A spectrum associated with Minkowski diagonal continued fraction

We prove a result on the structure of a Diophantine spectrum associated with Minkowski diagonal continued fraction

Rape Messaging

When feminists began advocating for rape reform in the 1970s, the rape message was clear: rape was not a crime to be taken seriously because women lie. After decades of criminal law reform, the legal requirement that a woman vigorously resist a man’s sexual advances to prove that she was raped has largely disappeared from the statute books, and, in theory, rape shield laws make a woman’s prior sexual history irrelevant. Yet, despite what the law dictates, rape law reforms have not had a “trickle-down” effect, where changes in law lead to changes in attitude. Women are still believed to be vindictive shrews so police continue to code rape allegations as “unfounded,” and prosecutors continue to elect not to prosecute many rape cases. To many, “no” can sometimes still mean “yes.” In short, criminal law reforms have only marginally succeeded at deterring rape and increasing conviction rates for rape. At the same time, criminal law reforms have entrenched gender norms and endorsed the message that acquaintance rapes are less worthy of harsh punishment. This Article argues against further ex post criminal law reforms and posits that efforts should shift to ex ante public health interventions. This Article draws from recent successful experiences with public health interventions in destigmatizing AIDS and denormalizing tobacco and advocates for a robust public health campaign to denormalize rape. It presents a detailed proposal for changing rape messaging, denormalizing rape, and ensuring better outcomes for victims

Estimation of Solutions of Differential Systems with Delayed Argument of Neutral Type

Tato disertační práce pojednává o řešení diferenciálních rovnic a systémů diferenciálních rovnic. Hlavní pozornost je věnována asymptotickým vlastnostem rovnic se zpožděním a systémů rovnic se zpožděním. V první kapitole jsou uvedeny fyzikální a technické příklady popsané pomocí diferenciálních rovnic se zpožděním a jejich systémů. Je uvedena klasifikace rovnic se zpožděním a jsou zformulovány základní pojmy stability s důrazem na druhou metodu Ljapunova. Ve druhé kapitole jsou studovány odhady řešení rovnic neutrálního typu. Třetí kapitola se zabývá systémy diferenciálních rovnic neutrálního typu. Jsou odvozeny asymptotické odhady pro řešení i pro derivace řešení. V závěru kapitoly jsou uvedeny příklady a srovnání výsledků s pracemi jiných autorů. Výpočty byly prováděny pomocí programu MATLAB. Poslední, čtvrtá kapitola, se zabývá asymptotickými vlastnostmi systémů se speciálním typem nelinearity, tzv. sektorové nelinearity. Jsou odvozeny vlastnosti řešení a derivace řešení. Základní metodou pro důkazy je v celé práci druhá Ljapunovova metoda a použití funkcionálů Ljapunova-Krasovského.This dissertation discusses the solutions to the differential equation and to systems of differential equations. The main attention is paid to study of asymptotical properties of equations with delay and systems of equations with delay. In the first chapter are given physical and technical examples described by differential equations with delay and their systems. The classification of equations with delay is given and basic notions of theory of stability are formulated (mainly with the emphasis on the Lyapunov second method). In the second chapter estimates of solutions of equations of neutral type are studied. The third chapter deals with systems of differential equations of neutral type. Asymptotic estimates for solutions and their derivatives are proved. At the end of the chapter examples and comparisons of our results and of other authors are given. The calculation were performed with the MATLAB software. Last, the fourth chapter deals with asymptotical properties of systems having a special type of nonlinearities, so called ``sector nonlinearities''. Properties and estimations of solutions and derivatives are derived. The basic tools used in the dissertation are the Lyapunov second method and functionals of Lyapunov-Krasovskii type.