PushPush is NP-Hard in 3D

We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open

学校のいじめ問題に関する研究(Ⅰ)

はじめに 1.今日的ないじめの特徴 2.今日的ないじめ問題の本質 3.大学生の中にある「いじめ」の記憶 3.1アンケート調査の結果 3.2アンケート結果の分析 4.大学生の「いじめ問題」に関する考え方 4.1アンケート調査の結果 4.2アンケート結果の分析 おわり

南宋朝創草期の財政問題の一考察

はじめに 一　南宋朝創草期の経済状態 二　国家財政との関連 (イ)張浚の場合－四川地域 (ロ)劉光世の場合－江糴地域 (ハ)和糴の場合 (ニ)塩の場合 (ホ)見銭関子の場合 (ヘ)告牒等の場合 三　史料にみられるその他の税目 おわり

One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case

A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this model. We show by a complete one loop analysis that all ultraviolet divergences are removable with a few renormalization constants in a way consistent with the above structure.Comment: 24 pages, figures using axodraw; version 2: a new ref item [4] added to cite efforts to all orders, typos fixed and minor rewordin

Bounded-Degree Polyhedronization of Point Sets

URL to paper listed on conference siteIn 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. [1]

Report of the International Conference on the Perinatal and Infant Mortality Problem of the United States

Summary of the presentations and discussions at the International Conference on the Perinatal and Infant Mortality Problem of the United States, Washington, D. C., May 13 and 14, 1965, under the sponsorship of the National Center for Health Statistics, Public Health Service, U.S. Department of Health, Education, and Welfare

心の緊急事態と危機介入の問題 : 母親による子殺し事件を中心に

目に見える緊急事態への対応はかなりなされるようになってきているが、目に見えない心の緊急事態に対する対応、危機介入についてわれわれはどのような対応が必要で、実現可能なのか。ここらを探ってみた

DD-dimensions Dirac fermions BEC-BCS cross-over thermodynamics

An effective Proca Lagrangian action is used to address the vector condensation Lorentz violation effects on the equation of state of the strongly interacting fermions system. The interior quantum fluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized Thomson Problem counterterm background. The general analytical formulas for the $d$-dimensions thermodynamics are given near the unitary limit region. In the non-relativistic limit for $d=3$, the universal dimensionless coefficient $\xi ={4}/{9}$ and energy gap $\Delta/\epsilon_f ={5}/{18}$ are reasonably consistent with the existed theoretical and experimental results. In the unitary limit for $d=2$ and T=0, the universal coefficient can even approach the extreme occasion $\xi=0$ corresponding to the infinite effective fermion mass $m^*=\infty$ which can be mapped to the strongly coupled two-dimensions electrons and is quite similar to the three-dimensions Bose-Einstein Condensation of ideal boson gas. Instead, for $d=1$, the universal coefficient $\xi$ is negative, implying the non-existence of phase transition from superfluidity to normal state. The solutions manifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.Comment: Improved versio