Hammett constants (σ) can be important factor to understanding substitution and position effects on benzoic acid. This report describes a computational study of ∆G◦ and σ for six substituted benzoic acid (X= F,Cl ,OH ,NH2 ,CN,NO2 )and phenylacetic acid substituted (X=OH ,NH2 ) at para and meta positions ingas and aqueousphases by DFT method and comparesit to available experimental and theoretic...

The present note is an answer to complains of E.Weitz on [Sh 371]. We present a corrected version of a part of chapter VIII of Cardinal Arithmetic. 1. J * [a] = b : b ⊆ b and for every inaccessible µ, we have µ > sup(b ∩ µ). 2. pcf * (a) = tcf(a/D) : D is an ultrafilter on a, D ∩ J * [a] = ∅. 3. If |a| < min(a), for µ ∈ pcf(a) let b a µ = b µ [a] be a subset of a such that J ≤µ [a] = J <µ [a] +...

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

We give an arithmetic version of the recent proof of the triangle removal lemma by Fox [Fox11], for the group Fn 2 . A triangle in Fn 2 is a triple (x, y, z) such that x + y + z = 0. The triangle removal lemma for Fn 2 states that for every ε > 0 there is a δ > 0, such that if a subset A of Fn 2 requires the removal of at least ε · 2n elements to make it triangle-free, then it must contain at l...

A memory-hard function (MHF) f is equipped with a space cost σ and time cost τ parameter such that repeatedly computing fσ,τ on an application specific integrated circuit (ASIC) is not economically advantageous relative to a general purpose computer. Technically we would like that any (generalized) circuit for evaluating an iMHF fσ,τ has area × time (AT) complexity at Θ(σ ∗ τ). A data-independe...

and Applied Analysis 3 From the corresponding facts in the Aronszajn-Kolmogorov theorem of 17 , we have the following result. Lemma 2.3 see 17 . Let A be a σ-C∗-algebra,H a Hilbert space, and a map T : A ×A → B H be given such that, for all a1, a2, . . . , an ∈ A, [ T ( ai , aj )]n i,j 1 ∈ M n B H . 2.3 Then there exists a Hilbert space K and a map V : A → B H,K such that T a, b V a∗ ∗V b , ∀a,...

Let b(n, k) denote the number of permutations of {1, . . . , n} with precisely k inversions. We represent b(n, k) as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for b(n, k)/n! for a range of k including the maximum of the b(n, k)/n!. AMS Subject Classific...