has a countably infinite number of solutions, which are denoted by Wk(z) for integers k. Each choice of k specifies a branch of the Lambert W function. By convention, only the branches k = 0 (called the principal branch) and k = −1 are real-valued for any z; the range of every other branch excludes the real axis, although the range of W1(z) includes (−∞,−1/e] in its closure. Only W0(z) contains...

The excitation temperature is crucial for understanding the dynamic processes of a vacuum arc. traditional methods based on optical emission spectroscopy can only provide 1D or 2D distribution. Due to absorption effect, it difficult obtain accurate information about radiation emitted by This result in measurement errors even lead incorrect conclusions. To address these issues, we developed 3D t...

In this study, fruit quality characteristics of sweet cherry cultivars (Prunus avium L. cvs. 0900 Ziraat, Kordia, Lambert, Regina, Sweetheart) grown in Ordu province Turkey were investigated. The Kordia cultivar's mass, width, and length measured higher than Lambert Ziraat cultivars. However, it was observed that the width cultivar similar to Regina Sweetheart. It determined firmness Sweetheart...

Using the general theory developed by the author in the previous paper, the problems of thermophoresis and diffusio-phoresis have been examined with a view to elucidating the effect of a general gas-surface scattering law on the associated forces. It is found that, in thermo-phoresis, there exists a close coupling between the first anisotropic moment of the gas-surface scattering law and the so...

In the myasthenic syndrome sometimes associated with bronchogenic carcinoma (Eaton-Lambert syndrome) muscular weakness is caused by reduced acetylcholine release from motor nerve terminals (Elmqvist and Lambert, 1968). Guanidine is a potent drug in this condition (Lambert, 1966) but serious adverse reactions have been reported (Lambert and Howard, 1972; Cherington, 1976; Henriksson et al., 1977...

Darcy’s flow friction factor is expressed in implicit form in some of the relations such as Colebrook’s and have to be solved by iteration procedure because the unknown friction factor appears on both sides of the equation. Lambert W function is implicitly elementary but is not, itself, an elementary function. Implicit form of the Lambert W function allows us to transform other implicit functio...

– (p, q) (p > 2, q = 2). These infinite tiling series of cubes are the special cases of the classical Lambert-cube tilings. The dihedral angles of the Lambert-cube are πp (p > 2) at the 3 skew edges and π2 at the other edges. Their metric realization in the hyperbolic space H 3 is well known. A simple proof was described by E. Molnár in [10]. The volume of this Lambert-cube type was determined ...

In this paper, we study the extinction time of logistic branching processes which are perturbed by an independent random environment driven a Brownian motion. Our arguments use Lamperti-type representation is interesting on its own right and provides one to correspondence between latter family Feller diffusions spectrally positive Levy process. When perturbation (of diffusion) subordinator then...

On October 5, 2007, a group of antitrust scholars convened on Chicago’s near northside to discuss monopolization law. In the course of their freewheeling but fascinating conversation, a number of broad themes emerged. Those themes can best be understood in contrast to a body of antitrust scholarship that was born six miles to the south, at the University of Chicago. Most notably, the northside ...

The additive fault tolerant control (FTC) for delayed system is studied in this work. To design the additive control, two steps are necessary; the first one is the estimation of the sensor fault amplitude using a Luenberger observer with delay, and the second one consists to generate the additive fault tolerant control law and to add it to the nominal control of delayed system. The additive con...