We survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely related with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. We conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.

The nonFickian flow of fluid in porous media is complicated by the history effect which characterizes various mixing length growth of the flow, which can be modeled by an integro-differential equation. This paper proposes two mixed finite element methods which are employed to discretize the parabolic integro-differential equation model. An optimal order error estimate is established for one of ...

Our research proposes a simple game model that captures the incentives dictating the interaction between buyers and sellers and reveals the strategies that evolve in different scenarios, such as eBay auctions. In particular, we find seller history has a significant effect on player strategy. We prove that for simple reputation-based buyer strategies, a seller’s decision whether to cheat or not ...

Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Also a necessary condition is determined under which history dependent equilibria can occur. Some of th...

This paper proposes a Bayesian RC-frame finite element model updating (FEMU) and damage state estimation approach using the nonlinear acceleration time history based on nested sampling. Numerical (FEM) parameters are selected through sampling, their probability density is estimated history. In first step, we estimate error standard deviation select FEM that required to be updated by FEMU. secon...

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a survey of some of the main results and a guide to the literature.

One of a feasible and efficient method to retrofit structures is spraying shotcrete which is widely applied around the world. Shotcrete is concrete with fine aggregates which are sprayed through a hose and by air pressure coat at high velocity onto a surface. In the current research, three masonry schools from different regions of Iran are selected. The retrofitted wall surfaces have been prepa...

Longevity is a life-history trait that is shaped by natural selection. An unexplored consequence is how selection on this trait affects diversity and diversification in species assemblages. Motivated by the diverse rockfish (Sebastes) assemblage in the North Pacific, the effects of trade-offs in longevity against competitive ability are explored. A competition model is developed and used to exp...

-Machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense, as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization, though, an alternative generator definition was given: unifilar, edge-emitting hidden Mark...

This paper introduces timeline trees, which are partial models of partially observable environments. Timeline trees are given some specific predictions to make and learn a decision tree over history. The main idea of timeline trees is to use temporally abstract features to identify and split on features of key events, spread arbitrarily far apart in the past (whereas previous decision-tree-base...