Composites in offshore technology in the next century

The advisability of application of advanced composites in deep-water offshore technology is shown using risers and tendons as examples. Numerical estimations of the parameters of multilayered metal-composite risers are obtained. Two new processes of spatial braiding for creating the external jackets of compound tendons are considered. Advanced composites are the only possible choice for exploitation of deposits at depths greater than 1500 m. That is why they are the most promising structural materials for offshore technology in the next century. This report was presented at the Symposium “Composites for the Next Millennium” in honor of Stephen Tsai's 70th birthday, Tours, France, 2–3 July, 1999. Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 549–560, September–October, 1999.     

Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite

Within the framework of a unified mathematical model based on the Markov chain theory, an attempt is made to describe the distribution of static strength, the fatigue curve, and the accumulation of fatigue damages. It is assumed that the fatigue failure of a test specimen occurs after the destruction of some its critical microvolume consisting of two — elastic (brittle fibers) and plastic (matrix) — parts. In the second part, plastic strains accumulate as soon as the cyclic load exceeds some level. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 615–630, September–October, 2006.     

Adhesive ability of a heat-resistant double-chain polymer and the strength of CFRP based on it

The adhesive ability of a heat-resistant polyiminoquinazolindione (PIQD) binder, based on a double-chain polymer, and the physicomechanical characteristics of unidirectional CFRPs made with it are investigated. It is shown that, at room temperature, the strength of model adhesive joints (PIQD-steel wire) and of the CFRPs in shear and bending is rather low — about half of that of similar specimens based on an epoxy binder. At the same time, all their mechanical characteristics, to a large measure (50%), are retained at temperatures up to 450°C, which considerably exceeds the heat resistance of all polymer matrices used at the present time. The elastic modulus of the CFRPs in bending practically remains the same up to 450°C. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 535–546, July–August, 2008.     

Moisture absorption and mechanical and acoustic responses in shear of a glass fiber fabric/epoxy resin composite

An analysis of the mechanical and acoustic responses of a laminate composed of 12 layers of glass fiber fabric/epoxy resin and conditioned in environments with relative humidities of 0, 60, and 96% RH at 60°C is presented. The first part of the study consists in following the weight gain according to the duration of hygrothermal conditioning, and the second part—in test ing 45°-oriented specimens in uniaxial tension up to failure at constant imposed displacement rates, with registrating the acoustic emission to track the damage process. The influence of moisture content in the material showed up as a significant decrease in its shear modulus, shear stress, and acoustic emission with growing quantity of absorbed water. An exponential function is proposed for describing the relationship between the varying shear modulus and the shear strain. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 595–602, September–October, 2007.     

Kinematic models of refined theories concerning composite beams,plates, and shells

Kinematic models used for construction of energetically consistent theories of composite beams, plates, and shells were examined. A new representation of the solution of the three-dimensional theory of elasticity for a transversely isotropic body and concepts for movements in an orthotropic strip, obtained in the form of asymptotic expansions, were used for substantiated selection of correct kinematic models. A comparative analysis of the consistent theories with other existing versions of applied theories was given based on solution of test problems. The results of the numerical comparative analysis suggest with a high degree of certainty that the versions of the refined theories of beams, plates, and shells based on special kinematics and satisfying criteria of consistency are more precise and effective than theorems which do not satisfy these criteria. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow. Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 612–624, September–October, 1996.     

On the distribution of imaginary parts of zeros of the Riemann zeta function,II

We continue our investigation of the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to Montgomery’s pair correlation function and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function. The first author is supported by National Science Foundation Grant DMS-0555367. The second author is partially supported by the National Science Foundation and the American Institute of Mathematics (AIM). The third author is supported by National Science Foundation Grant DMS-0456615.     

Inverse problem of nondestructive optical testing of residual stresses in cyclindrical shells

We considered the inverse problem of determination of the stress-strain state of a circular cylindrical shell that consists of two heterogeneous parts joined by a circular seam. As the input data for this problem, the results of polarization-optical measurements are used. The problem is formulated within the framework of a model that considers residual stress as caused by the geometric incompatibility of elastic deformations. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 151–156, April–June, 1998.     

On the Average Discrepancy of Successive Tuples of Pseudo-Random Numbers over Parts of the Period

 In the present paper we give an upper and a lower bound for the average value of the discrepancy of non-overlapping s-tuples of successive elements of a first order congruential pseudo-random-number generator (with prime modulus and maximal period). The estimates are – up to logarithmic factors – sharp also for short parts of the period. Received 30 January 1997; in revised form 2 May 1997     

The probability of ruin in finite time

The Sparre Andersen model in the collective risk theory is investigated. We obtain the rate of convergence for the ruin probability after thenth payoff in the case where claim sizes are heavy tailed (say, subexponential). Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 304–309, July–September, 1999.     

On-line Tracking of a Smooth Regression Function

We construct an on-line estimator with equidistant design for tracking a smooth function from Stone–Ibragimov–Khasminskii’s class. This estimator has the optimal convergence rate of risk to zero in sample size. The procedure for setting coefficients of the estimator is controlled by a single parameter and has a simple numerical solution. The off-line version of this estimator allows to eliminate a boundary layer. Simulation results are given. This work is partially supported by a fellowship from the Yitzhak and Chaya Weinstein Research Institute for Signal Processing at Tel Aviv University.     

Investigation of mutual longitudinal displacements of structural elements upon welding

We present the results of experimental investigation and control over mutual displacements of elements in the process of welding of butt and T-joints and develop a computational method for determination of these displacements and estimation of their influence on the accuracy of welded structures. Paton Electric Welding Institute, Ukrainian Academy of Sciences, Kiev; Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 96–104, April–June, 1998.     

A new model family for the strength distribution of fibers in relation to their length

Based on the weakest-link model, a family of fiber strength distributions is investigated assuming a two-stage failure process. At the first stage, a weakest link is formed (instantly or gradually), but at the second one the fracture of this link takes place. The gradual accumulation of flaws is described with the aid of Markov chain theory. The adequacy of the models considered is verified by checking them against experimental strength data for E-glass and flax fibers of various lengths. It is found that the models are not less accurate, but are even better, in a number of cases, than the model based on the known modified Weibull model with a power-law relation between the fiber length and the scale parameter. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 179–192, March–April, 2006.     

Two theorems about maximal Cohen–Macaulay modules

This paper contains two theorems concerning the theory of maximal Cohen–Macaulay modules. The first theorem proves that certain Ext groups between maximal Cohen–Macaulay modules M and N must have finite length, provided only finitely many isomorphism classes of maximal Cohen–Macaulay modules exist having ranks up to the sum of the ranks of M and N. This has several corollaries. In particular it proves that a Cohen–Macaulay lo cal ring of finite Cohen–Macaulay type has an isolated singularity. A well-known theorem of Auslander gives the same conclusion but requires that the ring be Henselian. Other corollaries of our result include statements concerning when a ring is Gorenstein or a complete intersection on the punctured spectrum, and the recent theorem of Leuschke and Wiegand that the completion of an excellent Cohen–Macaulay local ring of finite Cohen–Macaulay type is again of finite Cohen–Macaulay type . The second theorem proves that a complete local Gorenstein domain of positive characteristic p and dimension d is F-rational if and only if the number of copies of R splitting out of divided by has a positive limit. This result relates to work of Smith and Van den Bergh. We call this limit the F-signature of the ring and give some of its properties. Received: 6 May 2001 / Published online: 6 August 2002 Both authors were partially supported by the National Science Foundation. The second author was also partially supported by the Clay Mathematics Institute.     

Instrumenting Mathematical Activity: Reflections on Key Studies of the Educational Use of Computer Algebra Systems

This paper examines the process through which students learn to make functional use of computer algebra systems (CAS), and the interaction between that process and the wider mathematical development of students. The result of ‘instrumentalising‘ a device to become a mathematical tool and correspondingly ‘instrumenting’ mathematical activity through use of that tool is not only to extend students' mathematical technique but to shape their sense of the mathematical entities involved. These ideas have been developed within a French programme of research – as reported by Artigue in this issue of the journal – which has explored the integration of CAS – typically in the form of symbolic calculators – into the everyday practice of mathematics classrooms. The French research –influenced by socio-psychological theorisation of the development of conceptual systems- seeks to take account of the cultural and cognitive facets of these issues, noting how mathematical norms – or their absence – shape the mental schemes which students form as they appropriate CAS as tools. Instrumenting graphic and symbolic reasoning through using CAS influences the range and form of the tasks and techniques experienced by students, and so the resources available for more explicit codification and theorisation of such reasoning. This illuminates an influential North American study– conducted by Heid – which French researchers have seen as taking a contrasting view of the part played by technical activity in developing conceptual understanding. Reconsidered from this perspective, it appears that while teaching approaches which ‘resequence skills and concepts’ indeed defer – and diminish –attention to routinised skills, the tasks introduced in their place depend on another –albeit less strongly codified – system of techniques, supporting more extensive and active theorisation. The French research high lights important challenges which arise in instrumenting classroom mathematical activity and correspondingly instrumentalising CAS. In particular, it reveals fundamental constraints on human-machine interaction which may limit the capacity of the present generation of CAS to scaffold the mathematical thinking and learning of students. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigations into the fire hazard of a composite made from aerated concrete and crushed expanded polystyrene waste

The study deals with experimental investigations into the fire hazard of a composite of density 150–350 kg/m³ made of aerated concrete and crushed expanded polystyrene waste. The results of fire tests showed that a single-flame source of low heat output (0.07 kW) did not influence the origination and spread of flame on the surface of test specimens, regardless their density. Upon exposing the specimens to a single burning item of moderate heat output (30.0 kW), during the first 600 s of exposure, neither flaming particles nor droplets originated, nor a lateral flame spread on the long specimen wing was observed. In the case of high heat output (112 kW), the specimens of densities 150 and 250 kg/m³ started to burn, but those of density 150 kg/m³, in addition, lost their integrity. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 255–264, March–April, 2008.     

Garch(1,1) process can have arbitrarily heavy power tails

We study the structure of solutions of Kesten’s equation (1.5), where a, b ⩾ 0 are the coefficients of the GARCH(1,1) process in (1.1). We prove that, for any b ∈ (0, 1) and any κ > 0 small enough, there exists a stationary GARCH(1,1) process with tail index κ. The research was partially supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation, grant no. T-15/07. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 196–210, April–June, 2007.     

Partial regularity for variational integrals with (s,\mu ,q)–Growth

We introduce integrands of –type, which are, roughly speaking, of lower (upper) growth rate ) satisfying in addition for some . Then, if , we prove partial –regularity of local minimizers by the way including integrands f being controlled by some N–function and also integrands of anisotropic power growth. Moreover, we extend the known results up to a certain limit and present examples which are not covered by the standard theory. Received: 17 February 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

A semantics for the first quartet by T. S. Eliot

We construct a semantics for tense logic based on the following central concepts: (a) state of affairs, (b) is simultaneous or earlier than (not later than), (c) is accessible, and (d) is realized, in which a bit of T. Eliot’s lyrics is interpreted. Supported by the Science Foundation of Serbia (grant No. 04M02A) through the Belgrade Mathematical Institute. Translated fromAlgebra i Logika, Vol. 38, No. 4, pp. 383–408, July–August, 1999.     

The two phase stochastic Stefan problem

 This work is concerned with existence for a stochastic free boundary problem arising in phase transition (the Stefan two phase problem). The existence of an invariant ergodic measure associated with the corresponding transition semigroup P(t) is also proved, together with an integration by parts formula for the generator of P(t). Received: 20 June 2001 / Revised version: 17 June 2002 / Published online: 24 October 2002 Mathematics Subject Classification (2000): 35K35, 35R15, 60H15 Key words or phrases: Stochastic Stefan problem – Invariant measures – Wiener process – Transition semigroup – Kolmogorov operator     

Vanishing integrals for Hall–Littlewood polynomials

It is well known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even). In a recent paper of Rains and Vazirani, Macdonald polynomial generalizations of these identities and several others were developed and proved using Hecke algebra techniques. However, at q = 0 (the Hall–Littlewood level), these approaches do not work, although one can obtain the results by taking the appropriate limit. In this paper, we develop a direct approach for dealing with this special case. This technique allows us to prove some identities that were not amenable to the Hecke algebra approach. Moreover, we are able to generalize some of the identities by introducing extra parameters. This leads us to a finite-dimensional analog of a recent result of Warnaar, which uses the Rogers–Szegő polynomials to unify some existing summation type formulas for Hall–Littlewood functions.