Methods and problems of analyzing process diagrams

Process diagrams of are widely used to develop conceptual database models, in particular to establish the types of relationships between process elements. For some types of process diagrams, methods have been developed for converting them into sets of relationships. However, there are objective reasons that make it difficult to convert process diagrams into adequate and complete sets of relationships.

Sparse complete sets for coNP: Solution of the P versus NP problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Sparse complete sets for coNP: Solution of the P versus NP problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Sparse complete sets for coNP: Solution of the P versus NP problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Sparse complete sets for coNP: Solution of the P versus NP problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Unextendible Sets of Mutually Unbiased Basis Obtained from Complete Subgraphs

We propose a method, based on the search and identification of complete subgraphs of a regular graph, to obtain sets of Pauli operators whose eigenstates form unextendible complete sets of mutually unbiased bases of n-qubit systems. With this method we can obtain results for complete and inextensible sets of mubs for 2, 3, 4 and 5 qubits.

Integrability, intertwiners and non-linear algebras in Calogero models

For the rational quantum Calogero systems of type A1⊕A2, AD3 and BC3, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra ‘odd’ charges appearing for integral couplings. Formulæ for the energy eigenstates are used to tabulate the low-level wave functions.

John James Audubon's overlooked “Great Work”: his Ornithological biography

John James Audubon's five-volume Ornithological biography (1831–1839), published as the textual companion to The birds of America (1827–1838), remains a rich source of information about North America's avifauna. Issued separately from the prints for both practical and economic reasons, this classic but often forgotten work contained individual biographical accounts of each species shown in the illustrations, based upon the naturalist's decades of field observations. The demands associated with the publication and marketing of the prints compelled Audubon to wait until the end of 1830 before he began to write it, just as the first volume of 100 plates was being completed. Assisted throughout the endeavour by Scottish ornithologist William MacGillivray, who edited Audubon's manuscripts and provided scientific descriptions of each species, the naturalist published the first volume in 1831 in both Edinburgh and Philadelphia, the latter to secure the US copyright. A second Philadelphia edition appeared in 1832. Succeeding volumes were published in Edinburgh in 1834, 1835, 1838, and 1839, following the completion of each of the remaining three volumes of plates. An American edition of the second volume was published in 1835, but almost three-quarters of the copies were destroyed in a Boston fire. With sales of the last three volumes lagging, significantly fewer than 750 complete sets were ever sold.