Recursive proof of the Bell-Kochen-Specker theorem in any dimension n>3n>3

We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\leq d<n\leq 2d$). As an application of the method we find the smallest proofs known in dimension five (29 vectors), six (31) and seven (34), and different sets matching the current record (36) in dimension eight.Comment: LaTeX, 7 page

Multiqubit symmetric states with high geometric entanglement

We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram

In 1993, Mermin (Rev. Mod. Phys. 65, 803--815) gave lucid and strikingly simple proofs of the Bell-Kochen-Specker (BKS) theorem in Hilbert spaces of dimensions four and eight by making use of what has since been referred to as the Mermin(-Peres) "magic square" and the Mermin pentagram, respectively. The former is a $3 \times 3$ array of nine observables commuting pairwise in each row and column and arranged so that their product properties contradict those of the assigned eigenvalues. The latter is a set of ten observables arranged in five groups of four lying along five edges of the pentagram and characterized by similar contradiction. An interesting one-to-one correspondence between the operators of the Mermin-Peres square and the points of the projective line over the product ring ${\rm GF}(2) \otimes \rm{GF}(2)$ is established. Under this mapping, the concept "mutually commuting" translates into "mutually distant" and the distinguishing character of the third column's observables has its counterpart in the distinguished properties of the coordinates of the corresponding points, whose entries are both either zero-divisors, or units. The ten operators of the Mermin pentagram answer to a specific subset of points of the line over GF(2)[$x$]/$$. The situation here is, however, more intricate as there are two different configurations that seem to serve equally well our purpose. The first one comprises the three distinguished points of the (sub)line over GF(2), their three "Jacobson" counterparts and the four points whose both coordinates are zero-divisors; the other features the neighbourhood of the point ($1, 0$) (or, equivalently, that of ($0, 1$)). Some other ring lines that might be relevant for BKS proofs in higher dimensions are also mentioned.Comment: 6 pages, 5 figure

Observables have no value: a no-go theorem for position and momentum observables

A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments adde

Attitudes and practises with regard to emptying of onsite systems in Maputo, Mozambique

Rapid urbanisation as well as the rising need for water from industries and agriculture is intensifying freshwater scarcity in delta cities such as Maputo, Mozambique. Environmental pollution caused through the disposal of untreated wastewater and faecal sludge is additionally increasing water competition, posing a serious hazard to public health. Safe water reuse could hereby significantly lower the pressure on freshwater resources, still cities in developing countries lack knowledge, tools and capacities to integrate reuse into the overall (waste)water and faecal sludge management. With a city-wide onsite coverage of 90% it is essential to understand prevailing attitudes and practises along the faecal sludge management chain in order to quantify the end-use potential. This issue has been addressed through a survey of around 1,200 households in Maputo conducted by a cooperation of the Technical University of Delft and the Water and Sanitation Programme of the World Bank

Drastic reduction in density of Blattella germanica and Periplaneta americana cockroaches after the application of fenitrothion and lindane in Dema, Zimbabwe

Field studies were conducted in villages near the peri urban Dema area, Seke district, Zimbabwe, in order to understand the effect of the insecticides fenitrothion and lindane on Periplaneta americana and Blattella germanica cockroaches. A total of 63, 72 and 71 rooms were used for control, fenitrothion and lindane respectively. The mean density per room for P. americana before spraying was 43.5, 42.7 and 44.1 for the control, fenitrothion and lindane respectively. The mean density per room for B. germanica before spraying was 51.4, 50.2 and 47.1 for the control, fenitrothion and lindane respectively. A reduction in population density of P. americana was 3.2%, 83.8% and 99.3% in the control, fenitrothion and lindane rooms respectively. A reduction in population density of B. germanica was 87.8% and 82.8% in fenitrothion and lindane rooms respectively. An increase of 9.9% in the control rooms was observed. The majority of P. americana cockroaches died one month post spray with fenitrothion killing 78.2% and lindane 37.4% of all cockroach collections. However, the number of dead B. germanica cockroaches was almost of the same order for fenitrothion (71.9%) and lindane (74.5%). The residual effect of fenitrothion was 3 months on both cockroach nymph species and that of lindane was 1 month. In conclusion, both fenitrothion and lindane had impact on cockroach density, and fenitrothion showed a residual effect of 3 months

The generalized Kochen-Specker theorem

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference have been adde

Knock down and insecticidal activity of the plants Tagetes minuta, Lippia javanica, Lantana camara, Tagetes erecta and Eucalyptus grandis on Anopheles arabiensis mosquitoes

The knock down and insecticidal effects of the plants Tagetes minuta, Lippia javanica, Lantana camara, Tagetes erecta and Eucalyptus grandis were evaluated against Anopheles arabiensis mosquitoes in thatched round huts in Mumurwi village. Leaves from these plants were smouldered in order to provide mosquito repellent smoke. Complete knock down was provided 40 minutes after mosquitoes were exposed to smoke of T. erecta, 60 minutes to smoke of T. minuta and E. grandis and 120 minutes to smoke of L. javanica. Complete knock down of mosquitoes could not be provided by L. camara within the 140-minute exposure period. The KT50 (time required to knock down 50% of the mosquitoes) values were 24.985 minutes (T. minuta), 34.473 minutes (T. erecta), 59.119 minutes (L. javanica), 59.828 minutes (L. camara) and 25.245 minutes (E. grandis). The KT90 (time required to knock down 90% of the mosquitoes) values were 48.060 minutes (T. minuta), 50.169 minutes (T. erecta), 178.341 minutes (L. javanica), 140.220 minutes (L. camara) and 47.998 minutes (E. grandis). Mortality rates 24h after exposure were 40% (T. minuta), 100% (T. erecta), 75% (L. javanica), 90% (L. camara) and 100% (E. grandis). In conclusion, smoke from the plants T. erecta, T. minuta and E. grandis had very fast knock down rates with T. erecta, L. camara and E. grandis killing over 90% of the An. arabiensis mosquitoes. Plant smoke is important in mosquito control

Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has been corrected. Ref.[5] has been corrected, as has an error in Fig.3. Formatting error in Sec.4 has been corrected and the placement of tables and figures has been improved. A new paragraph has been added to Sec.4 and another new paragraph to the end of the Appendi