We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set Sn(132) of 132-avoiding permutations and the set A2n+1(132) of alternating, 132avoiding permutations. For every set p1, . . . , pk of patterns and certain related patterns q1, . . . , qk, our bijection restricts to a bijection between Sn(...

Recall that E denotes the number of red edges, and F denotes the total number of edges. Then E = ξF = ξNΛ′(1) with ξ defined appropriately. In this lecture we use the saddle point method to derive an approximation to coeff [∏kmax k=2 qk(z) MPk , zE ] , where qk(z) = 12 ((1 + z) n + (1− z)n) = ∑ r even ( k r ) zr. This coefficient counts the number of ways to choose which edges incident to the c...

Nutall's algorithm for the computation of PN(x) = E^o prx at xn = x0 + n\, n = 0, 1, 2, • • • requires converting PN(xn) to QN(n) ±?. N m = aann . Recursion is then carried out through Qk + , (n) = Qk + , (n 1) + gj(n), * = 0, 1, • • • , N 1. This requires the initial values fiv_r(0), r = 0, 1, 2, • • • , N. We present here explicit and easily programmable formulas for am as well as Q,v-r(0), i...

An echelon-use lithium-ion battery (EULB) refers to a powered used in electric vehicles when the capacity is attenuated less than 80% and greater 20%. Aiming at degradation of performance EULB unclear initial value state energy (SOE), estimations power (SOP) an are not accurate. SOP estimation method based on adaptive dual unscented Kalman filter (ADUKF) proposed. First, second-order resistor-c...

‖f ‖ ≤ Crq ‖f‖ 1−q/r ‖f ‖ was proved by Kolmogorov in [11] for f ∈W r ∞(R). Here ‖ · ‖ means ‖ · ‖L∞(R) and the sharp constant Crq = Kr−qK −1+q/r r is given in terms of the Favard constants Kp := 4 π ∑∞ n=0 [ (−1) 2n+1 p+1 . For the definition of the Sobolev space W r ∞(R) see e.g. [4, Ch. 1.5]. The first results of this type (the case q = 1, r = 2) were obtained by Hadamard in [9] and by Landa...

The subject of this work is the analysis and implementation of stabilized finite element methods on anisotropic meshes. We develop the anisotropic a priori error analysis of the residual-free-bubble (RFB) method applied to elliptic convection-dominated convection-diffusion problems in two dimensions, with finite element spaces of type Qk, k ≥ 1. In the case of P1 finite elements, relying on the...

The quakingviable mouse (qkv) is a spontaneous recessive mouse mutant with a deletion of approximately 1.1 Mb in the proximal region of chromosome 17. The deletion affects the expression of three genes; quaking (Qk), Parkin-coregulated gene (Pacrg) and parkin (Park2). The resulting phenotype, which includes dysmyelination of the central nervous system and male sterility, is due to reduced expre...

In an earlier paper Hubert, Mauduit and Sárközy defined the notion of binary lattice, they introduced the measures of pseudorandomness of binary lattices, and they constructed a binary lattice with strong pseudorandom properties with respect to these measures. Later further constructions of this type have been given by different authors. In this series we will study the measures of pseudorandom...