A durable purchased at time t 2 [0;1) provides a constant service ‡ow x0 in the interval [t; t + 1]. The price of the durable is reduced periodically: it is equal to p = p0=(1 + ) in the period of time [ ; + 1), 2 N, where 0. Assume that the interest rate equal to the rate of time preference: r = . Consider a consumer that at date t = 0 has no durable and a lifetime wealth w. His optimization p...

Spinel MgAl2O4  nanopowders were synthesized by one-step solid state reactions using Al(NO3)3.9H2O and MgSO4 raw materials at stoichiometric 1 : 2, Mg : Al molar ratio at a constant reaction temperature of 1000 ºC for 8 h (S1), 10 h (S2) and  24 h (S3). The synthesized materials were characterized...

Given a connected graph G = ( V , E ) $G=(V,E)$ and length function ℓ : → R $\ell :E\to {\mathbb{R}}$ we let d v w ${d}_{v,w}$ denote the shortest distance between vertex $v$ $w$ . A t $t$ -spanner is subset ′ ⊆ $E^{\prime} \subseteq E$ such that if ${d}_{v,w}^{^{\prime} }$ denotes distances in subgraph $G^{\prime} =(V,E^{\prime} )$ then ≤ }\le t{d}_{v,w}$ for all ∈ $v,w\in V$ We study size of ...

A parallel algorithm for generating t-ary tree sequences in reverse B-order is presented. The algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time O(1). The algorithm is executed on a CREW SM SIMD model, and is adaptive and cost-optimal. Prior to the discussion of the parallel algorithm a new sequential generation with O(1) average time ...

We introduce a new class of time-continuous recurrent neural network models. Instead declaring learning system's dynamics by implicit nonlinearities, we construct networks linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent with varying (i.e., liquid) time-constants coupled to their hidden state, outputs being computed numerical differe...

This paper studies a notion called polynomial-time membership comparable sets. For a function g, a set A is polynomial-time g-membership comparable if there is a polynomialtime computable function f such that for any x1; ; xm with m g(maxfjx1j; ; jxmjg), outputs b 2 f0; 1gm such that (A(x1); ; A(xm)) 6= b. The following is a list of major results proven in the paper. 1. Polynomial-time membersh...