Sentence examples for and hence forming from inspiring English sources

Since then, the study of four-manifolds and their invariants has undergone several further exciting developments, tying them deeply with ideas from symplectic geometry and pseudo-holomorphic curves, and hence forming further bridges with algebraic and symplectic geometry, but also connecting them more closely with knot theory and three-manifold topology.

The unconventional method was used to simulate the foamy oil behavior, that is the PVT cell was not rocked, avoiding a rapid artificial nucleation of the gas micro-bubbles and hence forming a separated gas phase.

In particular, they must come from equilibrium behavior tomorrow, and hence form part of a subgame perfect equilibrium today.

These interfaces are prone to fracture in such systems and hence form a weak point.

Under these conditions, only coalition cabinets commanding the support of several minority parties could muster legislative majorities and hence form a government.

The quartz and clay minerals in the coal provide different formation conditions and hence form different shapes of the shrinkage-induced pores.

In the near term, however, the demand to eliminate the debt ceiling won't accomplish much, since Republicans have somehow become convinced that debt-ceiling hikes are concessions to Democrats, and hence form a crucial and legitimate bargaining chip.

Most of the present province of Liaoning fell within the confines of the earliest Great Wall of China, built during the reign of Shihuangdi, the first Qin emperor (221 210 bce), and hence formed part of China from early times.

These bands have a filled shell and, hence, form a deep valence band.

Sectors such as agriculture and transport are heavily subsidized for their use of fossil fuels and hence form a strong lobby as well.

There is no phase separation and cracks of the membrane surface, suggesting that the synthesized composite films are homogeneous in nature and hence form a dense membrane.