solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

in this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional volterra-fredholm integro-differential equations. here, we use the so-called two-dimensional block-pulse functions.first, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. then, by using this matrices, the nonlinear two-dimensional vol...

Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...

FIELD and laboratory methodologies for measuring saturated hydraulic conductivity (Ks ) have been the focus of much attention because Ks is recognized to be one of the most sensitive parameters in predictive hydrological models.Direct measurements are preferred for its determination because indirect methods,usually based on soil textural characteristics combined with aggregate analyses, do not ...

Contaminants of emerging concern (CECs) are an unregulated suite of constituents frequently detected in environmental waters, which possess the potential to cause a host of reproductive and developmental problems in humans and wildlife. Degradation pathways of several CECs are well-characterized in idealized laboratory settings, but CEC fate and transport in complex field settings is poorly und...

Steganography is a way to communicate a message such that no one except the sender and recipient suspects the existence of the message. This type of covert communication lends itself to a variety of different purposes such as spy-to-spy communication, exchange of pornographic material hidden in innocuous image files, and other illicit acts. Computer forensic personnel have an interest in testin...