Effect of chemical nature of matrix on the strength of bonds with Armos aramide fibers

This investigation deals with adhesion between high-strength and high-modulus Armos aramide fibers (polyheteroarylene-co-p-phenyleneterephthalamide) and a series of different thermosetting matrices. The effect of the chemical nature of the matrix, time-temperature conditions of bond formation, and test temperature on the strength of the fiber-matrix interface was studied. Modified epoxy and heat-resistant matrices were used as adhesives. As a measure of adhesion, the shear adhesive strength ₀ determined by the fiber pull-out technique was used. It was found that both the adhesive strength and the fracture location in adhesive bonds depended on the nature of the matrix. At room temperature, chlorine-containing epoxy matrices provide the highest values of ₀, while the smallest strength of the interface is observed for bonds with heat-resistant (bismaleimide, oligomethacrylate) matrices. Fracture of adhesive bonds does not always occur at the fiber-matrix interface. A number of the specimens failed near the interface of the fiber. With temperature increase, the values of ₀ decrease. The adhesive strength falls especially drastically in the region of matrix softening. An advantage of heat-resistant matrices is that they retain 60–67% of ₀ value even at 250°C. The strength of unidirectional composites based on the investigated fibers and matrices was also estimated under different loading conditions such as tension, shear, compression, and bending. It was found that the strength in shear and compression did not correlate with the interface strength. The values of _c in bending and tension increased linearly with increase of ₀. The obtained dependences _c–₀ were compared with those of composites based on the SVM polyheteroarylene fibers determined by us earlier.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 391–406, May–June, 1998.     

Evaluation of Deformation and Strength Characteristics of Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste by the Methods of Mathematical Statistics

The possibilities of using various methods of mathematical statistics for processing and analyzing the results of deformation and strength tests on composites made from a low-density polyethylene and linen yarn production waste are evaluated. The hypothesis that the experimental strength data agree with the Gaussian distribution is examined by the Shapiro–Wilk test (W-test.) It is shown that the Gaussian distribution, both for systems unmodified and modified with diphenylmethane diisocyanate (DIC), is valid only for two parameters: the maximum tensile strength _max and the elastic modulus E _t. For the other parameters (the relative elongation _max corresponding to _max, the specific total work of failure A _b), and the specific work of failure to the tensile strength A _max), a non-Gaussian distribution is observed. An analysis of measurements for different specimens by the Bartlett test shows that the E _t data have equal variances for both systems (with and without DIC), but for the system containing DIC, the _max data have different variances. A two-factor ANOVA analysis reveals that DIC considerably affects the tensile strength and modulus of composites, but the influence of test conditions is a statistically significant factor only for the modulus. The coefficient of variation is considerably lower for _max than for E _t and can be used as a quantitative measure for the degree of heterogeneity of the composites investigated.     

On the On-line Number of Snacks Problem

In the number of snacks problem (NSP), which was originally proposed by our team, an on-line player is given the task of deciding how many shares of snacks his noshery should prepare each day. The on-line player must make his decision and then finish the preparation before the customers come to his noshery for the snacks; in other words, he must make decision in an on-line fashion. His goal is to minimize the competitive ratio, defined as _: C_A()/C_OPT(), where denotes a sequence of numbers of customers, C _OPT() is the cost of satisfying by an optimal off-line algorithm, and C _A() is the cost of satisfying by an on-line algorithm. In this paper we give a competitive algorithm for on-line number of snacks problem P1, the Extreme Numbers Harmonic Algorithm(ENHA), with competitive ratio 1+p(M-m)/(M+m), where M and m are two extreme numbers of customers over the total period of the game, and p is a ratio concerning the cost of the two types of situations, and then prove that this competitive ratio is the best one if an on-line player chooses a fixed number of shares of snacks for any sequence of numbers of customers. We also discuss several variants of the NSP and give some results for it. Finally, we propose a conjecture for the on-line NSP.     

Fibers in Ore Extensions

Let R be a finitely generated commutative algebra over an algebraically closed field k and let A=R[t;,] be the Ore extension with respect to an automorphism and a -derivation . We view A as the coordinate ring of an affine noncommutative space X. The inclusion RA gives an affine map : XSpecR, and X is a noncommutative analogue of A ¹×SpecR. We define the fiber X _p of over a closed point pSpecR as a certain full subcategory ModX _p of ModA. The category ModX _p has the following structure. If p has infinite -orbit, then ModX _p is equivalent to the category of graded modules over the polynomial ring k[x] with degx=1. If p is not fixed by , but has finite -orbit, say of size n, then ModX _p is equivalent to the representations of the quiver à _n–1 with the arrows all going in the same direction. If p is fixed by , then ModX _p is equivalent to either Modk or Modk[x]. It is also shown that X is the disjoint union of the fibers X _p in a certain sense.     

Self-intersections of 1-dimensional random walks

Summary Consider a random walk S _n on the integers, where the steps _i have mean 0 and variance ². Let T be the time of first self-intersection of the random walk. It is shown that, as , T grows at rate ^2/3. More precisely, T^2/3 has a non-degenerate limit distribution which can be described in terms of Brownian motion local time.Research supported by National Science Foundation Grant MCS80-02698.     

A note on the position of the centre of flexure of a beam of isotropic material having a section bounded by a parabola and a straight line

Zusammenfassung Die vorliegende Notiz behandelt das Problem der Auffindung des Biegungszentrums eines aus isotropem Material bestehenden Balkens, der einen durch eine parabolische und eine geradlinige Kante begrenzten Querschnitt besitzt. Die Last ist parallel zur geradlinigen Kante angenommen. Der Verfasser benützt zur Lösung der Aufgabe dasselbe Verfahren, dasSokolnikoff [1] für die Auffindung des Biegungszentrums eines halbkreisförmigen Balkens verwendete.

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Nomenclature x, y, z rectangular co-ordinates - l, m, n direction cosines of outward drawn normal - _x , _y , _z normal components of stress parallel tox, y, z axes - _xy , _yz , _zx shearing stress components in rectangular co-ordinates - u, v, w components of displacement - T (x, y) stress function in rectangular coordinates - Poisson's ratio - shear modulus - _yz , _zx , _xy shearing strain components in rectangular coordinates     

Noncommutative Valuation Rings of the Quotient Artinian Ring of a Skew Polynomial Ring

Let R be a Dubrovin valuation ring of a simple Artinian ring Q and let Q[X,] be the skew polynomial ring over Q in an indeterminate X, where is an automorphism of Q. Consider the natural map from Q[X,]_XQ[X,] to Q, where Q[X,]_XQ[X,] is the localization of Q[X,] at the maximal ideal XQ[X,] and set , the complete inverse image of R by . It is shown that is a Dubrovin valuation ring of Q(X,) (the quotient ring of Q[X,]) and it is characterized in terms of X and Q. In the case where R is an invariant valuation ring, the given automorphism is classified into five types, in order to study the structure of (the value group of ). It is shown that there is a commutative valuation ring R with automorphism which belongs to each type and which makes Abelian or non-Abelian. Furthermore, some examples are used to show that several ideal-theoretic properties of a Dubrovin valuation ring of Q with finite dimension over its center, do not necessarily hold in the case where Q is infinite-dimensional. Presented by A. VerschorenMathematics Subject Classifications (2000) 16L99, 16S36, 16W60.     

On the convergence order of accelerated root iterations

Summary A Gauss-Seidel procedure for accelerating the convergence of the generalized method of the root iterations type of the (k+2)-th order (kN) for finding polynomial complex zeros, given in [7], is considered in this paper. It is shown that theR-order of convergence of the accelerated method is at leastk+1+ _n (k), where _n (k)>1 is the unique positive root of the equation ⁿ --k-1 = 0 andn is the degree of the polynomial. The examples of algebraic equations in ordinary and circular arithmetic are given.     

Lattice separation and properties of Wallman type spaces

Summary In this paper, we are primarily concerned with the general Wallman spaces I_R (L) andI ^R L, associated with an abstract set X and a lattice of subsets of X,L. For a pair of latticesL ₁ L ₂ with L ₁ L ₂ we investigate first separation properties and finally we turn attention to the preservation of some of the properties introduced in connection withI ^R and the latticesW (L) andtW (L).     

Large Deviations of a Storage Process with Fractional Brownian Motion as Input

We study probabilities of large extremes of the storage process Y(t) = sup _t (X() - X(t) - c( - t)), where X(t) is the fractional Brownian motion. We derive asymptotic behavior of the maximum tail distribution for the process on fixed or slowly increased intervals by a reduction the problem to a large extremes problem for a Gaussian field.     

On the error term in the mean square formula for the Riemann zeta-function in the critical strip

For 1/2<<1 fixed, letE (T) denote the error term in the asymptotic formula for . We obtain some new bounds forE (T), and an _-result which is the analogue of the strongest _-result in the classical Dirichlet divisor problem.     

The convolution equation of Choquet and Deny on [IN]-groups

Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant     

Harmonic functions on nilpotent groups

For a probability measure on a locally compact groupG which is not supported on any proper closed subgroup, an elementF ofL (G) is called -harmonic if F(st)d(t)=F(s), for almost alls inG. Constant functions are -harmonic and it is known that for abelianG all -harmonic functions are constant. For other groups it is known that non constant -harmonic functions exist and the question of whether such functions exist on nilpotent groups is open, though a number of partial results are known. We show that for nilpotent groups of class 2 there are no non constant -harmonic functions. Our methods also enable us to give new proofs of results similar to the known partial results.     

Double Complexes and Cohomological Hierarchy in a Space of Weakly Invariant Lagrangians of Mechanics

For a given configuration space M and a Lie algebra G acting on M, the space V _0.0 of weakly G-invariant Lagrangians, i.e., Lagrangians whose motion equations left-hand sides are G-invariant, is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex by the method of spectral sequences, we arrive at the hierarchy in the space V _0.0: The double filtration {V _s.}, s = 0, 1, 2, 3, 4, = 0, 1, and the homomorphisms on every space {V _s.} are constructed. These homomorphisms take values in the cohomologies of the algebra G and the configuration space M. Every space {V _s.} is the kernel of the corresponding homomorphism, while the space itself is defined by its physical properties.     

Diffusion Equations and Geometric Inequalities

Let =(₀, ₁) be a fixed vector in R ² with strictly positive components and suppose ₀, ₁ > 0. Set = _{0 0} + _{1 1} and, if x ₀, x ₁ R ⁿ , set x = ₀ x ₀ + ₁ x ₁. Moreover, for any j {0, 1, }, let c _j : R ⁿ R be a continuous, bounded function and denote by p _j , c _j (t, x, y) the fundamental solution of the diffusion equation

Noetherian Equations for Matrices

Let L|K be a finite Galois extension. Using central simple algebras we deal with the crossed representations of G = Gal(L|K) over L which are defined as mappings X of G into GL_n(L) satisfying X = X X. The last equation is the Noetherian equation in case n=1. Furtheron, more general crossed projective representations are considered which obey an equation X X = Xf_, where f_, L.     

Inegalites de Sobolev pour les sous Laplaciens de certains groupes unimodulaires

Résumé On prouve des inégalités de type Sobolev pour les opérateurs (L-) oùL est un sous-Laplacien sur un groupe de Lie non moyenmable et le bout de son spectre.

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We prove Sobolev inequalities for (L-) whereL is a sub-Laplacian on a non-amenable group and is the bottom of its spectrum.

     

Pseudoanalyticity of continuous functions with the σ-preservation of angles

The following theorem is proved: Every continuous function satisfying the conditionK is pseudo-analytic. The conditionK is a generalization of the Men'shov condition, well known in the theory of analytic functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1051–1057, August, 1993.     

Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

The physical significance of the area of an isochromatic crack tip fringe loop

A relationship between the stress intensity factorsK ₁ andK ₂ and the area enclosed by a fringe loop is derived from certain characteristic geometrical features of static and dynamic isochromatic crack tip fringe loops. The influence of crack speed and the additional regular stress field _0x onto the angle of approach of isochromatics to the crack tip as well as the relation between oscillation, pulsation, and rotation of fringe loops and the quantitiesK ₁,K ₂, and _0x is discussed.

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Zusammenfassung Gewisse geometrische charakteristische Eigenschaften dienen zur Herleitung einer Beziehung zwischen den SpannungsintensitätsfaktorenK ₁ undK ₂ und der von den um die Rissspitze laufenden Isochromatenschleifen eingegrenzten Fläche. Der Einfluß der Rissgeschwindigkeit und des riss-parallelen Spannungsfeldes _0x auf den Einlaufwinkel der Isochromaten in die Riss-spitze wird untersucht, und die Kopplung zwischen dem Oszillations-, Pulsations- und Drehbewegungen der Isochromatenschleifen und den GrößenK ₁,K ₂ und _0x wird diskutiert.