Cyclic yield strength in definition of design limits for fatigue and creep

This study proposes a cyclic yield strength (CYS, σ^c_y) as a key characteristic for the definition of safe design for engineering structures operating under fatigue and creep conditions. CYS is defined on a cyclic stress-strain curve, while monotonic yield strength (MYS, σ^m_y) is defined on a monotonic stress-strain curve. Both values of σ^c_y and σ^m_y are identified using a 2-steps fitting procedure of the experimental stress-strain curves using Ramberg-Osgood and Chaboche material models. Comparison of σ^c_y and fatigue endurance limit σ^f_lim on the S-N fatigue curve reveals that they are approximately equal. Hence, basically safe fatigue design is guaranteed in purely elastic domain defined by the σ^c_y. A typical creep rupture curve in time-to-failure approach for creep analysis has 2 inflections corresponding to the σ^c_y and σ^m_y. These stresses separate 3 sections on the creep rupture curve, which are characterised by 3 different creep fracture modes and 3 creep deformation mechanisms. Thus, basically safe creep design is guaranteed in linear creep domain with brittle failure mode defined by the σ^c_y. These assumptions are confirmed for several structural low- and high-alloy steels for normal and high-temperature applications. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of prediction error variance

This note considers an estimate of the variance of the prediction error for a normal stationary time series based on the periodogram. It is shown that as T → ∞, the estimate converges almost surely to σ², the variance of the prediction error for the best linear predictor. By applying a result of Hannan [2] it thus follows that if in fitting an autoregression to the data x(1),…,x(T) the order k is greatly overstated, then the resultant estimate σ²_k of σ² will be biased downward.     

Über eine Defekt- und Verzweigungsrelation für die Ableitung meromorpher Funktionen

A well known inequality in Nevanlinna theory states that $$(*) \sum\limits_{a = |\infty } {\Theta (a,f^{(k)} ) \leqslant } {\text{ 1 + }}\tfrac{{\text{1}}}{{k + 1}} , k \geqslant 1$$ In this paper it is shown that (*) is sharp for all k≥1. The equality sign occurs if f is a solution of a Riccati differential equation with constant coefficients. Replacing Θ(a, f^(k)) in (*) by the deficiency σ(a,f^(k)) it is proved that in the corresponding inequality for \(\sum\limits_{a = |\infty } {\delta (a,f^{(k)} )} \) the bound 1+1/(k+1) fails to be best possible. In this connection several theorems are given about meromorphic functions with few multiple poles. It is also shown that in the class of Riccati differential equations with polynomial coefficients the equality sign in (*) characterizes the equations with constant coefficients.     

A GENERALIZATION OF COMPLETE GROUPS

Let G be a finite group and let G be the semi-direct product of a normal subgroup N and a subgroup K. In [1], conditions were found which are equivalent to the existence of a normal complement to N in G. We consider the structure of groups N for which the above condition always holds. Thus we use Bechtell's results to gain information on groups N such that if G is a semi-direct product of N and a subgroup K, then N is a direct factor of G, for all G. It is an old result that a group N is complete if and only if whenever N is a normal subgroup of G, then N is a direct factor of G, [4]. Hence it is not surprising that complete groups are part of our result. Moreover a group N is complete if and only if N is isomorphic to Aut(N) under the mapping σ(n) = σ _n , where σ _n is the inner automorphism induced by n. This remark leads us to consider groups N which contain a subgroup H such that H is isomorphic to Aut(N) under σ: H → Aut(N). All groups considered here are finite. The results found here do not parallel the results found in the author's dissertation for Lie algebras. There it is shown that only complete Lie algebras have the desired property. Thus, these results provide an example of when the theory of Lie algebras diverges from that of groups.     

On hereditarily strong Σ-spaces

In this paper the structure of hereditarily strong Σ-spaces (hsΣ-spaces, for short) is dealt with. The main result asserts that an hsΣ-space is the disjoint union of two σ subspaces one of which is an F_σ, the other a G_δ subset. Examples are given that in many ways, this decomposition cannot be improved. Then we investigate the question when an hsΣ-space is a σ-space. It is shown that a GO-space (or a first countable compactum) is metrizable iff it is an hsΣ-space, thereby proving a conjecture of J. van Wouwe. σ-spaces are characterized as being identical with perfect hsΣ-spaces. The question whether a Lindelöf, first countable hsΣ-space is a σ-space is shown to be independent of set theory. A characterization of hsΣ-spaces with no compact subsets of cardinality >2^ω is given.     

Self-Similarity and the Evaluation of Long-Time Nonhydrostatic Effects in Compositionally Driven Gravity Flows in Deep Surroundings

In the study of compositionally driven gravity currents involving one or more homogeneous fluid layers, it has been customary to adopt the hydrostatic assumption for the pressure field in each layer which, in turn, leads to a depth‐independent horizontal velocity field in each of these layers and significant simplifications to the governing equations. Under this hydrostatic paradigm, each layer will then have its motion governed by the well‐known reduced dimension shallow‐water equations. For the so‐called ‐layer or reduced gravity shallow‐water equations, similarity solutions for fixed volume gravity currents released in rectangular geometry have been found. Very few attempts have been made to evaluate contributions arising from the possible loss of hydrostatic balance in the context of the problems treated using the classic shallow‐water approach. Where such attempts have been pursued, they have usually been carried out in a time‐independent context or using layer‐averaged equations and very small amplitude disturbances. The vast majority of these studies into nonhydrostatic effects do not include any relevant numerical work to assess these effects. In this paper, we develop an approach for evaluating nonhydrostatic contributions to the flow field for bottom gravity currents in deep surroundings and rectangular geometry. Our approach makes no assumptions on the amplitudes of the disturbances and does not depend on layer‐averaging in the governing equations. We seek asymptotic expansions of the solutions to the Euler equations for a shallow fluid by using the small parameter δ², where δ is the aspect ratio of the flow regime. At leading order the equations enforce hydrostatic balance while those obtained at first order retain certain nonhydrostatic effects which we evaluate. Our method for evaluation of these first‐order contributions employs the self‐similar nature of the solution to the leading‐order equations in the new first‐order equations without any vertical averaging procedures being employed.     

A method of preventing cracking during heat treatment of thick-walled glass-fiber-reinforced plastic shells

To avoid cracking of thick-walled glass-fiber-reinforced plastic shells during heat treatment, it is suggested that the shells should be heat treated under pressure. This method is based on a comparison between the kinetics of the internal stresses σ_r.max(T) and strength σ _r ^str (T) during cooling. The authors give expressions for the optimum pressure, based on an elastic model of the material.     

Das Existenzproblem multivalenter Lösungen bei Differentialgleichungen

We consider linear differential equations $$w^{(n)} + \sum\limits_{i = 0}^{n - 1} {\sigma _i w^{(i)} = 0 in |z|}< 1.$$ If the coefficients σi inH ^∞ the solutions of theis equations have only a finite number of zeros and therefore these solutions are multivalent in |z|<1.     

The growth and decay of sonic waves in a radiating gas at high temperature

The propagation of a sonic discontinuity in an optically thick gray gas at temperature 10⁵°K or higher has been studied. The effects of radiation pressure and radiation energy density have been taken into account, while the profiles structured by radiant heat transfer are imbedded in the discontinuities under high temperature conditions of an optically thick medium. When the sonic discontinuity is propagating into a gas at rest, its velocity of propagation is found to be a constant which is the effective speed of sound in a radiating gas. The fundamental differential equations governing the growth of the sonic discontinuity are obtained and solved. It is concluded that if the sonic discontinuity is a compressive wave of order 1, then it terminates into a shock wave after a critical timet _c which has been determined. But on the other hand, when the sonic discontinuity is an expansion wave of order 1, then it will decay and will vanish ultimately. Particular cases of interest have been studied in details.     

Lp – Lq time decay estimate to the solution of the Cauchy problem for the system of equations describing nonlocal model of the thermoviscoelastic body

The aim of this paper is to present a new system of equations describing nonlocal model of thermoviscoelastic theory. We used the Papkin and Gurtin approach based on the constitutive relations for stress tensor σ(x), internal energy e(x) and heat flux q(x), with integral terms. Using the modified Cagniard-de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three-dimensional space. Basing on this matrix we represent in the explicit formula the solution of the Cauchy problem to this system of equations. Next, applying the method of Sobolev spaces, we proved the L^p–L^q time decay estimate to the solution of the Cauchy problem. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weak solutionsu(x,t) to parabolic partial differential equations with coefficients that depend uponu(yl, σ, (t,u(x,t))), 1 = 1, … k

The existence of weak solutionsu(x, t) to parabolic partial differential equations with coefficients that depend onu(y_l, σ_l(t, u(x, t))), l = 1,… k, is demonstrated using a retardation of the time arguments in the coefficients along with regularity and compactness results for solutions of linear parabolic partial differential equations.     

The number of labeled graphs placeable by a given permutation

Let S be a finite set and σ a permutation on S. The permutation σ* on the set of 2-subsets of S is naturally induced by σ. Suppose G is a graph and V(G), E(G) are the vertex set, the edge set, respectively. Let V(G) = S. If E(G) and σ*(E(G)), the image of E(G) by σ*, have no common element, then G is said to be placeable by σ. This notion is generalized as follows. If any two sets of {E(G), (σ¹)*(E(G)),…,(σ^l−1)* (E(G))} have no common element, then G is said to be I-placeable by σ. In this paper, we count the number of labeled graphs which are I-placeable by a given permutation. At first, we introduce the interspaced Ith Fibonacci and Lucas numbers. When I = 2 these numbers are the ordinary Fibonacci and Lucas numbers. It is known that the Fibonacci and Lucas numbers are rounded powers. We show that the interspaced Ith Fibonacci and Lucas numbers are also rounded powers when I = 3. Next, we show the number of labeled graphs which are I-placeable by a given permutation is a product of the interspaced Ith Lucas numbers. Finally, using a property of the generalized binomial series, we count the number of labeled graphs of size k which are I-placeable by σ. © 1996 John Wiley & Sons, Inc.     

The electron capture of H<Superscript>+</Superscript> ions in solid foils

The negative ion yields φ (H^?) and the neutral atom yields φ (H) of 0.6, 0.9, 1.2, 1.6 and 1.8 MeV H⁺ projectiles traversing various carbon foils have been measured. The experimental results showed that neither φ(H^?) nor φ(H) varies with the dwell time ^ at the same energy. φ(H)is larger than φ(H^?) by about 3–4 orders of magnitude. The charge exchanging between H⁺ ions and carbon foils was analyzed. It can be seen that the charge exchange is the most basic process. The experience formula of σ_c/σ_l has been gotten.     

Beispiele von Pseudo-Differentialoperator-Algebrenfl

Discussion of methods in theory of Partial Differential Operators (and Pseudo-Differential Operators) which are based on Gel'fand theory of commutative Banach Algebras. These methods all are discussed for the (non-compact) manifold Rⁿ, for L^p/-SobolefF spaces W_p,k (including k = ∞) and for operators of "Laplace-type", which, crudely, amounts to "elliptic type". Generalizations to general non-compact manifolds and to hypo-elliptic operators have been worked out in detail in [6], for example. Two types of symbol are introduced for a (Pseudo)-differential operator: the Laplace-symbol-quotient ^s (of order s) and the symbol σ. Among the results we have (a) necessary and sufficient criteria for the existence of an W^:p,-Fredholm inverse, (b) essential self-adjointness and (c) characterization of the essential spectrum of elliptic (Pseudo-) Differential operators.     

Kinetics of oxidation of aromatic ketones by peroxydisulphate catalysed by silver ions

The rates of peroxydisulphate oxidation of aromatic ketones have been found to be first order with respect to peroxydisulphate as well as of silver (I), but independent of the aromatic ketone. The effect of substituents on the rate of oxidation has been evaluated. The logk values have been plotted against the σ⁺ values, with ρ⁺=? 0.14. The reactivities of 1- and 2-acetyl naphthalene have been discussed. A mechanism of the oxidation of aromatic ketones based on reactive Ag⁺² species has been suggested.     

Conjugate gradient versus contraction mapping

The solution of linear equationsCu ⁰+b=0 foru ⁰ is considered here, withC a positive-definite and self-adjoint operator. Such equations arise when solving quadratic optimization problems and (for example) when solving partial differential equations using finite-difference methods. A standard solution technique is to approximateC by an operatorK which is easy to invert and then to construct an algorithm of the contraction-mapping type to useK ^–1 iteratively to help solve the original equation. Such algorithms have long been used for solving equations of this type. The aim of the paper is to show that, for eachK, a little-known generalization of the usual conjugate-gradient algorithm has advantages over the corresponding contraction-mapping algorithm in that it has better convergence properties. In addition, it is not significantly more difficult to implement. IfK is a good approximation toC, the resulting generalized conjugate-gradient algorithm is more effective than the usual conjugate-gradient algorithm.The computed results presented in Section 4 were obtained by P. Bluett while a research student at Imperial College.     

Optimal tactics for close support operations: Part VI,summary of numerical results

A new generation of C³ (command, control, and communication) models for military cybernetics has been developed in recent papers. Recursive equations for the solution of the C³-problem have been derived for an amphibious campaign with linear time-varying dynamics. Air and ground commanders are assumed to have different modes of intelligence and communications. Numerical results are summarized, and the relative importance of intelligence and communications is discussed.     

On σ-equivalence and χ-equivalence of graphs

We define a partial ordering on the set of σ-polynomials as well as a vertex splitting operation on the set of graphs, and introduce the notions of σ-equivalence and σ-uniqueness of graphs. Let σ(G) be the σ-polynomial of a graph G and (OVERBAR)σ(G) = σ(G^c). Let H = (G, v, A, B) be a vertex splitting graph of G. We prove that (OVERBAR)σ(G) ≤ (OVERBAR)σ(H) and the equality holds if and only if every vertex of A is adjacent to every vertex of B. This gives us an effective means to find σ-equivalent and χ-equivalent graphs. A necessary and sufficient condition for a graph to be χ-unique but not σ-unique is also obtained. © 1996 John Wiley & Sons, Inc.     

Translation-invariant linear forms on C0(G), C(G), Lp(G) for noncompact groups

Suppose G is a locally compact noncompact group. For abelian such G's, it is shown in this paper that L¹(G), C(G), and L^∞(G) always have discontinuous translation-invariant linear forms(TILF's) while C₀(G) and L^p(G) for 1 < p < ∞ have such forms if and only if $\text{G}\text{H}$ is a torsion group for some open σ-compact subgroup H of $\text{G}$. For σ-compact amenable G's, all the above spaces have discontinuous left TILF's.