Two theorems about the P versus NP problem be proved in this article (1) There exists a language L , that the statement L∈P is independent of ZFC. (2) There exists a language L∈NP , for any polynomial time deterministic Turing machine M , we cannot prove L is decidable on M .
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
The measurement of economies no longer by GDP alone, but by an Index that includes other important factors as well, a Social factors relativized GDP.
Social factors relativized GDP: GDP – GDP x GINI = K_Index Written differently: (1 – GINI) x GDP = K_Index Inflation indexed Version: (1 – GINI – Inflation) x GDP = K_Index_Infl.
Productivity Index: K_Index / Labor Force = K_PROD Inflation indexed Productivity Index: K_Index_Infl. / Labor Force = K_PROD_Infl.
Debt-to-K_Index: National debt / K_Index = K_Debt Debt-to-K_Index_Infl: National debt / K_Index_Infl. = K_Debt_Infl.
Eduardo Fernández 11 de Mayo 2018. Henri Falcón representa la única opción real de transición pacífica en el corto plazo. Toda campaña electoral es ocasión para discutir acerca de los problemas de la nación y las soluciones que se proponen para esos problemas. El primer día de esta campaña presidencial Henri Falcón presentó su propuesta […]
Diario El Universal Caracas 11/05/2018.-Las relaciones entre Estados Unidos y Venezuela se han deteriorado a tal punto que es difícil imaginar que pudieran recomponerse con facilidad y de una manera satisfactoria para ambas partes. Sin embargo, el propio agravamiento de las tensiones y sus previsibles consecuencias pudieran representar la ocasión para una revisión de lo […]
During the early 1830’s Bernard Bolzano, working in Prague, wrote a manuscript giving a foundational account of numbers and their properties. In the final section of his work he described what he called `infinite number expressions’ and `measurable numbers’. This work was evidently an attempt to provide an improved proof of the sufficiency of the criterion usually known as the `Cauchy criterion’ for the convergence of an infinite sequence. Bolzano had in fact published this criterion four years earlier than Cauchy who, in his work of 1821, made no attempt at a proof. Any such proof required the construction or definition of real numbers and this, in essence, was what Bolzano achieved in his work on measurable numbers. It therefore pre-dates the well-known constructions of Dedekind, Cantor and many others by several decades. Bolzano’s manuscript was partially published in 1962 and more fully published in 1976. We give an account of measurable numbers, the properties Bolzano proved about them, and the controversial reception they have prompted since their publication.
11-05-2018. Revisando la cronología previa y posterior a los sucesos ocurridos en PDVSA a partir de Noviembre de 2017, son muchas las conclusiones a las que se puede arribar acerca del porque de la deplorable situación actual de PDVSA. Todo inicia a partir de la implementación del plan siembra petrolera. Aunque su ejecución navegó por […]
Enrique Meléndez 11/05/2018. El señalamiento lo hizo el también Premio Nacional de Ciencias 2013 en un foro que organizó Conindustria el pasado miércoles 2 de mayo. Inició su intervención recordando que Venezuela sufre la patología de toda economía basada en las rentas petroleras y no en el fruto de las exportaciones agrícolas, industriales o de servicios – […]
11-05-2018. El presidente de la encuestadora Datanalisis, Luis Vicente León, explicó que los comicios previstos para el 20 de mayo, registrarán la participación más baja de electores durante un proceso electoral presidencial en la democracia venezolana. En su espacio de preguntas y respuestas de Venepress, León destacó que la oposición venezolana se encuentra “polifracturada” lo […]
The cooling of a quantity of boiling water all the way down to freezing by simply thermally connecting it to a thermal bath held at ambient temperature without external intervention would be quite unexpected. We describe the equivalent of a ‘thermal inductor’ composed of a Peltier element and an electric inductance, which can drive the temperature difference between two bodies to change sign by imposing a certain inertia on the flow of heat, thereby enabling continuing heat transfer from the chilling body to its warmer counterpart. We show theoretically and experimentally that such a process is possible and fully complies with the second law of thermodynamics. With further progress in thermoelectric materials, it could serve to cool hot materials well below ambient temperature without external energy supply.
