In this investigation the following general problem arises: Given a sequence of positive integers hypertension table buy avalide 162.5 mg low price, what is the expected length of its maximal monotonic nondecreasing subsequence heart attack 2013 effective avalide 162.5 mg. The solution depends upon the length of the sequence and the number of allowable integers arrhythmia practice strips order avalide 162.5mg with amex. Let F(p blood pressure too high avalide 162.5 mg with mastercard, q pulse pressure vs stroke volume avalide 162.5mg on-line,n) be the totality of F sequences of length n for a given p blood pressure chart for dogs order avalide 162.5mg without prescription, q choice where an F sequence of length n is defined as a sequence containing a maximum monotone nondecreasing subsequence of length n. Now consider the theorem for sequences of length M < M: choose a p, q satisfying p + q - M and (1), and fix n g M. Case 1: n = M: For any values of p, q > 0, there is only one F sequence, namely, 11 · · · 122 · · · 2. To remove the condition q < n - 1, we consider the case of sequence ending in 1 or 2. Here, the condition p < n - 1 must be imposed to satisfy the inductive hypothesis. Burge finds that the optimal strategy for sorting a set of data depends upon the amount of order (in the information-theoretic sense) already existing in the data; and he shows how to find an optimal sorting strategy given a measure of this order. As a consequence of (1) the subsequence must contain every number 1,2, · · ·, k at least once and hence it starts with the number 1 and ends with the number k. If the monotonic subsequence of length n is at the beginning (at the end) of the sequence there are M - n elements left, of which M - n - 1 can have arbitrary values, because M - n < pt for all i, while the first (last) of these elements can have all values except A; (except 1). Now consider the case where the monotonic subsequence is preceded by elements and followed by M - n - I elements. For n - M we have N = 1 and for n = M - 1 the above holds but we only have the first term i. A society is preparing 1560 ballots for an election for three offices for which there are 3, 4, and 5 candidates, respectively. In order to eliminate the effect of the ordering of the candidates on the ballot, there is a rule that each candidate must occur an equal number of times in each position as any other candidate for the same office. Of Ballots 260 182 78 234 52 130 104 312 208 Office 1 2 3 A D H A F I A E J B G J B G H B D I B G K C E L C F K the above tables just give the distribution for the first position on the ballot for each office. We must have the following (for simplicity we consider a total of 60 ballots): No. The problem is to determine a distribution of the candidates such that the system of linear equations for the number of each type of ballot, which contains more equations than unknowns, is solvable in positive integers. A trick solution to the problem can be obtained using 5 different ballots: add two fictitious names to the group of 3 and one to the group of 4. This would also provide a survey on the effect of ordering of the candidates on the ballot. Consider the differential equation Choose F(x) subject to the conditions so as to maximize >·(! This problem has arisen in connection with the construction of an optimal refracting medium. Let yn be the class of intcgrable, almost everywhere nonnegative, functions F(x) defined on the interval (0, 1) whose integral over (0, 1) is M. The proof of this assertion will depend on the following lemma, which is suggested by the usual calculus of variations devices. If a constant v and two absolutely continuous functions u(x) and A(x) can be found such that (i) /. Let C and C% be two closed curves in a plane, one totally surrounding the other, bounding an annular region. Let ^ be a harmonic function within the annular region, having a constant value on C and a constant value on C^. Prove (or disprove) that the same conclusion holds under the alternative constraint that the area bounded between the curves is fixed. Control Theory [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] D. For this reason our style will be semi-expository and the paper will be reasonably self-contained. The other purpose is to provide a method for generating scales for possible musical systems. The work in [1] has been made practical by Jorgenson [2], I am grateful to him and the referee for helpful suggestions. A (musical) scale is an increasing sequence of positive numbers /i,/2, · · · called notes or frequencies. A scale is n-tempered if for some positive n, the ratio /i+ M /i is called the octave. Thus, for this m and /, the product of m consecutive ratios of the form fi+ki / 1+fc(j i) spans I octaves. Since then it has displaced all its competitors, and is in almost universal use today. Later Ptolemy, the founder of trigonometry and refiner of Greek astronomy, investigated the superparticular series 2/1, 3/2, 4/3, 5/4, · · ·. By this we mean that when frequencies of these ratios are simultaneously sounded, the result is pleasing. The melodic is the impression received when notes are sounded in succession, while the harmonic, the impression when the sounding of notes is simultaneous. There is experimental justification for the theses that the melodic aspects of scales are conventional and learned, while there are convincing theories initiated by Helmholtz and based on experiment and deduction that there is a real basis for the harmonic aspect, that is independent of individual experience. The theory predicts that the superparticular ratios with small integers yield the most consonant simultaneous combination of sounds. The ratios based on superparticulars and shown in Table 2 were proposed by Ptolemy. From Table 3 we see that the deviation of just ratios from equal-tempered ratios is surprisingly small. Because of the "beat phenomena," (discussed in books on acoustics) the trained ear can detect pitch errors in the ratio of 2 simultaneously sounding notes to 1 cent or less, where ^ = 1 cent = 21/120° = 1. But the major 3rds (5/4) and minor 6ths (8/5) have errors of approximately 14 cents, while the minor 3rds (6/5) and major sixths (5/3) have errors of approximately 16 cents. The resulting dissonance, (very distinct on the organ) was intolerable tc many in the 16th, 17th, and 18th centuries, and delayed the universal adoption oi equal temperament. An optimal temperament is a temperament in which the ratios fifk approximate just ratios according to some criterion of optimality. This is a nonlinear system of 132 equations in 11 unknowns (we fix /i = 1): musically speaking, there are 12 distinct ratios of each kind (not counting repetition in octaves) and there are 11 kinds of ratios. The fundamental ratios 3/2 and 4/3 (perfect fifth and perfect fourth) are well approximated. The most irritating of these errors is the major 3rd and minor 6th, followed by the minor 3rds and major 6th. They are: minor second: major seventh, major second: minor seventh, minor 3rd: major sixth, major 3rd: minor sixth, perfect 4th: perfect 5th, diminished fifth: diminished fifth. For example, for each perfect 4th there is a complementary perfect 5th, and their errors are dependent. Moreover the errors in the seconds, sevenths and diminished 5th are of negligible importance. We shall consider therefore optimization over the intervals of the major and minor 3rds and pure fifths. With respect to perfect fifths, minor and major thirds are complementary, since Fi+3-Fi + Fi+7-Fi+3 = Fi+7-Fi. Observe that, however, if any 2 of the intervals Fi+3 - Ft, F,+7 - Fi+3, and Fi+7 - Ft, are just, the remaining one is just. For optimization, therefore, we consider only the intervals of the pure fifth and major 3rd. Observe that 3 consecutive major thirds must sum to 1200 cents, and just major 3rds are 386 cents. If all these consecutive 3rds are in equal use in a musical composition, these 14 cent errors are optimal. If some major 3rds are rarely used, we can make them larger than 400 cents and render the errors in the consecutive neighbors smaller. Also, we may wish the errors to be unequal to change "color"-have some major thirds "smooth" (small errors) and others rough (large errors). Since the renaissance almost all of Western music has been constructed of chords based on triads. A major triad on F) is the chord (F),F i+4,F i+7 }, here Fi+4-Fi is a major 3rd, Fi+7-Fi+4 a minor third and Fi+7-. This means that errors in the thirds from just intervals are less in absolute value than approximately 25 cents, and errors in perfect 5ths less than approximately 12 cents in absolute value. To do this we shall specify all the major thirds and optimize over the perfect 5ths. We use these to optimize over the fifths: Jsing (3) we can rewrite (4) as: the above is a system of 12 equations in 3 unknowns. Let A be an m x n matrix, x and b column vectors of dimension n and m, respectively. We shall use 2 such functions: and An optimal solution of Ax = b with respect to the norm · is an rc-vector x such that the vector x always exists and it effects the best "compromise" solution in the sense that the m-vector Ax is as close as possible to the m-vector b, (Closeness here is measured by our distance function ·. When · co is used it is possible to find xx as a solution of a linear programming problem. This distance function is a natural one for musical scales, because the worst departure from just intonation is made as small as possible. If j Axco-6 U = Ui^Ax^-b)^, u,r = ±1, 1 s k g r g m, and 0 belongs to the convex hull (uikAik: 1 ^ k g r], then Afco-i oo = -4j:-^ eo for all n-vectors x. We shall see below that because of special structure in the examples below x2 = *<», so that the least squares solution may be employed. Again, because of the simple structure of the scale equations a criterion of optimality can be employed which would not be useful in general. In general we could not expect more than n components of Ax -b to vanish for any x, but because of the special structure in the scale problem this can happen. We first consider equal temperament from the point of view of optimizing over the perfect fifths. For equal temperament we set a, = 400 and get from (5) (The set (6) is repeated 3 times. Since \Ax - b\x = 2 and 0 belongs to the convex hull of {-A l,A2,A3, A4}, Ax is a best uniform approximation of b also. This temperament called the common model meantone temperament, or simply meantone temperament, was the most used single temperament for approximately 200 years. The 8 relative minor triads are very consonant with minor 3rds in absolute error of 5. The urge for the general use of more than 8 major and minor triads led to the development of well-tempering. Bach was reported to have said he was not in favor of equal temperament, so that his "well-tempered Clavier" must have had a temperament such as the Werkmeister # 1 in mind. The optimal interpolatory solution of the above system is unique and 8 equations are satisfied. For these 9 equations to be satisfied (T) must be consistent with «i = 90, «2 = 294, «3 = 96 and «4 = 102. They are "1 "2 "3 "4 90 90 90 300 294 294 96 96 102 102 96 102 There are no others. If k letters are drawn at random and without replacement from the box, then the sample may contain some twin pairs. If many twin pairs result to the extent that the probability of that happening is small, then the randomness of the selection process is suspect and evidence for a pairwise association exists. In this paper we introduce statistics for testing the null hypothesis that there is no pairwise association for this model and two companion models. Using only the assumption of randomness we find exact and asymptotic formulas for these statistics and we point to some applications. In order to define the problem explicitly, it is instructive to exhibit the manner in which it arose. More important, however, is the fact that the formulas are applicable in several other settings where the model (sometimes subtly) fits. For the past several years many swine herds throughout the United States have experienced a problem of tuberculosis lesions. In 1972 the Meat Inspection Regulations were amended so as to require the entire carcass condemned if lesions are found in more than one site. This change along with the increase in the price of hogs has brought this problem to its present significance; it particularly affects the farmers and meat packers. As in most epidemiologic investigations, many issues surface including the necessity to account for about twenty-five host, parasite and environmental factors. Roughly, the empty house is filled with pregnant sows and when the piglets become a certain age, they are moved to a nursery. In addition to several management-health questions, the following emerged: Is there any evidence based on the data that suggests that the health situation would significantly improve if (through design or renovation) there were no between-pen contact under the heat lamps? Implicit here is the idea that if there are lesions (one or more) from pigs farrowed in a given pen, then such are more likely to be found via its paired pen; i. In these cases the oe pairs represent the pairs for which we are testing for pairwise association. Let X be a random variable denoting the number of marked oe pairs (pairs sharing common facilities and for which infection is observed). Let f(n, k) denote the number of distinct selections of k letters from the n letters of the sequence such that no oe pair is selected. If k is the total number of infected individuals in a group of n and if a is an integer, then the probability that X is larger than or equal to a is where r is the number of oe pairs; r = n/2 if n is even and r = (n~ l)/2 if n is odd. The hypothesis, H0, of no pairwise association may be tested by setting a equal to the number of observed marked pairs so that P(X ^ a) is the probability of getting an arrangement at least as extreme as the one we observe under the assumption of randomness. For the n even case, all selections of k letters for which no oe part is present can be realized by first selecting k oe pairs and then choosing one letter from each pair.
Once more blood pressure normal value order 162.5mg avalide mastercard, while the U-operator and Fundamental Formula were proving their worth algebraically hypertension nos definition cheap avalide 162.5mg visa, they popped their heads up again in differential geometry in work of Koecher: Ux arises naturally out of the inversion map j(x) = -x- 1 by Ux = (aj lx)- 1 for aj lx the usual differential (best linear approximation) of the nonlinear map j at the point x blood pressure bottom number is high order 162.5mg avalide with amex. A Springer [Sp] to base an entire theory and classification of Jordan algebras on the operation of inversion heart attack 2o13 order avalide 162.5 mg with amex. This identity is relatively easy to derive by an argument appealing to Zariski density and change of unit element blood pressure by palpation order 162.5 mg avalide free shipping. It was Jake who showed how to change units in Jordan algebras (passing from] with unit 1 to an "isotope" with unit u blood pressure 9058 buy generic avalide 162.5 mg, for any invertible u) and demonstrated the power of this method in Jordan theory. This is a generalization of the determinant for matrices, more generally of the "reduced norm" on finite-dimensional associative algebras. He showed that the generic norm could be defined for any finite-dimensional power-associative algebra, i. The key idea was that the "generic element" satisfied a generic minimum polynomial xn - 0"1(X)Xn - 1 +. For ordinary associative matrix algebras these are just the usual trace and determinant, and the generic minimum polynomial is the characteristic polynomial. The key player here was the generic norm N(·),since the minimum polynomial could be recovered as N(i1 - x) = i n - 0"1 (x)i n - 1 +. Any quadratic form Q is the generic norm of a jordan algebra of "degree 2", x 2 - T(x)x + Q(x)l = 0. Only certain very special cubic forms, such as with the Albert algebra, arise as generic norms of "degree 3" Jordan algebras, x 3 - T (x)x 2 + S(x)x- N(x)1 = 0. We no longer say, with Cartan, that the exceptional Lie group Ј5 arises as a group of transformations preserving a certain cubic form on 2 7-dimensional space; we say that Ј5 arises as the group of linear transformations on the 27-dimensional Albert algebra that preserve the generic norm, or equivalently, the surface N (x) = 1. Similarly, F4 arises not as the isotropy group of a point on the cubic surface, but as the isotropy group of the identity element, or better, as precisely the automorphism group of the Albert algebra. Like Athena springing full grown from the mind of Zeus, this theory sprang grown full from the mind of Jake. This was the first truly ring- jacobson at his 75th birthday celebration, t h eore tic ap - 1985, with Efim Zelmanov. The Jordan product xyx does not have a left or right like the associative product xy; it has an inside and an outside. If there is a scalar available, these outer ideals are the same thing as ideals (two-sided, b oth inner and outer). Saltman Nathan Jacobson has had an important and deep influence on the theory of central simple algebras despite the fact that he wrote on the subject only at isolated points of his career. His contributions can be divided into distinct time periods, separated by periods when he published in other areas. His influence was not only exercised by means of research papers but also through his exposition of known results in monographs. In that work he traced the connection between cyclic algebras and twisted polynomial rings. The deepest part concerned the so-called Schur index, which is the degree of the division algebra associated to a central simple algebra. In his thesis Jake shows that the Schur index of a cyclic algebra can be computed by knowing the factorization of a polynomial in the twisted polynomial ring. Though this work dates to 1934, the point of view is still being exploited and generalized, for example, in the work of Louis Rowen. In the then-current theory of central simple algebras, an important place was occupied by the socalled Noether-Skolem Theorem, which concerned automorphisms of these algebras. He proved that every derivation of a central simple algebra, trivial on the center, was inner. His next result had no automorphism version: Jake proved that every derivation on the center extended to the whole algebra, a result clearly false for automorphisms. These observations turned out to be crucial in the theory, then just begun, of so-called p-algebras, which are central simple algebras of prime characteristic p and degree a power of p. Jake could rewrite cyclic algebras of degree p in terms of derivations instead of automorphisms. The next paper on central simple algebras, of particular note, is on another topic still. In [15] Jacobson began his study of central simple algebras with involution, a subject he concerned himself with until the end of his career. An involution of A is an anti -automorphism of order 2, and for the moment an involution will always be the identity on the center F of A. If A= EndF(V), then involutions correspond to similarity classes of symmetric or antisymmetric nonsingular bilinear forms on V. In the symmetric case (that of a quadratic form) the involution is called orthogonal, a concept that generalizes to an arbitrary central simple A. Given a quadratic form, one can define the useful and important Clifford algebra and even Clifford subalgebra. This was the important first result in a continuing long program of many people. Tignol) that has extended many parts of the theory of quadratic forms to involutions. An involution on A, still trivial on the center, which is not orthogonal is called symplectic. If S c A is the space of elements fixed by a symplectic involution, then there is a form p on S, called the Pfaffian, whose square is a form of the determinant restricted to S. In [79] Jake showed that the function field L of the zero set of the Pfaffian was a so-called "generic! That is, A 0 F L has Schur index 2 in the nontrivial cases, and any other field with this property is a specialization of L. This was the first (and best understood) example of what one calls generalized Brauer-Severi varieties. If A is a central simple algebra with center F and F is the algebraic closure ofF, then A 0 F F is isomorphic to a ring of matrices Mn(F). However, this map can be defined on A itself and is then called the reduced norm n: A ~ F. Jake showed that this polynomial carries a surprising amount of information about the algebra-structure of A. Namely, he showed that a linear map f: A ~ B that preserves 1 and preserves the norm, must be an isomorphism or anti-isomorphism. This result is a special case of the Jordan theory in [76], where it arises, in the above form, only after combining other results. The Third International Mathematics and Science Study documented how mathematics teaching in the U. Politicians, noticing that citizens now care about education, have instituted quick fixes such as highstakes standardized tests, with budgets cut, principals fired, and students failed if they do not measure up. Most large states are suffering dire teacher shortages, especially in urban schools; mathematics is one of the subjects suffering the most. Most of the population thinks that learning mathematics is learning terms and practicing procedures, as do most elementary school teachers and some middle and high school teachers. Even if a consensus were reached about what to teach and how, it takes time for teachers to learn new material and adjust to new teaching methods. Three times through a lesson is a good rule of thumb for mastering a new teaching technique; for most K-12 teachers this means three years. And districts, for the most part, have not accepted the fact that teachers need time every day to discuss and reflect on teaching and mathematics with their colleagues. So how could a bunch of mathematics teachers get all these cats on the same track and steer the oceanliner of U. These organizations appreciated the fact that a knowledgeable group had organized the subject and laid out general recommendations. Many (probably not most) teachers began to rethink their teaching methods, and many districts tried new curricula. Since we may never have a national curriculum, this is the closest we will get to national standards. The updated version of the Standards, released this year under the title Principles and Standards for School Mathematics, was written with significant input from mathematicians; this was not the case with the 1989 Standards. Principles and Standards is intended to be read by many different groups: mathematics teachers and supervisors, local and state educational administrators, mathematicians, politicians, parents, and business and community leaders. Readers will find little gems of mathematics lessons, such as the young child who discovers, using a calculator, that one cannot ever get to 100 by counting by 3s, then uses other mathematical props to explain why. In addition to text there are mathematical illustrations, diagrams and graphs, reproductions of student work, references to "E-examples" (interactive activities or video clips on the Standards Web site), and photographs of classrooms showing ways of organizing a mathematics class other than by having students sit in rows of desks, listening or writing. Principles and Standards is carefully organized: the edges of pages are color-coded by grade band, with the ten standards listed down the side as tabs. So it is easy to find, say, "Geometry" in grades 9-12, or "Reasoning and Proof" in pre-K-2. The Web version is especially convenient for novices in mathematics education: one does not have to invest the time or money to order a paper copy. Chapter 8, "Working Together to Achieve the Vision", outlines what must be done and by whom to successfully reform mathematics education. Much of the vitriol in the "math wars" that broke out in the 1990s comes from deeply held beliefs about mathematics education: that traditional Euclidean geometry is the best, or the worst, way to teach mathematical reasoning; that paper-andpencil calculation is the key to , or a major impediment to , understanding numbers; that calculators should not be used until paper-and-pencil arithmetic has been mastered or that they should replace paper-and-pencil arithmetic. Mathematics education research does not give definitive answers to these questions, and many thoughtful teachers would agree with parts of each opinion. We need to set aside our differences and get down to the urgent business of convincing the American citizenry that teachers and schools need respect and financial support, convincing administrators that teachers need continuing professional development, convincing current and future teachers that knowing more mathematics is a vital professional requirement, and convincing students that it is possible and important to understand mathematics. Who can argue with a document that sets forth, in a very clear and well-organized manner, the consensus agenda for the subject matter to be learned in the K-12 cycle? There is no consensus on teaching mathematics, and perhaps in the best of all possible worlds, there need not be one. The danger is that the individual user, for whatever reason, cannot or will not read the document critically; the danger is greatest with regard to teaching methods. A teacher can read it and "check off" mathematical topics, but cannot read it and "check off" teaching methods, even though I firmly believe that there are many teachers and mathematics supervisors around the country who will do just that. The last time the bar was raised too high, the result was the so-called "new math", which cannot be judged a success by any measure. Thus, more attention can be given to understanding the number Herbert Clemens is professor of mathematics at the University of Utah. What is perhaps underappreciated in such debates is the fact that rote learning is not the enemy of mathematical understanding, but an essential vehicle to it. For example, many if not most students cannot develop an intuition for abstraction and symbolic manipulation without first correctly manipulating a lot of symbols. Perhaps one of the principal disappointments in the"math wars" has been the failure of the participants to acknowledge that appreciation of this fact is shared by both sides. But, as is natural for a document prepared and vetted by a large cross-section of the professional community, it reflects the fact that our community has a long way to go to get the balance right. The evolution of the reading wars finally led to the recognition of the necessary balance and constructive tension between "phonics" and "whole language". Of course we all believe that teachers should teach with conceptual insight and clarity and should use all the tools at their disposal to convey the mathematical essence clearly and persuasively to as many students as possible. But let us not forget that training "by rote" is a less dangerous weapon in the hands of a teacher of limited mathematical preparation and understanding than are attempts to foster understanding in others that one does not have oneself. Perhaps students at the secondary level find proof so difficult because their only experience with writing proofs has been in a high school geometry course, so they have a limited perspective. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts. And if that is the case, how on earth can we ask teachers to foster these skills in their students, except perhaps with vehicles (not yet invented) that work in a "teacher-proof" context? The "math people" are busy at an easier job, earning four times as much at some dot-com enterprise down the street. Let us be very careful about asking teachers for more than we have any right to expect. We run the risk of disrespecting the profession and its high level of skill and dedication and of foisting upon it the responsibility for remedying a deficiency that we as a society cause by the reward structure we have designed and perpetrated. Of course, when it comes to my own area, geometry, I must admit that I cringed when I read: Geometric ideas are useful in representing and solving problems in other areas of mathematics and in real-world situations, so geometry should be integrated when possible with other areas. Elements of the larger picture include: a) Here is a document that says that it is the ideas in mathematics that count. Four of the ten standards are about ideas-problem solving, reasoning and proof, communication, and connections. In pre-K-2, students should learn "addition facts"-the sums of all pairs of single-digit numbers. In 3-5 they should also learn the multiplication tables and "develop fluency" with whole-number arithmetic-all four operations. In 6-8 they should "develop and analyze algorithms for computing with fractions, decimals and integers, and develop fluency in their use. A mathematically attentive reader will find items that jar at all levels and in most parts of the document, at least the ones that I looked at. On page 144, lines 4-7, the indicated calculation appears to produce a fifthgrader 2 meters tall and an adult with a height of 2. On a higher level, on page 314, it is explained how to set up a coordinate system to produce a manageable proof that the medians of a triangle are concurrent. However, the "best", or mathematically most natural, proof of this is coordinate-free, with vectors, which are one of the recommended techniques, along with coordinates, in the first bullet of the third geometry expectation (page 308). Or, just across on page 315, why is so much effort expended with no attempt to formulate the precise relation between a transformation and a matrix: that the k -th column of the matrix is the image of the k-th standard basis Roger Howe is professor of mathematics at Yale University.
Clinical presentation can vary from incidentally discovered hypoglycemia to encephalopathy blood pressure 210 over 110 purchase avalide 162.5mg with visa. Sulfonylureas act to increase insulin secretion by the beta cells of the pancreas blood pressure yahoo order 162.5 mg avalide free shipping. Insulin acts to decrease lipolysis which then decreases production of fatty acids blood pressure medication beginning with m order avalide 162.5 mg with visa. This in turn blood pressure medication bystolic side effects generic avalide 162.5mg on-line, decreases ketone body (as ketones are synthesized from fatty acid breakdown) formation resulting in hypoketotic hypoglycemia heart attack the song avalide 162.5mg with amex. Following initial fluid resuscitation heart attack or stroke buy generic avalide 162.5mg on-line, the serum sodium should be corrected over 2448 hours. The brain has been found to make "idiogenic osmoles" in order to preserve cerebral oncotic pressure and to prevent neuronal shrinkage. Administering too much free water (such as D5W) too quickly can lead to cerebral edema and seizures, thus the hypernatremic dehydration must be corrected slowly. Although it may seem paradoxical to treat polyuria with a diuretic, depletion of sodium (due to diuretic therapy) results in increased reabsorption of sodium and water in the proximal tubule. Fludrocortisone is a mineralocorticoid agonist used to treat deficiency of aldosterone. Fluid restriction is dangerous in the face of diabetes insipidus as it can lead to severe dehydration in a short period of time. Insulin has no benefit in this patient, although diabetes mellitus usually also presents with polyuria, polydipsia, and weight loss. The breakdown may be so severe as to put the neonate at risk for bilirubin encephalopathy and require exchange transfusion. Gallstones may occur causing hepatomegaly in those with pyruvate kinase deficiency. This accumulation of copper results from impaired incorporation of copper into ceruloplasmin and decreased biliary copper excretion. Typically, the first organ to demonstrate signs of dysfunction from copper deposition is the liver. Deposition of copper in Descemet membrane, known as Kayser-Fleischer rings, may be absent in young children. Polyuria is not a common symptom, but renal dysfunction can occur causing Fanconi syndrome. Avoidance of milk products and other products, such as some medications or candy that contain lactose, is important. If started early in the neonatal period, this diet can prevent the formation of nuclear cataracts, usually the sole manifestation of this disease. Eliminating gluten would be the treatment for celiac disease, while providing increased amounts of folate may be helpful in pyruvate kinase deficiency. It is associated with coarse facial features, clouding of the corneas, deafness, airway obstruction, hydrocephalus, thickening of the cardiac valve leaflets, cardiomyopathy, congestive heart failure, poor growth and development, mental retardation, and early death often secondary to cardiopulmonary problems. Hypophosphatemic rickets is characterized by low serum phosphate caused by abnormal renal phosphate loss. Vitamin D deficiency rickets results from poor absorption and/or poor intake of vitamin D. Dark-skinned, breastfed individuals born in the winter are at particular risk for vitamin D deficiency rickets. Breast milk is known to have insufficient vitamin D; and supplementing breastfed children is recommended. Children with cystic fibrosis may also have vitamin D deficiency rickets caused by poor vitamin D absorption due to pancreatic insufficiency. Finally, children with 22q11 deletion syndrome may have hypocalcemia, but this is typically due to the congenital absence of parathyroid glands. The dietary supplements and bone marrow therapy seem to be more successful when instituted prior to onset of neurologic symptoms. Babies with this defect may have a severe lactic acidosis with resultant tachypnea, hypotonia, lethargy, and coma in the first few days of life, or the disease may not manifest itself for months to years until the child is stressed by infection, prolonged fasting, or other conditions requiring increased gluconeogenesis. Treatment centers on reducing gluconeogenesis (the major pathway is through pyruvate) by providing a high-fat, low-carbohydrate diet, normalizing blood sugars, and administering sodium bicarbonate and carnitine. Beta-hydroxybutyrate and acetoacetate are ketone bodies and play a prominent role in diabetic ketoacidosis. Some patients also have opalescent dentin (dentinogenesis imperfecta), and many develop conductive hearing loss in adolescence. At least four types have been described, with differing modes of inheritance and varying degrees of severity. Phenotypically, people with achondroplasia have rhizomelic short stature, flat nasal bridge, and prominent forehead. Those with histiocytosis X demonstrate sharply demarcated osteolytic lesions on x-ray rather than osteopenia. Children with rickets may have leg bowing and/or flared wrists noted on x-ray in addition to osteopenia. Osteogenesis imperfecta is the only choice that has blue sclera associated with it. The metabolic acidosis and phosphate loss seen in this disorder lead to growth failure and vitamin D-resistant rickets. Congenital adrenal hyperplasia typically demonstrates hyperkalemia and hypernatremia. Impaired metabolism of the common essential amino acid phenylalanine to tyrosine leads to build-up of phenylpyruvic acid and phenylethylamine. These products as well as excess phenylalanine lead to central nervous system damage. The screening is performed by collecting blood spots on filter paper at the time of discharge from the hospital to home and before 7 days of life. Infants discharged at less than 24 hours of age should have the screening test repeated prior to 14 days of life. Reducing phenylalanine in the diet will then reduce the serum levels and help reduce the consequences of the disease, which include brain damage, mental retardation, seizures, athetosis, hyperactivity, and behavioral problems. The diet is difficult to adhere to , and creates increased stress on the child and the family, which adds to the complexity of the disease. Pancreatic secretions contain sodium at 120140 meq/L, potassium at 515 meq/L, chloride at 100150 meq/L, bicarbonate at 100 meq/L; bile contains sodium at 120140 meq/L, potassium at 515 meq/L, chloride at 80120 meq/L, and bicarbonate at 40 meq/L. Knowledge of body fluid composition is useful in understanding the metabolic derangement seen. Typically, bilious vomiting results in isotonic dehydration and either a neutral pH or acidic pH. This contrasts with pure gastric losses, such as those seen in pyloric stenosis, where the dehydration typically results in a hypochloremic, metabolic alkalosis. Classic findings are aminoaciduria, phosphaturia, and glycosuria with resultant hyperchloremic metabolic acidosis with normal anion gap. There are multiple causes of this disorder including inborn errors of metabolism 142 6: Fluids, Electrolytes, and Metabolic Disorders 33. Defective or total lack of galactose1-phosphate uridyl transferase causes an inability to convert galactose into glucose. Galactose-1-phosphate is then converted to glucose-1-phosphate by the enzyme in question. Without the enzyme, galactose-1-phosphate accumulates, causing parenchymal damage to the kidneys, liver, and brain. Indirect hyperbilirubinemia, acidosis, and urosepsis (classically due to E coli), frequently are seen at presentation. Other manifestations include hypoglycemia, hepatomegaly, vomiting, seizures, and cataracts. The resultant hypochloremic metabolic alkalosis can be profound, and must be corrected prior to surgery. The incidence is approximately 1/150 male infants and 1/750 female infants and the risks are greatly increased in male infants born to mothers who had pyloric stenosis. It is an X-linked trait with affected males typically presenting as neonates with extreme hyperammonemia while citrulline levels are significantly reduced. Therapy includes a restricted dietary protein intake and special foods with only essential amino acids, l-citrulline, and sodium phenylbutyrate. Pulmonary symptoms include chronic cough and sputum production, persistent radiographic changes (hyperinflation, atelectasis), wheezing, nasal polyps, and digital clubbing. There are capabilities to do newborn screening, but this is not in widespread use at this time. Such aggressive fluid resuscitation is the mainstay of preventing and treating shock. Use of hypotonic fluids results in loss of fluid intracellularly, cell lysis, and potentially life-threatening cerebral edema. Other fluids such as albumin and blood can be used for volume expansion, but usually are not as readily available as crystalloid solutions in emergent rehydration situations. Depending on the degree, severity, and nature of the volume loss, two to three isotonic fluid boluses of normal saline (154 meq/L of sodium and chloride) may be required. Answers: 3343 143 One reason is that sodium will effectively stay in the intravascular space and help to expand the intravascular volume because it does not readily cross intracellularly. The second reason is the record of safety in administering isotonic fluid as opposed to hypertonic or hypotonic fluid. Even in cases of severe hypernatremic or hyponatremic dehydration, the additional sodium and free water provided with even two to three boluses of the isotonic fluid is negligible in its impact on the serum sodium level, especially when repleting the intravascular space of a patient in shock or near shock. Males and females are affected equally, though diagnosis in males is often delayed outside the newborn period until they experience a "saltlosing" crisis (usually in the second week of life after maternal mineralocorticoids are metabolized) or show evidence of increased masculinization. Many states have added 17-hydroxyprogesterone levels to the newborn screening in order to detect those male infants without ambiguous genitalia. The findings on physical examination of a prominent clitoris and labial fusion are suggestive of virilization, and further support the diagnosis of adrenal insufficiency. Although a viral gastroenteritis could explain the dehydration in an older infant or child, it would be less likely in a neonate of this age. In stressed children (ie, those experiencing illness or saltlosing crisis) a "stress" dosage should be administered of the glucocorticoid that is two to three times the daily calculated replacement. Many causes of macrosomia (eg, previous large-for-gestational age infants and maternal diabetes) are associated with abnormal glucose metabolism. The additional findings of ear anomalies could implicate a calcium abnormality (eg, DiGeorge anomaly/sequence), but the child has no heart murmur and is not failing to thrive at this point, making this a less likely diagnosis. Physical findings are characterized by macrosomia, microcephaly, visceromegaly, and macroglossia. Other associated anomalies are an increased incidence of hemihypertrophy, omphaloceles, cryptorchidism, and renal tumors. Transmission is often from a sporadic mutation on chromosome 11p15, although autosomal dominant inheritance is also seen. Mild to moderate mental deficiency has been reported in this disorder and is thought to be related to neonatal hypoglycemia. Smallfor-gestational-age infants and premature infants both have increased incidence of symptomatic hypoglycemia. A majority of their glucose problems are related to deficient glycogen stores, muscle protein, and body fat needed for metabolization to meet energy requirements. Infants born to diabetic mothers also experience an increased incidence of hypoglycemia. However, hypoglycemia in infants of diabetic mothers is not due to insufficient stores, but is due to hyperinsulinemia and low glucagon levels. Beckwith-Wiedemann syndrome infants also experience hyperinsulinemia which causes hypoglycemia. Treatment for these infants is the same as for other causes of hyperinsulinism; supportive administration of intravenous glucose at a rate of 68 mg/kg/min. At times, more aggressive treatments are warranted (eg, increased rates of glucose administration and supplementation of regulatory hormones by injections of steroids and growth hormone). When ingested, a small quantity can cause a rather toxic ingestion because one teaspoon (5 cc) of this liquid contains an amount of salicylate equivalent of 22 adult aspirin. Salicylate ingestions are impressive in the unique metabolic derangements comprised of a mixed respiratory alkalosis with metabolic acidosis. Initially, the salicylate is absorbed rapidly and directly stimulates the respiratory center causing tachypnea and a respiratory alkalosis. Eventually, lactic acid levels, along with other metabolic acid levels, begin to rise in the serum resulting in a severe acidosis. Symptoms of hyperpnea, tachycardia, lethargy, vomiting, dehydration, and coma can occur. Treatment is directed at primarily supportive care until the toxicity has been corrected. Acetaminophen overdose leads to initial nonspecific symptoms, followed by liver dysfunction. Ethanol ingestion is not associated with a respiratory alkalosis but is associated with a metabolic acidosis. These management steps along with good supportive care will minimize the duration of toxicity and facilitate rapid recovery of the patient with the least amount of adverse effects. Patients with salicylate toxicity typically are approximately 5%10% dehydrated and have experienced losses of potassium and hydrogen via the urine. Therapy includes both aggressive rehydration and alkalinization of the urine with administration of sodium bicarbonate. In severe ingestions, hemodialysis may be necessary if the quantity Answers: 4454 145 of ingestion, level of salicylates, and observed toxicity are not responding to conventional measures. These precursors exist in elevated amounts in the skin creating the reactions to ultraviolet light. This disease is an autosomal recessive disorder resulting in absence of the betalipoproteins in the plasma.
Please send this information to: Committee on Staffing arteria meningea anterior buy avalide 162.5mg fast delivery, Department of Mathematics heart attack 30s buy avalide 162.5mg low price, University of Utah blood pressure medication reviews purchase 162.5mg avalide with visa, 155 S heart attack 4 blocked arteries buy avalide 162.5mg with amex. The University of Utah is an Equal OpportunityI Affirmative Action Employer and encourages applications from women and minorities and provides reasonable accommodation to the known disabilities of applicants and employees arteria bulbi vestibuli order 162.5mg avalide with mastercard. Hildebrandt Research Assistant Professorships Description: these positions for up to three years are designed to provide mathematicians with favorable circumstances for academic career development in research and teaching blood pressure medication with the least side effects order 162.5 mg avalide with visa. These positions may be combined with other postdoctoral fellowships, giving additional reductions in teaching responsibility. Grant amount: Salary is competitive, and there are opportunities for supplemental summer salary. Application information: Application forms and further important information are available at http: I / University of Wisconsin-Madison Van Vleck Assistant Professorship Description: the Department of Mathematics invites applications for possible Van Vleck assistant professorships to begin on August 27, 2001. Eligibility: Ordinarily only those applicants who have received their doctorates since 1998 will be considered. Preference will be given to candidates who are likely to interact well with other members of the department. Deadline: the application deadline is December 15, 2000, although applications will continue to be considered until all available positions are filled. Applicants should also arrange to have three or four letters of recommendation sent to the above address. The University of Wisconsin is an Affirmative Action/ Equal Opportunity Employer and encourages applications from women and minorities. Teaching duties for the entire three-year instructorship are 9 onesemester courses. The hiring committee will select candidates based on excellence in teaching and research. The teaching load consists of three courses per year, two in one semester and one in the other semester. The teaching assignment normally includes introductory courses for undergraduates as well as specialized graduate courses. Eligibility: To be eligible for a fall 2000 appointment, a candidate must complete all requirements for the Ph. Current research interests of our faculty include: algebraic geometry, commutative algebra, complex geometry, foliations, functional analysis, harmonic analysis, low-dimensional topology, mathematical biology, operator theory, partial differential equations, probability and statistics, real and complex analysis, representation theory, Riemannian geometry, and wavelets. Deadline: We will begin reviewing applications on December 1, 1999, and continue reviewing applications until all positions are filled. Application information: Applicants should submit a curriculum vitae, thesis abstract, statement of research plans and interests, and should arrange for four letters of recommendation. Application materials and inquiries should be sent to the Chauvenet Search Committee, Department of Mathematics, Washington University in Saint Louis, Campus Box 1146, One Brookings Drive, St. Washington University is an Affirmative Action/ Equal Opportunity Employer and specifically invites and encourages women and minorities to apply. Travel and Study Abroad Alexander von Humboldt Foundation Research Fellowships Description: the Humboldt Foundation grants 500 Humboldt Research Fellowships annually to highly qualified scholars holding doctorates under the age of 40, enabling them to undertake long-term periods of research (6-12 months) in the Federal Republic of Germany. Applications are decided upon by a Selection Committee, which is composed of eminent German scholars from all disciplines. Eligibility: Application requirements include high academic qualifications, academic publications, a specific research plan, and for humanities scholars a good command of the German language. Family allowances, travel expenses, and language courses are covered by the fellowship. Deadline: Applications may be submitted at any time; however, the actual selection committees meet in March, July, and November. Applications should be submitted 5 months before the meeting at which the candidate wishes to be considered. Application information: Interested scholars may contact the Alexander von Humboldt Foundation, Jean-PaulStr. Yale University josiah Willard Gibbs Instructorships/Assistant Professorships Description: Offered to men and women with the doctorate who show definite promise in research in pure mathematics. Nominations for awards must be made by eminent German scholars; direct applications are not accepted. Eligibility: Scholars must have a position as a full/ associate professor and an internationally recognized research record. Application information: Nominators may contact the Alexander von Humboldt Foundation, Jean-Paul-Str. American-Scandinavian Foundation Description: Grants and fellowships for study or research in Scandinavia (Denmark, Finland, Iceland, Norway, and Sweden). Necessary language competence, financial need, and merit in pursuing the study program in Scandinavia are considered in making these awards. Application information: Write to the Exchange Division, the American-Scandinavian Foundation, 15 E. Administrator Exchange Program also offers an eightweek summer seminar in Italy which is open to college and university faculty and teachers (grades 9-12) of Latin, Greek, and the Classics. In addition to the general eligibility requirements, each applicant must meet the specific subject, level, and language fluency requirements for the countries to which he/she applies; these requirements are detailed in the application booklet. Grant amount: Grants to teach abroad include round-trip transportation for the participant (except Canada and the United Kingdom). Application information: the application booklet should be requested from the Fulbright Teacher Exchange Program, 600 Maryland Ave. The principal duties will be to do research and to teach a graduate course in the area of your specialty. Eligibility: Offered to young mathematicians with doctorates who show definite promise in research. Grant amount: Salary equivalent to that of assistant professor in the mathematics department. Marshall Scholarships Description: Up to forty scholarships are offered by the British Government to U. Fulbright Teacher & Administrator Exchange Program Description: Sponsored by the United States Department of State, this program offers international exchange opportunities for two-year and four-year college faculty members and elementary and secondary school teachers and administrators. Currently the program conducts exchanges with thirty-one countries in Eastern and Western Europe, Latin America, Africa, and Canada. Applicants for the project development visits need to demonstrate that a joint proposal for collaborative research will be prepared during their visit for submission to the National Science Foundation for funding. Acceptable topics include physics; chemistry; mathematics and computer sciences; earth, atmospheric, and oceanographic sciences; biological sciences; environmental sciences; engineering; archaeology and anthropology; geography; psychology; science and technology policy; economics; linguistics; or the history and philosophy of science. Student Program Fulbright and Related Grants for Graduate Study and Research Abroad Description: For graduate study or research in any field in which the project can be profitably undertaken abroad. National Science Foundation International Research Fellows Program Description: the International Division of the National Science Foundation administers a program to introduce scientists and engineers in the early stages of their careers to research opportunities abroad. The program provides support to carry out research at science and engineering establishments in foreign countries for periods of three to twenty-four months. Applications from women and minorities and for work in developing countries are especially encouraged. Research may be done in any field of science and engineering supported by the National Science Foundation. Appropriate host institutions are institutions of higher education, science and engineering centers, and nonprofit industrial and government research institutes. Eligibility: Eligible applicants, in addition to being citizens or permanent residents of the United States, must have earned a doctoral degree within six years of the date of application or expect to receive their degree by the award date. Grant amount: Awards will consist of round-trip economy airfare, in-country travel, a modest living allowance, health insurance, and dependent allowance for visits of six months or more. Application information: Interested persons should contact the National Science Foundation for details and application materials. Applications must include a letter of invitation from the proposed host institution. Grant amount: Tuition and living allowance worth approximately $27,000, depending upon course. Application information: Application forms are available from representatives on campuses of colleges and universities participating in the program. Six of the 46 awards are available to members of the International Federation of University Women to study in any country other than their own. Upon completion of studies, fellowship recipients are expected to return to their home countries to pursue professional careers. Directory of fellowships, grant support programs of government agencies, foundations, corporations, and business and professional organizations. American-Scandinavian Foundation Description: Scandinavian scholars are awarded graduate fellowships to study in the U. Application information: For information write to the appropriate society in Scandinavia cooperating with the American-Scandinavian Foundation (The DenmarkAmerica Foundation, Fiolstraede 24, 3. Education, University of Iceland, Neshaga 16, 107 Reykjavik, Iceland; the Norway-America Association, Radhusgt. Financial Aid for Minorities in Engineering and Science Financial assistance, scholarship and fellowship programs, resources for further information, 1999, Garrett Park Press, P. Grant amount: the number of awards varies each year according to total funds available. Sources of Fellowship Information Some of the publications listed below are available at school or college and university libraries or in the reference room of a good public library. Indexes organize grants by sponsor, field of study, academic level, and type of award, amount of support, destination. Identifies awards targeted for women, for minorities, and for other specific populations. Academic Year Abroad 2000/2001 Describes 2,617 academic-year and semester-length programs, offered by U. Key information on application procedures and requirements, academic credit, addresses and phone contacts, costs, fields of study, languages of instruction, housing, travel and orientation. Introductory section on planning study abroad and on how to read study-abroad literature. Indexes to sponsor institutions, consortia, fields of study, cost ranges, and special options such as internships, student teaching, and independent study. Study Features detailed descriptions of more than 600 fellowships, grants, scholarships and paid internships. For undergraduates, graduate students and postdoctoral students as well as working professionals. Professor in Mathematics Preference will be given to candidates in Algebraic Geometry, Topology or Algebra. Applicants are expected to have a strong research record and leadership in their field of expertise. Please submit applications with a curriculum vitae and a list of publications no later than November 30, 2000 to the Dekan der MathematischNaturwissenschaftlichen Fakultat der Universitat Zurich, Prof. Central Bureau Publications the Central Bureau is the agency funded by the education ministries of the U. Vacation Study Abroad 2000/2001 A guide to 2,239 short-term and summer programs offered by U. Etheridge, University of Oxford, England Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. Specific results are given, including extensive references to current literature for their general form. The successful candidate will have academic credentials qualifYing for appointment at the rank of fuii professor at the University of Louisville. Applicants are expected to have a strong and ongoing research record, demonstrated excellence in undergraduate and graduate education, commitment to faculty development, and possess superior leadership and communication skills. The following experiences will be viewed favorably: successful grant writing, curriculum and program development, graduate teaching and involvement with professional organizations. The Chair is the educational and administrative head of the department, and as such is solely responsible for all aspects of the coordination of the department. This includes financial and academic authority, and being the spokesperson to the upper administration. Research strengths of the department are in algebra, analysis, combinatorics, probability and statistics. For further details about the University of Louisville visit the wet site http:/ / The review process will begin immediately and continue until the position is filled or the search is closed. Dickson Instructor-Open to mathematicians who have recently completed or will soon complete the doctorate in mathematics, and whose work shows remarkable promise in mathematical research and teaching. These positions are intended for mathematicians whose work has been of outstandingly high caliber. Appointees are expected to have the potential to become leading figures in their field. Introduction the Report of the Treasurer is presented annually and discusses the financial condition of the Society as of the immediately preceding fiscal year end and the results of its operations for the year then ended. This section contains summary information regarding the operating results and financial condition of the Society for 1999.
In mid-1969 arrhythmia guidelines 2011 cheap 162.5 mg avalide amex, even though warned against it by dispensary personnel heart attack zone cheap avalide 162.5 mg, he suddenly increased his dosage to more than 300 arteria digitalis palmaris communis avalide 162.5mg cheap,000 units daily blood pressure chart related to age purchase avalide 162.5 mg line. During this final 3month period blood pressure wrist band cheap 162.5mg avalide otc, Gerald consumed an estimated 300 million units of vitamin A! His doctors warned him about the dangers of excessive vitamin A and cut off his access to vitamin A from the dispensary blood pressure variations cheap avalide 162.5 mg without prescription. Over the next year, Gerald gradually increased his juice intake to one gallon per day, which caused him to accumulate excess amounts of carotene pigment in his body tissues. At the time of his death, according to medical reports,ts,16 Gerald had severe scarring (cirrhosis) of his liver. In rats, both excessive intake and deficiency of vitamin A in the mother can result in deformed offspring. Many of her female friends were so enthralled by this book that they talked of little else for several months. There, extensive examination found that she had an extra urine-carrying tube (ureter) running from her left kidney to her vagina. They also indicate the variety of ways in which people have been exposed to such large dosages. Children have been hurt by the actions of well-meaning relatives who themselves had been misled by faddists. Both children and adults have been harmed by eating excessive amounts of foods rich in vitamin A. The list of toxic effects of vitamin A reported in scientific journals19-22 is quite long: loss of appetite; weight loss; loss of hair; anemia; blurred vision; retinal bleeding; protruding eyeballs; extreme drying and thickening of the skin; widespread itching; great pain and tenderness of the arm and leg bones, especially in children; abnormal bone growth; bleeding tendency; cracking of the lips; mouth ulcers; increased brain and spinal fluid pressure with headache and papilledema (mimicking brain tumor); irritability in children; and birth defects in children born to mothers who took megadosages of vitamin A. Curiously, vitamin A deficiency can produce some similar problems: bleeding tendency;13 birth defects; 21 ·22 skin difficulty;1 and increased brain and spinal fluid pressure. Never take 25,000 or more units of vitamin A daily or give more than 5,000 units to a small child, even if a doctor advises you to do so. Vitamin A Can Help or Harm 47 read from many sources on child care and sought the advice of her pediatrician, but she was also an enthusiastic believer in vitamins. After all, she thought, what could be more wholesome and "natural" than vitamins and the oil of a fish? By the time Frankie was six months old, he had developed an extravagant liking for fish liver oil and was occasionally allowed to drink directly from the bottle. At age 22 months, following a tonsillectomy, doctors noted that he was anemic, his liver and spleen were enlarged, the ends of his fingers had become clubshaped, and most of his hair had fallen out. At age 30 months, because of continuing anemia and enlarged spleen, Franklie was brought to a respected medical center where the diagnosis of chronic vitamin A poisoning was made. Since the burning pain prevented her from sleeping, she was able to continue this dosage faithfully until the next afternoon-ingesting a total of 1,300,000 units of vitamin A during a 27-hour period! Somehow he became convinced that daily supplements of vitamin A would relieve some of his minor ailments and prolong his life, so he began taking 50,000 to 100,000 units daily. Medical examination revealed that his liver was hard and enlarged, and his blood vitamin A content was more than 30 times normal. But Gerald just could not believe that anything as "wholesome" as a vitamin could really have made him sick. After brooding a few days about the injustice of being disallowed his favorite vitamin, he persuaded his wife to prepare fresh carrot juice daily using a blender. He began drinking a quart of it daily, obtained from 2 to 3 pounds of blended carrots. That he survived such massive dosage as long as he did must stand as a testimonial to the magnificent capacity of the human body to adjust to extremes of nutrition abuse. But at one month of age, the child became progressively listless and began to lose weight. Fortunately, doctors were able to relieve the blockage and kidney function returned to normal three months later. They were also aware of reports of similarly deformed newborn animals born of females who, during pregnancy, had been fed huge doses of vitamin A by research workers. How to Avoid Trouble with Vitamin A All of these case reports indicate how dangerous large amounts of vitamin A can be. Teenagers and adults have overdosed themselves on the theory that "if some is good, more is better. The list of toxic effects of vitamin A reported in scientific journals10- 22 is quite long: loss of appetite; weight loss; loss of hair; anemia; blurred vision; retinal bleeding; protruding eyeballs; extreme drying and thickening of the skin; widespread itching; great pain and tenderness of the arm and leg bones, especially in children; abnormal bone growth; bleeding tendency; cracking of the lips; mouth ulcers; increased brain and spinal fluid pressure with headache and papilledema (mimicking brain tumor); irritability in children; and birth defects in children born to mothers who took megadosages of vitamin A. Remember that all fat-soluble vitamins when taken in excess can accumulate in the body to reach toxic levels. This amount is easily obtained from a balanced diet which includes green and yellow vegetables, fruit, a reasonable amount of dairy products, eggs, and occasional portions of liver or other organ meats. These cities were notorious for being blanketed with such heavy smoke that even strong winds could clear the sky only momentarily. Palm was the first to observe and suggest a connection between sunlight and childhood. The next big advance came in 1919 when Me1lanby reported a technique for producing rickets in young animals and then curing it with cod liver oil. In 1922, McCollum and co-workers reported success in partially separating the active ingredient from cod liver oil and named it "vitamin D. Forms of Vitamin D Vitamin D is a general term for a family of compounds which exhibit vitamin D activity. Well, "vitamin Dh" which was studied during the early years of vitamin D research, was later found to be a mixture. So the term "vitamin Di" was abandoned along with most of the research involving it. The scientific name for natural vitamin D3 is cholecalciferol, which is formed by action of sunlight on a cholesterol derivative in the skin; and that for vitamin D 2 is ergocalciferol, made by ultraviolet radiation of ergosterol, a plant sterol plentiful in yeast. But it was not until 1931 that pure, crystalline vitamin 03 was isolated from cod liver oil by a long, laborious process. The exact chemical structure of vitamin Da was eventually determined in 1936 by the German scientist and Nobel Prizewinner, Adolf Windaus. This is the chief way of producing vitamin D nowadays for fortifying foods like milk, and for producing supplement capsules. Functions of Vitamin D Vitamin D is essential for normal bone growth and development. Together with parathyroid hormone, it regulates phosphorus and calcium metabolism and promotes calcium absorption from the intestines. Vitamin D maintains normal blood phosphorus and calcium concentrations so long as excessive intakes of the vitamin are not taken for long periods. It promotes normal bone calcification and helps provide needed inorganic phosphates for the body by activating the enzyme, alkaline phosphatase. After prolonged shortage of calcium in the diet, vitamin D comes to the rescue by increasing calcium absorption and keeping the blood calcium from dropping too low and threatening the heart muscle which depends on proper calcium concentrations. To do this, calcium is mobilized from bones, and this can lead to bone softening (osteomalacia). Without sufficient vitamin D, there will be inadequate absorption of calcium from food, calcium will be mobilized from bones, and abnormal bone tissue devoid of calcium will be made. Vitamin D and parathyroid hormone are also needed to harden (calcify) the soft "osteoid" tissue in growing bones. Unless rickets is corrected very early by a vitamin D supply, its victims will become permanently deformed. They must first be converted by successive actions of two specific enzymes, one in the liver and one in the kidneys, into 1,25dihydroxy-vitamin D 2 and 0 3, hormone-like substances. This condition is different from osteoporosis, a type of bone loss prevalent in postmenopausal women. In 1979, the Mayo Clinic reported on 52 women with this problem who were from 54 to 75 years old. X-ray examinations showed that all of them had abnormally low spinal bone (vertebral) density, and that each had suffered at least one fractured vertebra. All were in negative calcium balance, losing more calcium each day in their urine and feces than they were getting in a normally adequate diet, but calcium and vitamin D supplements had not helped them. When 27 of these 52 patients were compared with 27 women the same age who did not have osteoporosis, it was found that the osteoporotic patients absorbed much less calcium from their food. They also had lower blood levels of parathyroid hormone and 1,25-dihydroxy-vitamin Da, the active form of vitamin D that had been discovered by Dr. Twenty-four of the patients were given tiny doses of "super-D" for 7 days while 13 patients were given a placebo. The "double-blind" experiment showed that 21 of the 24 patients getting "super-D' had good increases in calcium absorption and the other three improved when their dosage was doubled. The 1-week treatment was repeated after one month and again after six months, at which time all 24 of the treated patients were in positive calcium balance-with increased calcium absorption and no more loss of calcium from their bones. I wonder how many of these improved patients, as they left the Mayo Clinic to return home, realized their good fortune in not having sought treatment at the hands of spine manipulators or other quacks. Although this treatment is very expensive and is still considered experimental, it illustrates the 'miraculous' potential of medical science. The Food and Nutrition Board6 also advises that: Although vitamin D can readily be formed by the action of sunlight on the skin, the amount formed is dependent on a number of variables, including length and intensity of exposure and color of skin. One report (Loomis 7) concluded that heavily pigmented skins can prevent up to 95 percent of ultraviolet radiation from reaching the deeper layers of the skin, where vitamin D is synthesized. In areas where sunlight is limited seasonally or where there is considerable atmospheric pollution, ultraviolet energy from the sun may be insufficient for adequate formation of vitamin D in the skin. Black children who live in areas with minimal sunlight would thus be more likely than white children to develop rickets, but fortification of milk with vitamin D has largely eliminated this disease in the United States. It is noteworthy that black children can tolerate higher daily dosages of vitamin D than white children. Yes, it is adequate except for abnormal conditions, such as lack of parathyroid hormone, inability to absorb fats and fat-soluble vitamins, or inability to convert vitamin D to its active forms. Lower levels of vitamin D are found in grains, vegetable oils, butter, cheese, milk (rich source if fortified with D 2), and livers of beef, pork and lamb. Remember, though, most adults obtain all or most of their vitamin D requirement from the action of sunlight on the skin. A Two-Edged Sword In 1928, Hess and Lewis8 reported the spectacular cure of 12 children with rickets by treatment with 5 mg of irradiated ergosterol (the Steenbock process). Mild toxic effects were observed in all 12 children, and severe toxic reactions occurred in 3 of them. Despite this early warning, it took 30 years before reports of vitamin D poisonings began to decline. Because vitamin D could cure bone-softening and rickets, the idea flourished that it might benefit all forms of arthritis. During that year he began to feel arthritic pain and stiffness which slowly worsened and gradually involved his ankles, knees, shoulders, wrists, elbows, fingers and hips. Three years later, doctors at a large eastern teaching hospital examined Archie and diagnosed rheumatoid arthritis. He was treated with 12 injections of a gold salt at weekly intervals and sent home with his arthritis somewhat improved. He returned to the same hospital for a checkup three years later in 1944, and again his weight and blood tests were normal. At home, Archie was frustrated by the failure of the big clinic to do more to a11eviate his arthritis. Upon his repeated complaints early in 1945, his family doctor prescribed a half-million units of vitamin D daily. He finally stopped in September 1946 because he developed really worrisome symptoms. His fingernails became quite tender and developed ye11ow deposits under the nails. He began to experience nausea, loss of appetite, and excessive urination even at night. In December 1946, three months after stopping the vitamin D supplements, Archie (now 59 years old) returned to the original hospital clinic. Here, examinations revealed that he had lost 33 pounds in one year (to a mere 125 pounds) and was anemic. Tests revealed serious kidney impairment with probable damage from calcium deposits. A minimal amount of cream and butter was allowed, and he was told to force himself to drink 4 quarts of fluids daily. After 20 months, the calcium deposits in his eyes had nearly cleared and Vitamin D Can Help or Harm 51 his blood calcium level and blood count were back to normal. With the help of one son who returned to the homestead, Archie still worked his farm, but he never fully recovered and could work only an hour or two a day. A Trio of Tortured Tots About the year 1960, three infants were growing up in the same neighborhood in a large Italian city. Though the three were healthy and had received proper vitamin supplementation since birth, each mother decided her child needed extra vitamin D above what the doctor had ordered. So for one month Lucia was given, instead of the recommended 400 units per day, a daily average of 83,000 units. Marissa got the moderately high dosage of 8, 700 units each day for 4 months while Alessandro was overloaded with 200,000 units per day for 15 days. The duration of overdosing varied because it stopped abruptly when each child was taken to the excellent pediatric clinic in that Italian city. Marissa, who had received the lowest overdosage, did not suffer any of the following, but Lucia and Alessandro did: fever, paleness, dry skin, loss of appetite, and neurological symptoms such as instability and extreme restlessness. All three recovered fully-Marissa took only 6 days, Lucia took 15 days, and poor Alessandro was not well until the 25th day of treatment. The physicians who published this report10 included the records of nine other infants admitted to their clinic with vitamin D intoxication between 1960 and 1964. He felt fine, but he was judged to have a borderline case of rickets because x-ray examinations of his wrists showed poor bone density, and the bones of his skull felt "peculiar" to his family doctor.
