Here we will follow some of the presentation from Werner, Manby, and Knowles. 1 Density fitting is a way to approximate the usual two-electron integrals, (pq|rs) = dr 1 dr 2 φ p (r 1)φ q (r 1) 1 r 12 φ r (r 2)φ s (r 2), (1) where we have assumed real orbitals. We may also consider this electron repulsion integral as the repulsion between two generalized electron densities,

Abstract In this paper, fixed point and coincidence results are presented for multivalued generalized φ-weak contractive mappings on complete metric spaces, where φ : [0, +∞) −→ [0, +∞) is a lower semicontinuous function with φ(0) = 0 and φ(t) > 0 for all t > 0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995).

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ri...

A new generalization of the Gray map is introduced. The new generalization Φ : Z 2 → Z k−1 n 2 is connected with the known generalized Gray map φ in the following way: if we take two dual linear Z2k -codes and construct binary codes from them using the generalizations φ and Φ of the Gray map, then the weight enumerators of the binary codes obtained will satisfy the MacWilliams identity. The cla...

Let the underlying process Y be a semimartingale taking values in an interval I. Let φ : I → R be a difference of convex functions, and let X := φ(Y ). A typical application takes Y to be a positive price process and φ(y) = log y for y ∈ I = (0,∞). Then [the floating leg of] a forward-starting weighted variance swap or generalized variance swap on φ(Y ) (shortened to “on Y ” if the φ is underst...

jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

For connectivity of random geometric graphs, where there is no density for underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show that for this random geometric graph, the connectivity threshold Rn, converges almost surely to a constant 1−2φ where 0 < φ < 1/2, which for standard Cantor distribution is 1/3. We also show that ‖Rn − (1− 2φ)‖1 ∼ 2...

A proper total weighting of a graph G is mapping φ which assigns to each vertex and edge real number as its weight so that for any uv , Σ e ∈ E ( v ) φ( )+φ( ≠ u ). k,k ')-list assignment L set k permissible weights ' weights. An -total with z V ∪ called ')-choosable if every there exists weighting. As strenghtening the well-known 1-2-3 conjecture, it was conjectured in [Wong Zhu, Total choosab...

In this paper we propose a generalization of the usual deBruijn identity that links the Shannon differential entropy (or the Kullback–Leibler divergence) and the Fisher information (or the Fisher divergence) of the output of a Gaussian channel. The generalization makes use of φ -entropies on the one hand, and of φ -divergences (of the Csizàr class) on the other hand, as generalizations of the S...