying spectral methods to mechanical engineering, and Bill Kuhn for allowing me to introduce the course on which this book is based. The basic idea is to assume that the unknown u(x) can be approximated by a sum of N + 1 "basis functions" n (x): N u(x) uN (x) = n=0 an n (x) (1. The different spectral and pseudospectral methods differ mainly in their minimization strategies. The example is the linear, one-dimensional boundary value problem: uxx - (x6 + 3x2)u = 0 u(-1) = u(1) = 1 the exact solution is (Scraton, 1965) u(x) = exp([x4 - 1]/4) (1. In order to satisfy the boundary conditions independently of the unknown spectral coefficients, it is convenient to write the approximation as u2:=1 + (1-x*x)*(a0 + a1*x + a2*x*x); u2 = 1 + (1 - x2)(a0 + a1 x + a2 x2) where the decision to keep only three degrees of freedom is arbitrary. The residual for this approximation is Resid:= diff(u,x,x) - (x**6 + 3*x**2)*u; R(x; a0, a1, a2) = u2,xx - (x6 + 3x2)u2 R = (2a2 + 2a0) - 6a1 x - (3 + 3a0 + 12a2)x2 - 3a1 x3 + 3(a0 - a2)x4 +3a1 x5 + (-1 - a0 + 3a2)x6 - a1 x7 + (a0 - a2)x8 + a1 x9 + 10a2 x10 (1. If we arbitrarily choose the points xi = (-1/2, 0, 1/2), this gives the three equations: eq1:=subs(x=-1/2,Resid); eq2:=subs(x=0,Resid); eq3:=subs(x=1/2,Resid); eq1 1683 659 a0 + a1 - 256 512 eq2 = -2(a0 - a2) 1683 659 a0 - a1 - eq3 = - 256 512 = - 1171 49 a2 - 1024 64 1171 49 a2 - 1024 64 (1. Could we have anticipated this, and used a trial solution with just two degrees of freedom for the same answer The answer to the first question is that choosing powers of x as a basis is actually rather dangerous unless N, the number of degrees-of-freedom, is small or the calculations are being done in exact arithmetic, as true for the Maple solution here. In an algebraic manipulation language, different rules apply as explained in Chapter 20. The second answer is: Collocation is the simplest choice which is guaranteed to work, and if done right, nothing else is superior. To understand why, however, we shall have to understand both the standard theory of Fourier and Chebyshev series and Galerkin methods (Chapters 2 and 3) and the theory of interpolation and cardinal functions (Chapters 4 and 5). The third answer is: once the basis set has been chosen, there are only two optimal sets of interpolation points for each basis (the Gauss-Chebyshev points and the Gauss-Lobatto points); both are given by elementary formulas in Appendices A and F, and which one is used is strictly a matter of convenience. Indeed, one can show that for this problem, all the odd powers of x have zero coefficients. Symmetries of various kinds are extremely important in practical applications (Chapter 8). First, the method is not necessarily harder to program than finite difference or finite element algorithms. When N is sufficiently small, Chebyshev and Fourier methods yield an analytic answer.

Colloquially symptoms 2 days before period order 40 mg pepcid with mastercard, the middle income trap is referred to as "growing old before getting rich symptoms tonsillitis order pepcid 40 mg mastercard. Gill and Homi Kharas jnc 8 medications pepcid 40mg discount, "The Middle-Income Trap Turns Ten symptoms exhaustion purchase pepcid on line," World Bank, August 2015, 7. The chosen technologies represented potentially "revolutionary" new industries in emerging fields, which could allow Chinese companies to "surpass" rather than simply "catch up" to the international technological frontier. After the turmoil of the Great Leap Forward and the Cultural Revolution, policymakers found the Chinese economy had fallen far behind advanced economies and de-emphasized rhetoric about surpassing in favor of "catching up. China Economic and Security Review Commission, Hearing on Chinese Views of Strategic Competition with the United States, June 24, 2020, 1. Naughton, in the 2006 Medium- and Long-Term Plan, the types of technology to be targeted were "ill defined" relative to highly specific targets set in later industrial policies. China Economic and Security Review Commission, Hearing on Chinese Views of Strategic Competition with the United States, June 24, 2020, 3. Naughton described as the "crucial brains" behind Chinese economic policy,96 convened a working group of financial and economic regulators to compare the fallout from 2008 with shifts in the global economy after the Great Depression. Using the strength of its economic and technological competitiveness, China should act as a cautious creditor nation, working to shape global institutions around its interests. With this program, Beijing saw an opportunity to surpass rather than simply catch up to the United States and other global leaders by focusing on technologies without entrenched market incumbents where Chinese entrants could develop a first-mover advantage. For example, it directed * Compulsory education denotes the years of education required under government law. In China, nine years of education are compulsory, from kindergarten to middle school. Organization for Economic Co-operation and Development, "Education in China: A Snapshot," October 2016, 10. In practice, this transfer occurred through a variety of legal and illicit means, ranging from forced technology transfer from foreign companies using the Chinese market as leverage to acquisitions of foreign technology and talent to commercial espionage by Chinese government actors. Naughton argued Beijing initiates private companies into the "national team" through purchasing contracts and regulatory support. Army War College, noted in testimony before the Commission, Beijing works to advance the position of these companies "both at home and in global markets. This process assists Chinese national champions in surpassing and supplanting global market leaders. The strategy reiterated that "for many countries," innovation formed the "core strategy for pursuing competitive advantage. The success of this strategy is reflected, in part, in the rapid rise in R&D expenditures by U. The policy asserted that fundamental research should remain unrestricted "to the maximum extent possible" in order to preserve the creativity and collaboration necessary for healthy innovation, while proprietary or national security-related research should be restricted. Harvard scholar Julian Gewirtz argued General Secretary Xi holds an "expansive" concept of "big security" that extends to the security of key industries "related to the lifeline of the national economy. Chinese chipmakers have so far been unsuccessful at mastering the intricate production processes required to fabricate the most cutting-edge chips widely used in consumer electronics, with the Semiconductor Industry of America estimating China as being at least two generations behind as of 2018. Translating theory and design into manufacturing requires a combination of engineering and scientific expertise, managerial talent, trade secrets, and multibillion-dollar production facilities that only a few companies located in Taiwan, South Korea, the United States, and Japan have achieved. This report served as the impetus for the Trump Administration to impose tariffs on U. Coordinated by the Cyberspace Administration of China, an overarching legal framework was first established in the 2017 Cybersecurity Law and expanded through subsequent laws (e. In Commission testimony, Janka Oertel, director of the Asia program at the European Council on Foreign Relations, said, "For China, Europe has become a key battleground in the strategic competition with the United States for economic and technological supremacy. Poland, Estonia, Romania, Latvia, Slovenia, and the Czech Republic have also signed agreements with the United States confirming their 5G suppliers would not be subject to control by a foreign government, a de facto exclusion of Huawei. For more, see Department of Homeland Security Cyber and Infrastructure Security Agency, "5G Wireless Networks: Market Penetration and Risk Factors," July 2019.

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Education: self-management education should focus on teaching patients the importance of recognizing their own level of control and signs of progressively worsening asthma symptoms medications that cause tinnitus buy pepcid 40 mg mastercard. Educational strategies should also focus on environmental control and avoidance strategies treatment solutions generic pepcid 40 mg fast delivery, as well as on medication use and adherence (e in treatment 1-3 order online pepcid. Expert Panel Report 3: Guidelines for the Diagnosis and Management of Asthma treatment jaundice order pepcid discount, 2007. Or at least two minor criteria (allergic rhinitis, wheezing unrelated to colds, or blood eosinophil count > 4 %). Prolonged observation (minimum 8 h) in setting able to manage respiratory failure is optimal. The passive movement of water is decreased and airway secretions are dehydrated with very low surface liquid layer. Cilia become compressed inhibiting ciliary clearance and cough clearance, bacteria thrive; immune function is also abnormal at the airway surface. Repeated and chronic infection leads to airway damage and bronchiectasis in the lung and dysfunction of other organs.

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When housed in plastic shoeboxes medicine for sore throat cheap pepcid amex, rats should be provided with some type of bedding material such as processed hardwood chips or ground corncobs treatment jalapeno skin burn order 20 mg pepcid visa. For newly weaned rats symptoms mono buy cheap pepcid 40mg on-line, it is advisable to gang house the animals for several days after receipt (e treatment notes discount pepcid 40mg with amex. This is particularly true if the animals are to be introduced to an automatic water system for the first time. Each rat should be checked daily to ensure that an adequate supply of fresh food and water is available. The Guide does not specify any particular lighting cycle for rats; however, a 12 hour light/12 hour dark cycle is routinely used for this species. Physical and Physiological Parameters Physical and physiological parameters for laboratory rats are listed in Table 1. Diseases Various diseases and adverse health conditions of laboratory rats are identified and briefly described in Table 1. Caused by bacterium Clostridium piliforme; may occur in mice, rats, gerbils, hamsters, guinea pigs, rabbits, cats, dogs, nonhuman primates, horses, and other species; has been reported in Europe, North America, and Asia; most outbreaks in laboratory rats and mice have occurred in conventional colonies; usually subclinical; signs may include diarrhea, poor coat, and sudden death in young; focal necrosis in liver and inflammation of ileum. Caused by bacterium Bordetella bronchiseptica that is a common inhabitant of the respiratory tract of rats and mice; may cause pneumonia usually in association with a primary pathogen such as mycoplasma. Caused by bacterium Pasteurella pneumotropica, an opportunistic organism; associated with abortion and respiratory, ear, reproductive, mammary gland, conjunctival and skin lesions; usually a co-pathogen with respiratory pathogens such as Sendai virus and mycoplasma. Caused by Paramyxovirus; extremely contagious; clinically inapparent chronic infection or clinically apparent acute infection; variable signs may include chattering, mild respiratory distress, prolonged gestation, poor growth, and death in young; concurrent pulmonary infections may occur. Caused by Coronavirus; highly contagious; one of the most common viruses in laboratory rats; virus is present in tissues of infected rats for only about 7 days; suckling rats may have mild transient signs (e. Caused by Pneumovirus; common infection in laboratory rodents worldwide; active infection lasts about 9 days; natural infections are subclinical in euthymic rodents. Condition of young rats and mice characterized by annular constriction and subsequent edema, necrosis, and sloughing of the tail; much more common in rats; may be prevented by providing relative humidity S50%. The most commonly used guinea pig strains are albino outbreds of the Dunkan-Hartley and Hartley varieties. Although these guinea pigs are a bit more expensive than the standard Hartley guinea pig, the absence of hair and intact immune system of the hairless guinea pig makes it an attractive alternative for dermal studies, such as delayed contact hypersensitivity or photoirritation and photosensitization studies. Consequently, the hairless guinea pig seems to be gaining in popularity among scientists involved in dermatological research. Handling and Restraint Although the guinea pig is probably the most nervous and panicky species used in research, it generally will not scratch or bite when picked up, provided it is well supported. It is advisable to approach and handle the guinea pig in a quiet and confident manner to avoid inducing any unnecessary stress in the animal. Housing Because guinea pigs cannot jump or climb very well, they may be housed in relatively shallow cages with solid bottoms or wire flooring. If solid-bottom caging is used, the animals should be provided with some type of bedding material, such as processed hardwood chips. Water may be supplied to guinea pigs using water bottles or by an automatic watering system. Each guinea pig should be checked daily to ensure that it has an adequate supply of fresh, uncontaminated food and water. Like humans and nonhuman primates, guinea pigs require regular doses of vitamin C (ascorbic acid) to avoid developing scurvy. Fortunately, commercial diets are available that contain an adequate supplement of vitamin C for this species. The health of each animal should be verified at the time of receipt and on a daily basis thereafter by trained and qualified personnel. Guinea pigs can be rather messy laboratory animals because they quickly foul their cages and seem to enjoy spilling their food and playing with their water sippers. Therefore, the condition of the cages and bedding should be monitored closely and cleaned regularly to provide a suitable habitat for the animals. The Guide does not specify any particular lighting cycle for guinea pigs; however, a 12 hour light/12 hour dark cycle is routinely used for this species.

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