An odd prime p is called a Wieferich prime if 2p−1 ≡ 1 (mod p); alternatively, a Wilson prime if (p− 1)! ≡ −1 (mod p). To date, the only known Wieferich primes are p = 1093 and 3511, while the only known Wilson primes are p = 5, 13, and 563. We report that there exist no new Wieferich primes p < 4×1012 , and no new Wilson primes p < 5×108. It is elementary that both defining congruences above h...

Let ψm be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 ≤ m ≤ 11. We extend this by finding ψ12 and ψ13. We also present an algorithm to find all integers n ≤ B that are strong pseudoprimes to the first m prime bases; with a reasonable heuristic assumption we can show that it takes at most B2/3+o(1) time.

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estim...

Introduction: The primary aim of facial reanimation surgery is to restore tone, symmetry, and movement to the paralyzed face. Hypoglossal-facial end-to-side anastomosis provides satisfactory facial reanimation in the irreversible proximal injury of the facial nerve. This study discussed the facial function results of end-to-side anastomosing of hypoglossal nerve to facial nerve when the i...

Increased spontaneous mutation is associated with increased cancer risk. Here, by using a model system, we show that spontaneous mutation can be increased several hundred-fold by a simple imbalance between the first two enzymes involved in DNA base excision repair. The Saccharomyces cerevisiae MAG1 3-methyladenine (3MeA) DNA glycosylase, when expressed at high levels relative to the apurinic/ap...

Two surprising new outcomes of the reaction of Lewis bases with dihalodiboranes(4) are presented, including sp(2)-sp(3) diboranes in which the Lewis base unit is bound to a highly sterically congested boron atom, and a rearranged double base adduct. The results provide a fuller understanding of the reactivity of diboranes, a poorly-understood class of molecule of critical importance to syntheti...

The present study tests the hypothesis that changes in the strong inorganic ion concentrations contribute significantly to the acid-base disturbance that develops during hemorrhage in the arterial plasma of rats in addition to lactate concentration ([Lac-]) increase. The physicochemical origins for this acid-base disorder were studied during acute, graded hemorrhage (10, 20, and 30% loss of blo...

The plasmatic strong ion difference (SID) is the difference between positively and negatively charged strong ions. At pH 7.4, temperature 37 degrees C and partial carbon dioxide tension 40 mmHg, the ideal value of SID is 42 mEq/l. The buffer base is the sum of negatively charged weak acids ([HCO3(-)], [A-], [H2PO4(-)]) and its normal value is 42 mEq/l. According to the law of electroneutrality,...

We propose a new strategy called the 'Protected DNA Probes (PDP) method' in which appropriately protected bases selectively bind to the complementary bases without the removal of their base protecting groups. Previously, we reported that 4-N-acetylcytosine oligonucleotides (ac(4)C) exhibited a higher hybridization affinity for ssDNA than the unmodified oligonucleotides. For the PDP strategy, we...