Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

Internal resonance of an L-shaped beam with a limit stop .1. Free vibration

Real-life structures often possess piecewise stiffness because of clearances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex mode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple internal resonances, which involve interactions among the first five modes and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the natural frequency of a higher mode. The conditions for the existence of internal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbone curves. A method to compute such intersections by using only one harmonic in the free vibration solution is proposed. (C) 1996 Academic Press Limited

Internal resonance of an L-shaped beam with a limit stop .2. Forced vibration

A limit stop is placed at the elbow of an L-shaped beam whose linear natural frequencies are nearly commensurable. As a result of this hardening device the non-linear system exhibits multiple internal resonances, which involve various degree of coupling between the first five modes of the beam in free vibration. A point load is so placed as to excite several modes and the resulting forced vibration is examined. In the undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with multiple branches and interactions between the first four modes. The amplitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Consequently parts of the resonance curve may be eliminated, with the resulting response comprising different distinctive branches. (C) 1996 Academic Press Limited

Some theorems in asymptotic analysis

Basing ourselves on the analysis of magnitude of order, we strictly prove fundamental lemmas for asymptotic integral, including the cases of infinite region. Then a general formula for asymptotic expansion of integrals is given. Finally, we derive a sufficient condition for an ordinary differential equation to possess a solution of the Frobenius series type at finite irregular singularities or branching points.

Understanding the ex-ante cost of liquidity in the limit order book: A note

This paper estimates a new measure of liquidity costs in a market driven by orders. It represents thecost of simultaneously buying and selling a given amount of shares, and it is given by a single measure of ex-ante liquidity that aggregates all available information in the limit order book for a given number of shares. The cost of liquidity is an increasing function relating bid-ask spreads with the amounts available for trading. This measure completely characterizes the cost of liquidity of any given asset. It does not suffer from the usual ambiguities related to either the bid-ask spread or depth when they are considered separately. On the contrary, with a single measure, we are able to capture all dimensions of liquidity costs on ex-ante basis.

Do tissue carbon and nitrogen limit population growth of weevils introduced to control waterhyacinth at a site in the Sacramento-San Joaquin Delta, California?

Waterhyacinth (Eichhornia crassipes(Mart.) Solms), is a serious problem in the Sacramento Delta. Two weevil species (Neochetina bruchi Hustache and N. eichhorniae Warner) have been introduced as biological control agents. The purpose of this study was to test the hypothesis that nitrogen (N) in the tissue of waterhyacinth was not sufficient to support weevil growth and reproduction. Because it grows better on plants with high N content and because it has a greater impact on the growth of high N plants, N. bruchi may be a more effective biological control agent in the Sacramento Delta.

Bag and size limit analyses for red drum in Northern and Southern Regions of the U.S. Atlantic

Assessments of the Atlantic red drum for the northern (North Carolina and north) and southern (South Carolina through east coast of Florida) regions along the U. S. Atlantic coast were recently completed. The joint Red Drum Technical Committee (SAFMC/ASMFC) selected the most appropriate catch matrix (incorporating an assumption on size of recreationally-released fish), selectivity of age 3 relative to age 2, and virtual population analysis (FADAPT). Given gear- and age-specific estimates of fishing mortality (F) for the 1992-1998 period, analyses were made of potential gains in escapement through age 4 and static spawning potential ratio (SPR) from further reductions in fishing mortality due to changes in slot and bag limits. Savings from bag limits were calculated given a particular slot size for the recreational fishery, with no savings for the commercial fisheries in the northern region due to their being managed primarily through a quota. Relative changes in catch-at-age estimates were used to adjust age-specific F and hence calculated escapement through age 4 and static SPR. Adjustment was made with the recreational savings to account for release mortality (10%, as in the stock assessment). Alternate runs for the northern region commercial fishery considered 25% release mortality for lengths outside the slot (instead of 0% for the base run), and 0% vs. 10% gain or loss across legal sizes in F. These results are summarized for ranges of bag limits with increasing minimum size limit (for fixed maximum size), and with decreasing maximum size limit (for fixed minimum size limit). For the southern region, a bag limit of one-fish per angler trip would be required to attain the stated target of 40% static SPR if the current slot limit were not changed. However, for the northern region, a bag limit of one-fish per angler trip appears to be insufficient to attain the stated target of 40% static SPR while maintaining the current slot limit. (PDF contains 41 pages)

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.