A non-canonical example to support P is not equal to NP

Abstract

Abstract：The more unambiguous statement of the P versus NP problem and the judgement of its hardness, are the key ways to find the full proof of the P versus NP problem. There are two sub-problems in the P versus NP problem. The first is the classifications of different mathematical problems (languages), and the second is the distinction between a non-deterministic Turing machine (NTM) and a deterministic Turing machine (DTM). The process of an NTM can be a power set of the corresponding DTM, which proves that the states of an NTM can be a power set of the corresponding DTM. If combining this viewpoint with Cantor's theorem, it is shown that an NTM is not equipotent to a DTM. This means that "generating the power set P(A) of a set A" is a non-canonical example to support that P is not equal to NP.

Influence of alloying elements on the microstructure and properties of Ti2AlNb

“…At present, the alloy composition in the range of Ti- (20)(21)(22)(23)(24)(25)(26) Al- (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) Nb O-phase alloys has shown a better match between higher strength and plasticity, so the study of the relationship between the organization and properties of the Ophase alloys is mostly focused on this composition range [16] [17] . Some studies have shown that the increase of Nb content in alloys can improve the strength, room temperature plasticity, and toughness of alloys.…”

“…% W alloys at r ¼ 208 MPa and T ¼ 760 C. However, an excessive amount of W will lead to the generation of β-phase, which will adversely affect the creep resistance of the alloys. Yang et al [29] prepared the alloy at r ¼ 208 MPa and T ¼ 760 C by powder metallurgy. Yang et al [29] prepared Ti-22Al-23.4Nb-1.6W alloy by powder metallurgy method and found W could promote the dissolution of the α2 phase and O phase in the solid solution stage and refine the (B2+O) lath microstructure.…”

“…Yang et al [29] prepared the alloy at r ¼ 208 MPa and T ¼ 760 C by powder metallurgy. Yang et al [29] prepared Ti-22Al-23.4Nb-1.6W alloy by powder metallurgy method and found W could promote the dissolution of the α2 phase and O phase in the solid solution stage and refine the (B2+O) lath microstructure.…”

Review—Status of Zinc-Silver Battery

“…Pulse charging method can eliminate high plateau voltage and increase the capacity, but it does not work at low current density. 55,56 High plateau voltage can also be . TG curve and its first derivative for stoichiometric CP AgO.…”

Research on Enzyme Pretreatment of Polylactic Acid/Cotton Blended Fabric under Ultrasonic Wave

“…The development of this fiber will promote the development of the circular economy, and be very meaningful to the adjustment of textile industry frame.Pretreatment of fibers can remove the natural impurities in the fiber, the sizing agent and greasy dirt adhering on the fiber surface due to the fabric manufacture process and etc. And this treatment will provide fibers with good whiteness property and supply qualified intermediate product for the dyeing, printing and afterfinish processes [5][6][7][8] . A popular pretreatment technology generally contains desizing, scouring and bleaching.…”