1,722,076 research outputs found
Syringomatous Eccrine Carcinoma of the Vulva
No full textBackground: Skin adnexal neoplasms of the vulva are uncommon, and malignant adnexal neoplasms of the vulva are rare. Case: A case of syringomatous eccrine carcinoma arising in the perineum is presented, and the literature reviewed. Conclusions: Non-squamous malignancy of the vulva should be considered. All suspicious lesions of the vulva should be biopsied.Peer reviewe
lamW: Lambert-W Function
No full textImplements both real-valued branches of the Lambert-W function (Corless et al, 1996) without the need for installing the entire GSL.To cite package "lamW" in publications use
Lambert W function in hydraulic problems
Get PDFDarcy’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 functions in explicit form without any kind of approximations or simplifications involved. But unfortunately, the Lambert W function itself cannot be solved easily without approximation. Two original transformations in explicit form of Colebrook’s relation using Lambert W function will also be shown. Here will be shown efficient procedure for approximate solutions of the transformed relations
Lambert W function in hydraulic problems
Get PDFDarcy'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 functions in explicit form without any kind of approximations or
simplications involved. But unfortunately, the Lambert W function itself cannot be solved
easily without approximation. Two original transformations in explicit form of Colebrook's
relation using Lambert W function will also be shown. Here will be shown ecient procedure
for approximate solutions of the transformed relations
Generalization of the Lambert W function
No full textThe Lambert W function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics,
physics, or population dynamics just to mention a few. In this paper we construct and study in great detail a generalization of the Lambert W which involves some
special polynomials and even combinatorial aspects
Asymptotic Series of Generalized Lambert W Function
No full textHerein, we present a sequel to earlier work on a generalization of the Lambert W function. In particular,
we examine series expansions of the generalized version providing computational means for
evaluating this function in various regimes and further confirming the notion that this generalization
is a natural extension of the standard Lambert W function
Primes and the Lambert W function
No full textThe Lambert W function, implicitly defined by
W
(
x
)
e
W
(
x
)
=
x
, is a relatively “new” special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can also be used to gain a new perspective on the distribution of the prime numbers
Lambert W random variables and their applications in loss modelling
Get PDFSeveral distributions and families of distributions are proposed to model
skewed data, think, e.g., of skew-normal and related distributions. Lambert W
random variables offer an alternative approach where, instead of constructing a
new distribution, a certain transform is proposed (Goerg, 2011). Such an
approach allows the construction of a Lambert W skewed version from any
distribution. We choose Lambert W normal distribution as a natural starting
point and also include Lambert W exponential distribution due to the simplicity
and shape of the exponential distribution, which, after skewing, may produce a
reasonably heavy tail for loss models. In the theoretical part, we focus on the
mathematical properties of obtained distributions, including the range of
skewness. In the practical part, the suitability of corresponding Lambert W
transformed distributions is evaluated on real insurance data. The results are
compared with those obtained using common loss distributions
Gecikmeli diferansiyel denklemlerde lambert W fonksiyonu uygulamaları
No full textGecikmeli diferansiyel denklemler, sistemlerin davranışlarındaki değişim karakterinin sadece şimdiki durumlarına değil aynı zamanda geçmişteki durumlarına da bağlı olabileceği yaklaşımının matematiksel olarak modellenmesine olanak sağlayan bir denklem grubudur. Bu denklem grubunun çözüm metotları ve çözümlerin kalitatif özellikleri adi diferansiyel denklemlerdekinden farklıdır. Tezin ilk bölümünde gecikmeli diferansiyel denklemlerin örnek modellerle tanıtılması, sınıflandırılması ve temel çözüm metotlarından olan adımlar yönteminin bir uygulamayla açıklanması yapılacaktır. Tezin ikinci bölümünde Lambert W fonksiyonu ve bu fonksiyonun gecikmeli diferansiyel denklemlerdeki uygulamalarında kullanılacak olan üstel matris yöntemi ve matris fonksiyonları kavramları tanıtılacaktır. Yine bu bölümde adi diferansiyel denklemlerde de kullanılan, gecikmeli diferansiyel problemlerinin çözümlerinin kalitatif değerlendirmesini yapabilmek için gereken kararlılık ve salınımlılık tanımları verilecektir. Tezin üçüncü bölümünde Lambert W fonksiyonunun belirli sınıf bir gecikmeli diferansiyel denklem problemine uygulanması incelenecektir. Örnek skaler ve sistem gecikmeli diferansiyel denklem problemleri üzerinde farklı parametrelerle Lambert W fonksiyonunun uygulanma adımları ve çözümleri incelenecektir.Çözümleri daha anlaşılır şekilde ortaya koyabilmek için sadece sembolik gösterim değil problemin çözüm adımlarındaki nümerik değerler de bazı problemlerde verilecektir. Skaler problem ve sistem problem için Lambert W fonksiyonu dallarına ait çözümlerinin baslangıç değer fonksiyonuyla denkleştirme metodu anlatılacak ve örnek uygulma gösterilecektir.Sonuç bölümünde tezin krıtik tespitleri tekrar ifade edilecek, tezin sunduğu yeniliğin anlamı, önemi ve kısıtları tekrar belirtilecektir.Delay differential equations are class of equations that can be considered as a tool for the mathematical modelling of the approach of not admitting the present state of the system as the sole criteria but presuming the historical states of the systems to have effect on the instantaneous character of change of the system as well. The solution methods and qualitative properties of delay differential equations are different from the ordinary differential equations.In the 1st chapter of the thesis delay differential equations will be introduced through some sample models. Its classification will be given and one of its main solution methods – method of steps – will be explained on an application.In the 2nd chapter of the thesis Lambert W function will be introduced together with the matrix exponential method and functions of matrices concepts which will have part on the application steps of Lambert W function on delay differential equations. Also in this chapter stability and oscillation concepts of ordinary differential equations will be reviewed for being a basis for the qualitative analysis of the solutions of the delay differential problems.In chapter 3 it will be reviewed how Lambert W function is applied to a specific class of delay differential equations. It will be anayzed the steps of applying the Lambert W function on scalar and system delay differential equations through examples and solutions derived by the method. To make the solutions of the method more apparent not only the symbolic results will be shown but also the numerical values of the application steps will be given in some examples. For both scalar and system problems, the method of equating the Lambert W function branches to the initial function will be explained and applied on a sample problem. In the results section key findings of the thesis will be rephrased and the importance, meaning and constraints of the original output of the thesis will be restated
- …
