The dual purpose of this article is to establish bilinear Poincaré-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling.

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

Multi-supply voltage design using Cluster Voltage Scaling (CVS) is an effective way to reduce power consumption without performance degradation. One of the major issues in this method is performance and power overhead due to insertion of Level Converting Flip-Flops (LCFF) at the interface from lowsupply to high-supply clusters to simultaneously perform latching and level conversion. In this pap...

The Grøstl hash function is one of the five finalists in the third round of SHA-3 competition hosted by NIST. In this paper, we propose some improved (pseudo) preimage attacks on the Grøstl hash function by using some techniques, such as subspace preimage attack and the guess-and-determine technique. We present the improved pseudo preimage attacks on 5-round Grøstl-256 hash function and 8-round...

On account of its application to the present and future analysis of the virtual photon correction to the hadronic properties by means of lattice QCD simulation, we initiate the study of the finite size scaling effect on the QED correction using low energy effective theory of QCD with QED. For this purpose, we begin with formulating a new QED on the space with finite volume. By adapting this for...

Let d ≥ 4 and let u be a global solution to the focusing masscritical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d u with spherically symmetric H x initial data and mass equal to that of the ground state Q. We prove that if u does not scatter then, up to phase rotation and scaling, u is the solitary wave eQ. Combining this result with that of Merle [15], we obtain that in dimensions d ≥ 4...

We report a scaling of the mean matter density with the width of the saturated Lyα absorptions. This property is established using the “pseudo-hydro” technique (Croft et al. 1998). It provides a constraint for the inversion of the Lyα forest, which encounters difficulty in the saturated region. With a Gaussian density profile and the scaling relation, a simple inversion of the simulated Lyα for...

The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions and satisfy the universal scaling relation predicted by the Buda-Lund h...

In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling lters and wavelet lters) can be factored as the product of primitive parau-nitary matrices, a pseudo identity matrix pair, an invertible matrix, and the canonical Haar matrix. Compared with the f...