The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Long-term preservation of Neozygites tanajoae (Entomophthorales : Neozygitaceae) in cadavers of Mononychellus tanajoae (Acari : Tetranychidae)

To determine the effect of storage on fungal survival, mummified cadavers of the cassava green mite pathogen, Neozygites tanajoae were placed at different conditions of temperature and relative humidity. The best condition for long-term preservation was -10 degrees C. At this condition, the fungus retained viability for 10 years when the experiment was terminated, with a decrease in sporulation with time. Cadavers placed at 4 degrees C and 5% RH sporulated for 2 years, while the fungus survived for only 7 days at 25 degrees C and 50% RH.

Preservation of Phakopsora pachyrhizi uredospores

This study compared different temperatures and dormancy-reversion procedures for preservation of Phakopsora pachyrhizi uredospores. The storage temperatures tested were room temperature, 5 degrees C, -20 degrees C and -80 degrees C. Dehydrated and non-dehydrated uredospores were used, and evaluations for germination (%) and infectivity (no. of lesions/cm(2)) were made with fresh harvested spores and after 15, 29 76, 154 and 231 days of storage. The dormancy-reversion procedures evaluated were thermal shock (40 degrees C/5 min) followed or not by hydration (moist chamber,24 h). Uredospores stored at room temperature were viable only up to a month of storage, regardless of their hydration condition. Survival of uredospores increased with storage at lower temperatures. Dehydration of uredospores prior to storage increased their viability, mainly for uredospores stored at 5 degrees C, -20 degrees C and -80 degrees C. At 5 degrees C and -20 degrees C, dehydrated uredospores showed increases in viability of at least 47 and 127 days, respectively, compared to non-dehydrated spores. Uredospore germination and infectivity after storage for 231 days (7.7 months), could only be observed at -80 degrees C, for both hydration conditions. At this storage temperature, dehydrated and non-dehydrated uredospores exhibited 56 and 28% of germination at the end of the experiment, respectively. Storage at -80 degrees C also maintained uredospore infectivity, based upon levels of Infection frequency, for both hydration conditions. Among the dormancy-reversion treatments applied to spores stored at -80 degrees C, those involving hydration allowed recoveries of 85 to 92% of the initial germination.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

The systematic use of intraoperative vascular Doppler ultrasound during microsurgical subinguinal varicocelectomy improves precise identification and preservation of testicular blood supply

Objective: To evaluate the impact of systematic use of intraoperative Doppler ultrasound during microsurgical subinguinal varicocele repair. Design: Prospective clinical study. Setting: Andrology laboratory and male infertility section of the urology department of a tertiary care hospital. Patient(s): Two hundred and thirteen men with clinical varicocele. Intervention(s): Subinguinal microsurgical varicocele ligation using an intraoperative vascular Doppler flow detector. Main Outcome Measure(s): Number of veins ligated, lymphatic spared, arteries identified or accidentally ligated. Result(s): A statistically significant greater number of arteries were identified and preserved when intraoperative vascular Doppler was used. In addition, the average number of internal spermatic veins ligated was statistically significantly greater in the same group. Accidental artery ligation occurred in two cases (1.1%) in which the Doppler was not applied. There was no statistically significant difference in number of lymphatics spared between groups. Conclusion(s): Our findings showed that concomitant use of intraoperative vascular Doppler during microsurgical varicocelectomy allows more arterial branches to be preserved, and more internal spermatic veins are likely to be ligated. This device should be considered an attractive tool to improve surgical outcomes and safety. (Fertil Steril (R) 2010; 93: 2396-9. (C)2010 by American Society for Reproductive Medicine.)

Comparison Between Perfadex and Locally Manufactured Low-Potassium Dextran Solution for Pulmonary Preservation in an Ex Vivo Isolated Lung Perfusion Model

Introduction. Lung tranplantation, a consolidated treatment for end-stage lung disease, utilizes preservation solutions, such as low potassium dextran (LPD), to mitigate ischemia reperfusion injury. We sought the local development of LPD solutions in an attempt to facilitate access and enhance usage. We also sought to evaluate the effectiveness of a locally manufactured LPD solution in a rat model of ex vivo lung perfusion. Methods. We randomized the following groups \?\adult of male Wistar rats (n = 25 each): Perfadex (LPD; Vitro life, Sweden); locally manufactured LPD-glucose (LPDnac) (Farmoterapica, Brazil), and normal saline solution (SAL) with 3 ischemic times (6, 12, and 24 hours). The harvested heart lung blocks were flushed with solution at 4 C. After storage, the blocks were connected to an IL-2 Isolated Perfused Rat or Guinea Pig Lung System (Harvard Apparatus) and reperfused with homologous blood for 60 minutes. Respiratory mechanics, pulmonary artery pressure, perfusate blood gas analysis, and lung weight were measured at 10-minute intervals. Comparisons between groups and among ischemic times were performed using analysis of variance with a 5% level of significance. Results. Lungs preserved for 24 hours were nonviable and therefore excluded from the analysis. Those preserved for 6 hours showed better ventilatory mechanics when compared with 12 hours. The oxygenation capacity was not different between lungs flushed with LPD or LPDnac, regardless of the ischemic time. SAL lungs showed higher PCO(2) values than the other solutions. Lung weight increased over time during perfusion; however, there were no significant differences among the tested solutions (LPD, P = .23; LPDnac, P = .41; SAL, P = .26). We concluded that the LPDnac solution results in gas exchange were comparable to the original LPD (Perfadex); however ventilatory mechanics and edema formation were better with LPD, particularly among lungs undergoing 6 hours of cold ischemia.

Long-term outcomes of radical cystectomy with preservation of prostatic capsule

We report our results of orthotopic ileal neobladder after radical cystectomy with prostatic adenomectomy with regard to urinary continence, sexual outcome and disease control. Between March 2003 and July 2004, 22 men with bladder transitional cell carcinoma (mean age 65.0) were analyzed. They underwent radical cystectomy with prostatic adenomectomy with preservation of the prostatic capsule, seminal vesicles and orthotopic ileal neobladder. Urinary continence was assessed after 2 days, 2 months, 6 months and 1 year. Preservation of sexual function was defined as the ability to have sexual intercourse and was assessed after 2-, 6-, and 12-months postoperatively. Overall survival and cancer-specific survival were assessed. Median postoperative follow-up was 60 months. Daytime and nighttime urinary continence after 48 h was 47 and 14%, respectively. After 2, 6 and 12 months, these rates were 74 and 16%, 85 and 26%, and 94 and 31%, respectively. Sexual intercourse was achieved in 69% of patients. Overall survival rate was 68%, and cancer-specific survival rate was 73%. Overall survival rates according to pathologic stage for pT0, pT1, pT2 and pT3 were 100, 60, 71 and 57%, and cancer-specific survival were 100, 80, 71 and 57%, respectively. Urinary continence and sexual function achieved by radical cystectomy with prostatic adenomectomy with orthotopic ileal neobladder seem to be similar to those achieved by the conventional technique with satisfactory oncologic results.

Gangliosides Are Important for the Preservation of the Structure and Organization of RBL-2H3 Mast Cells

Gangliosides are known to be important in many biological processes. However, details concerning the exact function of these glycosphingolipids in cell physiology are poorly understood. in this study, the role of gangliosides present on the surface of rodent mast cells in maintaining cell structure was examined using RBL-2H3 mast cells and two mutant cell lines (E5 and D1) deficient in the gangliosides, GM(1) and the alpha-galactosyl derivatives of the ganglioside GD(1b). The two deficient cell lines were morphologically different from each other as well as from the parental RBL-2H3 cells. Actin filaments in RBL-2H3 and E5 cells were under the plasma membrane following the spindle shape of the cells, whereas in D1 cells, they were concentrated in large membrane ruffles. Microtubules in RBL-2H3 and E5 cells radiated from the centrosome and were organized into long, straight bundles. The bundles in D1 cells were thicker and organized circumferentially under the plasma membrane. The endoplasmic reticulum, the Golgi complex, and the secretory granule matrix were also altered in the mutant cell lines. These results suggest that the mast cell-specific alpha-galactosyl derivatives of ganglioside GD(1b) and GM(1) are important in maintaining normal cell morphology. (J Histochern Cytochem 58:83-93, 2010)

Ridge Preservation With Acellular Dermal Matrix and Anorganic Bone Matrix Cell-Binding Peptide P-15 After Tooth Extraction in Humans

Background: Preventing ridge collapse with the extraction of maxillary anterior teeth is vital to an esthetic restorative result. Several regenerative techniques are available and are used for socket preservation. The aim of this study is to analyze by clinical parameters the use of acellular dermal matrix (ADM) and anorganic bovine bone matrix (ABM) with synthetic cell-binding peptide P-15 to preserve alveolar bone after tooth extraction. Methods: Eighteen patients in need of extraction of maxillary anterior teeth were selected and randomly assigned to the test group (ADM plus ABM/P-15) or the control group (ADM only). Clinical measurements were recorded initially and at 6 months after ridge-preservation procedures. Results: In the clinical measurements (external vertical palatal measurement [EVPM], external vertical buccal measurement [EVBM], and alveolar horizontal measurement [AHM]) the statistical analysis showed no difference between test and control groups initially and at 6 months. The intragroup analysis, after 6 months, showed a statistically significant reduction in the measurements for both groups. In the comparison between the two groups, the differences in the test group were as follows: EVPM = 0.83 +/- 1.53 mm; EVBM = 1.20 +/- 2.02 mm; and AHM = 2.53 +/- 1.81 mm. The differences in the control group were as follows: EVPM = 0.87 +/- 1.13 mm; EVBM = 1.50 +/- 1.15 mm; and AHM = 3.40 +/- 1.39 mm. The differences in EVPM and EVBM were not statistically significant; however, in horizontal measurement (AHM), there was a statistically significant difference (P<0.05). Conclusion: The results of this study show that ADM used as membrane associated with ABM/P-15 can be used to reduce buccal-palatal dimensions compared to ADM alone for preservation of the alveolar ridge after extraction of anterior maxillary teeth. J Periodontol 2011;82:72-79.

Agribusiness Opportunity Costs and Environmental Legal Protection: Investigating Trade-Off on Hotspot Preservation in the State of So Paulo, Brazil

Prior to deforestation, So Paulo State had 79,000 km(2) covered by Cerrado (Brazilian savanna) physiognomies, but today less than 8.5% of this biodiversity hotspot remains, mostly in private lands. The global demand for agricultural goods has imposed strong pressure on natural areas, and the economic decisions of agribusiness managers are crucial to the fate of Cerrado domain remaining areas (CDRA) in Brazil. Our aim was to investigate the effectiveness of Brazilian private protected areas policy, and to propose a feasible alternative to promote CDRA protection. This article assessed the main agribusiness opportunity costs for natural areas preservation: the land use profitability and the arable land price. The CDRA percentage and the opportunity costs were estimated for 349 municipal districts of So Paulo State through secondary spatial data and profitability values of 38 main agricultural products. We found that Brazilian private protected areas policy fails to preserve CDRA, although the values of non-compliance fines were higher than average opportunity costs. The scenario with very restrictive laws on private protected areas and historical high interest rates allowed us to conceive a feasible cross compliance proposal to improve environmental and agricultural policies.