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The method of alternating projections is used to examine how regularity of operators associated to the $${{\bar{\partial }}}$$ -Neumann problem percolates up the $${{\bar{\partial }}}$$ -complex. The approach revolves around operator identities—rather than estimates—that hold on any Lipschitz domain in $${{\mathbb {C}}}^n$$ , not necessarily bounded or pseudoconvex. We show that a geometric rate of convergence in von Neumann’s alternating projection algorithm, applied to two basic projection operators, is equivalent to $${{\bar{\partial }}}$$ having closed range. This implies that compactness of the $${{\bar{\partial }}}$$ -Neumann operator percolates up the $${{\bar{\partial }}}$$ -complex whenever $${{\bar{\partial }}}$$ has closed range at the corresponding form levels.

Sobolev irregularity of the Bergman projection on a family of domains containing the Hartogs triangle is shown. On the Hartogs triangle itself, a sub-Bergman projection is shown to satisfy better Sobolev norm estimates than its Bergman projection.

Cephalosporin antimicrobials can be utilized for the treatment of sepsis in neonatal foals, particularly when an aminoglycoside is contraindicated. Some cephalosporins, however, are not utilized because of cost, sporadic availability, or uncertainty about efficacy. The plasma disposition of ceftazidime, a third-generation cephalosporin with a broad spectrum of activity against a wide variety of gram-negative bacteria and minimal renal side effects has not been reported in neonatal foals. In this study, the plasma disposition of single intravenous (IV) and intramuscular (IM) doses of ceftazidime in neonatal foals was determined. Six healthy one to two-day-old foals were given 25 mg/kg of ceftazidime by IV and IM routes in a cross-over design, with a 48-h washout period between doses. Non-compartmental analysis was used to estimate plasma pharmacokinetic parameters. Median t1/2 was 2 h and median AUC0-last was 364 µg h/ml for both IV and IM administration. Median Cmax after IM administration was 101 µg/ml, with a median Tmax of 0.7 h. Relative bioavailability of IM injection was 90%. There were no statistically significant differences between estimated IV and IM pharmacokinetic parameters. Plasma concentrations remained above the human CLSI susceptible breakpoint for Enterobacteriaceae for over 8 h following IV and IM administration.

An integral solution operator for $${\bar{\partial }}$$ is constructed on product domains that include the punctured bidisc. This operator is shown to satisfy $$L^p$$ estimates for all $$1\le p

Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $\gamma$. A surprising consequence of the analysis is that, whenever $\gamma$ is irrational, the Bergman projection is bounded only for $p=2$., Comment: 21 pages, 2 figures

A sufficient condition for to have closed range is given for pseudoconvex, unbounded domains in .

A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the "fatness" of domains. This range of $p$ is shown to be sharp.

A classical observation of Riesz says that truncations of a general $\sum_{n=0}^\infty a_n z^n$ in the Hardy space $H^1$ do not converge in $H^1$. A substitute positive result is proved: these partial sums always converge in the Bergman norm $A^1$. The result is extended to complete Reinhardt domains in $\C^n$. A new proof of the failure of $H^1$ convergence is also given., Comment: Polynomial density argument added. Several typos corrected

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in C n , via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.

Solution operators for the equation ∂ ¯ u = f are constructed on general product domains in C n . When the factors are one-dimensional, the operator is a simple integral operator: specific derivatives of f are integrated against iterated Cauchy kernels. For higher dimensional factors, the solution is constructed by solving sub- ∂ ¯ equations with modified data on the factors. Estimates in several norms are proved.

Let Ω ⋐ C n \Omega \Subset \mathbb {C}^{n} be a domain with smooth boundary, whose Bergman projection B B maps the Sobolev space H k 1 ( Ω ) H^{k_{1}}(\Omega ) (continuously) into H k 2 ( Ω ) H^{k_{2}}(\Omega ) . We establish two smoothing results: (i) the full Sobolev norm ‖ B f ‖ k 2 \|Bf\|_{k_{2}} is controlled by L 2 L^2 derivatives of f f taken along a single, distinguished direction (of order ≤ k 1 \leq k_{1} ), and (ii) the projection of a conjugate holomorphic function in L 2 ( Ω ) L^{2}(\Omega ) is automatically in H k 2 ( Ω ) H^{k_{2}}(\Omega ) . There are obvious corollaries for when B B is globally regular.

Let B be the Bergman projection associated to a domain Ω on which the \({\bar\partial}\) -Neumann operator is compact. We show that arbitrary L2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a consequence, functions not contained in \({C^{\infty}(\overline{\Omega})}\) that are mapped by B to \({C^{\infty}(\overline{\Omega})}\) are explicitly described.

We give three proofs of the fact that a smoothly bounded, convex domain in ℝn has defining functions whose Hessians are non-negative definite in a neighborhood of the boundary of the domain.

We give an example of a permutation of integers which preserves all convergent Fourier series and makes some divergent Fourier series converge.

Let $$\Omega \subset \subset \mathbb{C}^{n}$$ be a smoothly bounded domain. Suppose Ω has a defining function, such that the sum of any q eigenvalues of its complex Hessian is non-negative. We show that this implies global regularity of the Bergman projection, B j-1, and the $$\bar{\partial}$$ -Neumann operator, N j , acting on (0,j)-forms, for $$j\in\{q,\ldots,n\}$$ .

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

We show that the existence of a certain family of plurisubharmonic functions on a bounded domain in Cn implies that the ∂-Neumann operator associated to the domain is compact. Our condition generalizes previous work of Catlin on compactness of the ∂-Neumann operator.

The effects of intravenous administration of variable-dose flumazenil (0, 0.001, 0.005, 0.01, and 0.1 mg/kg) after ketamine (3 mg/kg) and midazolam (0.0 and 0.5 mg/kg) were studied in 18 healthy unmedicated cats from time of administration until full recovery. End-points were chosen to determine whether flumazenil shortened the recovery period and/or modified behaviors previously identified and attributed to midazolam. Overall, flumazenil administration had little effect on recovery or behaviors. One minute after flumazenil administration, all cats were recumbent but a greater proportion of cats which received the highest dose assumed sternal recumbency with head up than any other group. Although not significant, those cats that received the highest flumazenil dose also had shorter mean times for each of the initial recovery stages (lateral recumbency with head up, sternal recumbency with head up and walking with ataxia) than any of the other treatment groups that received midazolam. For complete recovery, flumazenil did decrease the proportion of the cats that was sedated, but did not shorten the time to walking without ataxia. Based on this study, the administration of flumazenil in veterinary practice, at the doses studied, to shorten and/or improve the recovery from ketamine and midazolam in healthy cats cannot be recommended.

First published in Proceedings of the American Mathematical Society in volume 130 and issue 1, published by the American Mathematical Society.

The effects of intravenous administration of variable-dose midazolam (0, 0.05, 0.075, 0.1, 0.3 and 0.5 mg/kg) and ketamine (3 mg/kg) were studied in twenty-four healthy unmedicated cats from time of administration until full recovery. End-points were chosen to determine the optimal dose to allow a short period of restraint without noxious stimuli, a short period of restraint with noxious stimuli and endotracheal intubation. Recovery characteristics, as well as undesirable behaviours observed during recovery, were also recorded. The dose of midazolam to achieve lateral recumbency with head down was found to be 0.016 mg/kg in 50% of the population (ED50) and 0.054 mg/kg in 95% (ED95) of the population. A midazolam dose of 0.286 mg/kg was required to prevent conscious perception of a stimulus to the ulnar nerve in 50% of the population and 0.652 mg/kg in 95% of the population. The ED50 and ED95 of midazolam required to prevent swallowing in response to a laryngoscope placed on the back of the tongue were found to be 0.265 mg/kg and 0.583 mg/kg, respectively. The ED50 doses of 0.265 mg/kg for intubation and 0.286 mg/kg for restraint with noxious stimulation were close to the tested dose of 0.3 mg/kg. At that dose, the lack of responses lasted 3.67 +/- 2.27 min for laryngoscope and 2.50 +/- 2.20 min for ulnar nerve stimulation, with recovery to walking with ataxia taking 41.50 +/- 15.18 min and complete recovery taking 3.6 +/- 1.3 h. The predominant behavioural pattern during recovery was found to be normal, but some cats also exhibited abnormal behavioural patterns. Nine of the twelve cats exhibited an abnormal arousal state, with 4 being restless and 5 being sedated. Seven of the twelve cats exhibited an abnormal behaviour when approached, with three of the cats being more difficult to approach and four of the cats being easier to approach. Eight of the twelve cats exhibited an abnormal behavioural pattern when restrained, with the cats equally divided between more difficult and easier to restrain. Five of the twelve cats vocalized more during the recovery. The ED50 of 0.042 mg/kg to induce chemical restraint without a noxious stimulus is close to the tested dose of 0.05 mg/kg. At that dose, cats remained lateral with head down for 5.49 +/- 4.02 min, took 25.96 +/- 5.77 min to walk with ataxia and 1.7 +/- 0.4 h for complete recovery. The predominant behavioural patterns during recovery were normal, with several cats exhibiting some abnormal patterns. Two cats were sedated, one cat was more difficult to approach, one cat was easier to restrain and three cats were more vocal.

Emerging technologies that use spread spectrum and frequency hopping signals may enable more efficient use of the high-frequency (HF) band. High-powered HF radar is an example of this technology where channels are used that appear to be unoccupied and the frequency hopping signal of the HF radar has been remarkably free from interfering with conventional spectrum occupants. Considering future application of HF systems of this type, it is of interest to examine the availability of free channels in the frequency range between 3 and 30 MHz for bandwidth (BW) availability and time duration. This paper discusses the characteristics of channels that are available for use in the HF spectrum based on spectrum measurements by the Navy's Relocatable Over-the-Horizon Radar (ROTHR) located in the southeast section of Virginia. In particular, the ROTHR data being analyzed are from the spectrum monitor (SM). The SM is a subsystem of the ROTHR which measures the power level in 3-kHz intervals for frequencies between 5 and 28 MHz, the radar's operating frequency range. Measurements of the HF spectrum were analyzed for the fall and winter seasons at the radar's location. The analysis consisted of estimating the number of clear channels of various widths in selected megahertz bands over the ROTHR's operating frequency range. Characteristics of available channels are presented in various graphical forms which include clear channel availability, probability of at least one clear channel of a specified width, and duration of clear channels as a function of frequency. The Weibull distribution is proposed as an analytical model for investigating channel duration. Analysis results indicate which portion of the HF spectrum is most likely to have available bandwidths and what their expected durations are as a function of season and time of day.

The effects of intravenous administration of variable-dose midazolam and ketamine (3 mg/kg) were studied in twelve healthy unmedicated cats from time of administration until full recovery. A range of midazolam doses (0.0, 0.05, 0.5, 1.0, 2.0 and 5.0 mg/kg) was chosen, so that beneficial and/or detrimental effects could be documented and the therapeutic window for further study determined. One minute after administration of ketamine, all cats had assumed a lateral position, mostly with head up. Muscle tone was increased (100%), apneustic breathing pattern evident in 92% of cats, chewing without stimulation of the oropharyngeal area was observed in most cats (97%), but most cats did not salivate (87%). At 2.5 min after completion of ketamine injection and 1 min after administration of saline, a similar picture was observed, except that salivation was evident. All cats chewed or swallowed in response to a finger or laryngoscope placed in the oropharyngeal area and, while most cats were not aware of a noxious stimulus to the tail, some cats were aware of a noxious stimulus to the paw. Recovery from ketamine alone was rapid and smooth with cats rolling into sternal recumbency and then cautiously walking with ataxia. Recovery to walking without incoordination was also rapid (< 2 h) and no abnormal behavioural patterns were observed during recovery. Administration of midazolam after ketamine, had beneficial effects and the therapeutic window for midazolam was found to lie between 0.05 mg/kg and 0.5 mg/kg. Administration of any dose of midazolam after ketamine caused a greater proportion of cats to assume a laterally recumbent position with head down compared with ketamine alone, however, the time period of recumbency was only significantly longer with a midazolam dose of 2.0 mg/kg or above. Doses of midazolam of 0.5 mg/kg or above decreased muscle rigidity but did not affect salivation or respiratory pattern observed in cats which received ketamine alone. A significantly greater proportion of cats which received ketamine and midazolam 0.5 mg/kg or above did not swallow in response to a finger or a laryngoscope placed in the mouth compared with that which received ketamine alone. The length of time in which cats did not swallow was only significantly longer at midazolam doses of 1.0 mg/kg and above. At midazolam doses of 0.5 mg/kg or above, the proportion of cats without a nociceptive response to a tail or paw clamp was significantly greater than cats which received ketamine alone. The time period without nociceptive response, however, was not influenced by midazolam administration. The time taken for cats which received ketamine and midazolam 0.05 mg/kg or 0.5 mg/kg to assume sternal position, walk with ataxia, walk without ataxia, behave normally when approached or restrained and recover normal arousal state was not significantly different from cats which received ketamine alone. Ketamine and midazolam 5.0 mg/kg significantly prolonged all recovery times compared with ketamine alone. Unfortunately, a greater proportion of cats which received ketamine and midazolam 0.5 or 5.0 mg/kg exhibited detrimental behavioural effects. These were more likely to be adverse and included restlessness, vocalization and difficulty approaching and restraining cats. In this study, an effect of sex of the cats was found, with male cats taking a significantly longer to recover to sternal recumbency and walk with ataxia, while female cats took longer to recover to a normal arousal state.

Congenital left ventricular aneurysm is a rare condition characterized by a protrusion or outpouching of a portion of the ventricular wall with broad connection to the ventricular cavity, which may or may not be associated with paradoxical systolic expansion. Only four cases of congenital left ventricular aneurysm diagnosed by prenatal ultrasonography have been reported so far, with the earliest diagnosis at 26 weeks' gestation. 1-3 In all four cases the pregnancy proceeded uneventfully to term, and all neonates were asymptomatic after birth and at follow-up examination between 4 months and 2 years. 1-3 In this report we describe a case of fetal hydrops secondary to a left ventricular aneurysm diagnosed at 19 weeks' gestation. To our knowledge, this is the first case in which a congenital cardiac aneurysm resulted in severe fetal compromise.

The successful performance of a high-frequency (HF) over-the-horizon radar (OTHR) is dependent upon the environment in which the radar must operate. This study investigates measured power levels of noise and signal characteristics in the HF environment of an operational OTHR system located in Amchitka, Alaska. These measurements were acquired by the Navy's AN/TPS-71 radar (ROTHR) spectrum monitor and represent a new source of HF environmental measurements for noise characteristics, channel availability, and expected duration of various channel widths as a function of frequency, time of day, and season of year. The analysis and results presented are based on HF environmental measurements obtained over the 5–28 MHz frequency band by a receiver with a very low noise figure, an efficient antenna, high dynamic range, and which was seldom internally noise limited. The analysis of this data has provided information on power levels associated with noise and HF users in the geographic region of the radar. Clear channel availability results are based on a threshold level defined by empirical distribution functions (EDF) of the measured power levels from the ROTHR site in Amchitka, Alaska.

A new proof of Oka's lemma is given for smoothly bounded, pseudoconvex domains $D\subset\mathbb{C}^n$. The method of proof is then also applied to other convexity-like hypotheses on the boundary of $D$.

Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the ""other side"" of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.|Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the ""other side"" of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.

Proofs of two results about a monomial ideal -- describing membership in auxiliary ideals associated to the monomial ideal -- are given which do not invoke resolution of singularities. The AM--GM inequality is used as a substitute for taking a log resolution of the monomial ideal.

We construct bounded, plurisubharmonic functions with maximally large Hessians near the boundary of a smoothly bounded convex domain in Cn. As a corollary, the equality of the order of contact of the boundary with complex analytic varieties (the D'Angelo type) and the order of contact with complex lines is demonstrated.

We present several generalizations of the Riemann-Lebesgue lemma. Our approach highlights the role of cancellation in the Riemann—Lebesgue lemma.

Seasonal capture of adult sugar beet root maggots, Tetanops myopaeformis (Roder), was monitored with Blickenstaff & Peckenpaugh sticky-stake traps at 83 commercial sugar beet fields in Idaho during 1980-1984. Published models of postdiapause larval development were inadequate predictors of adult £ light activity and capture. Forecasts of peak adult capture were improved by accounting for larval development before 1 April and for suppression of adult £light activity when maximum daily air temperature was

Toeplitz operators on strongly pseudoconvex domains in $\mathbb{C}^n$, constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The mapping properties of these operators on $L^p$, as the power of the distance varies, are established.

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold., Comment: To Appear in Ann. Inst. Fourier

This volume is the proceedings of a conference held at Ohio State University in May of 1999. Over sixty mathematicians from around the world participated in this conference and principal lectures were given by some of the most distinguished experts in the field. The proceedings volume contains fully refereed research articles from some of the principal speakers, including: Salah Baouendi (UCSD), David Barrett (Univ. Michigan), Bo Berndtsson (Goteborg), David Catlin (Purdue Univ.), Micheal Christ (Berkeley), John D'Angelo (Univ. Illinois), Xiaojun Huang (Rutgers), J. J. Kohn (Princeton), Y.-T. Siu (Harvard), and Emil Straube (Texas A & M).