Fission-fragment energy correlation measurements for 252Cf(sf) and structures in far-out asymmetric fission

Fragment-mass and kinetic-energy distribution measurements for ²⁵²Cf(sf) have been extended to the far-out asymmetric low-yield fission region of M_H = 190 compared with the existing data that go up to M_H ≈ 168. The mass yield Y(m) shows a shoulder for M_H ≈ 163 and an important enhancement for M_H ? 176. The 〈E_K〉(m), σ_EK(m) and, to a lesser extent, Y(m) distributions show strong and correlated amplitude fluctuations for M_H ? 170. These data indicate strong and rapid changes in deformation of the nascent fragments and the coexistence of more than one deformed-shell stabilized scission configuration for the same mass splits. These structures and those present in the relatively high-yield regions are discussed in terms of the static macro-microscopic potential-energy calculations.     

A method for automatic identification of water and fat images from a symmetrically sampled dual-echo Dixon technique

Sampling water and fat signals symmetrically (i.e., at 0° and 180° relative phase angles) in a dual-echo Dixon technique offers high intrinsic tolerance to phase fluctuations in postprocessing and maximum signal-to-noise performance for the separated water and fat images. However, identification of which image is water and which image is fat after their separation is not possible based on the phase information alone. In this work, we proposed a semiempirical automatic image identification method that is based on the intrinsic asymmetry between the water and fat chemical shift spectra. Specifically, the approximately bimodal feature of the fat spectra and the observation that most in vivo tissues are either predominantly water or predominantly fat are used to construct a spectrum-based algorithm. Additional refinement is accomplished by considering the spatial distribution of the tissues that may have a coexistence of water and fat. The final improved algorithm was tested on a total of 131 three-dimensional patient datasets collected from different scanners and found to yield correct water and fat identification in all datasets.     

Ultradistributional boundary values of harmonic functions on the sphere

We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calderón and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.     

Identifying defective sets using queries of small size

We examine the following version of a classic combinatorial search problem introduced by Rényi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y$ of $X$, which is known to have exactly $d$ elements, by means of testing, for as few as possible subsets $A$ of $X$, whether $A$ intersects $Y$ or not. We are primarily concerned with the non-adaptive model, where the family of test sets is specified in advance, in the case where each test set is of size at most some given natural number $k$. Our main results are nearly tight bounds on the minimum number of tests necessary when $d$ and $k$ are fixed and $n$ is large enough.     

Multi-set neighbor distinguishing 3-edge coloring

Let $G$ be a graph without isolated edges, and let $c:E\left(G\right)\to \{1,\dots ,k\}$ be a coloring of the edges, where adjacent edges may be colored the same. The color code of a vertex $v$ is the ordered $k$-tuple $(a_1,a_2,\dots ,a_k)$, where $a_i$ is the number of edges incident with $v$ that are colored $i$. If every two adjacent vertices of $G$ have different color codes, such a coloring is called multi-set neighbor distinguishing. In this paper, we prove that three colors are sufficient to produce a multi-set neighbor distinguishing edge coloring for every graph without isolated edges.     

A discrete convolution involving Fourier sine and cosine series and its applications

ABSTRACT

In this paper, we introduce a discrete convolution involving both the Fourier sine and cosine series. We study Young's type inequality and a discrete transform related to this convolution and solve in closed form a class of discrete Toeplitz plus Hankel equations.     

Discrete minimisers are close to continuum minimisers for the interaction energy

Under suitable technical conditions we show that minimisers of the discrete interaction energy for attractive-repulsive potentials converge to minimisers of the corresponding continuum energy as the number of particles goes to infinity. We prove that the discrete interaction energy \(\Gamma \)-converges in the narrow topology to the continuum interaction energy. As an important part of the proof we study support and regularity properties of discrete minimisers: we show that continuum minimisers belong to suitable Morrey spaces and we introduce the set of empirical Morrey measures as a natural iscrete analogue containing all the discrete minimisers.     

The Obstacle Version of the Geometric Dynamic Programming Principle: Application to the Pricing of American Options Under Constraints

We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201–236, 2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.