We consider the homogeneous Dirichlet problem for anisotropic parabolic equationut−∑i=1NDxi(|Dxiu|pi(x,t)−2Dxiu)=f(x,t) in cylinder Ω×(0,T), where Ω⊂RN, N≥2, is a parallelepiped. The exponents of nonlinearity pi are given Lipschitz-continuous functions. It shown that if pi(x,t)>2NN+2,μ=supQT⁡maxi⁡pi(x,t)mini⁡pi(x,t)<1+1N,|Dxiu0|max⁡{pi(⋅,0),2}∈L1(Ω),f∈L2(0,T;W01,2(Ω)), then has unique solution ...

The purpose of this study was to explore the effect of applying task-based activities on students’ listening comprehension improvement. It also aimed at providing evidence to show how shifting from a traditional language teaching approach into the TBLT approach can positively affect the process of learning listening skill. To do this, 80 participants were selected from three English language in...

© 2 0 0 1 m a s s a c h u s e t t s i n s t i t u t e o f t e c h n o l o g y, c a m b r i d g e , m a 0 2 1 3 9 u s a — w w w. a i. m i t. e d u m a s s a c h u s e t t s i n s t i t u t e o f t e c h n o l o g y — a r t i f i c i a l i n t e l l i g e n c e l a b o r a t o r y 1 ABSTRACT The image comparison operation – assessing how well one image matches another – forms a critical component...

Any σ ∈ Gal(L1L2/K) restricted to L1 or L2 is an automorphism since L1 and L2 are both Galois over K. So we get a function R : Gal(L1L2/K)→ Gal(L1/K)×Gal(L2/K) by R(σ) = (σ|L1 , σ|L2). We will show R is an injective homomorphism. To show R is a homomorphism, it suffices to check the separate restriction maps σ 7→ σ|L1 and σ 7→ σ|L2 are each homomorphisms from Gal(L1L2/K) to Gal(L1/K) and Gal(L2...

Abstract This study explored the effect of speaking task on midclause pausing characteristics in L1 and L2 speech same speakers to gain further insights into potential relationship between pause location stages production. Participants included English learners French ( n = 29) or Spanish 27) from publicly available, longitudinal LANGSNAP corpus. completed two oral tasks their L2: a picture-bas...

We prove the Gagliardo–Nirenberg-type multiplicative interpolation inequality ‖v‖L1(Rn) ≤ C‖v‖ 1/2 Lip′(Rn)‖v‖ 1/2 BV(Rn) ∀v ∈ Lip ′(Rn) ∩ BV(R), where C is a positive constant, independent of v. Here ‖·‖Lip′(Rn) is the norm of the dual to the Lipschitz space Lip 0(R) := C 0,1 0 (Rn) = C0,1(Rn) ∩C0(R) and ‖ · ‖BV(Rn) signifies the norm in the space BV(Rn) consisting of functions of bounded vari...

There is substantial debate over the mental representation of regular past tense forms in both first language (L1) and second language (L2) processing. Specifically, the controversy revolves around the nature of morphologically complex forms such as the past tense –ed in English and how morphological structures of such forms are represented in the mental lexicon. This study focuses on the resul...