Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

Smoothing singularities of Riemannian metrics while preserving lower curvature bounds

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Variable dentition in a Chinese insectivore, by Wilfred H. Osgood.

v.20:no.27(1937)

Investigações sobre doenças de Psittacideos

The present paper colligates the notions acquired in previous investigations, already published, and new observations upon diseases of the psittacidae, liable to be confused with psittacosis of parrots. The author calls attention to the indifference with regard to this question shown by investigators, even by those who dealt with the study of this disease on the occasion of the latest outbreak of psittacosis, in flagrant contrast with the researches upon the alterations induced by pathogenic agents of other diseases transmissible to man, when these agents pass through animals or when the latter are depositaries of the virus. This remark considerably enhances the importance of the presence paper from a hygienic and epidemiologic point of view, representing moreover a contribution to general knowledge and to veterinary medicine. The researches carried out since the appearance of the latest outbreak of psittacosis,-which occurred simultaneously with an epizooty in parrots lodged in aviary of the park of Agua Branca (Directory of Animal Industry of the State São Paulo)-led to the verification of the frequent existence in these animals of various diseases liable to be confused with psittacosis. These diseases are due to two kinds of pathogenic agents: virus and bacteria. In the first group there are to be found the diseases occasioned by the virus of human psittacosis, discovered by Western, Bedson and Simpson, and the disease me with in parrots coming from traders in S. Paulo. The infections by bacteria of the genus Salmonella and by those of other genera belong to the second group. As differential characters of the two infections due to virus, delineated on the strength of notions drawn from a detailed experimental study and from the literature on this subject, the following are given: ¹ Samples of our virus were sent, for comparison, to various investigators of psittacosis. Amongst them, Prof. M. Rivers acceded to our request; he found its nature to be different from that of the virus of psittacosis studiedby him. We are very much obliged to him for the attention he paid to this verification. Virus of psittacosis - Infectiousness: man, monkey, rabbit, mouse, hen, canary. Neurotropic affinity. Inclusions: small, protoplasmic. Exsiccation: the virus has good power of preservation. Symptoms: inactivity, drowsiness, frequent diarrhoea, oculo-nasal discharge and cough, coma. Duration: 4 to 5 days. Bodily lesions: congestion of intestines, splenomegaly. Virus of S. Paulo - Infects only psittacidae, particularly those of the genus Amazona. No localization in the nervous system. Large, nuclear. Is rapidly destroyed. Inactivity, inappetency, adynamia (drooping of the wings, indifference, leaning its beak against the bars of the cage in order not to fall down); profuse diarrhoea, of whitish stools, at times enterorrhagia; prolonged coma. 2 to 8 days. Foci of yellowish necrosis in liver, spleen and lung. At times, congestion of intestines. Characteristic features common to the two viruses.-They act in great dilutions, filter through tight candles though being partly retained, are preserved under glycerine or Bedson's solution, are stable at 55°C. heat and are destroyed by physical and chemical agents. Both virus diseases are very seldom met with in psittacidae: only once, amongst numberless sick parrots, the author met with a disease of the virus differring from that of psittacosis. This disease, greatly transmissible to man, ought to be more frequent, if it were common in parrots. On the contrary, bacteria cause diseases in these animals with great frequency, presenting variable characters, from a severe epizootic form, rapidly mortal, to ambulatory or silent forms, for the most part developing towards a cure or assuming a chronic character. Amongst the bacteria which cause the infection of this group the salmonellae predominate and amongst them the bacterium discovered by Nocard, as well as a species which in the course of this study is characterized under the name of Salmonella nocardi. The author believes that in the epizooty from which Nocard isolated his bacterium there was association of the virus-disease inducing the epizooty of that epoch in Paris with the bacterial disease, as must have happened in Argentina, where the disease was transmitted to man, and Santillan, according to Barros, isolated from the sick parrots bacteria of the genus Salmonella. The diseases of the two groups, that due to virus and that due to bacteria, are differentiated: Virus-diseases - Evolution: rapid, nearly always followed by death. Symptoms: sadness, profuse diarrhoea, of whitish stools, at times enterorrhagia, complete inappetency, adynamia, indifference, prolonged coma. Clinical forms: acute and subacute. Lesions: Foci of necrosis in liver and spleen without cellular reaction around the focus, yellow liver, multiple serositis. Presence of protoplasmic or nuclear granulations. Bacteriology: Complete lack or inconstant presence of bacteria in the organs and blood. Infectiousness of the organs and blood after filtration: positive. Bacterial diseases - Varies from one week to a month or more, not always fatal. Sadness, partial inappetency, tremblings, intensive thirst, mucous or mucosanguineous diarrhoea, lack of adynamia (reacts to stimulations and moves well at any time of the disease, though showing little disposition to locomotion), soiling of feathers. Frustrate, acute, subacute and chronic. Hepatic and intestinal cogestion, foci of necrosis in liver, spleen and lung with cellular reaction around the focus. Lack of granulations. Constant presence of bacteria in the organs and blood. Negative. The analysis of the litterature shows that the characteristic features of the diseases in parrots referred to parrot psittacosis, more frequently approach the bacterial diseases here described of these animals, a hypothesis which is reinforced by the observation of the greater frequency of infections...

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Análise citológica e cariométrica da ação da colchina sôbre a espermatogênese dos hemípteros

The action of colchicine upon the spermatogenesis of Triatoma infestans, (Hemipt. Heteroptera), has been studied and the different categories of giant spermatids that appear during the treatment have been compared with the nuclear volumes of the whole series of normal spermatogenetic stages. The following facts have been ascertained: 1) 4 hours after the treatment the gonial mitotic metaphases, and the 1st. and 2nd. metaphases of meiosis are stopped. The prophasic stages of meiosis and diakynesis appear to be normal. After 9 days of treatment, all the tetrads are broken in the meiotic metaphases and the cells appear with 44 and 22 chromosomes respectively, scattered in the cytoplasm. 2) At 9 days, practically all spermatogenetic stages have disappeared except for a few cysts of spermatogonia, and practically the whole testicle is full of cysts of spermatozoa and spermatid, with some large zones of necrosis with pycnotic nuclei. The spermatids appear to be of different sizes and the statistical analysis of the nuclear volumes gives a polymodal hystogram with 4 modes, whose volumes are in the ratio of 1:2:4:8. Ripe spermatozoa seem to have a certain volume variability, that has not been possible to analyse quantitatively. All these facts confirm what DOOLEY found in the colchicinized Orthoptera testicle. 3) The caryometric analysis conducted statistically on the normal stages of the spermatogenesis (resting spermatogonia, gonial prophases, leptotene, "confused stage", diakynesis, and spermatid) revealed the following facts: a) Considering the volume of the resting, spermatogonia as 1, their mitotic prophases have a volume of 2. Some rare prophases appear to have a volume of 4 and probably belong to tetraployd spermatogonia normally present in the testicle of Hemiptera. b) The first spermatocyte at the beginning of the auxocitary growth (leptotene) has a volume of 2, which is equal to that of them gonial prophase. It grows further during the "confused stage" and reduplicates, reaching thus the volume of 4. Diakynesis has a rather variable nuclear volume and it is higher than volume 4. This is probably of physico-chemical nature and not a growth increase. c) The spermatid at the beginning of the spermiogenetic process has a volume of 1 which is very constant and homogeneous. 4) These results can be summarized concluding that the meiotic process begins from a spermatogonium at the end of his mitotic interphasic growth (vol. 2) and instead of entering into the mitotic prophase transforms itself into the leptotene spermatocyte. During the diplotene ("confused stage") the volume of the nucleus doubles once more and reaches volume 4. In consequence of the two successive meiotic divisions the spermatid, although having an haploid number of chromosomes, has a nuclear volume of 1, just like the diploid spermatogonium. The interpretation of this strange result probably comes from the existence of the "tertiary split" in the chromosomes of the haploid set, that has been illustrated in the Hemiptera by HUGUES SCHRADER and in Orthoptera by MICKEY and co-workers. The tertiary split indicates that the chromosomes of the haploid set are constituted from almost two chromonemata, and this double constitution corresponds to the double cycle of reduplication that takes place during the spermatogenesis starting from the resting gonia. In Triatoma infestans the tertiary split appears in the chromosomes in the 1st. and 2nd. metaphases and in the diakynesis. In the blocked metaphases at the 9th. day of colchicinization some of the 44 elements scattered in the cytoplasm, show, when properly oriented, the split very clearly. Some new and strange facts revealed by SCHRADER and LEUCHTEMBERGER in Arvelius suggest the possibility of other interpretations of the rhythmic growth in special cases. There appears the necessity of more knowledge about the multiple or simple constitution of the chromosomes in somatic and spermatogonial mitosis.

El Riesgo y las estrategias en la evaluación de los fondos de inversión de renta variable

El objetivo de este trabajo consiste en proponer una medida de performance adecuada para los fondos de inversión de renta variable. Las características específicas de este tipo de carteras inducen a tomar un enfoque basado en la L.M.C., por lo que se escoge como medida de riesgo el riesgo total de la cartera (pσ). Se introducen las estrategias pasivas y activas en el análisis, con lo que se consigue desarrollar una medida de performance que, además de medir la rentabilidad por gestión efectiva, la pondera en función del grado de actividad asumido por la cartera a evaluar.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Safe dissection of the distally based anterolateral thigh flap.

Background The distally based anterolateral thigh (ALT) flap is an interesting reconstructive solution for complex soft tissue defects of the knee. In spite of a low donor site morbidity and wide covering surface as well as arch of rotation, it has never gained popularity among reconstructive surgeons. Venous congestion and difficult flap dissection in the presence of a variable anatomy of the vascular pedicle are the possible reasons.Methods An anatomical study of 15 cadaver legs was performed to further clarify the blood supply of the distally based ALT. Our early experience with the use of preoperative angiography and a safe flap design modification that avoids distal intramuscular skeletonization of the vascular pedicle and includes a subcutaneous strip ranging from the distal end of the flap to the pivot point is presented.Results The distally based ALT presents a constant and reliable retrograde vascular contribution from the superior genicular artery. Preoperative angiography reliably identified and avoided critical Shieh Type II pedicled flaps. The preservation of a subcutaneous strip ranging from the distal flap end to the upper knee was associated with the absence of venous congestion in a short case series.Conclusions Preoperative angiography and a flap design modification are proposed to allow the safe transfer of the distally based ALT to reconstruct soft tissue defects of the knee.

Experimental investigation of transient natural convection cooling of high prandtl number fluid with variable viscosity

Report for the scientific sojourn at the James Cook University, Australia, between June to December 2007. Free convection in enclosed spaces is found widely in natural and industrial systems. It is a topic of primary interest because in many systems it provides the largest resistance to the heat transfer in comparison with other heat transfer modes. In such systems the convection is driven by a density gradient within the fluid, which, usually, is produced by a temperature difference between the fluid and surrounding walls. In the oil industry, the oil, which has High Prandtl, usually is stored and transported in large tanks at temperatures high enough to keep its viscosity and, thus the pumping requirements, to a reasonable level. A temperature difference between the fluid and the walls of the container may give rise to the unsteady buoyancy force and hence the unsteady natural convection. In the initial period of cooling the natural convection regime dominates over the conduction contribution. As the oil cools down it typically becomes more viscous and this increase of viscosity inhibits the convection. At this point the oil viscosity becomes very large and unloading of the tank becomes very difficult. For this reason it is of primary interest to be able to predict the cooling rate of the oil. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of high Prandtl fluid considering the variable viscosity effects.

Welfare Implications of Public Education Spending Rules

In this paper, we quantitatively assess the welfare implications of alternative public education spending rules. To this end, we employ a dynamic stochastic general equilibrium model in which human capital externalities and public education expenditures, nanced by distorting taxes, enhance the productivity of private education choices. We allow public education spending, as share of output, to respond to various aggregate indicators in an attempt to minimize the market imperfection due to human capital externalities. We also expose the economy to varying degrees of uncertainty via changes in the variance of total factor productivity shocks. Our results indicate that, in the face of increasing aggregate uncertainty, active policy can signi cantly outperform passive policy (i.e. maintaining a constant public education to output ratio) but only when the policy instrument is successful in smoothing the growth rate of human capital.