A novel superstring-inspired gravitational theory in four spacetime dimensions is proposed as a sum of the modified $(R+\alpha R^2)$ gravity motivated by Starobinsky inflation and Bel-Robinson-tensor-squared term eleven-dimensional M-theory dimensionally reduced to dimensions. The Starobinsky-Bel-Robinson action has only two parameters, which makes it suitable for verifiable physical applicatio...

We prove sharp Lieb-Thirring inequalities for Schrödinger operators with potentials supported on a hyperplane and we show how these estimates are related to LiebThirring inequalities for relativistic Schrödinger operators.

In this paper, we study rank two semifields of order q that are of scattered type. The known examples of such semifields are some Knuth semifields, some Generalized Twisted Fields and the semifields recently constructed in [12] for q ≡ 1(mod 3). Here, we construct new infinite families of rank two scattered semifields for any q odd prime power, with q ≡ 1(mod 3); for any q = 2, such that h ≡ 1(...

1 School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; [email protected] (Y.J.); [email protected] (Y.-N.Z.) 2 Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China 3 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China; [email protected] 4 State Nuclear Power Technology R & D Cent...

Birth Control or the Limitation of Offspring [3] was written by American eugenics [5] and birth control [6] advocate William J. Robinson [4]. First published in 1916, the final edition (fortyeighth) was published in 1936, the same year that Robinson died. As a medical doctor and author, Robinson used his influence to promote propaganda for ?fewer and better babies,? by focusing on contraception...

So far we have talked about the expectation of random variables, and moved on to the variance or the second moment. However, neither of these methods is strong enough to produce the tight bounds needed for some applications. We have already stated that if all you are given is the variance of a r.v., then Chebyshev’s Inequality is essentially the best you can do. Thus, more information is needed...

We present a formula for the values of the sign representations of the complex reflection groups G(r, p, n) in terms of its image under a generalized Robinson-Schensted algorithm.

We propose an analogue of Solomon’s descent theory for the case of a wreath product G Sn, where G is a finite abelian group. Our construction mixes a number of ingredients: Mantaci-Reutenauer algebras, Specht’s theory for the representations of wreath products, Okada’s extension to wreath products of the Robinson-Schensted correspondence, and Poirier’s quasisymmetric functions. We insist on the...

are known as Lieb-Thirring bounds and hold true with finite constants Lγ,d if and only if γ ≥ 1/2 for d = 1, γ > 0 for d = 2 and γ ≥ 0 for d ≥ 3. Here and in the following, A± = (|A| ± A)/2 denote the positive and negative parts of a self-adjoint operator A. The case γ > (1 − d/2)+ was shown by Lieb and Thirring in [21]. The critical case γ = 0, d ≥ 3 is known as the Cwikel-Lieb-Rozenblum inequ...

Consider the Schrödinger operators H± = −d/dx ± V (x). We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and several sharp results concerning the spectral properties of H±.