Recently, Eisenbrand, Pach, Rothvoß, and Sopher studied the function M(m, n), which is the largest cardinality of a convexly independent subset of the Minkowski sum of some planar point sets P and Q with |P | = m and |Q| = n. They proved that M(m, n) = O(m2/3n2/3+m+n), and asked whether a superlinear lower bound exists for M(n, n). In this note, we show that their upper bound is the best possib...

In this paper, persents the definitions of strongly prime ideal, strongly prime N-subgroup, Pseudo-valuation near ring and Pseudo-valuation N-group. Some of their properties have also been proven by theorems. Then it is shown that, if N be near ring with quotient near-field K and P be a strongly prime ideal of near ring N, then is a strongly prime ideal of ‎‎, for any multiplication subset S of...

Article history: Available online 17 July 2008

3 Proof of Theorem 1 9 3.1 Estimation of the g1 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Estimation of the g3 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Estimation of the g2 term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Putting everything together. . . . . . . . . . . . . . . . . . . . . ....

Cyber Security requires cryptology for the basic protection. Among different ECRYPT technologies, stream cipher plays a central role in advanced network security applications; in addition, pseudo-random number generators are placed in the core position of the mechanism. In this paper, a novel method of pseudo-random number generation is proposed to take advantage of the large functional space d...

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered he...

Twin brothers and their maternal uncle with a previously undescribed neonatal progeroid syndrome are presented. In addition to progeroid features, they had pseudo-obstruction of the urinary and gastrointestinal tracts, severe leucocytosis, liver dysfunction, and low complex III and IV in muscle but not in liver. Previously described neonatal progeroid syndromes and syndromes featuring pseudo-ob...

A series of mono-amide-functionalized pillar[5]arenes with different lengths of N-ω-aminoalkyl groups as the side chain on the rim were designed and synthesized, which all formed pseudo[1]rotaxanes in the crystal state. And these pseudo[1]rotaxanes could be transformed into [1]rotaxanes or open forms in the crystal state. In addition, they were also studied in solution by (1)H NMR spectroscopy.

We establish a composition theorem of Stepanov almost periodic functions, and, with its help, a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition, we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a r...