In this paper it is shown that the Hartogs triangle $${\mathbf{T}}$$ in $${\mathbf{C}}^2$$ a uniform domain. This implies Sobolev extension Furthermore, weak and strong maximal extensions of Cauchy-Riemann operator agree on triangle. These results have numerous applications. Among other things, they are used to study Dolbeault cohomology groups with coefficients complement .

I give my personal perspective on the past, present, and future of weak neutral current experiments, emphasizing the experimental inputs; the theoretical difficulties and inputs; the role of model independent and global analyses; and the implications at each stage. • Introductory Comments • The Discovery Phase (unification) • The Second Generation (the standard model confirmed) • The Third Gene...

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.

Based on agglutination, complement fixation, bactericidal, and opsonization tests, it is evident that suspensions of a Bacteroides sp. isolated from the mouse intestine and given by parenteral routes do not initiate antibody formation in mice. Rats also respond poorly to the antigenic stimulus. In contrast, suspensions of other bacterial species isolated from the rodent intestine are highly imm...

ht + (uh+ u+ uxy)x = 0 (1.2) which were first obtained by Boiti et al [1] as a compatibility condition for a “weak” Lax pair. A Kac-Moody-Virasoro type Lie algebra for eqs. (1.1) and (1.2) were given by Paquin and Winternitz [2]. Moreover, Sen-yue Lou [3] showed that eqs. (1.1) and (1.2) do not pass the Painlevé test, both in the ARS algorithm and in the WTC approach. Equations (1.1) and (1.2) ...

There exists a utilitarian tradition à la Sidgwick of treating equal generations equally in the form of anonymity. Diamond showed that no social evaluation ordering over infinite utility streams satisfying the Pareto principle, Sidgwick’s equity principle, and the axiom of continuity exists. We introduce two versions of egalitarianism in the spirit of the Pigou-Dalton transfer principle and the...

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate – exhibited by a random Gaussian matrix. We then show that this moment condition is necessary, up to a log log factor. In addition, we explore the Compati...

By the famous theorem of Morse and Hedlund, a word is ultimately periodic if and only if it has bounded subword complexity, i.e., for sufficiently large n, the number of factors of length n is constant. In this paper we consider relational periods and relationally periodic sequences, where the relation is a similarity relation on words induced by a compatibility relation on letters. We investig...