Abstract:
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].

Abstract:
I want to show one possibility to proof the Collatz conjecture, also called 3n+1 conjecture, for any natural number N. For this, I limit my analysis on the direct odd follower of every natural odd number and show the connections between the already by one reached numbers and their followers, to find an recurrence over all ranges [1,N_{i}], to proof the conjecture.

Abstract:
The well-known Dixmier conjecture asks if every algebra endomorphism of the first Weyl algebra over a characteristic zero field is an automorphism. We bring a hopefully easier to solve conjecture, called the $\gamma,\delta$ conjecture, and show that it is equivalent to the Dixmier conjecture. Up to checking that in the group generated by automorphisms and anti-automorphisms of $A_1$ all the involutions belong to one conjugacy class, we show that every involutive endomorphism from $(A_1,\gamma)$ to $(A_1,\delta)$ is an automorphism ($\gamma$ and $\delta$ are two involutions on $A_1$), and given an endomorphism $f$ of $A_1$ (not necessarily an involutive endomorphism), if one of $f(X)$,$f(Y)$ is symmetric or skew-symmetric (with respect to any involution on $A_1$), then $f$ is an automorphism.

Abstract:
Data on the public's cancer beliefs were collected by means of a postal survey (anonymous questionnaire). Two general practices based in Nottingham and in Mansfield, in east-central England, sent questionnaires to registered patients aged 30 to 70 years. 1,808 completed questionnaires were returned for analysis, 56.5 per cent from women.Women were less likely to underestimate overall cancer incidence, although each sex was more likely to cite a sex-specific cancer as being amongst the most common cancer site. In terms of risk factors, men were most uncertain about the role of stress and sexually-transmitted diseases, whereas women were more likely to rate excessive alcohol and family history as major risk factors. The majority of respondents believed the public health care system should provide cancer screening, but significantly more women than men reported having benefiting from the nationally-provided screening services. Those who were older, in better health or had longer periods of formal education were less worried about cancer than those who had illness experiences, lower incomes, or who were smokers. Actual or potential participation in bowel screening was higher amongst those who believed bowel cancer to be common and amongst men, despite women having more substantial worries about cancer than men.Our results suggest that men's and women's differential knowledge of cancer correlates with women's closer involvement with screening. Even so, men were neither less positive about screening nor less likely to express a willingness to participate in relevant screening in the future. It is important to understand gender-related differences in knowledge and perceptions of cancer, if health promotion resources are to be allocated efficiently.In England, enthusiasm for cancer screening has led to the establishment of organised national programmes, with direct costs being met by the publicly-funded National Health Service (NHS). Since the late-1980s, all women within p

Abstract:
We conjecture that in the chiral limit of QCD the spectrum of hadrons is comprised of decoupled, reducible chiral multiplets. A simple rule is developed which identifies the chiral representations filled out by the ground-state hadrons. Our arguments are based on the algebraic structure of superconvergence relations derived by Weinberg from the high-energy behavior of pion-hadron scattering amplitudes.

Abstract:
In this work we use the number classification in families of the form 6n+1, and 6n+5 with n integer (Such families contain all odd prime numbers greater than 3 and other compound numbers related with primes). We will use this kind of classification in order to attempt an approach to Goldbach strong conjecture. By means of a geometric method of binary bands of numbers we conceive a new form of study of the stated problem.

Abstract:
An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is believed that statistical information from these simulations is accurate, but no one has offered a rigourous proof of this. In order to give mathematicians a clear goal in understanding this problem, we state a precise mathematical conjecture about molecular dynamics simulation of a particular system. We believe that if the conjecture is proved, we will then understand why molecular dynamics works.

Abstract:
This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the Connes Embedding Conjecture. It contains new proofs of equivalence of the Connes Embedding Conjecture, Positivstellensatze for trace positive polynomials, Kirchberg's Conjecture, and Tsirelson's Problem.

Abstract:
This article is a collected information from some books and papers, and in most cases the original sentences is reserved about twin prime conjecture.