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DYNAMIC VIBRATION DAMPERS FOR CONSOLE INSTRUMENTS

The maximum efficiency of dynamic vibration dampers (DD) is achieved at optimal values of their parameters. Inertial DD are tuned according to their own frequency and damping, and the optimal values of the absorber parameters depend on the spectral composition of the suppressed oscillations. For nonlinear DD, the optimal values of parameters (for example, gap or precompression) also depend on the intensity of external influences on the object. For multi-element DDs, the number of damper inertial elements should also be optimized. The conditions for optimal tuning of the inertial DD are the conditions of antiresonance. In this work, the tuning of an impact DD with viscous friction has been studied. To determine the optimal value of the gap between the mass of the absorber and its body, a nonlinear problem was solved by the method of point transformations. The influence of deviations from the optimal setting of the shock DD on the amplitude of oscillations is determined. It has been established that small deviations from the optimum cause significant increments in the oscillation range (by 2...5 times), which leads to the need to tune the shock DD with high accuracy. The sensitivity of the vibration damper to the optimization error of its parameters is estimated in the work. In addition, the tuning features of multi-element DDs built into the boring bar for eight types of absorbers were studied with varying their design features. When studying the frequency characteristics, the ratio of the maximum values A0 max/AD max was taken as a measure of efficiency, where A0 max is the oscillation amplitude in the system without a damper. The influence of the diametral clearance and the axial compression force on the efficiency of various types of DDs has been established.

Comparison of coupling constant by using momentum spectra and event shape variables in different interactions

We describe in this paper the quantum chromodynamics prediction to calculate the strong coupling constant by using event shape variables as well as momentum spectra. By fitting the dispersive model and employing our parameters on event shape distribution, we obtain the perturbative value of [Formula: see text] = 0.1305 ± 0.0474 and also the non-perturbative value of α0 = 0.5246 ± 0.0516 GeV for electron–proton interactions. Next, by using momentum spectra for the same interactions, we obtain αs = 0.1572 ± 0.029. Our values in both methods are consistent with those obtained from electron–positron annihilations measured previously. When we find coupling constant for different flavours, we observe that they do not affect our results considerably. This is in accordance with quantum chromodynamics theory. All these features will be explained in the main text.

A monotonicity property for generalized Fibonacci sequences

Abstract Given k ≥ 2, let a n be the sequence defined by the recurrence a n = α 1 a n–1 + … + α k a n–k for n ≥ k, with initial values a 0 = a 1 = … = a k–2 = 0 and a k–1 = 1. We show under a couple of assumptions concerning the constants α i that the ratio a n n a n − 1 n − 1 $\frac{\sqrt[n]{a_n}}{\sqrt[n-1]{a_{n-1}}}$ is strictly decreasing for all n ≥ N, for some N depending on the sequence, and has limit 1. In particular, this holds in the cases when all of the α i are unity or when all of the α i are zero except for the first and last, which are unity. Furthermore, when k = 3 or k = 4, it is shown that one may take N to be an integer less than 12 in each of these cases.

Space- and time-resolved observation of extreme laser frequency upshifting during ultrafast-ionization

A 65-fs, 800-nm, 2-TW laser pulse propagating through a nitrogen gas jet has been experimentally studied by 90° Thomson scattering. Time-integrated spectra of scattered light show unprecedented broadening towards the blue which exceeds 300 nm. Images of the scattering region provide for the first time a space- and time-resolved description of the process leading quite regularly to such a large upshift. The mean shifting rate was as high as δλ/δt ≈ 3 Å/fs, never observed before. Interferometry shows that it occurs after partial laser defocusing. Numerical simulations prove that such an upshift is consistent with a laser-gas late interaction, when laser intensity has decreased well below relativistic values (a0 ≪ 1) and ionization process involves most of the laser pulse. This kind of interaction makes spectral tuning of ultrashort intense laser pulses possible in a large spectral range.

Polynomials whose coefficients are generalized Tribonacci numbers

Let an denote the third order linear recursive sequence defined by the initial values a0=a1=0 and a2=1 and the recursion an=pan-1+qan-2+ran-3 if n⩾3, where p,q, and r are constants. The an are generalized Tribonacci numbers and reduce to the usual Tribonacci numbers when p=q=r=1 and to the 3-bonacci numbers when p=r=1 and q=0. Let Qn(x)=a2xn+a3xn-1+⋯+an+1x+an+2, which we will refer to as a generalized Tribonacci coefficient polynomial. In this paper, we show that the polynomial Qn(x) has no real zeros if n is even and exactly one real zero if n is odd, under the assumption that p and q are non-negative real numbers with p⩾max{1,q}. This generalizes the known result when p=q=r=1 and seems to be new in the case when p=r=1 and q=0. Our argument when specialized to the former case provides an alternative proof of that result. We also show, under the same assumptions for p and q, that the sequence of real zeros of the polynomials Qn(x) when n is odd converges to the opposite of the positive zero of the characteristic polynomial associated with the sequence an. In the case p=q=r=1, this convergence is monotonic. Finally, we are able to show the convergence in modulus of all the zeros of Qn(x) when p⩾1⩾q⩾0.

Abstract 3563: Soy protein isolate consumption does not prevent biochemical failure after radical prostatectomy in high risk men: A randomized controlled trial

Abstract Epidemiologic and experimental data suggest that soy consumption may prevent prostate cancer and be beneficial for men with prostate cancer. Soy intake and risk of prostate cancer are inversely correlated; soy isoflavones inhibit growth of prostate cancer cells and reduce prostate carcinogenesis in animal models. We tested the hypothesis that soy consumption reduces biochemical recurrence after radical prostatectomy in a randomized controlled clinical trial with a soy protein supplement versus a casein-based placebo in men at increased risk for PSA failure in the first 2 years after radical prostatectomy. PSA was tested at 2-month intervals in year 1 and every 3 months in year 2. Eligibility criteria were: Gleason sum of >8, extra-capsular extension, seminal vesicle invasion, positive surgical margins, positive lymph nodes, and/or a preoperative PSA of >20 ng/ml. Biochemical recurrence was defined a priori as reaching a PSA value of α0.07 ng/ml, confirmed twice. A two-year PSA failure rate in eligible subjects of approximately 30% was expected, based on data from NYU and previous literature. With a planned sample size of 128 evaluable subjects per arm, the study had 80% power to detect a 50% reduction in PSA failure rate at a 2-sided significance level of 0.05. The soy protein isolate and placebo (generously provided by Solae LCC, St Louis, MO) were identical in composition, except for the protein source (19.2-19.8 g protein/day); the soy product provided daily 23.5 mg genistein and 40.9 mg total isoflavones (aglycone equivalents); the placebo was devoid of any soy-specific constituents. Accrual did not reach the intended level and 172 subjects were randomized and enrolled, of whom 142 were evaluable (completed two years on study or developed confirmed recurrence within two years). Soy protein consumption did not alter recurrence rate or time-to-recurrence (TTR). Of the 74 evaluable subjects in the soy arm 22 (30%) recurred as did 22 (32%) of the 68 subjects in the placebo arm recurred. The mean TTR was 40.7 + 29.3 (SD) weeks in the soy group and 44.5 + 28.0 weeks in men on placebo. Statistical analysis on intention-to-treat basis confirmed the absence of an effect on these primary endpoints. The drop-out rate was 17% and there were <5% missing values, none of which impacted the primary endpoints. Compliance by self-report was excellent and is being confirmed by serum isoflavone levels. There were no treatment-related adverse events, except a few cases of constipation. We previously ruled out effects of the intervention on anti-thyroid activity and iron status in a subset of subjects. Thus, soy consumption is safe, but unlikely to benefit men after radical prostatectomy, although the results of this study do not rule out preventive effects of soy prior to prostate cancer development. (Supported by NIH grants CA27790, CA166195 & RR029879 and the Prevent Cancer Foundation) Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 3563. doi:1538-7445.AM2012-3563

Transport control within a microtube

Investigation of the entrainment of gases induced by a surface wave propagating along the wall of a microtube is conducted by using a relaxed model with slip velocity boundary conditions. Flow patterns tuned by critical reflux values a0, Knudsen numbers, Reynolds numbers, and the wave number are demonstrated. Results show that once the cross section of the microtube is narrowed down (slip velocity increasing) there are earlier backward flows and the flow pattern is much more complicated. Our results should be useful for the design of micro total analytical systems.

Study on the structure and energy of the (0001) surface of α-Al2O3 substrate

There are three different structures of the α-Al2O3(0001) crystal surface b ecause different atoms are terminated on the outermost layer. Our calculations a re based on the density functional theory in local density approximation, and on ultra-soft pseudopotential methods, with the valence orbital expanded in plane- wave by using three-dimensional periodic boundary conditions in κ-space, first ly, the calculation result is that α-Al2O3(0001) crystal surface structure which the outermost layer is terminated by a single layer of Al atoms is much mo re stable than the other two structures. Secondly, a rhombohedral primitive cell is employed to perform cell optimizations, with ten atoms in the unit cell, and the calculated equilibrium parameters are:a0＝0.48178nm,γ＝120.16, which are in excellent agreement with recent experimental values(a0＝0.47591nm ),with a difference of less than 1.3%. Moreover, our calculations are performed with a su per-cell slab model in vacuum environment, in which the outermost layer is termi nated by single Al atoms. By investigating the four-layer relaxation and Al-O a toms population of the surface, we obtain results that the top single Al layer i s an inward relaxation of 0.0792 nm—0.098nm, that is, the second-layer O atoms are turned into the top layer,and the top O and Al atoms population analysis sho w that the valence electrons are concentrated on the surface oxygen ions with a greater probability,it is obvious that the α-Al2O3(0001) crystal surface ap pears in the O-surface state,which is discussed from the microstructure of α-Al 2O3(0001)crystals in details.

Transport along deformable microfabricated channel

Investigation of the entrainment of fluids induced by a wavy deformation along walls in a flat-plane microchannel is conducted by using the relaxed model with velocity-slip boundary conditions. Flow patterns tuned by critical reflux values a0 and Reynolds number are demonstrated especially for the free pumping case. Results show that once the cross-section of the microchannel is narrowed down (velocity-slip increases) there will be earlier backward flows.

On the length of lemniscates.

We show that for a polynomial p(z) = z + . . . the length of the level set E(p) := {z : |p(z)| = 1} is at most 9.173 d, which improves an earlier estimate due to P. Borwein. For d = 2 we show that the extremal level set is the Bernoullis’ Lemniscate. One ingredient of our proofs is the fact that for an extremal polynomial the set E(p) is connected. For a monic polynomial p of degree d we write E(p) := {z : |p(z)| = 1}. A conjecture of Erdős, Herzog and Piranian [4], repeated by Erdős in [5] and elsewhere, is that the length |E(p)| is maximal when p(z) := z + 1. It is easy to see that in this conjectured extremal case |E(p)| = 2d+O(1) when d→∞. The first upper estimate |E(p)| ≤ 74d2 is due to Pommerenke [8]. Recently P. Borwein [2] gave an estimate which is linear in d, namely |E(p)| ≤ 8πed ≈ 68.32d. Here we improve Borwein’s result. Let α0 be the least upper bound of perimeters of the convex hulls of compact connected sets of logarithmic capacity 1. The precise value of α0 is not known, but Pommerenke [10] proved the estimate α0 < 9.173. The conjectured value is α0 = 3 3/222/3 ≈ 8.24. Theorem 1 For monic polynomials p of degree d |E(p)| ≤ α0d < 9.173d. A similar problem for rational functions turns out to be much easier, and can be solved completely by means of Lemma 1 below. ∗Supported by EPSRC grant GR/L 35546 at Imperial College and by NSF grant DMS9800084

Non‐LTE Models and Theoretical Spectra of Accretion Disks in Active Galactic Nuclei. II. Vertical Structure of the Disk

We have calculated several representative models of vertical structure of an accretion disk around a supermassive Kerr black hole. The interaction of radiation and matter is treated self-consistently, taking into account departures from LTE for calculating both the disk structure and the radiation field. The structural equations are described in detail, and various approximations are discussed. We have demonstrated that departures from LTE are very important for determining the disk structure, even at the midplane, as well as the emergent radiation, particularly for hot and electron-scattering-dominated disks. We have shown that at least for the disk parameters studied in this paper, non-LTE effects tend to reduce the value of the Lyman jump with respect to the LTE predictions, regardless whether LTE predicts an emission or absorption jump. We have studied the effects of various values of viscosity on the model structure and predicted spectral energy distribution. The viscosity is parameterized through a parameter α0 that describes the vertically averaged viscous stress, two power-law exponents, ζ0 and ζ1, and the division point md between these two forms. The disk structure and emergent radiation is sensitive mainly to the values of α0, while the other parameters influence the disk structure to a much lesser extent. However, although the detailed shape of the predicted spectrum is sensitive to adopted value of α0, the overall appearance of the spectrum is quite similar.

Newton Method of Successive Approximations for the Linearization of the Calibration Curves of Chromium, Copper, Lead, Manganese, Silver, and Thallium in Zeeman Graphite Furnace Atomic Absorption Spectrometry

A new approach for the linearization of calibration curves in graphite furnace atomic absorption spectrometry (GFAAS) with Zeeman background correction was tested experimentally in an intermediate concentration region before rollover. The computational procedure employed the Newton method of successive approximations and was based on the theoretical model of L'vov et al. The calculations were based on three measured parameters: the rollover absorbance, Ar; the sensitivity ratio at the rollover point, R′; and the original background-corrected peak absorbances Az. This computational procedure generated corrected normalized integrated absorbance values A0,n with the slope identical to the slope of the original linear part of the calibration curve. The new computational procedure was employed for the linearization of calibration curves of chromium, copper, lead, manganese, silver, and thallium in Zeeman GFAAS under stabilized temperature platform furnace (STPF) conditions. Overall, the new computational procedure was able to extend the linear range of the calibration curves by a factor of 2–3 for the tested elements.

Bacterial Deposition in Porous Media: Effects of Cell-Coating, Substratum Hydrophobicity, and Electrolyte Concentration

Deposition of seven bacterial strains on spherical glass and Teflon collectors was studied in vertical down-flow columns at an ionic strength (I) of 0.1 M. The various bacteria had either one of the following types of major cell−surface constituents: nonpolysac charide (NP), amphiphilic (AMPH), or anionic polysaccharide (AP) macromolecules. Deposition was analyzed in terms of the clean bed collision efficiency α0 (the probability of a cell to attach upon reaching a substratum free of cells) and a blocking factor B (the ratio of the area blocked by an attached cell to the geometric area of a cell). The value of α0 decreased from 1.0 to about 0.01 in the following order of cell−surface constituents/collector combina tions: NP/Teflon and AMPH/Teflon > NP/glass > AMPH/glass, AP/Teflon, and AP/glass. The value for B, at a Peclet number of 1 × 105, increased from about 3 to 18 in the order NP/low cell charge < NP or AMPH/high cell charge < AP/high cell charge. This indicates that cell−cell repulsion enhances ...

Chaotic transport by dipolar vortices on a β-plane

During the meandering motion of a dipolar vortex on a β-plane mass is exchanged both between the dipole and the ambient fluid and between the two dipole halves. The mass exchange (as well as the meandering motion) is caused by variations of the relative vorticity of the vortices due to conservation of potential vorticity. Previous studies have shown that a modulated point-vortex model captures the essential features in the dipole evolution. For this model we write the equations of motion of passive tracers in the form of a periodically perturbed integrable Hamiltonian system and subsequently study transport using a ‘dynamical-systems theory’ approach. The amount of mass exchanged between different regions of the flow is evaluated as a function of two parameters: the gradient of ambient vorticity, β, and the initial direction of propagation of the dipole, α0. Mass exchange between the dipole and the surroundings increases with increasing both β and α0. The exchange rate (amount of mass exchanged per unit time) increases with β and has a maximum for a particular value of α0 (≈ 0.62π). Dipolar vortices in a rotating fluid (with a sloping bottom providing the ‘topographic’ β-effect) show, in addition to the relative vorticity variations, a second perturbation that leads to exchange of mass. The points where vorticity is extreme approach each other as the dipole moves to shallower parts of the fluid and separate as the couple moves to deeper parts. This mechanism is studied independently and it is shown to lead to a stronger exchange between the dipole halves and the ambient fluid but no exchange between the two dipole halves.

Thermal rate constants in collinear atom transfer reactions by optimizing the position of the reactants/products dividing surface

On the basis of Miller–Schwartz–Tromp [J. Chem. Phys. 79, 4889 (1983)] formula for the flux autocorrelation function, and its derivation in hyperspherical coordinates by Park and Light [J. Chem. Phys. 94, 2946 (1991)], we study the sensitivity of the thermal rate constant, k(T), for a collinear transfer reaction calculated within the framework of the finite basis set approximation, to the position of the dividing surface between reactants and products, s0=ρα0. Illustrating 2D numerical examples of calculating k(T) for symmetric, H3, and nonsymmetric, Mu–H2 and Mu–D2, potential surfaces by optimizing the value of α0 are given. In all cases (symmetric and nonsymmetric potential surfaces) the optimal dividing surface has to be chosen such that dk(T)/dα0=0. For symmetric potential surfaces tan(2α0)=(mBM/mAmc)1/2, whereas, for highly nonsymmetric potential surfaces, the optimal dividing surface has to be chosen numerically. It is shown that with very limited basis set this numerical stationary solution may be associated with an inflection point rather than a minimum, and therefore k(T) is not necessarily an upper bound to the true thermal rate.

Theory of the threshold exponent in anomalous absorption spectra of metallic Cs

The threshold exponent α0 of anomalous soft X-ray absorption spectra of metallic Cs in the theory of Nozières and De Dominicis is calculated. The value of α0 for Cs is obtained experimentally as 0.06 or 0.07 which is considerably smaller than those for K and Rb and could not have been explained even qualitatively by predecessors. By a proposed model the localized 4f-orbital is pulled in by the 5p-hole that is created by absorption of a soft X-ray, resulting in the screening of the 5p-hole. From this model we obtained the value of α0 = 0.05, in agreement qualitatively with the experimental results. For K and Rb, the obtained values for α0 in the present study are 0.27 and 0.25, respectively, in satisfactory agreement with the experimental results.

Ｖ形環状切欠材の回転曲げ疲労強度に及ぼす析出硬化の影響

The effect of precipitation hardening on rotary bending fatigue strength of circumferential V-notched specimens was investigated at room temperature by using two commercial steels, i.e., 18 Ni maraging steel and an austenitic heat resisting steel, JIS SUH38. The rotary bending fatigue tests were carried out on the as solution-treated, peak-aged and over-aged specimens.The fatigue limits of the smooth specimens as well as all of the notched specimens were not influenced by precipitation hardening in 18 Ni maraging steel. Non-propagating cracks were found in all the notched specimens having the stress concerntration factor, α, of 6.2 except the over-aged specimens. It was also found that the stress concentration factor at the branching point, α0, is nearly 4. In SUH38, the fatigue limits of the smooth specimen and the notched specimen with α of 2.1 were found to increase with precipitation hardening, while the fatigue limits for the other notched pecimens having α larger than 2.1 did not change in spite of precipitation hardening. The value of α0 was nearly equal to 2 in the as solution-treated specimens and 4 in the other aged specimens. Furthermore, nonpropagating cracks were easier to be formed in SUH38 than in 18 Ni maraging steel and in the as solution-treated specimens than in the aged specimens.Discussions were finally made on the fatigue limits by dividing them into the fatigue limit for crack initiation, σw1 and the fatigue limit for crack propagation, σw2. Especially the behavior of nonpropagating cracks was discussed on the basis of roughness-induced crack closure.

Analytical Expressions for the Composition Dependence of Stacking Fault Energies and Probabilities in Binary Silver Systems

The following straight-line relationship between the stacking-fault probability α and alloying concentration has been obtained by fitting published data: lnα=lnα0+Kα [C/(1+C)]. In this expression, C=X/X*, where X is the alloying concentration and X* is the solubility limit (both in atomic percent) at either the peritectic or the eutectic temperature, α0 is the stacking-fault probability for pure silver and Kα is an experimental constant. The value of α0, obtained by extrapolation, is 3.13±0.14×10−3; Kα is usually within the range 6.2±0.5, but is lower in those binary systems alloyed with the hcp elements Mg, Zn, and Cd. Similarly, an analytical expression relating stacking-fault energy γ and alloying concentration may be written as lnγ=lnγ0+Kγ [C/(1+C)]2,where γ0 is the stacking-fault energy of silver. The value of Kγ for the Ag–Sn, Ag–In, and Ag–Al systems ranges from −10.0 to −10.5, but is −6.5 in the Ag–Zn system. The relationship between α and γ is discussed on the basis of these equations.

Thermal Diffusion and Self-Diffusion in Ammonia

The temperature dependence of the isotopic thermal-diffusion factor α0 for ammonia has been investigated with the help of an equimolar mixture of 14NH3 and 15NH3. A 10-tube metal swing-separator as well as a two-bulb glass apparatus were used for these measurements. The value of α0 increases with temperature, its value being 0.00±0.02 at 242°K to 0.09±0.03 at 496°K, in disagreement with the values obtained by Watson and Woernley, who observed a definite inversion in the sign of α0 at temperature ∼290°K. The present set of observed values of α0 also disagrees with the theoretical calculation of Monchick and Mason. Possible causes of this disagreement are: (1) inadequacy of the potential model, (2) neglect of inelastic collisions, and (3) formation of dimers. The self-diffusion coefficient of ammonia has also been studied in the temperature range of 233° to 353°K with a two-bulb apparatus. There is marked disagreement between observed and calculated values at low temperatures. This is also explained in terms of dimerization.

Isotopic Thermal-Diffusion Factor of Argon

An extensive investigation of the isotopic thermal-diffusion factor α0 of argon in the mean temperature range 127° to 653°K has been carried out with a four-tube swing separator employed previously in similar work with helium and neon. Because of a linear variation of α0 with T in the low-temperature region, the mean temperature T̄ = (T2—T1)/ln(T2/T1 ) has been used instead of the arithmetic mean of T1 and T2. This temperature assignment has been verified by varying the temperature gradient significantly. The experimentally determined value of α0 increases from 0.068±0.015 at T̄ = 127°K to 0.485±0.035 at T̄ = 653°K, in fair agreement with earlier experiments. Just as for helium and neon, a Lennard-Jones 12:6 potential model fails to account for the observed temperature variation of argon α0 values. The best fit for an exp—six force model occurs for α = 17 and ε/k = 176°K. Using these force parameters, the best fit with experimental viscosity data yields rm = 3.535 Å. These parameters are then used to calculate the diffusion coefficient and second virial coefficient for argon. There is fair agreement with the experimental values of these other transport coefficients.