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->• 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), ■ ■ ■ , z"(w), with domains of definition Ai, • ■ • , A", are said to be independent iff P{ flLx A*[z*M Set] }/P{ f|Li A*l = LTt-i P{A*tz*W £c*]}/P(At) for every real Cx, • • • , 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,
(j**SUv*L. 1872.] LIVING GLACIE. ttSOE California. "L*~ 547 the distance, a water-fall, rippling from the rocks, Avith a sense of motion so Avonderfully conveyed as to arrest the attention even of the most casual beholder. Near by, a cabin of logs. In the foreground a woman, with her hand resting on the arched neck of a young horse, which is the most conspicuous figure on the canvas. A jockey and a boy complete the group. Its catalogued title is simply, " Nelly." . As a work of art, it is a revelation of symmetrical outline and warmth of coloring, delicate in conception, exquisite in finish. The other — a companion picture — represents a similar cabin, upon whose threshold a woman is arrested by a pony express-rider, bearing a telegraphic dispatch. In the light and joy and illumination of her face, one can easily understand why it should be called, "After the Race." These two paintings express, in color, the story here related — a story containing more fact than fiction. They are not for sale, having been painted as a gift for Charles Swinford and wife, who reside in San Francisco, by an artist living in Rome, whose Avorks are rapidly rising in value. His name is Paul. LIVING GLACIERS OF CALIFORNIA. ON one of the yellow days of October, 1871, when I was among the mountains of the "Merced group" following the foot-prints of the ancient gla-. ciers that once flowed grandly from their ample fountains, reading what I could of their history as written in moraines, cations, lakes, and carved rocks, I came upon a small stream that was carrying mud of a kind I had never seen. In a calm place, where the stream widened, I collected some of this mud, and observed that it was entirely mineral in composition, and fine as flour, like the mud from a fine-grit grindstone. Before I had time to reason, I said, " Glacier mud—mountain meal! " Then I observed that this muddy stream issued from a bank of fresh quarried stones and dirt, that was sixty or seventy feet in height. This I at once took to be a moraine. In climbing to the top of it, I was struck with the steepness of its slope, and with its raAY, unsettled, plantless, new-born appearance. The slightest touch started blocks of red and black slate, followed by a rattling train of smaller stones and sand, and a cloud of dry dust of mud, the Avliole moraine being as free from lichens and weather - stains as if dug from the mountain that very day. When I had scrambled to the top of the moraine, I saw what seemed to be a huge snow-bank, four or five hundred yards in length, by half a mile in width. Imbedded in its stained and furrowed surface were stones and dirt like that of Avhich the moraine Avas built. Dirt- stained lines curved across the snowbank from side to side, and when I observed that these curved lines coincided Avith the curved moraine, and that the stones and dirt were most abundant near the bottom of the bank, I shouted, "A living glacier I" These bent dirt-lines show that the ice is following in its different parts with unequal velocity, and these imbedded stones are journeying down, to be built into the moraine, and they gradually become more abundant as they approach the moraine, because there the motion is slower. 548 'LIVING GLA'cTERS OF CALIFORNIA. [Dec. On traversing my new-found glacier, I came to a crevasse, down a wide and jagged portion of which I succeeded in making my way, and discovered that my so-called snow-bank was clear, green ice, and, comparing the form of the basin which it occupied with similar adjacent basins that were empty, I was led to the opinion that this glacier was several hundred feet in depth. Then I went to the "snow-banks" of Mts. Lyell and McClure, and, on examination, Avas convinced that they also were true glaciers, and that a dozen other snow-banks seen from the summit of Mt. Lyell, crouching in shadow, were glaciers, living as any in the world, and busily engaged in completing that vast work of mountain-making accomplished by their giant relations now dead, which, united and continuous, covered all the range from summit to sea. But, although I was myself thus fully satisfied concerning the real nature of these ice masses, I found that my friends regarded my deductions and statements with distrust; therefore, I determined to collect proofs of the common, measured, arithmetical kind. On the twenty-first of August last, I planted five stakes in the glacier of Mt. McClure, which is situated east of Yosemite Valley, near the summit of the range. Four of these stakes were extended across the glacier, in a straight line, from the east side to a point near the middle of the glacier. The first stake was planted about twenty-five yards from the east bank of the glacier; the second, ninety-four yards; the third, 152, and the fourth, 225 yards. The positions of these stakes were determined by sighting across from bank to bank, past a plumb-line, made of a stone and a black horse-hair. On observing my stakes on the sixth of October, or in forty-six days after being planted, I found that stake No. 1 had been carried down stream eleven inches; No. 2, eighteen inches : No. 3, thirty-four, and No. 4, forty-seven inches. As stake No. 4 was near the middle of the glacier, perhaps it was not far from the point of maximum velocity — forty-seven inches in forty-six days, or one inch per day. Stake No. 5 was planted about midway between the head of the glacier and stake No. 4. Its motion I found to be, in forty-six days, forty inches. Thus these ice-masses are seen to possess the true glacial motion. Their surfaces are striped with bent dirt-bands, and are bulged and undulated by ine- quallfpfs in the bottom of their basins, causing an upward and downward swedg- ing, corresponding to the horizontal swedging as indicated by the curved dirt-bands. The Mt. McClure glacier is about one- half of a mile in length, and the same in width at the broadest place. It is crevassed on the south - east corner. The crevasse runs about south-west and north-east, and is several hundred yards in length. It is nowhere more than one foot in width. The Mt. Lyell glacier, separated from that of McClure by a narrow crest, is about a mile.in width by a mile in length. I have planted stakes in the glaciers of "Red Mountain" also, but have not yet observed them. The Sierras adjacent to the Yosemite Valley are composed of slate and granite, set on edge at right-angles to the direction of the range, or about north 300 east, and south 300 west. Lines of cleavage cross these, running nearly parallel with the main range; and the granite of this region has a horizontal cleavage or stratification. The first-mentioned of these lines have the fullest development, and give direction and character to many valleys and canons, and determine the principal features of many rock-forms. No matter how hard, how domed or homogeneous the granite may be, it still possesses these lines of cleav e, which 1872.] LIVING GLACIERS OF CALIFORNIA. 549 require only simple conditions of moisture, time, etc., for their development. But I am not ready to discuss the origin of these planes of cleavage, which make this granite so easily denudable, nor their full significance Avith regard to mountain structure in general. I will only say here, that oftentimes the granite contained between two of these north 300 east planes is softer than the rock outside, and has been denuded, leaving vertical walls, as determined by the direction of the cleavage, thus giving rise to those narrow-slotted canons, called "devil's slides" "devil's lanes" "devil's gateways" etc. In many places, in the higher portions of the Sierras, these slotted canons are filled with "snow" which I thought might prove to be ice; might prove to be living glaciers, still engaged in cutting into the mountains, like endless saws. To decide this question, on the twenty-third of August last, I set two stakes in the narrow-slot glacier of Mt. Hoffman, marking their position by sighting across from Avail to wall, as I did on the McClure glacier; but on visiting them, a .month afterward, they had been melted out, and I was unable to decide anything Avith any great degree of accuracy. On the fourth of October last, I stretched a small trout-line across the glacier, fastening both ends in the solid banks, which at this place were only sixteen feet apart. I set a short, inflexible stake in the ice, so as just to touch the tightly- drawn line, by which means I was enabled to measure the flow of the glacier with great exactness. Examining the stake in twenty-four hours after setting it, I found that it had been carried down about three-sixteenths of an inch. At the end:of four days, I again examined it, and found that the whole downward motion was thirteen-sixteenths of an inch, showing that the flow of this glacier was perfectly regular. In accounting for those narrow-lane canons, so common here, I always referred them to ice-action in connection with special conditions of cleavage, and I was gratified to find that their formation was still going on. This Hoffman glacier is about 1,000 feet long by fifteen to thirty feet wide, and perhaps loo feet deep in the deepest places. I go back to the mountains to complete these observations. These are the first fruits, and the rest of the crop I Avill bring in when I come to study in the Coast Range.
"Separation of ethyle (ethule, ethereum, = 4c + 5 h.)." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 14(92), pp. 543–544