As new applications of Schrödinger type inequalities obtained by Jiang (J. Inequal. Appl. 2016: Article ID 247, 2016) in the Schrödingerean Hardy space, we not only obtain the representation of Schrödingerean harmonic functions but also give a sufficient and necessary condition between the Schrödingerean distributional function and its derivative in the Schrödingerean Hardy space.

Many decision problems can be formulated as mathematical optimization models. While deterministic optimization problems include only known parameters, real-life decision problems almost invariably involve parameters that are subject to uncertainty. Failure to take this uncertainty under consideration may yield decisions which can lead to unexpected or even catastrophic results if certain scenar...

In this paper we prove a new chain rule formula for the distributional derivative of the composite function v(x) = B(x, u(x)), where u :]a, b[→ Rd has bounded variation, B(x, ·) is continuously differentiable and B(·, u) has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space va...

We prove that if t 7→ u(t) ∈ BV(R) is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields ut + f(u)x = 0, then up to a countable set of times {tn}n∈N the function u(t) is in SBV, i.e. its distributional derivative ux is a measure with no Cantorian part. The proof is based on the decomposition of ux(t) into waves belongin...

We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...

Let f be a distribution (generalised function) on the real line. If there is a continuous function F with real limits at infinity such that F ′ = f (distributional derivative) then the distributional integral of f is defined as ∫ ∞ −∞ f = F (∞)−F (−∞). It is shown that this simple definition gives an integral that includes the Lebesgue and Henstock–Kurzweil integrals. The Alexiewicz norm leads ...

Nahla A Belal CBAS: Context Based Arabic Stemmer Arabic morphology encapsulates many valuable features such as word’s root. Arabic roots are being utilized for many tasks the process of extracting a word’s root is referred to as stemming. Stemming is an essential part of most Natural Language Processing tasks, especially for derivative languages such as Arabic. However, stemming is faced with t...

Arabic morphology encapsulates many valuable features such as word’s root. Arabic roots are being utilized for many tasks; the process of extracting a word’s root is referred to as stemming. Stemming is an essential part of most Natural Language Processing tasks, especially for derivative languages such as Arabic. However, stemming is faced with the problem of ambiguity, where two or more roots...

Many syntactic approaches view word order as a derivative property of phrase-structure. An alternative is that word order is a learned property of constructions or even lexemes. What distributional patterns might provide evidence of lexeme-specific word order? A minimal grammatical pair is presented from Yurok, an Algic language of northwestern California. Words of the same general category and...