Given the increasing demand pressure on water resources coupled with supply holdups and institutional failures, fresh-water resources are increasingly susceptible to depletion and could potentially add to water stress in India. A vast demand-supply gap necessitates water conservation, including recycling measures. India has a great potential in wastewater treatment, and one of the ways to address it is decentralisation of wastewater treatment given its environmental benefits. Based on the Contingent Valuation Method (CVM), this study assesses Delhi urban householdsâ willingness to pay for the Operation & Maintenance (O&M) costs of a local Wastewater Treatment Plants (WWTP) that supplies residential complexes treated water for toilet-flushing. The study found that if freshwater prices rise sufficiently for consumers, they may be willing to subsidise a decentralized WWTP to cover at least their non-potable water uses. In addition, the co-provision of such public goods can become an important supplement to urban municipal finance.
Security breaches of the cryptocurrency exchanges usually cause the price fluctuation in the market. Approximately one hundred cryptocurrency thefts, including hacks and scams, has occurred since 2012 to 2018, half of which are hacks of Bitcoins. Based on the thirty Bitcoin hacks, this study portrays the general price pattern during the hack. And it illustrates the link between the size of the hack and the subsequent price change of Bitcoin. The tests reveal that the larger the volume of the hack, the stronger the price drop. However, a similar obvious relationship does not exist for the recovery of the price. The study might be the first piece of research focus on the hacks and the price pattern in a short time period.
On behalf of the American Association of Neurological Surgeons/Congress of Neurological Surgeons Joint Section on Disorders of the Spine and Peripheral Nerves, it is my great privilege to introduce these Guidelines for the Management of Acute Cervical Spine and Spinal Cord Injuries. These guidelines represent the initial installment of a more comprehensive guidelines initiative from the Joint Section on behalf of all practicing neurosurgeons and their patients. The Section is grateful to the small working group who devoted considerable time and effort to the generation of this outstanding document. We would like to formally recognize the Joint Section on Trauma for their important collaboration on this project. The Section would also like to acknowledge and thank the parent organizations, the American Association of Neurological Surgeons and the Congress of Neurological Surgeons, for their guidance of and support for this project, most notably through the efforts of the American Association of Neurological Surgeons/ Congress of Neurological Surgeons Guidelines Committee. The Section is also deeply indebted to Michael Apuzzo and the staff of Neurosurgery for their advice and editorial assistance in preparing this document for publication. The application of Neurosurgeryâ s rigorous peer-reviewed editorial process has clearly enhanced the quality, balance, and stature of this document. Perhaps most importantly, Neurosurgery has provided an extraordinary vehicle for the widespread dissemination and ultimate incorporation of these guidelines to improve the care and enhance the outcomes of patients with traumatic cervical spine and spinal cord injuries. One of the truly important functions of organized neurosurgery is the generation of evidenced-based clinical practice guidelines. Properly developed, such guidelines can answer important questions, resolve uncertainty, identify areas of deficient knowledge and opportunities for future scientific investigation, standardize treatment, and improve the quality of care and the outcomes for patients. The now widely disseminated head trauma guidelines, for example, have clearly made a difference in the outcomes of patients with severe head injury. Guidelines development is a highly structured process with rigorous methodological criteria and exacting standards. It is a time-, labor-, and resource-intensive process that has served as a significant obstacle to more widespread guidelines development throughout neurosurgery. In the past, clinical practice guidelines have been developed by publicly supported epidemiologists and methodologists who understood study design, data analysis, and the guidelines process, but not the disease. This absence of context and clinical perspective significantly limited the value and relevance of their results. Alternatively, clinician-generated guidelines often took the form of methodologically flawed consensus panels and expert opinion, also of limited value. The Joint Spine Section recognized the importance of evidence-based clinical practice guidelines and the challenges of their development. The appropriate clinical expertise, strict adherence to established methodological standards for guidelines development, and considerable resource investment for the development, dissemination, and maintenance of the guidelines documents were deemed crucial to our guidelines initiative. Cervical spine and spinal cord injury was chosen as the initial guidelines topic because of the personal, social, and economic devastation of these injuries, their complex nature, and the high level of uncertainty, as reflected in wide practice variations, as to the value and indications for many of the aspects of evaluation and treatment. The clinical practice guidelines contained in this supplement to Neurosurgery represent a remarkable effort. They address the key issues related to the evaluation and management of these complex conditions that are relevant to the treating physician. In every chapter, the pertinent issues are succinctly stated, the published data are comprehensively presented in the evidentiary tables, and the evidence is thoroughly discussed and critically evaluated throughout the text. The linkage between the quality of the evidence and the strength of the recommendations was not a âblack boxâ process but an open, deliberative exercise by skilled experts guided by a rigorous set of standards. Despite the strength and potential value of this document, it is important to acknowledge the inherent limitations of clinical practice guidelines. This, or any other, evidence-based clinical practice guidelines document does not represent the definitive source of knowledge on the stated topic. Rather, it represents recommendations of varying strength and certainty based on an analysis of the best available published data. These data, however, are often conflicting, flawed, or incomplete, and there are unavoidable elements of potential bias from subjectivity, perspective, and experience of the individuals and group involved in the analysis and interpretation of these data. In essence, proof is a relative term based on the interpretation of evidence. Furthermore, it is subject to different standards. A relevant example comes from the field of jurisprudence, where the standard of proof (i.e., guilt) for criminal trials is âbeyond a reasonable doubt,â whereas the standard for civil courts must simply reflect âa preponderance of evidenceâ or âmore likely than not.â These different standards evolved because of the perceived different consequences of a wrongful verdict. Moreover, as Stephen Haines likes to note, the verdict ânot guiltyâ does not mean innocent; it merely says not proved. Such are the vagaries associated with the interpretation of even scientific evidence. Principled people can look at the same evidence and come to different conclusions subject to their own personal perspective, experience, and stake in the result. Nevertheless, the Joint Section and Guidelines Development Group went to great lengths to identify and avoidâor at least minimizeâthese potential problems. The working group adopted the most widely recognized and rigorous standards for guidelines development. A diverse panel of experts with expertise in spine, trauma, and epidemiology brought relevant clinical, scientific, and methodological competence to enhance both the analytical and the deliberative aspects of this process. Periodic outside reviews were routinely obtained for topics or areas of contention or uncertainty to add additional perspective and balance. Above all, the process was accountable and transparent at every stage. Ultimately, we offer these guidelines as a living document to those professionals who treat patients with traumatic spinal injury. We hope each practitioner will critically evaluate these guidelines and come to his or her own conclusion on how, whether, and when to implement its recommendations. It may be used either as a reference or as a basis for standardized protocols of evaluation and management of the patients with traumatic spinal injury. For clinical and basic science researchers, we hope that it will identify and catalyze scientific investigation in areas of deficient knowledge. As a Section, we stand firmly behind this important document and will continuously update the recommendations as new knowledge and understanding is developed. We sincerely believe that these guidelines can improve the care and enhance the outcomes of patients with traumatic injuries to the cervical spine and spinal cord.
1. Introduction.The classical Sturmian theorem of ordinary differential equations deals with functions u(x) and v(x) which are, respectively, solutions of differential equations(1) Um-^^j+tumO,(2) Mv=-l{J^+yv = 0.Under the assumption that "F is larger than M" (in the sense that a(x) Ă€ a(x) > 0 and c(x) ÂŁ y(x)) one can infer information about all solutions of (2) from knowledge about a particular nontrivial solution of (1)-i.e. if u(xx) = u(x2)=0 then every solution of (2) has a zero in [xx, x2].These ideas have been generalized to second order elliptic equations by several authors ([l]-[4]) considering elliptic operators and also by Protter [5] and Swanson [6] considering the nonselfadjoint case.Given a proper relation among the coefficients of F and M and that Lu=0 has a nontrivial solution with nodal domain Ă, then it can be shown that every solution of Mv = 0 has a zero in Ă2.While all the above proofs of this fact make essential use of some sort of ordering among elliptic operators, the nature of this ordering is never defined in operator-theoretic terms.The results of §2 below suggest that it is an order relationship between certain resolvents of the differential operators F and M which underlies the separation properties characteristic of Sturmian theorems.It will be shown that quite general operator equations in a Banach space 3S satisfy a type of Sturmian theorem if the operators' resolvents satisfy prescribed positivity requirements with respect to a cone SP.In order to apply this theory to differential operators, one must first establish the corresponding positivity properties for their resolvents.This is done in §3 for sufficiently regular nonselfadjoint second order elliptic operators, and the general theory of §2 is then applied in the proof of two Sturmian theorems and the establishment of criteria for certain Green's functions to be positive.
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Spectral Theory in Mathematical Physics
Quantum chaos and dynamical systems
Stability and Controllability of Differential Equations
Historians have recently given much attention to the active, formative role of state governments in the American economy before the Civil War.1 The states exercised nearly exclusive control over many aspects of economic life, and in such areas as labor, banking, and corporation policy the federal government interfered relatively little. The consequence was considerable decentralization of power in policymaking, together with variations in policy from state to state.2 Perhaps in no policy area were variations so dramatic as in state legislation on banking. In some states banking was prohibited outright, while in others the state government itself established and operated banks, sometimes on a monopoly basis. Elsewhere, safety funds were established and banks required to meet minimum standards of specie reserve and the like; and in a few states, stringent regulatory policies were pursued, with public commissioners given considerable discretion in administering policy.3
Let $\{X(t), t = \cdots -1, 0, 1, \cdots\}$ be a $P$ dimensional zero mean stationary Gaussian time series, $X(t) = \begin{pmatrix}X_1(t)\\X_2(t)\\\vdots\\X_P(t)\end{pmatrix}$ we let $R(\tau) = EX(t)X' (t + \tau)$, where $R(\tau) = \{R_{ij}(\tau), i,j = 1, 2, \cdots P\}$, and $F(\omega) = (2\pi)^{-1} \sum^\infty_{\tau=-\infty}e^{-i\omega\tau}R(\tau)$. It is assumed that $\sum^P_{i,j=1} \sum^\infty_{\tau=-\infty} |\tau| |R_{ij}(\tau)| < \infty$, and hence $F(\omega)$ exists and the elements possess bounded derivatives. It is further assumed that $F(\omega)$ is strictly positive definite, all $\omega$. Knowledge of $F(\omega)$ serves to specify the process. $F(\omega)$, and $S$, the covariance matrix of $x = \begin{pmatrix}x_1 \\ x_2\ \\ vdots\\x_P\end{pmatrix}$, a Normal $(0, S)$ random vector are known to enjoy many analogous properties. (See [7].) To cite two examples, the hypothesis that $X_i(s)$ is independent of $X_j(t)$ for $i \neq j = 1, 2, \cdots P$, any $s, t$, is equivalent to the hypothesis that $F(\omega)$ is diagonal, all $\omega$, while the hypothesis that $x_i$ is independent of $x_j$, for $i \neq j = 1, 2, \cdots P$ is equivalent to the hypothesis that $S$ is diagonal. The conditional expectation of $x_1$, given $x_2, \cdots x_P$ is \begin{equation*}E(x_1\mid x_2, \cdots x_P) = S_{12}S^{-1}_{22}\begin{pmatrix}x_2 \\ \vdots \\ x_P\end{pmatrix}, S = \bigg(\begin{array}{c|c} S_{11} & S_{12} \\ \hline S_{21} & S_{22}\end{array} \bigg)\end{equation*}. The corresponding regression problem for stationary Gaussian time series goes as follows. If \begin{equation*}E\{X_1(t)\mid X_2(s), \cdots X_P(s), s = \cdots -1, 0, 1, \cdots\} = \sum^P_{j=2} \sum^\infty_{s=-\infty} b_j(t - s)X_j(s)\end{equation*} then $B(\omega)$, defined by $B(\omega) = (B_2(\omega), \cdots B_P(\omega)), B_j(\omega) = \sum^\infty_{s=-\infty} b_j(s)e^{i\omega s}$ satisfies \begin{equation*}B(\omega) = F_{12}(\omega)F_{22}^{-1}(\omega), \quad F(\omega) = \bigg(\begin{array}{c|c}f_{11}(\omega) & F_{12}(\omega) \\ \hline F_{21}(\omega) & F_{22}(\omega)\end{array} \bigg).\end{equation*} It is interesting to ask how well these and similar analogies carry over to sampling theory and hypothesis testing. Goodman [3] gave a heuristic argument to support the conclusion that $\hat{F}_X(\omega_k)$, a suitably formed estimate of the spectral density matrix $F(\omega_k)$ has the complex Wishart distribution. The question is met here by the following results. Firstly if $\hat{F}_X(\omega_l), l = 1, 2, \cdots M$ are estimates of the spectral density matrix, each consisting of averages of $(2n + 1)$ periodograms based on a record of length $T$, with the $\omega_l$ equally spaced and $(2n + 1)M \leqq \frac{1}{2} T$, then it is possible to construct, on the same sample space as $X(t), M$ independent complex Wishart matrices $\hat{F}{\bar{\bar{X}}}(\omega_l), l = 1, 2, \cdots M$ such that $\{\hat{F}_X(\omega_l), l = 1, 2, \cdots M\}$ converge simultaneously in mean square to $\{\hat{F}_{\bar{\bar{X}}}(\omega_l), l = 1, 2,\cdots M\}$, as $n, M$ get large. Secondly, it is legitimate to use the natural analogies from multivariate analysis to test hypotheses about time series. One example is presented, as follows. The likelihood ratio test statistic for testing $S$ diagonal is $|\hat{S}|/\mathbf{\prod}^P_{i=1} \hat{s}_{ii}$ where $\hat{S} = \{\hat{s}_{ij}$ is the sample covariance matrix. The analogous statistic $\psi$ for testing $X_i(s), X_j(t)$ independent, $i,j 1 = 2, \cdots P$ from a record of length $T$ is $\psi = \prod^M_{l=1} \lbrack|\hat{F}_X(\omega_l)|/\prod^P_{i=1} \hat{f}_{ii}(\omega_l)\rbrack$ where $\hat{F}_X(\omega_l) = \{\hat{f}_{ij}(\omega_l)\}$ are the sample spectral density matrices as above. Letting ${\bar{dbar{\psi}}} = \prod^M_{l=1} \lbrack|\hat{F}_{\bar{\bar{x}}}(\omega_l)|/\prod^P_{i=1} \hat{h}_{ii}(\omega_l)\rbrack$ where $\hat{F}_{\bar{\bar{x}}}(\omega_l) = \{\hat{h}_{ij}(\omega_l)\}$ are the independent complex Wishart matrices referred to above, we show $EC_{n,M} |\log \psi - \log {\bar{\bar{\psi}}} \rightarrow 0$ for large $n, M$, where $C_{n,M}$ are chosen to make the result non-trival. The method of proof applies to any statistic which is a product over $l$ of sufficiently smooth functions of the entries of $\hat{F}_X(\omega_l)$. Applications to estimation and testing in the regression problem will appear elsewhere [8]. The distribution theory of functions of complex Wishart matrices has been well investigated by a number of authors [3] [5] [6], and hence can be easily applied here to statistics like ${\bar{\bar{\psi}}}$. The results above are shown for $P = 2$, it is clear that the proofs extended to any (fixed) finite $P$. The proofs proceed as follows, via a theorem which has somewhat more general application. For each $T$, let $X$ be the $2 \times T$ random matrix $X = \binom{X_1}{X_2} = \begin{pmatrix}X_1(1), \cdots, X_1(T)\\X_2(1), \cdots, X_2(T)\end{pmatrix}$ and let the $2T \times 2T$ covariance matrix $\Sigma$ be given by $\Sigma = \begin{pmatrix}\sum_{11} \sum_{12} \\ \sum_{21} \sum_{22}\end{pmatrix}$ where $\Sigma_{ij} = EX_i'X_j. \{\hat{F}_X(\omega_l)\}$, the sample spectral density matrices described above based on a record of length $T$, are each of the form $\hat{F}_X(\omega_l) = T^{-1}XQX'$ where $Q$ is a $T \times T$ circulant matrix with largest eigenvalue $ = T(2n + 1)^{-1} \leqq \frac{1}{2}M < <T$. We define circulant matrices $\bar{\Sigma}_{ij}$ which approximate $\Sigma_{ij}$, and a random matrix $\bar{X}$ on the sample space of $X$, $\bar{X} = \binom{\bar{X}_1}{\bar{X}_2} = \begin{pmatrix}\bar{X}_1(1), \cdots, \bar{X}_1(T)\\\bar{X}_2(1), \cdots, \bar{X}_2(T)\end{pmatrix}$ with $E\bar{X}_i'\bar{X}_j = \bar\Sigma_{ij}$. The $2T$ eigenvalues of the block circulant matrix $\bar\Sigma = \begin{pmatrix}\bar\Sigma_{11} \bar\Sigma_{12} \\ \bar\Sigma_{21} \bar\Sigma_{22}\end{pmatrix}$ will be the $2T$ eigenvalues of the $T$ matrices $\{F(2\pi j/T),j = 1, 2, \cdots T\}$. The distribution of random matrices of the form $T^{-1}\bar{X}Q\bar{X}'$ where $Q$ is any circulant matrix are relatively simple to investigate due to the fact that all circulant matrices commute, and their eigenvalues may be exhibited as simple functions of the elements. Circulant quadratic forms in random vectors with circulant covariance matrices are well known in the literature, (See [1] and references cited there). Let $\hat{F}_{X,Q} = T^{-1}XQX'$ and $\hat{F}_{\bar{X},Q} = T^{-1}\bar{X}Q\bar{X}'$ where $Q$ is now any $T \times T$ (real or complex) quadratic form with largest absolute eigenvalue $\leqq q$. The main Theorem allows the replacement of $X$ by $\bar{X}$ in the analysis, and is, that under the assumptions on $F(\omega)$ and $R(\tau)$, for any $T$, \begin{equation*}\tag{1.1} E \operatorname{tr} (\hat{F}_{X,Q} - \hat{F}_{\bar{X},Q})(\hat{F}_{X,Q} - \hat{F}_{\bar{X}, Q})^{\ast'} \leqq cq^2/T^2\end{equation*} where $c$ is a constant depending only on $F(\omega)$ and $R(\tau)$. A lemma, essentially allowing the replacement of $F(\omega)$ by a suitably chosen step-function, together with the application of (1.1) gives the results concerning the $\{\hat{F}_X(\omega_l)\}$ an $\lambda$. Since $\hat{R}(\tau)$, the sample (circularized) autocorrelation function is also of the form $T^{-1}XQX'$ with $Q$ circulant we obtain an easy corollary on the distribution of $\{\hat{R}(\tau)\}$.
The Korean family planning program from 1964 to 1968 is considered in its entirety. The program is financed primarily by Korean government appropriations (averaging about $2 million in past years from central and local budgets) but also is supported substantially by foreign agencies such as the Population Council SIDA and AID. The Planned Parenthood Federation of Korea working in cooperation with the government is financed by about $200000 yearly from Korean government and foreign sources. The program has offered the IUD condom and vasectomy to every couple without charge. Accomplishments include adoption of the loop or vasectomy by 1/3 of couples with wife below age 45 elicitation of the best response among illiterate and low-income families and in rural areas reduction of crude birth rate by roughly 10% as of 1968 by IUDs inserted through mid-1968 and launching a pill program for IUD drop-outs starting with an unknown method a population of 30 million was informed of it and their approval won. Approaches used in the program have included strong governmental policy; implementation through the existing health structure; decentralization of functions to local and provincial government levels; payment by government of physicians and fieldworkers involved as well as vasectomy acceptors for work lost; high fieldworker density; fixation of target quotas with positive and negative sanctions on workers; and full use of mass media. Problems to be dealt with involve funding doctorless and remote areas and termination rates. The problems have been obtaining the funds; areas that are doctorless and that are remote; the training of workers; funds for maintenance and supply systems; shortcomings of the present contraceptive methods; and the changing of field-worker duties.
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Diverse Approaches in Healthcare and Education Studies
Abstract Capital and Management in Socialist Economies The idea, that an economy can be operated by methods of central planning to realize the economic optimum like the model of a private business corporation, proved to be successful only in the first periods of (âextensiveâ) industrialization. Growing product differentiation increased the danger of disallocation of resources. The solution of microeconomic allocation problems turned out to be most unsatisfactory. Since 1962, reforms try to decentralize decision making in the individual enterprise striving mostly for production aims planned centrally. The problem of appropriate investment and success criteria for the systemâs management remains unsolved. While in sectors of the economy, where large sums of capital are needed, ex ante central planning is necessary, the problem is different in manufacturing industry. Here, an efficient selection from the abundance of continually and acceleratingly renewing technical progress can be made only with decentralized rules of efficiency, which, however, must be based on market prices. But the choice of a soviet director is limited by problems of financing and supply. He may calculate approximately the technical effect of investment, but he cannot evaluate its economic effect, since prices have been set since long and do not reflect the permanently changing relations of scarcity of resources, Besides, the certain profit from selling established products is frequently preferred to the risk of innovation. The industrial reform of 1965 has focused on the relation of the profit from sold production and the invested capital stock. It emphasizes the importance of investment financing from enterprize profits and credit (in contrast to the usual allotment of means for investment by central authorities). A greater flexibility in fulfilling the plan can be observed, but managementâs investment choices are still very limited. The centrally planned supply of investment cannot keep pace with increased decentralized investment demands. The reason for the stated inferiority of socialist economies in realizing technical progress is ultimately the absence of a capital market. Its role for most investment decisions can be substituted only most imperfectly by central planning.
A gas or vapor bubble moving in translation in a liquid and varying its volume propels itself by a rocket effect, which occurs in foams moving in pressure or temperature fields with a non-zero gradient. It is notably observed in boiling and centrifugal pump operation, which latter features the following two characteristic bubble types : __ 1. Gas bubbles, which are apt to emerge faster from the pump than the liquid; 2. Vapor bubbles (cavitalion). When a bubble in translatory motion implodes, energy is transferred: potential pressure energy is converted info kinetic implosion energy, which in turn becomes kinetic translation energy. The instrument for this energy transfer process is a "micro-jet" following the bubble. It is shown that a considerable increase in kinetic translation energy density occurs, which is converted into potential pressure energy on impact against a solid obstacle. The resulting pressures (10,000 kg/sq.cm) explain the mechanical aspect of cavitation erosion. Several experimental results have confirmed these theoretical considerations. The development of a rotoscope is also described, this being a device enabling a centrifugal pump impeller (for example) to be "stopped" so that only the relative motion of the flow particles remains. Unlike with a stroboscope, time exposures can he taken with this device. With more thorough knowledge of foam mechanisms, and especially of cavitalion bubble behavior, it should be possible to design cavitation erosion-proof impeller blades.
The principles of unity and complexity introduced into the Polish State budget in 1951 are no longer fully observed. In particular, certain funds administered by local councils have appeared gradually in the last years, on the basis of the budget law of 1958 which admitted making some budget expenses dependent on definite budget revenues. Moreover, some funds have been created outside the local budgets. These deserve special attention as a new phenomenon which becomes increasingly important for the local councils activities and especially for councils of the lowest level. The development of decentralized funds seems to be desirable firstly in the economic micro-regions, such as villages and towns, in order to accelerate their development. The augmentation of the role of decentralized funds would also be advisable in counties and provinces provided they constitute regions with specific economic structure. Decentralized funds should be first of all used to finance local investments, the more so that this would be in accordance with the main destination of the funds already administered by local councils. In this way, decentralized funds could in the future be transformed into the local investment budgets. The considerable development of decentralized funds in this country, in particular of those of the lowest level of local administration, seems, moreover, to prove that local budgets at this level, which since 1951 have been incorporated into the State budget, are not fully adequate for financing local councils activities. This suggests that a reform of local budgets of the lowest level is advisable, which would make their administration more similar to that of decentralized funds. The author considers in detail the perspectives and conditions of s'uch a reform of the local budgets of the lowest level, as well as the prospects and conditions of further development of the decentralized funds if no budget reform takes place. He discusses especially the links between decentralized funds and local budgets in this last case. The other subject of the author's consideration is the advisability of financing the local councils activities by bank credit or by credit granted by central funds administered by budget authorities
This paper is concerned with repetitive sequential play in finite statistical games (decision problems) from the statistician's point of view. We shall assume that the statistician's move at stage $k$ may depend on the previous $k - 1$ moves of Nature as well as the random variable $\mathbf{X}_k = (X_1, \cdots, X_k)$, where the $X_i$ are independent observations (r.v.'s) (possibly vector-valued) from the sequence of statistical games, $k = 1, 2, \cdots$. The play is repetitive in the sense that each component game is identical in structure, with only the moves of the statistician and Nature changing. Furthermore, we impose no assumptions regarding the behavior of the parameter sequence of Nature's moves. The statistician does have the added disadvantage that the finite class of distributions in the component game is not fully specified. However, he does know that class in question has: either (i) all members with discrete distributions or (ii) all members with $q$-dimensional a.e. continuous Lebesgue densities. This same problem when the distributions are fully known has been treated in [6] for statistical as well as more general games in which Nature's space is finite. In the case where the distributions are completely specified but the history of the past moves is unknown to the statistician, see [20], [22], [27], and [28]. The development in this paper is closely connected to and motivated by these results, particularly those of the preceding paper [27]. If for fixed $N$, the empirical distribution $p_N$ of Nature's moves is known, then the statistician could use as a rule for each of the $N$ component games a strategy Bayes against $p_N$ having risk $\phi(p_N)$. In all the papers cited in the previous paragraph, the aim was to construct for the statistician, when $p_N$ is unknown and $N$ not specified, a sequence of randomized decision functions whose $N$th average loss minus $\phi(p_N)$ approaches zero (or has an upper bound approaching zero) in a suitable sense as the number of repetitions of play, $N$, increases. However, in the case of statistical games, all of the above results require that the finite class of distributions be fully specified. In this paper we remove that assumption by estimating the distributions sequentially based on past moves and observations. Then in the present play of the component game the statistician substitutes these estimators into a procedure which is Bayes against the empirical distribution of Nature's previous moves. The resulting sequence of procedures is shown to be "asymptotically good" in the sense that the average loss over the $N$ games $W_N$ minus the Bayes risk $\phi(p_N)$ approaches zero (in an appropriate sense) as $N$, the number of games played, increases. In Section 2 we introduce notation and preliminaries. Section 3 discusses play in repetitive games and defines the proposed sequential procedures $\mathbf{t} = \{\mathbf{t}_k\}$. In Section 4 we prove preliminary results upon which all proofs are founded. Section 5 considers the discrete case giving uniform (in sequences of Nature's moves) convergence theorems (as $N \rightarrow \infty$) for the quantity $W_N - \phi(p_N)$. Theorem 5.1 is a uniform convergence theorem of $O(N^{-\frac{1}{2}})$ of the expected value of $W_N - \phi(p_N)$ for finite discrete classes, each member of which is non-degenerate and satisfies a certain tail probability condition. Under the same conditions, Theorem 5.2 gives uniform convergence to zero in probability for the quantity $N^{\frac{1}{2}} (\log N)^{-1} \{W_N - \phi(p_N)\} \text{as} N \rightarrow \infty$. Uniform convergence of $W_N - \phi(p_N) \rightarrow 0$ in probability for general non-degenerate finite discrete class is presented in Theorem 5.3. Section 6 treats the estimation problem for densities needed to form the randomized strategy sequences $\mathbf{t}$ in the continuous case. The results stated are based on a paper by Cacoullos [3] generalizing the univariate results of Parzen [15]. In Section 7, we present results for the continuous case. Theorem 7.1 and its corollary give uniform convergence of $W_N - \phi(p_N)$ to zero in probability and of its expectation to zero, respectively. The finite continuous classes of Theorem 7.1 are very general in the sense that each member is a continuous a.e. density. Finally, in Section 8 we draw certain conclusions and relate our results to similar results obtained elsewhere. The novelty of the paper rests in the fact that through the past history of Nature's moves and the observations connected with past play, one can construct a sequential strategy, $\mathbf{t} = \{\mathbf{t}_k\}$, with very little knowledge about the finite class of distributions, which approaches asymptotic "optimal" play. The lack of knowledge on the finite class of distributions distinguishes this work from the related "repetitive type" problems in games and/or decision theory treated in [1], [2], [4], [6], [7], [8], [9], [10], [12], [17], [18], [19], [20], [21], [22], [24], [25], [26], [27], [28], and [29]. For possible applications of this work see Neyman [14], especially his Example 3 and his discussion relating to the work of Blackwell [2].
Case reports of three residents of Ontario with clinical histoplasmic chorioretinitis are presented. The diagnosis was made on the basis of the clinical appearance, the presence of calcified lesions in the chest, a negative skin test to tuberculin, and a positive skin test to toxoplasmin. All patients were treated with intravenous amphotericin B. Except for transitory elevation of blood urea nitrogen, there were no serious complications from the drug and in all cases the lesions in the eyes were improved. Histologic or cultural proof of the presence of fungus in the eye is not available, but clinical and laboratory findings can combine to point to the diagnosis of histoplasmosis. In such cases, since vision is at stake, treatment with amphotericin B should be considered.
Professor Keeping's book is a text for a one-year course (90-100 hours) for students having a knowledge of elementary calculus-second or third year students.It is unusually complete in that it is difficult to think of a topic which is not treated, at least briefly, but which one might like to see included in such a course.As would be expected of a widely ranging book at this level, many results are stated without proof but it is by no means a " how to do it" book.In addition to the usual elementary probability theory, standard distributions, and classical estimation and testing, one finds, e.g. the cumulants and Ar-statistics, sampling techniques, sequential and nonparametric procedures, fixed, random and mixed models as well as latin square and incomplete block designs considered, and a last chapter which looks at multivariate problems and introduces stochastic processes.There is a laudable concern for the power of the tests discussed and the required non-central distributions are introduced.Appropriate tables, a large number of exercises (with answers) and a thirty page appendix on various mathematical topics are included as well.The price paid for the virtue of comprehensiveness is, of course, the brevity of some particular parts; one cannot have everything.However, one might reasonably suggest that the briefer the treatment the more precise should be the statements.This book is somewhat marred by puzzling, misleading, or false statements, e.g. both the sample and population moments are defined to be the " rth moment of X about zero"; "If T is sufficient, so is any function of T" (p.125); the variance of a maximum likelihood estimator is asserted to be the Cramer-Rao lower bound; in discussing the Mann-Whitney U-test, it is not clear at given points just what alternatives are being considered and while one statistic is described as the test statistic, we are instructed to reject for small values of another.
(1) As it is shown in the answering rate itself, concern of top management on the rationalization of business finance is very sincere. (2) As for depreciation system, contraction of depreciation terms and general or partial widening of the rooms for arbitrary depreciation are earnestly desired. (3) Corporate tax has been intensely criticized, and opinion of the majority takes its revision as a premise for financial rationalization. (4) Regarding budget system, opinion of the majority asserts concentrative management, but not a few recognize the necessity of decentralized system. (5) Upon internal audit and concept of cost, a fundamental shift from the traditional idea is fairly evident.
One of the features of the text is an elaborate code which is used to refer to certain axioms, definitions, and theorems.For example, TIr is the Theorem on Irrational Numbers, which runs as follows: "If a non-zero rational number 'r is combined with an irrational number p by any one of the four operations of arithmetic, the result produced is an irrational number; in symbols, r + p, r -p, p -r, rp, r/p, p/r are irrational numbers."According to the author 1 s preface, "Experience in classroom teaching shows that the students use the code with alacrity and effectiveness in making full and concise proofs, " This reviewer feels that the book under review is a worthy addition to the literature; but on the whole he found the exposition somewhat clumsy.In a few places terms are used before they are explained (e.g."empty set," page 99) and in c some places no explanation is offered where one is clearly required, (e.g.01 is used, but never defined.Since 31 is defined, the reviewer presumes that no knowledge of factorials is assumed.)Functions are never mentioned, even though the use of functions could have simplified the treatment considerably.These objections, however, may possibly be regarded as minor.Finally, the exercises in the book are many in number and generally non-computational in nature.
Abstract : The year 1935 marked the establishment of the General Headquarters Air Force, the first official recognition that the development of effective airpower necessitated authority for independent action. The purpose of this monograph is to show the organizational growth of the Army air arm from 1935 to September 1945 and to trace the ideas and influences that affects its development. Most significant of these was the continuous effort to attain an autonomous air force, one with a large degree of control over its own affairs internally and the necessary voice in determining its operational activities. Important internal developments included the establishment and implementation of an Air Staff, the application of management devices, the improvement of programming methods, the consolidation of AAF Headquarters offices, and decentralization of command responsibilities.
exists for every i (Theorem 9 of [3]).Following Levy the state i is called stable or instantaneous according as gt-as finite or infinite.We refer to [2 ] for the foundations of the theory of Markov chains under consideration.Although knowledge of these foundations will be necessary for a thorough understanding of what follows, we shall strive to make the present paper readable by itself.Let i be a stable state with q,>0; such a state always exists unless P{x(t) =x(0), 0^t<°° }=l [8, p. 375].Suppose that P{x(0)>=*} =1.LetX=X,(w) be the "first sojourn time" in the state i, namely the length of the first tinterval in which x(t, w)=i (seeTheorem 1 of [2]).Then P{\^t} =l-e~">', t^O [3, p. 54].Let j be an arbitrary state (not oo!) and defineIf J9*i, a is the "first entrance time intoj"; ii j = i, a is the "second entrance time into i" (the first being zero by hypothesis).It is easily shown that a is a random variable in the broad sense, namely a measurable w-iunction defined on a measurable w-set whose probability may be less than one.We define its distribution function in the broad sense by Fij(t)=P{a^t}.Now it can be proved that the two random variables X and a-X (which may be zero with positive probability) are independent^).This is a special case of Theorem 5 of [2], but we give a simple proof as follows.Let us first note that the distribution of a -X may be derived as follows.It can be shown that(3) a(w) considered as a point on the i-axis is the limit from the right of points of Sj(w) ={t: x(t, w) =j}; hence we havewhere h = 2~m, ra->âą oo.Now for each 5 > 0 define two random variables X,=X,(w) and a, = aa(w) on the set {w: x(s, w)=i} as follows: X"(w) is the supremum of T such that x(t, w)=i, s^t<s + T; as(w) is the infimum of t such that t>\"(w) and x(t, w) =j.Thus X0 and a0 reduce to the previous X (2) The random variables Zi(w), â â â , z"(w), with domains of definition Ai, âą â âą , A", are said to be independent iff P{ flLx A*[z*M Set] }/P{ f|Li A*l = LTt-i P{A*tz*W ÂŁc*]}/P(At) for every real Cx, âą âą âą , ck.(3) In fact, the set Sj(w) is dense in itself (see [2, §4, (ii)]).
Among the greatest obstacles in the postwar recovery of steel industry in Japan were. counted the shortage of coal, the removal of subvention to the iron and steelprices and -decentralization of large steel firms. A tragic atmosphere thus clouded was pushed away by the breakout of the Korean Incident (June 1950). Again the prices became enhanced. The export was extended and the production increased. Thence came a chance of modernization of iron and steel industry in Japan. The scheme of this plan that had been plotted by the Rationalization Council in the first half of 1951 was encouraged in the second half by establishment of Japan Development Bank, institution of special overeas credit by the Bank of Japan and the favorable development in Capital market.Capital development and production increase of steel firms in Japan was suceessively realized -during the year of 1951. However, towards 1952 the period of reaction began so that an intensification of the sales competition gradually invited a drop in the steel prices, notwith-standing a temporary short boom due to a steel strike in the United States.In April 1952, the industrial control of the Occupation Forces ended and Japan was again allowed to enter an international economic circles.At this moment, owing to establishment of the European Coal and Steel Community, progress of modernization progress in several countries and recovery of the West-Germany iron and steel industry, the steel industry of Japan too was obliged to be entangled with the international contest.In 1953, the steel market again tended to a slight boom due to domestic investment and consumption but at the end of the same year decrease in bath munition demands and steel export again occurred. Without finding domestic demands, the steel products of Japan began to flow out overseas. At this time happily owing to a shortage of steel export from Europe Japanese products filled the markets of South America and India and enjoyed higher prices. It was also evident at the end of 1954 that the iron and steel industry in rapan again inclined to an expansive production.After such historical introduction, the author described in detail (1) the process of rationalization and financing concerned; (2) trends in the situations of raw materials for iron and steel; (3) domestic market and export; (4) some tendencies in special steels; and (5) future prospects.
Part I. Introduction 1. Prologue.Thus far, very little has been published on the general theory of formal modular invariants or covariants.Workers have, on the whole, obtained results for special, more or less isolated, cases; and although some beautiful and important general theorems have been proved, they are more or less unrelated.This is, of course, only natural in any division of knowledge in its formative state.Nevertheless, no worker in the field could fail to be conscious of a certain uniformity common to the special cases that have been studied in detail; though (alas !) this uniformity usually appeared to be broken ruthlessly in the next case studied.This breaking of an apparent law signified, however, merely that we did not know these special cases with a sufficient thoroughness of illuminating detail, or were trying unwittingly to make the laws conform to certain standards, unconsciously preconceived.This latter handicap was laid on us naturally enough by our thorough knowledge of algebraic invariants and the fact that this newer kind of covariants is, in many ways, strikingly like the older, classic covariants, though so tantalisingly different.Their similarity and their difference show themselves in the very beginning of the study: in the definitions, in the simplest examples.Perhaps the differences that first come to mind are those which are inherent in the fields of definition, which, in the case of classic covariants, is the field of reals or ordinary complex numbers and, in the case of modular covariants, is a Galois field, GF[pn], of order pn.These differences are too obvious to mention in detail, but one who has studied the beautiful proofs given by the old masters of invariant theory has been forced to the conclusion that most of the proofs seemed to use the properties of a field of characteristic zero, not in some accidental manner, but rather in veriest necessity.Growing from the surface differences between the two fields are two very important distinguishing characteristics of the two kinds of covariants.It * Part II was presented to the Society, September 7, 1920; Part III, December 28, 1921; Parts IV and V, December 27, 1922.
of Paul's chapters two definitions of the Christian ideal blend-' For as many as are led by the Spirit of God, these are sons of God'; John makes Jesus stake the future on the ' other Paraclete.'These texts represent all schools of New Testament thought.Indeed, the New Testament is just 'the book of the Spirit.'It is not necessary to repeat the old proofs that in it the ' Spirit of God' and the 'Spirit of Christ' are one, nor to argue that he who has another's spirit and none other is sure to grow really like him.He who receives God's Spirit becomes Christ-like and God-like.This third notion of true manhood is synonymous with the other two.' 1 C. Ryder Smith,