Despite overall psychotherapy efficacy (Lambert, 2013), many clients do not benefit (Reese, Duncan, Bohanske, Owen, & Minami, 2014), dropouts are a problem (Swift & Greenberg, 2012), and therapists vary significantly in success rates (Baldwin & Imel, 2013), are poor judges of negative outcomes (Chapman et al., 2012), and grossly overestimate their effectiveness (Walfish, McAlister, O'Donnell, &...

An approach for the analytical solution, free and forced, to systems of delay differential equations (DDEs) has been developed using the matrix Lambert function. To generalize the Lambert function solution for scalar DDEs to systems of DDEs, we introduce a new matrix, Q when the coefficient matrices in a system of DDEs do not commute. The solution is in the form of an infinite series of modes w...

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...

Johann Heinrich Lambert is best known for his work in physics. The law of Bouguer-Lambert-Beer on the absorbtion of light may be his most famous achievement. He is also well known in mathematics, for example for his proof of π and e being irrational numbers, for his work on non-additive probabilities and for his contribution to non-Euclidean geometry. He worked on numerous problems of natural s...

We present a concise overview of the modified Beer-Lambert law, which has been extensively used in the literature of near-infrared spectroscopy (NIRS) of scattering media. In particular, we discuss one form of the modified Beer-Lambert law that is commonly found in the literature and that is not strictly correct. However, this incorrect form of the modified Beer-Lambert law still leads to the c...

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...

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 ...