Successive projections on hyperplanes

AbstractAny sequence of points in Rn obtained by successive projections of a point on elements of a finite set of hyperplanes is bounded

Domain wall motion in thin ferromagnetic nanotubes: Analytic results

Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius

Phase Transition in Matched Formulas and a Heuristic for Biclique Satisfiability

A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. We study phase transition in a context of matched formulas and their generalization of biclique satisfiable formulas. We have performed experiments to find a phase transition of property "being matched" with respect to the ratio $m/n$ where $m$ is the number of clauses and $n$ is the number of variables of the input formula $\varphi$. We compare the results of experiments to a theoretical lower bound which was shown by Franco and Gelder (2003). Any matched formula is satisfiable, moreover, it remains satisfiable even if we change polarities of any literal occurrences. Szeider (2005) generalized matched formulas into two classes having the same property -- var-satisfiable and biclique satisfiable formulas. A formula is biclique satisfiable if its incidence graph admits covering by pairwise disjoint bounded bicliques. Recognizing if a formula is biclique satisfiable is NP-complete. In this paper we describe a heuristic algorithm for recognizing whether a formula is biclique satisfiable and we evaluate it by experiments on random formulas. We also describe an encoding of the problem of checking whether a formula is biclique satisfiable into SAT and we use it to evaluate the performance of our heuristicComment: Conference version submitted to SOFSEM 2018 (https://beda.dcs.fmph.uniba.sk/sofsem2019/) 18 pages(17 without refernces), 3 figures, 8 tables, an algorithm pseudocod

On variables with few occurrences in conjunctive normal forms

We consider the question of the existence of variables with few occurrences in boolean conjunctive normal forms (clause-sets). Let mvd(F) for a clause-set F denote the minimal variable-degree, the minimum of the number of occurrences of variables. Our main result is an upper bound mvd(F) <= nM(surp(F)) <= surp(F) + 1 + log_2(surp(F)) for lean clause-sets F in dependency on the surplus surp(F). - Lean clause-sets, defined as having no non-trivial autarkies, generalise minimally unsatisfiable clause-sets. - For the surplus we have surp(F) <= delta(F) = c(F) - n(F), using the deficiency delta(F) of clause-sets, the difference between the number of clauses and the number of variables. - nM(k) is the k-th "non-Mersenne" number, skipping in the sequence of natural numbers all numbers of the form 2^n - 1. We conjecture that this bound is nearly precise for minimally unsatisfiable clause-sets. As an application of the upper bound we obtain that (arbitrary!) clause-sets F with mvd(F) > nM(surp(F)) must have a non-trivial autarky (so clauses can be removed satisfiability-equivalently by an assignment satisfying some clauses and not touching the other clauses). It is open whether such an autarky can be found in polynomial time. As a future application we discuss the classification of minimally unsatisfiable clause-sets depending on the deficiency.Comment: 14 pages. Revision contains more explanations, and more information regarding the sharpness of the boun

Ground-state configurations in ferromagnetic nanotori

Magnetization ground states are studied in toroidal nanomagnets. The energetics associated to the ferromagnetic, vortex and onion-like configurations are explicitly computed. The analysis reveals that the vortex appears to be the most prominent of such states, minimizing total energy in every torus with internal radius $r\gtrsim10\,{\rm nm}$ (for Permalloy). For $r\lesssim10\,{\rm nm}$ the vortex remains the most favorable pattern whenever $R/\ell_{ex}\gtrsim1.5$ ($R$ is the torus external radius and $\ell_{ex}$ is the exchange length), being substituted by the ferromagnetic state whenever $R/\ell_{ex}\lesssim1.5$.Comment: 16 pages, 9 figures, 3 apendices, Revtex forma

Magnetisation switching in a ferromagnetic Heisenberg nanoparticle with uniaxial anisotropy: A Monte Carlo investigation

We investigate the thermal activated magnetisation reversal in a single ferromagnetic nanoparticle with uniaxial anisotropy using Monte Carlo simulations. The aim of this work is to reproduce the reversal magnetisation by uniform rotation at very low temperature in the high energy barrier hypothesis, that is to realize the N\'eel-Brown model. For this purpose we have considered a simple cubic nanoparticle where each site is occupied by a classical Heisenberg spin. The Hamiltonian is the sum of an exchange interaction term, a single-ion anisotropy term and a Zeeman interaction term. Our numerical data of the thermal variation of the switching field are compared to an approximated expression and previous experimental results on Co nanoparticles

Splenic infarction: an update on William Osler\u27s observations.

BACKGROUND: Osler taught that splenic infarction presents with left upper abdominal quadrant pain, tenderness and swelling accompanied by a peritoneal friction rub. Splenic infarction is classically associated with bacterial endocarditis and sickle cell disease. OBJECTIVES: To describe the contemporary experience of splenic infarction. METHODS: We conducted a chart review of inpatients diagnosed with splenic infarction in a Jerusalem hospital between 1990 and 2003. RESULTS: We identified 26 cases with a mean age of 52 years. Common causes were hematologic malignancy (six cases) and intracardiac thrombus (five cases). Only three cases were associated with bacterial endocarditis. In 21 cases the splenic infarction brought a previously undiagnosed underlying disease to attention. Only half the subjects complained of localized left-sided abdominal pain, 36% had left-sided abdominal tenderness; 31% had no signs or symptoms localized to the splenic area, 36% had fever, 56% had leukocytosis and 71% had elevated lactate dehydrogenase levels. One splenectomy was performed and all patients survived to discharge. A post hoc analysis demonstrated that single infarcts were more likely to be associated with fever (20% vs. 63%, p \u3c 0.05) and leukocytosis (75% vs. 33%, P = 0.06) CONCLUSIONS: The clinical presentation of splenic infarction in the modern era differs greatly from the classical teaching, regarding etiology, signs and symptoms. In patients with unexplained splenic infarction, investigation frequently uncovers a new underlying diagnosis

Magnetic Reversal in Nanoscopic Ferromagnetic Rings

We present a theory of magnetization reversal due to thermal fluctuations in thin submicron-scale rings composed of soft magnetic materials. The magnetization in such geometries is more stable against reversal than that in thin needles and other geometries, where sharp ends or edges can initiate nucleation of a reversed state. The 2D ring geometry also allows us to evaluate the effects of nonlocal magnetostatic forces. We find a `phase transition', which should be experimentally observable, between an Arrhenius and a non-Arrhenius activation regime as magnetic field is varied in a ring of fixed size.Comment: RevTeX, 23 pages, 7 figures, to appear in Phys. Rev.

Magnetization reversal of ferromagnetic nanodisc placed above a superconductor

Using numerical simulation we have studied a magnetization distribution and a process of magnetization reversal in nanoscale magnets placed above a superconductor plane. In order to consider an influence of superconductor on magnetization distribution in the nanomagnet we have used London approximation. We have found that for usual values of London penetration depth the ground state magnetization is mostly unchanged. But at the same time the fields of vortex nucleation and annihilation change significantly: the interval where vortex is stable enlarges on 100-200 Oe for the particle above the superconductor. Such fields are experimentally observable so there is a possibility of some practical applications of this effect.Comment: 8 pages, 9 figure

Tverberg-type theorems for intersecting by rays

In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set