We construct a family of compact 7-dimensional manifolds endowed with a weakly integrable generalized G2-structure with respect to a closed and non-zero 3-form. We relate the previous structures with SU(3)structures in dimension 7. Moreover, we investigate which types of SU(3)structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G2-structure with respect to a n...

We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The form of the distribution can be calculated analytically for any realization of disorder. For non-zero impurity concentration the distribution becomes a self...

Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension m1 +m2 − 1 in the product X := X1 1 ×X m2 2 of two Hadamard manifolds Xi i of dimension mi with negative curvature bounded away from zero. Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity o...

In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford in...

We study the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. Simple-zero and double-zero singularities are investigated when bifurcation parameters change near certain critical values. By performing center manifold reduction, the normal forms on the center manifold are derived to obtain the bifurcation diagrams of the model such as Hopf, homoc...

By using a multiscale analysis, we establish quantitative versions of the Besicovitch projection theorem (almost every projection of a purely unrectifiable set in the plane of finite length has measure zero) and a standard companion result, namely that any planar set with at least two projections of measure zero is purely unrectifiable. We illustrate these results by providing an explicit (but ...

Let A be a unital simple AT-algebra of real rank zero. Given an isomorphism γ1 : K1(A)→ K1(A), we show that there is an automorphism α : A → A such that α∗1 = γ1 which has the tracial Rokhlin property. Consequently, the crossed product A ⋊α Z is a simple unital AH-algebra with real rank zero. We also show that automorphism with Rokhlin property can be constructed from minimal homeomorphisms on ...

In this paper, we explore the geometric objects of conformal geometric algebra based on their IPNS (inner product null space) representation in some detail. Spheres of dimension 1 , 2 and three are objects of conformal geometric algebra. Usually, points in conformal geometric algebra are represented as ordinary spheres with zero radius, but what about circles with zero radius? We expect many pr...

There is consensus that modularity has many benefits from cost savings due to increased commonality to enabling a higher variety of products. Full modularity is, however, not always achievable. How engineering systems and products whose design is heavily influenced by technical constraints, such as weight or size limitations, tend to exhibit rather integral architectures is shown in this study....

A primitive relay channel (PRC) has one source(S) communicating a message to one destination (D) with thehelp of a relay (R). The link between R and D is consideredto be noiseless, of finite capacity, and parallel to the linkbetween S and (R,D). Prior work has established, for any fixednumber of channel uses, the minimal R-D link rate needed sothat the overall S-D messag...