Lossy trapdoor functions, introduced by Peikert and Waters (STOC ’08), are functions that can be generated in two indistinguishable ways: either the function is injective, and there is a trapdoor to invert it, or the function is lossy, meaning that the size of its range is strictly smaller than the size of its domain. Kakvi and Kiltz (EUROCRYPT 2012) proved that the Full Domain Hash signature s...

It is clear that Ak and Bk are subsets of Ck, and in fact Lehmer [3] proved that Ak ⊂ Bk ⊂ Ck. It is not difficult to show that Cp ⊂ Ap for a prime p, so that Ap = Bp = Cp. P. J. McCarthy [5] proved that Ak = Bk when k is not squarefree, and he asked if the result could be extended to all composite numbers k. This was done by P. Erdős [2], who proved that the set Bk \ Ak is infinite for every c...

Objective(s): The effects of PPAR-γ agonist alone and in combination with carvacrol and Zataria multiflora on inhaled paraquat (PQ) induced-systemic inflammation and oxidative stress were examined. Materials and Methods: Control group exposed to normal saline aerosol, one group exposed to 54 mg/m3 PQ aerosol and four groups exposed to PQ...

In order to investigate the effect of hemoperfusion (HP) on the clearance rate of paraquat (PQ) and develop a clearance model, 41 PQ-poisoned patients who acquired acute PQ intoxication received HP treatment. PQ concentrations were determined by high performance liquid chromatography (HPLC). According to initial PQ concentration, study subjects were divided into two groups: Low-PQ group (0.05-1...

Paraquat (PQ) is an herbicide used extensively in agriculture. This agent is also suspected to be a risk factor for Parkinson's disease (PD) by harming nigro-striatal dopamine neurons. There is likely, genetic-based, individual variability in susceptibility to PQ neurotoxicity related PD. In this study, we measured the delivery of PQ to the brain after three weekly injections of PQ at 5 mg kg(-...

The previous mapping lecture demonstrated how, in the absence of errors, STS mapping could be solved efficiently via a reduction to a well-known abstract problem called the consecutive-ones problem. The solution made use of a data structure called a PQ-tree which eloquently represents all possible orderings of the STS sites that are consistent with the data. The flaw in this approach, however, ...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

background: paraquat (pq) poisoning is highly fatal; and therefore, clinicians should be familiar with prompt approach to and poor prognostic features of this type of poisoning. hence, in this study, clinical profile, management and outcome of a series of patients with pq poisoning are presented. methods: a retrospective review of medical records of patients poisoned with pq who were treated at...

A ternary inclusion-exclusion polynomial is a polynomial of the form Q{p,q,r} = (zpqr − 1)(zp − 1)(zq − 1)(zr − 1) (zpq − 1)(zqr − 1)(zrp − 1)(z − 1) , where p, q, and r are integers ≥ 3 and relatively prime in pairs. This class of polynomials contains, as its principle subclass, the ternary cyclotomic polynomials corresponding to restricting p, q, and r to be distinct odd prime numbers. Our ob...