Deformations of Charged Axially Symmetric Initial Data and the Mass–Angular Momentum–Charge Inequality

We show how to reduce the general formulation of the mass–angular momentum–charge inequality, for axisymmetric initial data of the Einstein–Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors (Cha and Khuri, Ann Henri Poincaré, doi: 10.1007/s00023-014-0332-6, arXiv:1401.3384, 2014), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass–angular momentum–charge inequality in the maximal case.     

Stochastic modeling of quality of systems operating in a heterogeneous environment

We consider systems that are subject to an external mixed Poisson shock process. Each shock can result in a failure of a system with a given probability and is survived with the complementary probability. Each shock additionally decreases the quality function that describes the performance of a system, thus forming the corresponding stochastic process. Expectations (unconditional and conditional on survival) and relevant variability characteristics for the stochastic quality function are derived. Some monotonicity properties of the conditional quality function are investigated and the future values of this function are derived.     

L2‐signatures,homology localization,and amenable groups

Aimed at geometric applications, we prove the homology cobordism invariance of the L²‐Betti numbers and L²‐signature defects associated to the class of amenable groups lying in Strebel's class D(R), which includes some interesting infinite/finite non‐torsion‐free groups. This result includes the only prior known condition, that Γ is a poly‐torsion‐free abelian group (or a finite p‐group). We define a new commutator series that refines Harvey's torsion‐free derived series of groups, using the localizations of groups and rings of Bousfield, Vogel, and Cohn. The series, called the local derived series, has versions for homology with arbitrary coefficients and satisfies functoriality and an injectivity theorem. We combine these two new tools to give some applications to distinct homology cobordism types within the same simple homotopy type in higher dimensions, to concordance of knots in three manifolds, and to spherical space forms in dimension 3. © 2012 Wiley Periodicals, Inc.     

Signature invariants of covering links

We apply the theory of signature invariants of links in rational homology spheres to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, we derive an explicit formula to compute signature invariants of their covering links. Using the formula, we produce fused boundary links that are positive mutants of ribbon links but are not concordant to boundary links. We also show that for any finite collection of patterns, there are homology boundary links that are not concordant to any homology boundary links admitting a pattern in the collection.

     

On a Stochastic Survival Model for a System Under Randomly Variable Environment

In many cases, the survival probability of a system depends not only on the intrinsic characteristic of the system itself but also on the randomly variable external environment under which the system is being operated. In this paper we study a stochastic survival model for a system under random shock process which affects the survival of the system in a complicated way. The lifetime distribution of the system is derived, and the effect of environmental factors on the failure process of the system is also investigated.     

Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

Knot signature functions are independent

A Seifert matrix is a square integral matrix satisfying

To such a matrix and unit complex number there corresponds a signature,

Let denote the set of unit complex numbers with positive imaginary part. We show that is linearly independent, viewed as a set of functions on the set of all Seifert matrices.

If is metabolic, then unless is a root of the Alexander polynomial, . Let denote the set of all unit roots of all Alexander polynomials with positive imaginary part. We show that is linearly independent when viewed as a set of functions on the set of all metabolic Seifert matrices.

To each knot one can associate a Seifert matrix , and induces a knot invariant. Topological applications of our results include a proof that the set of functions is linearly independent on the set of all knots and that the set of two-sided averaged signature functions, , forms a linearly independent set of homomorphisms on the knot concordance group. Also, if is the root of some Alexander polynomial, then there is a slice knot whose signature function is nontrivial only at and . We demonstrate that the results extend to the higher-dimensional setting.

     

On generalized shock models for deteriorating systems

Standard assumptions in shock models are that failures of items are related either to the cumulative effect of shocks (cumulative models) or that they are caused by shocks that exceed a certain critical level (extreme shocks models). In this paper, we present useful generalizations of this setting to the case when an item is deteriorating itself, for example, when the boundary for the fatal shock magnitude is decreasing with time. Three stochastic failure models describing different impacts of shocks on items are considered. The cumulative effect of shocks is modeled in a way similar to the proportional hazards model. Explicit formulas for the corresponding survival functions are derived and several simple examples are considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.     

Comparison of nonlinear effects in amplitude and phase holograms recorded in photographic materials

Beam amplitudes of successive orders diffracted on holographic gratings are calculated and thus nonlinear effects in amplitude, bleached phase and reversal bleached phase holograms are compared. Then values of intermodulation noise are compared for the above three types of Fourier hologram of two circular holes.