Plurisubharmonic polynomials and bumping

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain \Omega\subset C^n in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with bdy(\Omega), at the site of the bumping, are explicitly realised. Generally, when \Omega\subset C^n, n\geq 3, the known methods lead to bumpings with high orders of contact -- which are not explicitly known either -- at the site of the bumping. Precise orders are known for h-extendible/semiregular domains. This paper is motivated by certain families of non-semiregular domains in C^3. These families are identified by the behaviour of the least-weight plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity.Comment: 24 pages; corrected typos, fixed errors in Lemma 3.3; accepted for publication in Math.

Diagonal Slice Four-Wave Mixing: Natural Separation of Coherent Broadening Mechanisms

We present an ultrafast coherent spectroscopy data acquisition scheme that samples slices of the time domain used in multidimensional coherent spectroscopy to achieve faster data collection than full spectra. We derive analytical expressions for resonance lineshapes using this technique that completely separate homogeneous and inhomogeneous broadening contributions into separate projected lineshapes for arbitrary inhomogeneous broadening. These lineshape expressions are also valid for slices taken from full multidimensional spectra and allow direct measurement of the parameters contributing to the lineshapes in those spectra as well as our own

Fellhanera gyrophorica, a new European species with conspicuous pycnidia

Fellhanera gyrophorica Sérus., Coppins, Diederich & Scheidegger is described as new from Europe Austria, Lithuania, Luxembourg, Poland, Switzerland and Ukraine. It is a sterile corticolous species with conspicuous and sometimes shortly stalked pycnidia whose outer walls produce gyrophoric acid. Its position in the genus Fellhanera (Pilocarpaceae) is tentative and further studies may necessitate its transfer to another genu

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

Modeling of the degradation of poly(ethylene glycol)-co-(lactic acid)-dimethacrylate hydrogels

Because of their similarity with extracellular matrix, hydrogels are ideal substrates for cell growth. Hydrogels made of synthetic polymers are excellent alternatives to natural ones and offer the key advantage of precisely controllable degradation times. In this work, hydrogels have been prepared from modified poly(ethylene glycol) macromonomers, functionalized on both ends first with a few lactic acid units, and then with methacrylate groups. A library of hydrogels has been prepared using free- radical polymerization of the macromonomers, by changing both the macromonomer concentration and their type, i.e., the number of lactic acid repeating units. The degradation kinetics of these hydrogels, caused by the hydrolysis of the lactic acid units, have been carefully monitored in terms of swelling ratio, mass loss, and Young’s modulus. A complete mathematical model, accounting for hydrogel degradation, swelling, and reverse gelation, has been developed and used to predict all the measured quantities until complete disappearance of the gels. The model is capable of accurately predicting the time evolution of all the properties investigated experimentally. To the best of our knowledge, this is the first study where such a systematic comparison between model predictions and experimental data is presented

An Exploratory Investigation of Some Types of Aeroelastic Instability of Open and Closed Bodies of Revolution Mounted on Slender Struts

Aeroelastic instability phenomena of isolated open and closed rigid bodies of revolution free to move under elastic restraint have been investigated experimentally at low speeds by means of models suspended at zero angles of attack and yaw on slender flexible struts from a wind tunnel ceiling. Three types of instability were observed - flutter similar to classical bending-torsion flutter, divergence, and an uncoupled oscillatory instability which consists in nonviolent continuous or intermittent small-amplitude oscillations involving only angular deformations. The speeds at which this oscillatory instability starts were found to be as low as about one-third of the speed at flutter or divergence and to depend on the shape of the body, particularly that of the afterbody, and on the relative location of the elastic axis. An attempt has been made to calculate the airspeeds and, in the case of the oscillatory phenomena, the frequencies at which these instabilities occur by using slender-body theory for the aerodynamic forces on the bodies and neglecting the aerodynamic forces on the struts. However, the agreement between the speeds and frequencies calculated in this manner and those actually observed has been found to be generally unsatisfactory; with the exception of the frequencies of the uncoupled oscillations which could be predicted with fair accuracy. The nature of the observed phenomena and of the forces on bodies of revolution suggests that a significant improvement in the accuracy of analytical predictions of these aeroelastic instabilities can be had only by taking into account the effects of boundary-layer separation on the aerodynamic forces

Organic-solvent-free extraction of carotenoids from yeast Rhodotorula glutinis by application of ultrasound under pressure

The extraction of Rhodotorula glutinis carotenoids by ultrasound under pressure (manosonication) in an aqueous medium has been demonstrated. The influence of treatment time, pressure, and ultrasound amplitude on R. glutinis inactivation and on the extraction of carotenoids was evaluated, and the obtained data were described mathematically. The extraction yields were lineal functions of those three parameters, whereas inactivation responded to a more complex equation. Under optimum treatment conditions, 82% of carotenoid content was recovered. Extraction of carotenoids in an aqueous medium was attributed to the capacity of ultrasound for cell disruption and emulsification. Cavitation caused the rupture of cell envelopes and the subsequent formation of small droplets of carotenoids surrounded by the phospholipids of the cytoplasmic membrane that would stabilize the emulsion. Analysis of the dispersed particle size of the extracts demonstrated that a fine, homogeneous emulsion was formed after treatment (average size: 230 nm; polydispersity <0.22). This research describes an innovative green process for extracting carotenoids from fresh biomass of R. glutinis in which only two unit operations are required: ultrasonic treatment, followed by a centrifugation step to discard cell debris. The extract obtained thanks to this procedure is rich in carotenoids (25 mg/L) and could be directly incorporated as a pigment in foods, beverages, and diet supplements; it can also be utilized as an ingredient in drugs or cosmetics

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random, Gaussian interactions of order p >= 2, and deterministic self-interactions u <= 0. We show that for nonzero u the effect of increasing the order of the interactions is to make the system more cooperative, in the sense that the fraction of extinct species is greatly reduced. Furthermore, we find that for p > 2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.Comment: 7 pages, 4 Postscript figure