Global Modulus Research Articles

Exponential bounds for the probability deviations of sums of random fields

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field. The motivation of the present study comes mainly from the dependence Monte Carlo methods.

Macro- and Micro-Scale Probing of the Mechanical Properties of DNA-Crosslinked Gels Using Embedded Inclusions

AbstractMechanical properties of a class of self-assembling hydrogels based on DNA hybridization were studied using rigid, embedded inclusions. Because inclusions can be deflected without direct contact with a manipulator (e.g., magnet) once they are embedded within the subject material, the measurement technique is well suited for monitoring instantaneous and time-varying changes in the mechanical properties of active materials as they respond to external stimuli. In gels crosslinked with complementary strands of oligonucleotides, hybridization chemistry and strand displacement mechanisms allow reversible assembly, shape change, and large changes in compliance through the application of particular strands of DNA. In earlier work using large (diameter ∼0.8 mm) magnetic beads, the scaling behavior of the global elastic modulus with crosslink density was determined. More recently, it was shown that a threefold increase in stiffness was possible by generating prestress in the DNA-crosslinked gel network. Currently, the gels are functionalized to support cell attachment and embedded with micro-fabricated nickel bars. Through the measurement of local elastic and shear moduli as well as Poisson’s ratios, cell-substrate interactions can be used as a means of evaluating the potential of DNA-crosslinked gels as active cellular engineering substrates and tissue engineering scaffolds.

Relationships between grade determining properties of Spanish scots and laricio pine structural timber

In a. sample made up of 3312 boards of scots pine (pinus sylvestris) and 3318 boards of laricio pine pinus nigra Van Saltzmannii), both of Spanish provenance, and ranging in size from 100x40x2500 mm to 200x70x4500 mm, previously tested in accordance with the procedure set forth in UNE EN 408 standard, the relationships between the grade determining properties considered in the UNE EN 338 standard (bending strength, global and local modulus of elasticity in bending, density) are studied. In addition to these variables, the modulus of elasticity was also considered, calculated by means of the measuring of the transmission speed of an ultrasonic pulse generated by a Sylvatest device. The global modulus of elasticity calculated by measuring the deformation at the neutral axis seems to be the best predictor of the ultimate bending strength, while the local modulus of elasticity proves to be difficult to obtain, and has a lower predictive quality, and so its elimination is suggested. The need to consider one single testing procedure to determine the global modulus of elasticity is also analyzed, along with the convenience of carrying out further studies regarding the use of ultrasonic techniques in order to predict the modulus of elasticity, due to the fact that the systems available are not sufficiently precise.

Local elastic modulus of atherosclerotic lesions of rabbit thoracic aortas measured by pipette aspiration method

Changes in mechanical properties of arteries during atherogenesis remain controversial. One of the reasons could be that they have been evaluated with parameters measured in a whole vessel, although the lesions are localized. The local elastic modulus of atherosclerotic lesions was measured by the pipette aspiration method in thoracic aortas of rabbits fed a cholesterol diet for 8, 16, 24 and 28 weeks. The global elastic modulus of the whole aorta was measured by the pressure–diameter test. The local modulus decreased from that of the normal tissue in 8 weeks and then increased during the cholesterol feeding period. The global modulus did not change until 24 weeks and increased by 28 weeks. Histological observation revealed that the initial soft lesion was mainly composed of foam cells, and the stiffening accompanied first the appearance of smooth muscle cells in the top layer of the hyperplastic intima and then calcification in its bottom layer. The global elastic modulus did not change until marked calcification occurred in the tissue. These results suggest that change in mechanical properties of atherosclerotic lesion is not simple and has a close correlation with its histology. Assessment of local mechanical properties is important for studying mechanical properties of atherosclerotic arteries.

Effectiveness of the global modulus of continuity on metric spaces

In the “δ—ε” — definition of continuity of a function ƒ between metric spaces, the value of δ depends on χ, ε and function ƒ as well. This kind of dependence can be described by a function, so called, “global modulus of continuity”, which maps the triple (ƒ, χ, ε) to corresponding δ. By a recent result of Repovš and Semenov (Proc. Int. Conf. Topol. (Trieste, 1993), G. Gentili (Ed.), Rent. Ist. Mat. Univ. Trieste, vol. 25, 1993, pp. 441–446), there is a continuous global modulus of continuity for the function space C( X, Y) of all continuous functions from a locally compact metric space X to an arbitrary metric space Y. Based on Weihrauch's framework on computable metric spaces (K. Weihrauch, Theoret. Comput. Sci. 113 (1993) 191–210), we show that there is a computable global modulus of continuity for C( X, Y), if X is an “effectively locally compact” metric space and Y is a computable metric space. The proof is a direct construction not depending on the proof of Repovš and Semenov.

Determination of the modulus of elasticity in bending of structural timber - comparison of two methods

Two different methods of determining the modulus of elasticity in bending were compared. In the one method, the deformation measurement is local as prescribed in European standard EN 408, and in the other one it is a global measurement, similar to what is stated in the methods used in North America and Australia. A total of 1825 beams of spruce and pine timber was tested. The result shows that there can be a substantial difference between the two methods, and that the ratio between the local and global modulus of elasticity is affected by different factors, such as the length between the reference points in the deformation measurement, the ratio between the modulus of elasticity and shear modulus and timber quality.

The asymptotic law of the local oscillation modulus of the empirical process

Abstract Stute (1982) investigated strong limit theorems for the global oscillation modulus of the empirical process. We present the description of the limiting behaviour of the local oscillation modulus ωn (an,x0) for sequences of positive constants {an} converging to zero and satisfying certain growth conditions. Our result is the finest limit law in this context and extends Levy's LIL for the Wiener process. We illustrate the usefulness of our result by presenting several applications including strong convergence rates for variable kernel density estimators, an a.s. representation of the bootstrap, asymptotics of perturbed sample quantiles and the LIL for the Kiefer process and the general quantile process.

Élasticité globale de panneaux sandwich : Détermination théorique et expérimentales par une méthode de vibrations propres

Experimental studies in dynamic bending and torsion, give a global flexure and a global torsion modulus for a sandwich panel of constant thickness. These global modulus connect, for bending and torsion states, strains and moments. We can easily calculate these global modulus with the strength materials computations.The study, of normal-mode frequencies of panel samples, can check the homogeneity of the industrial panel making.In fact, eigen-frequencies are very sensitive to dimensional variations in surface layer thickness or core shape of the sandwich.For the determination of the elastic modulus, only vibrations experiments give good results on materials with small core elastic modulus, because during panel testing, we don’t distort or crush the sandwich core.

Note on Hille’s exponential formula

In an earlier paper of the author it was shown that we would not be able to obtain a better estimate for Hille's first exponential formula than KWB(T1/2, T(.)f), where WB(6, T(.)f) is the global modulus of continuity of T(t)f, tE [0, B]. It is shown in this paper that this estimate can actually be achieved. Let T(t) be a strongly continuous semigroup of operators on a Banach space into itself, and let WL(b; T(* )f) be the rectified modulus of continuity in [0, L] given by: (1) WL(8; T(-)f) = {supllT(t) T(s), I ts 1/2. It remained to find if an estimation similar to (2) is valid fory = 1/2. This will be answered here positively as follows: THEOREM 1. Let { T(t); 0< t < X } be a strongly continuous semigroup on a Banach space B into itself. Then (3) f1exp(AT) T(t)fJf < (L1/2 + 1)WL(Tl/2, T(.)f) + Kr'/2 fffI where K is independent of r, t-<L-a and ry<6 for some y <1/2. PROOF. Following the proof of Theorem 2.1 in [1] we write