Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

A promising and simple method to quantify soil/manure mixing on beef feedlot pens

On beef cattle feed pen surfaces, fresh and decayed manure is mixed with base rock or soil (base). Quantifying this mixing has beneficial applications for aspects including nutrient and greenhouse gas budgeting. However, no practical methods exist to quantify mixing. We investigated if measuring element concentrations in: (A) fresh manure, (B) base material, and (C) pen manure offers a promising method to quantify manure/base mixing on pen surfaces. Using three operational beef feedlots as study sites, we targeted carbon (C), and silicon (Si), which are the two most abundant and easily measurable organic and inorganic elements. Our results revealed that C concentrations were strongly (>15 times) and significantly (P < 0.05) higher whereas Si concentrations strongly (>10 times) and significantly (P < 0.01) lower in fresh manure than base material at all three sites. These relative concentrations were not significantly impacted by manure decay, as determined by an 18-week incubation experiment. This suggested that both of these elements are suitable markers for quantifying base/manure mixing on pens. However, due to the chemical change of manure during decay, C was shown to be an imprecise marker of base/manure mixing. By contrast, using Si to estimate base/manure mixing was largely unaffected by manure decay. These findings were confirmed by measuring C and Si concentrations in stockpiled pen surface manure from one of the sites. Using Si concentrations is a promising approach to quantify base/manure mixing on feed pens given that this element is abundantly concentrated in soils and rocks.

A simple triggered vacuum gap

A simple triggered vacuum gap has previously been described by the authors in this journal (see ibid., vol.5, 415, 1972). Further studies have resulted in improvement of the performance with regard to sensitivity and consistency of the trigger characteristics and immunity from bridging due to metal particles eroded from the arc. The earlier design suffered from rather frequent bridging of the auxiliary gap and showed rather wide scatter in its trigger characteristics. In the present design thermally stable materials like fused quartz, machinable ceramic 'Supramica 500' (Mycalex Corporation of America), lead titanate, barium titanate (LCC HTD) and silicon carbide have been used to insulate the trigger electrode from the cathode. Consistent triggerings free from bridging, at relatively low voltages of 200-400 V have been obtained.

Delay characteristics of a simple triggered vacuum gap

Firing delays of a simple triggered vacuum gap are reported in this paper. The effects of insulating materials in the auxiliary gap, auxiliary gap current, main gap current and electrode separation on the delay have been investigated. The presence of insulating material in the auxiliary gap having low auxiliary gap resistance appears to exhibit large delay. Delay decreases considerably with increase of current in the auxiliary and the main gaps, but it increases with increase of electrode separation. The scatter in the delay is less than 25 ps and 500 ps with supramica (Mycalex Corporation of America) and silicon carbide respectively at lower values of auxiliary gap current and it becomes negligible for supramica at auxiliary gap currents greater than 6A. This investigation appears to indicate that the simple device can be used as a fast switch.

On the Specificity of Carbohydrate-Lectin Recognition The Interaction of a Lectin from Ricinus communis Beans with Simple Saccharides and Concanavalin A

A galactose-specific protein (RC1) isolated from Ricinus communis beans was found to give a precipitin reaction with concanavalin A. Its carbohydrate content amounted to 8–9% of the total protein and was found to be rich in mannose. The interaction of RC1 with galactose and lactose was measured in 0.05 M phosphate buffer containing 0.2 M NaCl (pH 6.8) by the method of conventional equilibrium dialysis. From the analysis of the binding data according to Scatchard method the association constant (Ka) at 5°C was calculated as 3.8 mM−1 and 1.2 mM−1 for lactose and galactose, respectively. In both cases the number of binding sites per molecule of RC1 with molecular weight of 120000 was found to be 2. From the temperature-dependent Ka values for the binding of lactose, the values of –5.7 kcal/mol and –4.3 cal × mol−1× K−1 were calculated for ΔH and ΔS, respectively. The addition of concanavalin A to RC1 or vice versa led to the formation of the insoluble complex RC1· ConA4 containing one molecule of RC1 and one molecule of tetrameric concanavalin A (ConA4) which could be dissociated upon addition of concanavalin A-specific sugars. The complex formation results in a time-dependent appearance of turbidity in the time range from 10s to 10 min. From the measurement of the time-dependent appearance and disappearance of the turbidity the formation (kf) and dissociation (kd) rate constants were calculated as 3 mM−1× s−1 and 0.07 ks−1 respectively. The ratio kf/kd (43μM −1), that corresponds to the association constant of complex RC1· ConA4, is higher than that of mannoside · ConA4 and thereby suggests that protein-protein interaction contributes significantly in stabilising glycoprotein · lectin complexes. The relevance of this finding to the understanding of the chemical specificities that are involved in a model cell-lectin interaction is discussed.

A simple non-linear D/A converter

A simple generalized technique for realizing a non-linear digital to analogue converter (N-DAC), based on the principles of ' segment of equal digital interval ' is described. The simplicity of the proposed technique is demonstrated by realizing an N-DAC having a square law transfer function.

Simple synthesis and spectroscopic studies on cobalt added ZnO nanocrystals

Cobalt doped zinc oxide nanoparticles were prepared through simple wet chemical method. X-ray diffraction studies confirm the prepared particles are in wurtzite structure. Scanning Electron Microscopy studies show the shape and morphology of the particles. To identify the presence of cobalt in ZnO, Energy Dispersive X-ray analysis was done. Optical absorption measurements show the presence of exciton peak at 375 nm. Photoluminescence studies were done with the excitation wavelength of 330 nm, which shows the emission because of exciton recombination and oxygen vacancy.

A simple method for large-scale preparation of chick embryo tRNA

A simple method for preparing bulk quantities of tRNA from chick embryo has been developed. In this method chick embryos were homogenized in a buffer of pH 4.5, followed by deproteinization with phenol. The aqueous layer was allowed to separate under gravity. The resulting aqueous layer, after two more phenol treatments, was directly passed through a DEAE-cellulose column and the tRNA eluted therefrom with 1 Image NaCl. The tRNA prepared by this method was as active as the one prepared at neutral pH.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.

Low-voltage and high-current delay characteristics of a simple triggered vacuum gap

Low-voltage and high-current switching delay characteristics of a simple triggered vacuum gap (TVG) are described using lead zirconate titanate as the dielectric material in the auxiliary gap. This TVG has superior performance at high currents (up to 14 kA was studied) with regard to delay, reliable firing and extended life as compared to the one using either supramica or silicon carbide. The total delay consists of three intervals: to break down the auxiliary gap, to propagate the trigger plasma and to break down the main gap. The data on the influence of the various parameters like the trigger voltage, current, energy and the main circuit energy are given. It has been found that the delay due to the first two intervals is small compared to the third.

A Simple Method of Obtaining the Band Strengths in the Electronic Spectra of Diatomic Molecules

Relative band strengths of diatomic molecules for which the product of Franck-Condon factor and r-centroid is approximately equal to 1 for (0,0) band can be determined by a simple method which will be in good agreement with the smoothed array of experimental values.

A simple method for the isolation of plant protoplasts

A simple protoplast isolation protocol that was designed to recover totipotent plant protoplasts with relative ease has been described. The key elements of the protocol are, tissue digestion at slightly elevated temperatures and use of protoplast-releasing enzymes that are stable and efficient at higher temperatures. Besides enzymes, the protoplast isolation cocktail consisted of an osmoticum (mannitol or MgSO4), and a protectant (CaCl2 2H2O), all dissolved in distilled water. The protocol has ensured reproducibility, higher yields and is gentle on protoplasts as the protoplasts obtained were amenable to cell wall regeneration and cell division. Plant regeneration was demonstrated forNicotiana tabacum cv. Thompson from protoplasts isolated by this method. Wall regeneration and cell division were obtained in other species. The merits of the protocol are, simple and easy-to-handle procedure, non-requirement of preconditioning of donor plant and explants, incubation without agitation, satisfactory yields, culturability of the protoplasts isolated and applicability of the protocol to a large number of species including mucilage-containing plants.

A simple model for protein thermal denaturation

Whether proteins denature in all-or-none fashion or in a continuous fashion is as yet an unresolved problem. The all-or-none process implies that while the process of denaturation is going on, only two kinds of protein molecules can exist. One is completely unchanged and the other is altered. The altered protein molecules are indistinguishable. Underlying the 'continuum' models is the assumption that all the chains in a protein globule undergo similar changes so that it is enough to consider a single chain.