Let Γ2 ⊆ Γ1 be finitely generated subgroups of GLn0 (Z[1/q0]). For i = 1 or 2, let Gi be the Zariski-closure of Γi in (GLn0 )Q, Gi be the Zariski-connected component of Gi, and let Gi be the closure of Γi in ∏ p-q0 GLn0 (Zp). In this article we prove that, if G1 is the smallest closed normal subgroup of G1 which contains G2 and Γ2 y G2 has spectral gap, then Γ1 y G1 has spectral gap.

In this note we study the mathematical theory of one particular algorithm for nonholonomic point-to-point path nding. The algorithm considered here is a \continuation" or \deformation" method, in which one starts with an admissible trajectory that goes from the desired initial point p to some point q0, and then tries to construct a one-parameter family of trajectories, whose terminal points qs ...

This paper presents a new procedure of partial deduction of various constraint logic programs. The procedure takes a program-goal pair (P0, Q0) as input and outputs a resultant program-goal pair (Pn, Qn). The procedure always terminates and the computational equivalence of the program-goal pairs (P0, Q0) and (Pn, Qn) is preserved. Pn is more efficient in solving Qn than P0 in solving Q0. Our pr...

We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely, ∆p(x)u := div ( |∇u|p(x)−2∇u ) = f(x) in Ω, for which we prove Harnack’s inequality when f ∈ Lq0 (Ω) if max{1, N p1 } < q0 ≤ ∞. The constant in Harnack’s inequality depends on u only through ‖|u|p(x)‖p2−p1 L1...

We develop a Bott-Borel-Weil theory for direct limits of algebraic groups. Some of our results apply to locally reductive ind-groups G in general, i.e., to arbitrary direct limits of connected reductive linear algebraic groups. Our most explicit results concern root-reductive ind-groups G, the locally reductive ind-groups whose Lie algebras admit root decomposition. Given a parabolic subgroup P...

Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic correlations, where the electronic excitations are coupled to the fractionalized excitations of a quantum fluctuating antiferromagnet on the square lattice. The re...

Motivated by typical questions from computational geometry (visibility and art gallery problems) and combinatorial geometry (illumination problems) we present an analogue of the Krein-Milman theorem for the class of star-shaped sets. If S ⊆ R is compact and star-shaped, we consider a fixed, nonempty, compact, and convex subset K of the convex kernel K0 = ck(S) of S, for instance K = K0 itself. ...

In a graph G, the all-paths transit function A(u, v), consists of set all vertices in G which lies some path connecting u and v. Convexity obtained by is called convexity. A partition P into two disjoint non-empty subsets Radon if convex hulls intersect. (P0, Q0) nonempty t-tolerant partition, for any S⊆P with |S|≤t, intersection 〈P0−S〉∩〈Q0−S〉≠∅. Here we study number respect to It minimum k suc...

The research proposes a hydrological model to forecast recessive flows and it estimates depletion coefficient for the "Jequetepeque" river, water from top of "Gallito Ciego",Contumazá, Peru. Recessive were used third break point flow hydrograph "Yonán" station period 1988-2019. An exponential category (ALVI) was used. Ranges coefficients 0.0148 &lt; α 0.0003 day-1, calibration 0.005 day-1were i...