Minimal cut sets of s–t networks with k-out-of-n nodes

In this paper, we extend traditional directed s–t network by letting nodes have k-out-of-n property: To generate output flows, a node must receive at least k flows from its n input links, where k is an integer assigned for the node and its value can be any number from 1 to n. To evaluate the system reliability, minimal cut sets for the extended network are defined for nodes. Under this definition, an extended network and its sink node have the same minimal cut sets. A new algorithm is designed to generate minimal cut sets for all nodes, starting with the source node and ending with the sink node. With different initializations, the algorithm can be applied for extended s–t networks with or without node failures.     

Exact equation and an algorithm for reliability evaluation of K-out-of-N:G system

An expression for reliability of K-out-of-N:G system is proposed. An algorithm for computing reliability of K-out-of-N system is given. It is an easy to implement, fast and memory efficient algorithm and helps to improve the computational efficiency considerably.     

Measurements of the viscosity of n-heptane,n-nonane,and n-undecane at pressures up to 70 MPa

New absolute measurements of the viscosity of n-heptane, n-nonane, and n-undecane are presented. The measurements were performed with a vibrating-wire instrument at temperatures of 303.15 and 323.15 K and pressures up to 70 MPa. The overall uncertainty in the reported viscosity data is estimated to be ±0.5%. A recently developed semiempirical scheme for the correlation and prediction of the thermal conductivity, viscosity, and self-diffusion coefficients of n-alkanes is applied to the prediction of the viscosity of n-heptane, n-nonane, and n-undecane. The comparison of these predicted values with the present high-pressure measurements demonstrates the predictive power of this scheme.     

Viscosity of binary mixtures. IV. Triethylamine with alkanes and monoalkylamines at 303.15 and 313.15 K

Viscosities and densities of seven binary mixtures of n-hexane, n-octane, isooctane, n-propylamine, n-butylamine, n-hexylamine, and n-octylamine with triethylamine have been measured at 303.15 and 313.15 K. Deviations of viscosities from a linear dependence on the mole fraction and values of excess Gibbs energy of activation G ^*E of viscous flow are attributable to the H-bonding and to the size of the alkylamine and alkane molecules.     

Reliability evaluation of multi-state weighted -out-of- systems

The k-out-of-n systems have been extensively studied in recent years. A binary weighted k-out-of-n model has also been reported in the literature. In this paper, we first compare two approaches for reliability evaluation of binary weighted k-out-of-n systems. We then provide two models of multi-state weighted k-out-of-n system models. Recursive algorithms are presented for reliability evaluation of these new models. The universal generating function approach is also used for reliability evaluation of multi-state weighted k-out-of-n systems.     

Reliability evaluation of furnace systems

This article reports an application of the k-out-of-n:F and the consecutive-k-out-of-n:F system reliability models in evaluation of the life distribution of furnaces used in a petro-chemical company. Different scenarios are used in modeling the reliability behaviors of the furnaces as a function of the reliabilities of the tubes in the furnaces. The life distribution of the furnace is used in making decisions on when to replace the furnace.     

Interplay of low and highT c phases in Bi-Sr-Ca-Cu-O superconductor

In the Bi-Sr-Ca-Cu-O system stringent conditions of heat-treatment lead to the formation of a mixture of both the low and highT _c phases and obtaining a single-phase material becomes extremely difficult. This study reports preparation of samples with single superconducting transitions at ∼ 75 K and ∼ 108 K; the compositions of which correspond ton=2,3 in the series Bi₂Sr₂Ca _n−1Cu _n O_{4 + 2n} . X-ray diffraction studies show that the lowerT _c material is a relatively pure phase while the higherT _c phase only co-exists with the lowerT _c phase. The most obvious effect of doping the system with lead is to make the reaction take place faster and thereby increase the volume fraction of the 110K phase.     

New insights into the assessment of k-out-of-n and related systems

k-out-of-n and related systems have received much attention in the recent past years. Hundreds of articles were devoted to various methods to assess them. In this article, we show that there exist very efficient algorithms to compute the reliability of k-out-of-n, l-to-h-out-of-n and consecutive k-out-of-n systems. k-within-r-out-of-n systems are intrinsically much harder. We study the performance of binary decision diagrams (BDDs) on these systems. Then, we propose a new approximation scheme. This algorithm is much more efficient in practice than already proposed methods.     

The viscosity of five liquid hydrocarbons at pressures up to 250 MPa

This paper reports new measurements of the viscosity of toluene, n-pentane, n-hexane, n-octane, and n-decane at pressures up to 250 MPa in the temperature range 303 to 348 K. The measurements were performed with a vibrating-wire viscometer and with a relative method of evaluation. Calibration of the instrument was carried out with respect to reference values of the viscosity of the same liquids at their saturation vapour pressure. The viscosity measurements have a precision of ±0.1% but the accuracy is limited by that of the calibration data to be ±0.5%. The experimental data have been represented by polynomial functions of pressure for the purposes of interpolation. The data are also used as the most precise test yet applied to a representation of the viscosity of liquids based upon hard-sphere theory.     

The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method

In this article, a special node called the k⁻-out-of-n node, which cannot receive more than a certain amount of flows, is newly introduced. The acyclic multistate-node network (AMNN) that unsatisfied the flow conservation law is then extended to the k-out-of-n AMNN by including the k⁻-out-of-n and k⁺-out-of-n nodes. A very simple universal generating function method (UGFM) based on some intuitive properties that characterize the structure of the k-out-of-n AMNN is developed to solve the k-out-of-n AMNN reliability. The correctness of the proposed UGFM will be analyzed and proven. An example with three special cases illustrates how the k-out-of-n AMNN reliability is evaluated using the proposed UGFM. To show that the proposed UGFM can also solve the AMNN reliability, the first case of the example demonstrates that the proposed UGFM without needing to remove redundant terms and collecting like terms is more efficient and reasonable than the best-known UGFM.     

A simple algorithm for evaluating the k-out-of-n network reliability

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. The minimal cut set (MC, an edge set) is one of the major and fundamental tools for evaluating network reliability. A k-out-of-n MC is a special MC in a k-out-of-n network in which some nodes must receive at least k flows from their n input edges, where k is an integer number between 1 and n. In this study, an alternative method is given first to define a MC using a node set (called MCN) in k-out-of-n networks. A very simple algorithm based on some intuitive theorems that characterize the structure of the MCN and the relationship between MC and MCN is developed to solve the k-out-of-n network reliability by finding the k-out-of-n MCs between two special nodes. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithm. The correctness of the proposed algorithm will be analyzed and proven. Two examples are illustrated to show how all k-out-of-n MCs are generated and verified in a k-out-of-n network using the proposed algorithm. The reliability of one example is then computing using one example.     

Viscosity and Liquid Density of Asymmetric Hydrocarbon Mixtures

Although a large body of viscosity data exists for simple mixtures of lighter n-alkanes, available information for heavy or asymmetric systems is scarce. Experimental measurements of viscosity and liquid densities were performed, at atmospheric pressure, in pure and mixed n-heptane, n-hexadecane, n-eicosane, n-docosane, and n-tetracosane from 293.15 K, or above the melting point, up to 343.15 K. The measured densities were correlated using the Peng–Robinson equation of state, and viscosities were modelled using the friction theory.     

A path-based algorithm for evaluating the k-out-of-n flow network reliability

Evaluating the network reliability is an important topic in the planning, designing and control of systems. The minimal path (MP, an edge set) set is one of the major, fundamental tools for evaluating network reliability. A k-out-of-n MP is a union of some MPs in a k-out-of-n flow network in which some nodes must receive flows from their k input distinctive edges (each input edge has one flow) to generate one flow, where k is an integer number between 2 and n. In this study, a very simple a-lgorithm based on some intuitive theorems that characterize the k-out-of-n MP structure and the relationship between k-out-of-n MPs and k-out-of-n MP candidates is developed to solve the k-out-of-n flow network reliability by finding the k-out-of-n MPs between two special nodes. The proposed algorithm is easier to understand and implement. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MPs are generated and verified in a k-out-of-n flow network using the proposed algorithm. The reliability of one example is then computing using the same example.     

Nonlinear surface impedance in “low” and “high”T c superconductors

The degradation of the surface impedanceZ = R + iX with rf power is a principal limit for measurements and applications. Such nonlinearities occur for normal conducting cavities by heating or electron loading. But superconductors show a much richer spectrum of causes for nonlinearities. The nonlinearities in the surface resistance δR ∞ γ H ⁿ and surface reactance δR ∞ α H ⁿ can be classified by the ratior = δX/δ R. This ratio differs in value, temperature, or frequency dependence for the different mechanisms, allowing a unique identification of those mechanisms. This identification is a prerequisite for an improved rf cavity design and improvement of superconducting materials.     

New bounds on the reliability of the consecutive k-out-of-r-from-n:F system

The main goal of this article is to show that the lower and upper bounds on the failing probability resp. reliability of consecutive k-out-of-r-from-n:F reliability systems developed by Sfakianakis, Kounias and Hillaris [M. Sfakianakis, S. Kounias, A. Hillaris, IEEE Trans. Reliability 1992;R-41:442–447] can be improved by applying fourth order Boole–Bonferroni bounds. Further we propose the application of the Hunter–Worsley bound in the framework of reliability system analysis, too. Numerical results of the formerly published test examples and harder problems are given. The computer code was written in and is available on request from the authors.     

Thermoelectric power in Gd3+-substituted Cu-Cd ferrites

Polycrystalline Cd _x Cu_1−x Fe_2−y Gd _y O₄ ferrites fory=0·0 and 0·1 were prepared by ceramic technique. X-ray diffractograms of powder samples show cubic symmetry withx⩾0·2 fory=0·0 and 0·1, while compositions withx=0·0 fory = 0·0 and 0·1 are tetragonal. The thermopower measurements for Gd³⁺-undoped ferrites in the temperature range 300 K to 788 K shown-type conductivity forx⩾0·2. The substitution of Gd³⁺ changedn-type conductivity of the compositions top-type. The mobilities calculated show decreasing trend on Gd³⁺ substitution. The values of activation energy ΔE and drift mobilityE _d suggest polaron formation in substituted samples. The conduction mechanism is explained on the basis of localized model and formation of Gd³⁺+Fe²⁺ stable pairs at B site and Cu¹⁺+Fe³⁺ at A site.     

Specific Heat Jump at Tc of High Tc Superconductors: Effect of Van Hove Singularity

In the BCS framework, exact expressions for the ratio between the jump in the specific heat at T _c and the normal phase specific heat are derived within the Van Hove singularity scenario. Analytical results are obtained for an isotropic s-wave and anisotropic d-wave pairing symmetries. Graphical solutions of the ratio as functions of _D /T _c and E _F /T _c , where _D is the cutoff energy and E _F is the Fermi energy, show significant deviations from the BCS value of 1.43.     

A new algorithm for generating minimal cut sets in k-out-of-n networks

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. A k-out-of-n network is a special network in that some nodes must receive at least k (>1) flows from all of their input edges (n). In real-life cases, many networks such as computer and telecommunications include k-out-of-n nodes for redundancy. The minimal-cut-node-set (MCN) is the major and fundamental tools for evaluating the k-out-of-n network reliability. In this study, a very simple algorithm based on some intuitive theorems that characterize the structure of the MCN is developed to solve the k-out-of-n network reliability. Compared to the existing algorithms, the proposed algorithm generates all k-out-of-n MCs without duplication based on fewer MCNs and fewer (k-out-of-n MC) candidates. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithms. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MCs are generated, verified, and implemented to evaluate the k-out-of-n network reliability using the proposed algorithm.     

The thermal conductivity of n-hexane,n-heptane,and n-decane by the transient hot-wire method

New absolute measurements of the thermal conductivity of liquid n-hexane, n-heptane, and n-decane are reported. The measurements have been carried out in the temperature range 300–370 K at atmospheric pressure in a transient hotwire instrument. The accuracy of the measurements is estimated to be ±0.5%. The density dependence of the thermal conductivity of n-hexane and n-heptane is found to be well described by a universal equation for the hydrocarbons based on a rough hard-sphere model. The measurements of the three hydrocarbons studied are also employed to generate more accurate effective core volumes, which are the only parameters characteristic of the fluid required for the application of the proposed universal scheme.     

Accommodating degradation results within a qualification procedure

A qualification procedure may comprise different tests which may either be successful or a failure. However, there are cases of degradation which should be taken into account. The reliability of a consecutive k-out-of-n:G set of tests is evaluated, along with the possibility of degradation. The problem is formulated as a difference equation that is transformed into a digital filter equation. Numerical results indicate improved chances of success for a set of tests that take into account the case of degradation.